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Search Results (129)

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Keywords = relaxation oscillation

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11 pages, 1848 KiB  
Communication
Broadband Optical Frequency Comb Generation Utilizing a Gain-Switched Weak-Resonant-Cavity Fabry–Perot Laser Diode under Multi-Wavelength Optical Injection
by Yuhong Tao, Qiupin Wang, Pu Ou, Guangqiong Xia and Zhengmao Wu
Photonics 2024, 11(10), 912; https://doi.org/10.3390/photonics11100912 - 27 Sep 2024
Viewed by 578
Abstract
We propose and experimentally demonstrate an approach for generating a wideband optical frequency comb (OFC) featuring multiple comb lines and wavelength tunability based on a gain-switched weak-resonant-cavity Fabry–Perot laser diode (WRC-FPLD) under multi-wavelength optical injection. The longitudinal mode interval of the utilized WRC-FPLD [...] Read more.
We propose and experimentally demonstrate an approach for generating a wideband optical frequency comb (OFC) featuring multiple comb lines and wavelength tunability based on a gain-switched weak-resonant-cavity Fabry–Perot laser diode (WRC-FPLD) under multi-wavelength optical injection. The longitudinal mode interval of the utilized WRC-FPLD is about 0.28 nm (35.0 GHz), and its relaxation oscillation frequency is about 2.0 GHz at 1.15 times the threshold current. Under current modulation with a power of 20.00 dBm and a frequency of 2.0 GHz, the WRC-FPLD is driven into the gain-switched state. By further introducing multi-wavelength injection light (MWIL) containing four power equalization comb lines with an interval of 0.56 nm, a wideband OFC featuring multiple comb lines and wavelength tenability can be obtained. The experimental results demonstrate that by gradually increasing the injection’s optical power, the number of produced OFC lines initially increases and then decreases. By meticulously adjusting the wavelengths of the MWIL and carefully selecting the matched injection power, the broadband OFC can be tuned across an extensive spectral range. Under optimized operation parameters, an OFC with 147 lines, and a bandwidth of approximately 292 GHz within a 10 dB amplitude, variation is achieved. In this case, the measured single-sideband phase noise at the fundamental frequency is about −115 dBc/Hz @ 10 kHz, indicating that the comb lines possess good stability and strong coherence. Full article
Show Figures

Figure 1

Figure 1
<p>A schematic diagram of the OI-GS WRC-FPLD experimental system. LDC: laser diode controller; MFS: microwave frequency synthesizer; BST: T-type bias tee; WRC-FPLD: weak-resonant-cavity Fabry–Perot laser diode; DFB-SL: distributed feedback semiconductor laser; TL: tunable laser; OC: optical circulator; FBGF: fiber Bragg grating filter; EDFA: erbium-doped fiber amplifier; VA: variable attenuator; PC: polarization controller; FC: fiber coupler; PM: power meter; OSA: optical spectrum analyzer; PD: photodetector; ESA: electrical spectrum analyzer; DSO: digital storage oscilloscope. Solid line: optical path; dashed line: electronic path.</p>
Full article ">Figure 2
<p>(<b>a</b>) The <span class="html-italic">P</span>-<span class="html-italic">I</span> curve of the WRC-FPLD at a free-running state; (<b>b</b>) the optical spectrum of the WRC-FPLD biased at 52.00 mA.</p>
Full article ">Figure 3
<p>The optical spectra (first column), time series (second column), and power spectra (third column) of the WRC-FPLD under current modulation with <span class="html-italic">f</span><sub>m</sub> = 2.0 GHz and <span class="html-italic">P</span><sub>m</sub> = 0 (<b>a1</b>–<b>a3</b>), <span class="html-italic">P</span><sub>m</sub> = 0.00 dBm (<b>b1</b>–<b>b3</b>), and <span class="html-italic">P</span><sub>m</sub> = 20.00 dBm (<b>c1</b>–<b>c3</b>). The gray curve denotes the noise floor in the power spectra.</p>
Full article ">Figure 4
<p>(<b>a</b>) The optical spectrum of the free-running DFB-SL biased at 50.00 mA under a temperature of 8.13 °C; (<b>b</b>) the optical spectrum of the DFB-SL subject to optical injection with an injection power of 10.00 dBm and a wavelength of <span class="html-italic">λ</span><sub>D</sub> + Δ<span class="html-italic">λ</span><sub>D</sub>; (<b>c</b>) the optical spectrum of the multi-wavelength injection light after adopting power equalization through an FBGF combined with an EDFA.</p>
Full article ">Figure 5
<p>The optical spectrum of the GS WRC-FPLD under multi-wavelength optical injection with <span class="html-italic">λ</span><sub>D</sub> = 1547.0294 nm and <span class="html-italic">P</span><sub>inj</sub> = 4.982 μW.</p>
Full article ">Figure 6
<p>(<b>a</b>) The number of comb lines of the generated OFC varied with injection power under <span class="html-italic">λ</span><sub>D</sub> = 1547.0294 nm; (<b>b</b>) the power for different comb lines of the generated OFC varied with injection power. The solid lines indicate the average of five measurements, and the length of the error bars indicate the standard deviation of the corresponding data.</p>
Full article ">Figure 7
<p>For <span class="html-italic">P</span><sub>inj</sub> = 4.982 μW and <span class="html-italic">λ</span><sub>D</sub> = 1547.0294 nm, (<b>a</b>) the power spectrum of the OFC generated by the OI-GS WRC-FPLD, (<b>b</b>) the fundamental signal centered at 2.0 GHz, (<b>c</b>) the single-sideband (SSB) phase noise of the fundamental signal, and (<b>d</b>) the SSB phase noise of the fundamental signal at a 10 kHz frequency offset as a function of the observing time.</p>
Full article ">
17 pages, 5175 KiB  
Article
Reliability Enhancement Methods for Relaxation Oscillator with Delay Time Cancellation
by Kunpeng Xu, Hongguang Dai, Zhanxia Wu, Zhibo Huang, Guoqiang Zhang, Xiaopeng Yu, Wechang Wang and Gang Xuan
J. Low Power Electron. Appl. 2024, 14(4), 47; https://doi.org/10.3390/jlpea14040047 - 26 Sep 2024
Viewed by 718
Abstract
Relaxation oscillators are preferred in low-frequency applications due to their lower power consumption and superior temperature stability. However, frequency errors arise from variations in the comparator’s offset voltage and delay time due to PVT changes. To address these issues, this paper proposes the [...] Read more.
Relaxation oscillators are preferred in low-frequency applications due to their lower power consumption and superior temperature stability. However, frequency errors arise from variations in the comparator’s offset voltage and delay time due to PVT changes. To address these issues, this paper proposes the low-power delay time cancellation (DTC) technique and several enhancement methods, including a novel offset trimming approach, an error state detection and recovery (ESDAR) circuit, and a specialized frequency-trimming method. Simulation results for an 8 MHz relaxation oscillator in a 40 nm CMOS process show that the proposed DTC technique and enhancements improve frequency variation due to power supply fluctuations to ±0.05% and reduce temperature-induced frequency variation to ±0.4%. Full article
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Impact of <span class="html-italic">V<sub>os</sub></span> and delay time <span class="html-italic">t<sub>d</sub></span> on comparator response; (<b>b</b>) reduction in <span class="html-italic">V<sub>os</sub></span> and <span class="html-italic">t<sub>d</sub></span> impact using DTC technique.</p>
Full article ">Figure 2
<p>Structure of the proposed oscillator.</p>
Full article ">Figure 3
<p>Timing waveforms of the proposed relaxation oscillator.</p>
Full article ">Figure 4
<p>Connections of the comparator and <span class="html-italic">R<sub>t</sub></span> (<b>a</b>) before the offset trimming; (<b>b</b>) during the offset measurement phase; (<b>c</b>) during the resistance setting phase.</p>
Full article ">Figure 5
<p>Oscillator tolerance to comparator delay time variations with and without offset trimming.</p>
Full article ">Figure 6
<p>Incorrect signals generated by control circuit resulting in incorrect clock when a sudden VDDA drop occurs without ESDAR circuit.</p>
Full article ">Figure 7
<p>Operating mechanism of the ESDAR circuit: (<b>a</b>) under normal condition, (<b>b</b>) during abrupt changes in VDDA.</p>
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<p>ESDAR circuit generating reset signals to restore correct oscillation following a sudden VDDA drop.</p>
Full article ">Figure 9
<p>Structure of frequency-trimming circuit.</p>
Full article ">Figure 10
<p>Proposed frequency-trimming process.</p>
Full article ">Figure 11
<p>Variations in <span class="html-italic">f</span><sub>0</sub> with respect to the change in <span class="html-italic">WT</span>, while keeping optimal <span class="html-italic">α</span>.</p>
Full article ">Figure 12
<p>Oscillator malfunctions due to an excessively high frequency.</p>
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<p>Flowchart for using bisection method to tune <span class="html-italic">WT</span> with the assistant of the ESDAR circuit.</p>
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<p>Frequency variation due to (<b>a</b>) power supply and (<b>b</b>) temperature fluctuations.</p>
Full article ">
33 pages, 14062 KiB  
Article
Parametric Characterization of Nonlinear Optical Susceptibilities in Four-Wave Mixing: Solvent and Molecular Structure Effects
by José L. Paz, Alberto Garrido-Schaeffer, Marcos A. Loroño, Lenin González-Paz, Edgar Márquez, José R. Mora and Ysaias J. Alvarado
Symmetry 2024, 16(10), 1263; https://doi.org/10.3390/sym16101263 - 25 Sep 2024
Viewed by 879
Abstract
We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a four-wave mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system [...] Read more.
We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a four-wave mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute–solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, the complete frequency space is considered through the pump–probe detuning, without restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation. Full article
(This article belongs to the Section Physics)
Show Figures

Figure 1

Figure 1
<p>Nonlinear refractive index as a function of pump detuning in frequency space <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mo>Δ</mo> <mn>1</mn> </msub> <mo>,</mo> <msub> <mo>Δ</mo> <mn>2</mn> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </semantics></math>, considering different transverse relaxation times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> <mo stretchy="false">(</mo> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 2
<p>Refraction index as a function of detuning for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, at different transversal relaxation times.</p>
Full article ">Figure 3
<p>Effect of transverse relaxation time T<sub>2</sub> on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math> (keeping all other parameters constant).</p>
Full article ">Figure 4
<p>Nonlinear refractive index as a function of pump- and probe-detuning, considering different ratios (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>1</mn> </msub> <mo>/</mo> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> </mrow> </semantics></math>) of relaxation times.</p>
Full article ">Figure 5
<p>Study of dispersive responses with pumping detuning (normalized) for particular processes: <math display="inline"><semantics> <mrow> <msub> <mo>ω</mo> <mn>2</mn> </msub> <mo>=</mo> <msub> <mo>ω</mo> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mo>ω</mo> <mn>2</mn> </msub> <mo>−</mo> <msub> <mo>ω</mo> <mn>1</mn> </msub> <mo>=</mo> <msub> <mover accent="true"> <mo>ω</mo> <mo>˜</mo> </mover> <mn>0</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mo>ω</mo> <mn>1</mn> </msub> <mo>−</mo> <msub> <mo>ω</mo> <mn>2</mn> </msub> <mo>=</mo> <msub> <mover accent="true"> <mo>ω</mo> <mo>˜</mo> </mover> <mn>0</mn> </msub> </mrow> </semantics></math>, as a function of the <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>1</mn> </msub> <mo>/</mo> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> </mrow> </semantics></math> ratio.</p>
Full article ">Figure 6
<p>Time effect of the ratio of relaxation times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> </mrow> </semantics></math> (3D) on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Effect of coupling between the molecular system and the thermal reservoir on the nonlinear refractive index for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Effect of coupling between the molecular system and the thermal reservoir on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Effect of coupling between the molecular system and the thermal reservoir (3D) on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Effect of total saturation <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> on the nonlinear refractive index for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Effect of total saturation <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> (2D) on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, as a function of the pump–probe detuning.</p>
Full article ">Figure 12
<p>Effect of total saturation <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> (3D) on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Effect of intramolecular coupling on the nonlinear refractive index for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, as a function of the pump–probe detuning.</p>
Full article ">Figure 14
<p>Effect of intramolecular coupling on the nonlinear refractive index for selected frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, as a function of normalized pump detuning.</p>
Full article ">Figure 15
<p>Effect of intramolecular coupling on the nonlinear refractive index for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, as a function of normalized pump detuning.</p>
Full article ">Figure 16
<p>Nonlinear absorption coefficient as a function of pump–probe detuning in frequency space parameterized by transverse relaxation times.</p>
Full article ">Figure 17
<p>Effect of transverse relaxation time T<sub>2</sub> on the nonlinear absorption coefficient as a function of pump detuning in the three processes shown.</p>
Full article ">Figure 18
<p>Effect of transverse relaxation time T<sub>2</sub> (3D) on the nonlinear absorption coefficient for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 19
<p>Effect of the ratio of relaxation times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> </mrow> </semantics></math> on the nonlinear absorption coefficient as function of <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 20
<p>Effect of the ratio of relaxation times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">T</mi> <mn>2</mn> </msub> </mrow> </semantics></math> on the nonlinear absorption coefficient in the three processes shown.</p>
Full article ">Figure 21
<p>The nonlinear absorption coefficient as function of pump-detuning and ratio of relaxation times.</p>
Full article ">Figure 22
<p>Effect of coupling between the molecular system and the thermal reservoir on the nonlinear absorption coefficient for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 23
<p>Nonlinear absorption coefficient as a function of pump beam detuning. We have taken into account different intensities of coupling between the molecular system and the thermal reservoir.</p>
Full article ">Figure 24
<p>Nonlinear absorption coefficient as a function of pumping detuning and system-reservoir coupling in the three selected frequency coordinates.</p>
Full article ">Figure 25
<p>Effect of total saturation <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> on the nonlinear absorption coefficient for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 26
<p>Effect of total saturation <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">S</mi> <mrow> <mn>12</mn> </mrow> </msub> </mrow> </semantics></math> (2D) on the nonlinear absorption coefficient for selected frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 27
<p>Nonlinear absorption coefficient as a function of pumping detuning and saturation parameter of pump-beam, in the three selected frequency coordinates.</p>
Full article ">Figure 28
<p>Effect of intramolecular coupling on the nonlinear absorption coefficient for any ratio of frequencies <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 29
<p>Effect of intramolecular (2D) coupling on the nonlinear absorption coefficient for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 30
<p>Effect of intramolecular (3D) coupling on the nonlinear absorption coefficient for given frequency ratios <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 31
<p>Comparison between scattering and absorption profiles at the frequency of interest when considering different ratios between pumping and test beam frequencies.</p>
Full article ">Figure 32
<p>Nonlinear refractive index as a function of pumping beam detuning for the processes <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> <mo>=</mo> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> <mo>=</mo> <mn>2</mn> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math>, considering different orders of perturbation according to Equation (16).</p>
Full article ">Figure 33
<p>Nonlinear absorption coefficient as a function of detuning in processes <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> <mo>=</mo> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <msub> <mo>Δ</mo> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mo>Δ</mo> <mn>2</mn> </msub> <mo>=</mo> <mn>2</mn> <msub> <mo>Δ</mo> <mn>1</mn> </msub> </mrow> </semantics></math>, considering different perturbation treatments (Equation (23)).</p>
Full article ">
16 pages, 1309 KiB  
Article
A Sub-0.01 °C Resolution All-CMOS Temperature Sensor with 0.43 °C/−0.38 °C Inaccuracy and 1.9 pJ · K2 Resolution FoM for IoT Applications
by Yixiao Sun, Jie Cheng, Zhizhong Luo and Yanhan Zeng
Micromachines 2024, 15(9), 1132; https://doi.org/10.3390/mi15091132 - 6 Sep 2024
Viewed by 703
Abstract
A high resolution, acceptable accuracy and low power consumption time-domain temperature sensor is proposed and simulated in this paper based on a 180 nm standard CMOS technology. A diode stacking structure is introduced to enhance the accuracy of the temperature sensing core. To [...] Read more.
A high resolution, acceptable accuracy and low power consumption time-domain temperature sensor is proposed and simulated in this paper based on a 180 nm standard CMOS technology. A diode stacking structure is introduced to enhance the accuracy of the temperature sensing core. To improve the resolution of the sensor, a dual-input capacitor multiplexing voltage-to-time converter (VTC) is implemented. Additionally, a low-temperature drift voltage-mode relaxation oscillator (ROSC) is proposed, effectively reducing the large oscillation frequency drift caused by significant temperature impacts on delay errors. The simulated results show that the resolution is as high as 0.0071 °C over 0∼120 °C with +0.43 °C/−0.38 °C inaccuracy and 1.9 pJ · K2 resolution FoM, consuming only 1.48 μW at a 1.2 V supply voltage. Full article
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<p>Operation principle of four typical temperature sensors.</p>
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<p>The structural diagram of the proposed temperature sensor.</p>
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<p>The time signal <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> </mrow> </msub> </semantics></math> as temperature increases and decreases.</p>
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<p>The schematic of the proposed temperature sensing core.</p>
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<p>The schematic of the proposed VTC.</p>
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<p>The change in signals <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>i</mi> <mi>p</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </semantics></math> over time.</p>
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<p>The comparator in the proposed VTC.</p>
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<p>The schematic of a conventional ROSC.</p>
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<p>The schematic of the proposed ROSC.</p>
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<p>The schematic of the aforementioned TDC.</p>
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<p>The <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>P</mi> <mi>T</mi> <mi>A</mi> <mi>T</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>C</mi> <mi>T</mi> <mi>A</mi> <mi>T</mi> </mrow> </msub> </semantics></math> generated by the temperature sensing core.</p>
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<p>The reference frequency generated by the relaxation oscillator.</p>
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<p>The simulated temperature error for different process corners.</p>
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<p>Power dissipation of the proposed temperature sensor.</p>
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22 pages, 7320 KiB  
Article
A CMOS Rail-to-Rail Class AB Second-Generation Voltage Conveyor and Its Application in a Relaxation Oscillator
by Radivoje Djurić and Jelena Popović-Božović
Electronics 2024, 13(17), 3511; https://doi.org/10.3390/electronics13173511 - 4 Sep 2024
Viewed by 564
Abstract
In this paper, we present a CMOS rail-to-rail second-generation voltage conveyor (VCII) suitable for low power applications, implemented in 180 nm CMOS technology with a supply voltage of ± 0.9 V. The proposed VCII consists of a current and voltage buffer operating in [...] Read more.
In this paper, we present a CMOS rail-to-rail second-generation voltage conveyor (VCII) suitable for low power applications, implemented in 180 nm CMOS technology with a supply voltage of ± 0.9 V. The proposed VCII consists of a current and voltage buffer operating in class AB. At the input of the voltage buffer, there is a bulk-driven differential amplifier, which provides a rail-to-rail input common-mode voltage. A common source output stage in class AB provides rail-to-rail at the output of the voltage buffer. The transistors are designed to operate in moderate inversion, achieving a relatively large current and voltage buffer bandwidth of 298.3 MHz and 173.2 MHz, respectively, with a power consumption of 157 μW. A sine wave with an amplitude of 1.5 Vpp and a frequency of 1 MHz on the output buffer has a total harmonic distortion of only 0.29%. The application of VCII in a relaxation oscillator with a frequency of up to 10 MHz is demonstrated, as well as its comparative characteristics with reference to other relevant square-wave generators published in the literature. Full article
(This article belongs to the Section Circuit and Signal Processing)
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<p>Equivalent model of VCII.</p>
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<p>Symbolic representation of the VCII.</p>
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<p>The current buffer of the proposed <math display="inline"><semantics> <mrow> <mi>V</mi> <mi>C</mi> <mi>I</mi> <msup> <mi>I</mi> <mo>−</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Current-transfer function Y−X and its derivative.</p>
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<p>Distortions of the CB at 1 MHz, as a function of the input current amplitude <span class="html-italic">I<sub>m</sub></span>.</p>
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<p>The proposed rail-to-rail voltage buffer.</p>
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<p>Voltage transfer function X−Z and its derivative.</p>
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<p>The current buffer and the voltage buffer transfer function.</p>
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<p>Schematic diagram of the current-driven NIC with <math display="inline"><semantics> <mrow> <msup> <mi>VCII</mi> <mo>−</mo> </msup> </mrow> </semantics></math>.</p>
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<p>The proposed relaxation oscillator based on a <math display="inline"><semantics> <mrow> <msup> <mi>VCII</mi> <mo>−</mo> </msup> </mrow> </semantics></math>: (<b>a</b>) schematic diagram, (<b>b</b>) static characteristic of the oscillator’s active part.</p>
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<p>The small-signal oscillator circuit for equivalent resistance determination.</p>
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<p>Typical voltage and current waveforms in the proposed oscillator at 1.045 MHz (<math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>F</mi> </msub> <mo>=</mo> <mn>22</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>6.5</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>).</p>
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<p>Static characteristics of the proposed oscillator with <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>F</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mrow> <mi>F</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>22</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>, and with two external resistances <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math>.</p>
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<p>The frequency of oscillation vs. <math display="inline"><semantics> <mi>C</mi> </semantics></math> and the relative error of the frequency estimation vs. frequency.</p>
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<p>Frequency-dependent negative impedance <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>1</mn> <mo> </mo> <mi>MHz</mi> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>5</mn> <mo> </mo> <mi>MHz</mi> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>=</mo> <mn>10</mn> <mo> </mo> <mi>MHz</mi> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Typical voltage and current waveforms in the proposed oscillator at 10 MHz, (<b>b</b>) The phase portrait at 10 MHz (<math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>F</mi> </msub> <mo>=</mo> <mn>22</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>=</mo> <mn>100</mn> <mo> </mo> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="sans-serif">Ω</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>0.79</mn> <mo> </mo> <mi>pF</mi> </mrow> </semantics></math>).</p>
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<p>Phase noise in the 1.049 MHz relaxation oscillator for three supply voltages: <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>0.81</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>0.90</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>0.99</mn> <mo> </mo> <mi mathvariant="normal">V</mi> </mrow> </semantics></math> (from bottom to top).</p>
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9 pages, 2276 KiB  
Article
Detection of Optogalvanic Spectra Using Driven Quasi-Periodic Oscillator Dynamics
by Mark Koepke
Atoms 2024, 12(8), 42; https://doi.org/10.3390/atoms12080042 - 19 Aug 2024
Viewed by 743
Abstract
The narrowband light from a scannable, single-mode dye laser influences the electrical properties of gas discharges. The variation in these properties as the laser wavelength λ is scanned yields the optogalvanic spectrum of the discharge (i.e., electrical conductivity vs. frequency). By connecting a [...] Read more.
The narrowband light from a scannable, single-mode dye laser influences the electrical properties of gas discharges. The variation in these properties as the laser wavelength λ is scanned yields the optogalvanic spectrum of the discharge (i.e., electrical conductivity vs. frequency). By connecting a neon lamp, capacitor, and power supply in parallel, an undriven relaxation oscillator is formed whose natural frequency f0 is affected by neon-resonant laser light and this λ-dependence of the relaxation oscillator frequency f0 yields a variant optogalvanic spectrum (i.e., f0 vs. frequency). In this paper, a driving force is effectively applied to an otherwise undriven oscillator when the incident light is chopped periodically at fd. For fdf0 and a sufficiently large driving force amplitude (laser intensity and the degree of neon resonance), the relaxation oscillator can be entrained so that f0 is locked on fd and is independent of λ. For the new chopped-light technique described here, fd is adjusted to be the subthreshold of the entrainment range, where the λ-dependence of f0 is advantageously exaggerated by periodic pulling, and the beat frequency |fdf0| vs. λ provides an optogalvanic spectrum with appealingly amplified signal-to-noise qualities. Beat frequency neon spectra are reported for the cases fd < f0 and fd > f0 and are compared with spectra obtained using the unchopped-light (i.e., undriven) method. Full article
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<p>System’s oscillation frequency and system’s beat frequency as a function of chopping frequency, i.e., driving frequency. (<b>a</b>) Beat frequency and (<b>b</b>) system’s oscillation frequency shows effects of periodic pulling and entrainment when driving and oscillation frequency values are close.</p>
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<p>Beat frequency (increasing vertically) vs. driving force frequency (increasing from left to right). Effect of incident laser light’s resonance with neon influences the relaxation oscillator’s natural frequency, while the Arnol’d tongue feature remains dominant. Here, the system’s natural frequency, approximated by the entrainment’s midpoint along <span class="html-italic">f</span><sub>d</sub> axis, decreases slightly as the laser light is scanned through the neon line. The blue line is the optogalvanic beat frequency spectrum (see Figure 6) for a given value of laser chopping frequency, i.e., driving frequency. Of interest is the blue line that is immediately to the left of the zero-beat-frequency region, i.e., entrainment region.</p>
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<p>Natural frequency vs. duty cycle. (<b>a</b>) Increasing laser intensity increases optogalvanic effect until heating effects dominate. (<b>b</b>) Optogalvanic effect increases (relaxation oscillator’s national frequency decreases) as chopping duty cycle increases.</p>
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<p>Isolation of two effects (widening and shifting). (<b>a</b>) Center of entrainment shifts as optogalvanic effect increases. (<b>b</b>) Entrainment width broadens as optogalvanic effect increases.</p>
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<p>Schematic diagram of experimental setup.</p>
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<p>Beat frequency spectra. Influence of optogalvanic effect on beat frequency for driving force frequency smaller or larger than the relaxation oscillator’s natural frequency.</p>
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<p>Influence of laser intensity and chopping duty cycle (D.C.) on optogalvanic spectral line amplitude and shape. Beat freq spectra for 100%-100%, 100%-50%, 50%-100% (ratio of intensity to duty cycle).</p>
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18 pages, 7142 KiB  
Article
Research on the Flow-Induced Vibration of Cylindrical Structures Using Lagrangian-Based Dynamic Mode Decomposition
by Xueji Shi, Zhongxiang Liu, Tong Guo, Wanjin Li, Zhiwei Niu and Feng Ling
J. Mar. Sci. Eng. 2024, 12(8), 1378; https://doi.org/10.3390/jmse12081378 - 12 Aug 2024
Viewed by 723
Abstract
An oscillating flow past a structure represents a complex, high-dimensional, and nonlinear flow phenomenon, which can lead to the failure of structures due to material fatigue or constraint relaxation. In order to better understand flow-induced vibration (FIV) and coupled flow fields, a numerical [...] Read more.
An oscillating flow past a structure represents a complex, high-dimensional, and nonlinear flow phenomenon, which can lead to the failure of structures due to material fatigue or constraint relaxation. In order to better understand flow-induced vibration (FIV) and coupled flow fields, a numerical simulation of a two-degrees-of-freedom FIV in a cylinder was conducted. Based on the Lagrangian-based dynamic mode decomposition (L-DMD) method, the vorticity field and motion characteristics of a cylinder were decomposed, reconstructed, and predicted. A comparison was made to the traditional Eulerian-based dynamic mode decomposition (E-DMD) method. The research results show that the first-order mode in the stable phase represents the mean flow field, showcasing the slander tail vortex structure during the vortex-shedding period and the average displacement in the in-line direction. The second mode predominantly captures the crossflow displacement, with a frequency of approximately 0.43 Hz, closely matching the corresponding frequency observed in the CFD results. The higher dominant modes mainly capture outward-spreading, smaller-scale vortex structures with detail displacement characteristics. The motion of the cylinder in the in-line direction was accompanied by symmetric vortex structures, while the motion of the cylinder in the crossflow direction was associated with anti-symmetric vortex structures. Additionally, crossflow displacement will cause a symmetrical vortex structure that spreads laterally along the axis behind the cylinder. Finally, when compared with E-DMD, the L-DMD method demonstrates a notable advantage in analyzing the nonlinear characteristics of FIV. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Simulation model diagram of a benchmark cylindrical structure: (<b>a</b>) computational domain; (<b>b</b>) computation mesh and reference nodes.</p>
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<p>Response of amplitude <span class="html-italic">y</span>/<span class="html-italic">D</span> versus reduced velocity <span class="html-italic">U*</span>. ( data from Khalak and Williamson [<a href="#B32-jmse-12-01378" class="html-bibr">32</a>], Pan, Cui, and Miao [<a href="#B33-jmse-12-01378" class="html-bibr">33</a>], Niaz B.Khan [<a href="#B35-jmse-12-01378" class="html-bibr">35</a>], and Li, Li and Liu [<a href="#B36-jmse-12-01378" class="html-bibr">36</a>]).</p>
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<p>Displacement rate of cylinder structures: (<b>a</b>) time history curve; (<b>b</b>) spectrum of displacement rate.</p>
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<p>Calculation process.</p>
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<p>Eigenvalues of L-DMD modes and the relationship between frequency and growth rate.</p>
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<p>The L-DMD modes 1–5 at 11 s and 13 s.</p>
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<p>Comparison of L-DMD and CFD vorticity fields reconstructed using 10 modes at 11 s: (<b>a</b>) L-DMD vorticity; (<b>b</b>) CFD vorticity.</p>
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<p>Comparison of the L-DMD and CFD vorticity fields at 13 s: (<b>a</b>) L-DMD vorticity; (<b>b</b>) CFD vorticity.</p>
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<p>Eigenvalues of the L-DMD modes and the majority of the characteristic values in the stable stage.</p>
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<p>The L-DMD modes 1-5 at 30 s and 40 s.</p>
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<p>The L-DMD vorticity (<b>left</b> column) and CFD vorticity (<b>right</b> column) reconstructed using 10 modes.</p>
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<p>Variations in vorticity at the reference nodes: (<b>a</b>) Point A; (<b>b</b>) Point B; (<b>c</b>) Point C; (<b>d</b>) Point D; (<b>e</b>) Point E; (<b>f</b>) Point F.</p>
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<p>Mode coefficient: (<b>a</b>) time-history curve; (<b>b</b>) spectrum.</p>
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<p>Time–history displacement rate of cylinder structures: (<b>a</b>) crossflow; (<b>b</b>) in-line.</p>
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<p>Motion trajectory rate characteristics: (<b>a</b>) Mode 1; (<b>b</b>) Mode 2; (<b>c</b>) Mode 3; (<b>d</b>) Mode 4; (<b>e</b>) Mode 5; (<b>f</b>) Mode 6.</p>
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<p>Loss value of L-DMD: (<b>a</b>) T = 34.80 to 35.00; (<b>b</b>) T = 54.35 to 54.55.</p>
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<p>Vorticity field reconstructed using 10 modes based on E-DMD.</p>
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30 pages, 6944 KiB  
Review
Modeling Electronic and Optical Properties of InAs/InP Quantum Dots
by Fujuan Huang, Gaowen Chen and Xiupu Zhang
Photonics 2024, 11(8), 749; https://doi.org/10.3390/photonics11080749 - 10 Aug 2024
Viewed by 884
Abstract
A theoretical investigation of electronic properties of self-assembled InAs/InP quantum dots (QDs) is presented, utilizing a novel two-step modeling approach derived from a double-capping procedure following QD growth processes, a method pioneered in this study. The electronic band structure of the QD is [...] Read more.
A theoretical investigation of electronic properties of self-assembled InAs/InP quantum dots (QDs) is presented, utilizing a novel two-step modeling approach derived from a double-capping procedure following QD growth processes, a method pioneered in this study. The electronic band structure of the QD is calculated by the newly established accurate two-step method, i.e., the improved strain-dependent, eight-band k p method. The impact of various QD structural parameters (e.g., height, diameter, material composition, sublayer, and inter-layer spacer) on electronic states’ distribution and transition energies is investigated. Analysis of carrier dynamics within QDs includes intraband and interband transitions. The calculation of the carrier transitions between two atomic states, providing insights into optical gain or loss within QDs, is in terms of dipole matrix element, momentum matrix element, and oscillation strength, etc. In addition, the time-domain, traveling-wave method (i.e., rate equations coupled with traveling-wave equations) is used to investigate the optical properties of QD-based lasers. Several optical properties of the QD-based lasers are investigated, such as polarization, gain bandwidth, two-state lasing, etc. Based on the aforementioned method, our key findings include the optimization of carrier non-radiative intraband relaxation through sublayer manipulation, wavelength control through emission blue-shifting and gain bandwidth via variation of sublayer, polarization control of QDs photoluminescence via excited states’ transitions, and the enhancement of two-state lasing in InAs/InP QD lasers by thin inter-layer spacers. This review offers comprehensive insights into QDs electronic band structures and carrier dynamics, providing valuable guidance for optimizing QD-based lasers and their potential designs. Full article
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<p>Schematic of overall modeling procedure. TDTW: time domain traveling wave.</p>
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<p>Schematics and geometries of (<b>a</b>) buried truncated pyramid shaped single InAs QD and (<b>b</b>) buried five-layer InAs QD stacks; and <span class="html-italic">h</span> and <span class="html-italic">D</span> are the height of dot and diameter of dot base, respectively.</p>
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<p>(<b>a</b>) Distribution of hydrostatic strain and (<b>b</b>) biaxial strain along the z-axis through the center of the quantum dot, as obtained from both the one-step and two-step models; and (<b>c</b>) the energy band edges for electrons, heavy holes, and light holes under strain, plotted along the (001) direction [<a href="#B38-photonics-11-00749" class="html-bibr">38</a>].</p>
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<p>(<b>a</b>) Distribution of hydrostatic strain and biaxial strain along the z-axis through the center of quantum dot stacks with spacer thicknesses of 30 nm (left panel) and 5 nm (right panel); and (<b>b</b>) schematic representations of bidirectional (left panel) and unidirectional (right panel) compressive strain accumulations. The left panel illustrates the conventional model, while the right panel depicts our multistep (novel) model applied to a deeply buried stack of five dot layers. Red arrowhead lines indicate the direction of cumulative strain, and green lines represent the total <span class="html-italic">ϵ<sub>zz</sub></span> along the growth direction [<a href="#B78-photonics-11-00749" class="html-bibr">78</a>].</p>
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<p>Comparison of transition energies (RT PL peak wavelengths) between calculated values and experimental data from [<a href="#B8-photonics-11-00749" class="html-bibr">8</a>,<a href="#B65-photonics-11-00749" class="html-bibr">65</a>] for (<b>a</b>) QDs with a 1.1 Q barrier and (<b>b</b>) QDs with a 1.15 Q barrier. The shaded regions represent the tunable ranges of PL peak wavelengths calculated using the two-step model for TP and FL QDs, while the areas with diagonal and solid borders denote results from the one-step model. In panel (<b>b</b>), error bars reflect the simulation outcomes for TP QDs using the two-step model with the specific quaternary material (x = 0.184, y = 0.392) as detailed in [<a href="#B8-photonics-11-00749" class="html-bibr">8</a>]. The deviations between the one-step model calculation and the experimental data are evident [<a href="#B74-photonics-11-00749" class="html-bibr">74</a>].</p>
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<p>(<b>a</b>) Distribution of strain tensors <math display="inline"><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> </semantics></math> along the z-axis through the center of the QD with and without a 1.27-monolayer (ML) GaP or GaAs sublayer. The inset shows the normalized strain distribution of the QD and wetting layer in three-dimensional space. (<b>b</b>) Distribution of the piezoelectric potential <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mi>p</mi> </msub> </mrow> </semantics></math> along the diagonal of the QD’s base plane in the (110) direction, comparing QDs with and without GaP or GaAs sublayers. The inset provides a normalized view of the piezoelectric potential distribution in three-dimensional space [<a href="#B75-photonics-11-00749" class="html-bibr">75</a>].</p>
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<p>Electron energy states for the quantum dot as a function of sublayer thickness (<span class="html-italic">d<sub>sub</sub></span>): (<b>a</b>) QD with a height of 1.5 nm and a GaP sublayer, (<b>b</b>) QD with a height of 3 nm and a GaP sublayer, (<b>c</b>) QD with a height of 1.5 nm and a GaAs sublayer, and (<b>d</b>) QD with a height of 3 nm and a GaAs sublayer [<a href="#B78-photonics-11-00749" class="html-bibr">78</a>].</p>
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<p>(<b>a</b>) Electron relaxation rate <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <msub> <mi>τ</mi> <mrow> <mi>s</mi> <mi>p</mi> <mi>o</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> from the ES to the GS as a function of GaP or GaAs sublayer thickness for the QD; and (<b>b</b>) The energy gap between the first ES and GS for QDs with GaP or GaAs sublayers [<a href="#B78-photonics-11-00749" class="html-bibr">78</a>].</p>
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<p>(<b>a</b>) Comparison of photoluminescence peak wavelengths from simulations and experimental data in [<a href="#B96-photonics-11-00749" class="html-bibr">96</a>] for samples with and without a 0.28 nm GaP sublayer. The shaded regions represent the calculated ranges of PL peak wavelengths as a function of dot base sizes and heights. The upper and lower bounds of these regions correspond to RT PL peak wavelengths from dots with lateral diameters of 40 nm and 30 nm, respectively. (<b>b</b>) Calculated tunable range of RT PL peak wavelengths for dots with varying heights and GaP sublayer thicknesses. A 1.09 ML GaP sublayer allows for an extension of up to 65 nm towards shorter wavelengths. By simultaneously adjusting both the sublayer thickness and dot height, a total tunable range of 195 nm can be achieved. The simulation assumes a fixed dot base diameter of 30 nm [<a href="#B79-photonics-11-00749" class="html-bibr">79</a>].</p>
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<p>RT PL emission spectra for five InAs quantum dot (QD) layers with different FCL thicknesses: (<b>a</b>) without a GaP sublayer and (<b>b</b>) with GaP sublayers of specific thicknesses. The bold solid lines indicate the overall PL spectra for these chirped QD configurations. The QD base diameter is consistently 30 nm [<a href="#B79-photonics-11-00749" class="html-bibr">79</a>].</p>
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<p>(<b>a</b>) HH, LH, SO states percentage in ground hole states of the closely QD stacks (spacer layer thickness <span class="html-italic">T<sub>S</sub></span> = 4 nm) with SLN from 2 to 5. (<b>b</b>) The probability density isosurfaces of the lowest electron states included in GS and the first ES for the three-layer QD stacks with 4 nm spacer layer [<a href="#B80-photonics-11-00749" class="html-bibr">80</a>].</p>
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<p>(<b>a</b>) PL emission spectrum of closely stacked three-layer QDs (<span class="html-italic">T<sub>S</sub></span> = 4 nm). The peak wavelengths of the ES and GS emission are indicated. (<b>b</b>) Transition intensity of TE and TM polarization for the closely stacked three-layer QDs (<span class="html-italic">T<sub>S</sub></span> = 4 nm) [<a href="#B80-photonics-11-00749" class="html-bibr">80</a>].</p>
Full article ">Figure 13
<p>Changes in the six lowest calculated electron energy levels as a function of <span class="html-italic">T<sub>S</sub></span> at room temperature. For a spacer thickness of approximately 10 nm, a nearly six-fold degenerate ES is formed by the anti-binding s-orbital <math display="inline"><semantics> <mrow> <mo>|</mo> <mfenced close="" open="|"> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mn>2</mn> </msub> </mrow> </mfenced> <mo>〉</mo> </mrow> </semantics></math> interacting with two binding p-orbitals <math display="inline"><semantics> <mrow> <mfenced close="" open="|"> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mn>3</mn> </msub> </mrow> </mfenced> <mo>〉</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mfenced close="" open="|"> <mrow> <msub> <mi mathvariant="sans-serif">Ψ</mi> <mn>4</mn> </msub> </mrow> </mfenced> <mo>〉</mo> </mrow> </semantics></math>. The insets display the corresponding 3D electron probability density isosurfaces for these degenerate states [<a href="#B78-photonics-11-00749" class="html-bibr">78</a>,<a href="#B117-photonics-11-00749" class="html-bibr">117</a>].</p>
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<p>(<b>a</b>–<b>d</b>) The progression of simulated optical spectra with varying bias currents at room temperature for spacer thicknesses <span class="html-italic">T<sub>s</sub></span> of 10 nm (left column) and 30 nm (right column), with inhomogeneous gain bandwidth of FWHM values of 35 meV (top row) and 40 meV (bottom row). In panel (<b>a</b>), the red patterned spectrum highlights the initiation of two-state lasing at wavelengths of approximately 1560 nm (ES) and 1640 nm (GS) at a bias current of 2 <span class="html-italic">I<sub>th</sub></span>. Panel (<b>c</b>) includes an inset that provides a detailed view of the spectral evolution between 25 and 29 mA bias currents. Panel (<b>d</b>) features insets displaying the distinctive output power characteristics in both the time domain (left) and frequency domain (right) at 5.5 <span class="html-italic">I<sub>th</sub></span> [<a href="#B117-photonics-11-00749" class="html-bibr">117</a>].</p>
Full article ">Figure 15
<p>The total <span class="html-italic">P</span>-<span class="html-italic">I</span> characteristics for 10 (solid) and 30 nm (dashed) with inhomogeneous gain bandwidth FWHM Δ<span class="html-italic">E</span> = 35 (blue) and 40 meV (red), and the insets depict the zoom-in total (upper left) and corresponding state-resolved <span class="html-italic">P</span>-<span class="html-italic">I</span> characteristics [<a href="#B117-photonics-11-00749" class="html-bibr">117</a>].</p>
Full article ">
54 pages, 6496 KiB  
Review
Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives
by Annalisa Quaini, Omer San, Alessandro Veneziani and Traian Iliescu
Fluids 2024, 9(8), 178; https://doi.org/10.3390/fluids9080178 - 4 Aug 2024
Viewed by 990
Abstract
Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For [...] Read more.
Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models in order to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, instead of reviewing all the ROM closures and stabilizations, we took a more modest step and focused on one particular type of ROM closure and stabilization that is inspired by large eddy simulation (LES), a classical strategy in computational fluid dynamics (CFD). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Indeed, LES-ROMs are modular and generally require minimal modifications to standard (“legacy”) ROM formulations. Furthermore, the computational overhead of these modifications is minimal. Finally, carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in science and engineering applications. LES-ROMs are constructed by leveraging spatial filtering, which is the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also “bridges” two distinct research fields (LES and ROMs) that have been disconnected until now. This paper is a review of LES-ROMs, with a particular focus on the LES concepts and models that enable the construction of LES-inspired ROMs and the bridging of LES and reduced-order modeling. This paper starts with a description of a versatile LES strategy called evolve–filter–relax (EFR) that has been successfully used as a full-order method for both incompressible and compressible convection-dominated flows. We present evidence of this success. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs (e.g., EFR-ROM). Several applications of LES-ROMs to the numerical simulation of incompressible and compressible convection-dominated flows are presented. Finally, we draw conclusions and outline several research directions and open questions in LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which we believe has a lot of potential in the practical numerical simulation of convection-dominated flows in science, engineering, and medicine. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics: Feature Papers, 2024)
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Figure 1

Figure 1
<p>Overall view of the energy cascade, from injection to dissipation of energy, and associated types of modeling.</p>
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<p>LES schematic showing the input flow variable, <math display="inline"><semantics> <mi mathvariant="bold">u</mi> </semantics></math>, that cannot be represented on a given coarse mesh, and the filtered flow variable, <math display="inline"><semantics> <mover> <mi mathvariant="bold-italic">u</mi> <mo>¯</mo> </mover> </semantics></math>, that can be accurately represented on the coarse mesh.</p>
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<p>Schematic of the concept proposed in [<a href="#B99-fluids-09-00178" class="html-bibr">99</a>].</p>
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<p>Images of a patient-specific AoD showing the true lumen and the false lumen.</p>
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<p>Simulation in a patient-specific AoD. Top left: pressure. Top right: velocity (in cm/s) in the descending aorta and at the entrance of the false lumen. The two bottom panels outline the complexity of the flow induced by the entry tear for the velocity (<b>left</b>) and the wall shear stress (<b>right</b>).</p>
Full article ">Figure 6
<p>Anatomies of several AoDs, pinpointing the diversity of the possible morphologies. Geometries reconstructed at Emory University with Vascular Modeling ToolKit [<a href="#B110-fluids-09-00178" class="html-bibr">110</a>].</p>
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<p>EFR simulation of the hemodynamics in a patient-specific AoD: TAWSS in different regions of the false lumen.</p>
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<p>Sobol’ indexes in a patient-specific geometry for the sensitivity of the TAWSS and the OSI to the radius <math display="inline"><semantics> <mi>α</mi> </semantics></math> (<b>left</b>), the inflow rate <span class="html-italic">Q</span> (<b>center</b>), and the geometry (<b>right</b>). Blue regions identify parts of the domain weakly affected by variations in the input in comparison with the other uncertainties.</p>
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<p>Rising thermal bubble: perturbation of potential temperature <math display="inline"><semantics> <msup> <mi>θ</mi> <mo>′</mo> </msup> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1020</mn> </mrow> </semantics></math> s computed with the EFR and <math display="inline"><semantics> <msub> <mi>a</mi> <mi>S</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>a</mi> <mi>D</mi> </msub> </semantics></math> with the coarser mesh (<b>first two panels</b>) and the finer mesh (<b>last two panels</b>).</p>
Full article ">Figure 10
<p>Density potential temperature fluctuation <math display="inline"><semantics> <msup> <mi>θ</mi> <mo>′</mo> </msup> </semantics></math> (<b>left</b>) and indicator function (<b>right</b>) for the EFR method with <math display="inline"><semantics> <msub> <mi>a</mi> <mi>S</mi> </msub> </semantics></math> (<b>top</b>) and <math display="inline"><semantics> <msub> <mi>a</mi> <mi mathvariant="script">D</mi> </msub> </semantics></math> (<b>bottom</b>). The mesh size is <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> m.</p>
Full article ">Figure 11
<p>Lift coefficient <math display="inline"><semantics> <msub> <mi>C</mi> <mi>L</mi> </msub> </semantics></math> computed by the FOM and the projection/data-driven ROM from [<a href="#B197-fluids-09-00178" class="html-bibr">197</a>] for different thresholds of cumulative energy.</p>
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<p>Pareto plots for the velocity and pressure: time-averaged relative <math display="inline"><semantics> <msup> <mi>L</mi> <mn>2</mn> </msup> </semantics></math> error versus relative wall time when the number of basis functions for the velocity is varied for the 2D (<b>left</b>) and 3D (<b>right</b>) cylinder tests.</p>
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<p>T-junction test case: instantaneous temperature field at <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> </mrow> </semantics></math> = 10,000 for an investigation on thermal striping, which is critical in nuclear engineering [<a href="#B200-fluids-09-00178" class="html-bibr">200</a>].</p>
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<p>Near-wall temperature history at <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math> for several <span class="html-italic">x</span> locations in the outlet branch.</p>
Full article ">Figure 15
<p>T-junction at <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>10</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics></math>: comparison of the near-wall temperature history at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math> between the FOM, the G-ROM, and the LES-ROMs for <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> </mrow> </semantics></math> (outlet branch).</p>
Full article ">Figure 16
<p>T-junction at <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> <mo>=</mo> <mn>10</mn> <mo>,</mo> <mn>000</mn> </mrow> </semantics></math>: comparison of the near-wall temperature history at <math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math> between the FOM, the G-ROM, and the LES-ROMs for <math display="inline"><semantics> <mrow> <mi>x</mi> <mo>=</mo> <mn>6</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>9</mn> </mrow> </semantics></math> (outlet branch).</p>
Full article ">Figure 17
<p>Simplified geometry of a TCPC. The vertical vessel is the vena cava (VC: superior at the top—SVC, inferior at the bottom—IVC). The pulmonary artery (PA) is the horizontal vessel. The inflow sections are at the SVC and at the IVC. This generates colliding fronts. The picture reports the results corresponding to two different surgical options. The difference is in the flow distribution from the IVC (the so-called hepatic flow distribution): <math display="inline"><semantics> <mrow> <mi>F</mi> <msub> <mi>D</mi> <mrow> <mi>L</mi> <mi>P</mi> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> is the fraction of hepatic flow directed to the left PA. An even flow distribution (i.e., <math display="inline"><semantics> <mrow> <mi>F</mi> <msub> <mi>D</mi> <mrow> <mi>L</mi> <mi>P</mi> <mi>A</mi> </mrow> </msub> <mo>≈</mo> <mn>50</mn> <mo>%</mo> </mrow> </semantics></math>) is desirable. Notice that the different <math display="inline"><semantics> <mrow> <mi>F</mi> <msub> <mi>D</mi> <mrow> <mi>L</mi> <mi>P</mi> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> are created by different offsets between the SVC and IVC.</p>
Full article ">Figure 18
<p>Rising thermal bubble: <math display="inline"><semantics> <msup> <mi>θ</mi> <mo>′</mo> </msup> </semantics></math> given by the ROMs and the FOM at time values within (<b>left</b>) and outside (<b>right</b>) the training dataset.</p>
Full article ">Figure 19
<p>Density current: <math display="inline"><semantics> <msup> <mi>θ</mi> <mo>′</mo> </msup> </semantics></math> given by the ROMs and the FOM at time values within (<b>top</b>) and outside (<b>bottom</b>) the training dataset.</p>
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23 pages, 1999 KiB  
Article
Numerical Solution of the Newtonian Plane Couette Flow with Linear Dynamic Wall Slip
by Muner M. Abou Hasan, Ethar A. A. Ahmed, Ahmed F. Ghaleb, Moustafa S. Abou-Dina and Georgios C. Georgiou
Fluids 2024, 9(8), 172; https://doi.org/10.3390/fluids9080172 - 27 Jul 2024
Viewed by 875
Abstract
An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only [...] Read more.
An efficient numerical approach based on weighted-average finite differences is used to solve the Newtonian plane Couette flow with wall slip, obeying a dynamic slip law that generalizes the Navier slip law with the inclusion of a relaxation term. Slip is exhibited only along the fixed lower plate, and the motion is triggered by the motion of the upper plate. Three different cases are considered for the motion of the moving plate, i.e., constant speed, oscillating speed, and a single-period sinusoidal speed. The velocity and the volumetric flow rate are calculated in all cases and comparisons are made with the results of other methods and available results in the literature. The numerical outcomes confirm the damping with time and the lagging effects arising from the Navier and dynamic wall slip conditions and demonstrate the hysteretic behavior of the slip velocity in following the harmonic boundary motion. Full article
(This article belongs to the Topic Fluid Mechanics, 2nd Edition)
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Figure 1

Figure 1
<p>Geometry of plane Couette flow.</p>
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<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 1 (plate moving at constant speed) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and Navier slip (<math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) for <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip), 1 (moderate slip), and 10 (weak slip). The results obtained with pdepe.m (<b>left column</b>) compare well with those of the WAFDM (<b>right column</b>).</p>
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<p>Evolution of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> using the pdepe function of MATLAB (solid) and the WAFDM (dashed) in Case 1 (plate moving at constant speed and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (Navier slip)) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <span class="html-italic">B</span> = 0.1 (strong slip), and 1 (moderate slip), and 10 (weak slip).</p>
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<p>Evolution of the volumetric flow rate <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 1 (plate moving at constant speed) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (Navier slip), 1, and 10: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) 1 (moderate slip).</p>
Full article ">Figure 4 Cont.
<p>Evolution of the volumetric flow rate <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 1 (plate moving at constant speed) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (Navier slip), 1, and 10: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) 1 (moderate slip).</p>
Full article ">Figure 5
<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip): (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> (Navier slip); (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Evolution of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip) for <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, 1, and 10. Time damping and lagging are observed.</p>
Full article ">Figure 7
<p>Instability of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip), and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip); (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> (weak slip).</p>
Full article ">Figure 9
<p>Evolution of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip), 1 (moderate slip), and 10 (weak slip).</p>
Full article ">Figure 10
<p>Hysteretic behavior of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. Note that the scale of the vertical axis changes.</p>
Full article ">Figure 10 Cont.
<p>Hysteretic behavior of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. Note that the scale of the vertical axis changes.</p>
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<p>Evolution of the volumetric flow rate <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (oscillating plate) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, 5, and 10: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip).</p>
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<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip): (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 12 Cont.
<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip): (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Evolution of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip) for <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, 1, and 10.</p>
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<p>Evolution of the solution <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>y</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip); (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> (weak slip).</p>
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<p>Evolution of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip), 1 (moderate slip), and 10 (weak slip).</p>
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<p>Hysteretic behavior of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. Note that the scale of the vertical axis changes.</p>
Full article ">Figure 16 Cont.
<p>Hysteretic behavior of the slip velocity <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 2 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>. Note that the scale of the vertical axis changes.</p>
Full article ">Figure 17
<p>Evolution of the volumetric flow rate <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> in Case 3 (single-plate oscillation) with <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>Λ</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, 1, and 10: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (strong slip); (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>B</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> (moderate slip, right).</p>
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13 pages, 1980 KiB  
Article
Plasmid DNA Complexes in Powder Form Studied by Spectroscopic and Diffraction Methods
by Aleksandra Radko, Sebastian Lalik, Natalia Górska, Aleksandra Deptuch, Jolanta Świergiel and Monika Marzec
Materials 2024, 17(14), 3530; https://doi.org/10.3390/ma17143530 - 17 Jul 2024
Viewed by 697
Abstract
Currently, new functional materials are being created with a strong emphasis on their ecological aspect. Materials and devices based on DNA biopolymers, being environmentally friendly, are therefore very interesting from the point of view of applications. In this paper, we present the results [...] Read more.
Currently, new functional materials are being created with a strong emphasis on their ecological aspect. Materials and devices based on DNA biopolymers, being environmentally friendly, are therefore very interesting from the point of view of applications. In this paper, we present the results of research on complexes in the powder form based on plasmid DNA (pDNA) and three surfactants with aliphatic chains containing 16 carbon atoms (cetyltrimethylammonium chloride, benzyldimethylhexadecylammonium chloride and hexadecylpyridinium chloride). The X-ray diffraction results indicate a local hexagonal packing of DNA helices in plasmid DNA complexes, resembling the packing for corresponding complexes based on linear DNA. Based on the Fourier-transform infrared spectroscopy results, the DNA conformation in all three complexes was determined as predominantly of A-type. The two relaxation processes revealed by dielectric spectroscopy for all the studied complexes are connected with two different contributions to total conductivity (crystallite part and grain boundaries). The crystallite part (grain interior) was interpreted as an oscillation of the polar surfactant head groups and is dependent on the conformation of the surfactant chain. The influence of the DNA type on the properties of the complexes is discussed, taking into account our previous results for complexes based on linear DNA. We showed that the type of DNA has an impact on the properties of the complexes, which has not been demonstrated so far. It was also found that the layer of pDNA–surfactant complexes can be used as a layer with variable specific electric conductivity by selecting the frequency, which is interesting from an application point of view. Full article
(This article belongs to the Special Issue Liquid Crystals and Other Partially Disordered Molecular Systems)
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<p>FT-MIR spectra of pure components (pDNA, CTMA, HDP and BAC) and obtained complexes: pDNA–CTMA (<b>a</b>), pDNA–HDP (<b>b</b>) and pDNA–BAC (<b>c</b>).</p>
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<p>XRD patterns for pDNA-based complexes with three different surfactants.</p>
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<p>The dielectric dispersion (<b>a</b>) and absorption (<b>b</b>) as well as real part of specific electric conductivity (<b>c</b>) for pDNA complexes. The legend in (<b>a</b>) is the same for all graphs.</p>
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<p>Real (<b>a</b>) and imaginary (<b>b</b>) part of the impedance for all complexes studied; legend in (<b>a</b>) is valid for (<b>b</b>).</p>
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<p>Nyquist plot for complexes studied: pDNA–BAC (<b>a</b>), pDNA–CTMA (<b>b</b>) and pDNA–HDP (<b>c</b>) as well as an impedance spectrum with fitting result for pDNA–HDP complex (<b>d</b>). Black line represents the best fit of Equation (1) to the experimental data (open points); the red line represents fitted data for the grain boundaries (<span class="html-italic">R</span><sub>1</sub>), while the green line represents the grain interior (crystallite part of the sample—<span class="html-italic">R</span><sub>2</sub>). Calculated equivalent circuit: two RC parallel connected in series (<b>e</b>).</p>
Full article ">Figure A1
<p>Comparison of FT-MIR spectra of bulk plasmid DNA (pDNA) and linear DNA (dsDNA). Results for linear DNA are presented in [<a href="#B20-materials-17-03530" class="html-bibr">20</a>].</p>
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20 pages, 4818 KiB  
Article
Research on a Distributed Photovoltaic Two-Level Planning Method Based on the SCMPSO Algorithm
by Ang Dong and Seon-Keun Lee
Energies 2024, 17(13), 3251; https://doi.org/10.3390/en17133251 - 2 Jul 2024
Cited by 1 | Viewed by 668
Abstract
In response to challenges such as voltage limit violations, excessive currents, and power imbalances caused by the integration of distributed photovoltaic (distributed PV) systems into the distribution network, this study proposes at two-level optimization configuration method. This method effectively balances the grid capacity [...] Read more.
In response to challenges such as voltage limit violations, excessive currents, and power imbalances caused by the integration of distributed photovoltaic (distributed PV) systems into the distribution network, this study proposes at two-level optimization configuration method. This method effectively balances the grid capacity and reduces the active power losses, thereby decreasing the operating costs. The upper-level optimization enhances the distribution network’s capacity by determining the siting and sizing of distributed PV devices. The lower-level aims to reduce the active power losses, improve the voltage stability margins, and minimize the voltage deviations. The upper-level planning results, which include the siting and sizing of the distributed PV, are used as initial conditions for the lower level. Subsequently, the lower level feeds back its optimization results to further refine the configuration. The model is solved using an improved second-order oscillating chaotic map particle swarm optimization algorithm (SCMPSO) combined with a second-order relaxation method. The simulation experiments on an improved IEEE 33-bus test system show that the SCMPSO algorithm can effectively reduce the voltage deviations, decrease the voltage fluctuations, lower the active power losses in the distribution network, and significantly enhance the power quality. Full article
(This article belongs to the Topic Advances in Power Science and Technology)
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<p>Distribution network PV integration structure.</p>
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<p>Two-level planning framework for distributed photovoltaics.</p>
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<p>Oscillatory convergence curve.</p>
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<p>Progressive convergence curve.</p>
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<p>Test results of various benchmark functions.</p>
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<p>Iteration comparison of different particle swarm optimization algorithms.</p>
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<p>Model solution flowchart.</p>
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<p>IEEE-33 node system.</p>
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<p>Annual solar intensity and load status.</p>
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<p>24-hour load trend in Jiangsu.</p>
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<p>Charging and discharging schematic of energy storage devices across five scenarios.</p>
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<p>Active power loss over time across five scenarios.</p>
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21 pages, 2528 KiB  
Article
On Dark Matter and Dark Energy in CCC+TL Cosmology
by Rajendra P. Gupta
Universe 2024, 10(6), 266; https://doi.org/10.3390/universe10060266 - 18 Jun 2024
Cited by 1 | Viewed by 1215
Abstract
Relaxing the temporal constancy constraint on coupling constants in an expanding universe results in Friedmann equations containing terms that may be interpreted as dark energy and dark matter. When tired light (TL) was considered to complement the redshift due to the expanding universe, [...] Read more.
Relaxing the temporal constancy constraint on coupling constants in an expanding universe results in Friedmann equations containing terms that may be interpreted as dark energy and dark matter. When tired light (TL) was considered to complement the redshift due to the expanding universe, the resulting covarying coupling constants (CCC+TL) model not only fit the Type Ia supernovae data as precisely as the ΛCDM model, but also resolved concerns about the angular size of cosmic dawn galaxies observed by the James Webb Space Telescope. The model was recently shown to be compliant with the baryon acoustic oscillation features in the galaxy distribution and the cosmic microwave background (CMB). This paper demonstrates that dark energy and dark matter of the standard ΛCDM model are not arbitrary but can be derived from the CCC approach based on Dirac’s 1937 hypothesis. The energy densities associated with dark matter and dark energy turn out to be about the same in the ΛCDM and the CCC+TL models. However, the critical density in the new model can only account for the baryonic matter in the universe, raising concerns about how to account for observations requiring dark matter. We therefore analyze some key parameters of structure formation and show how they are affected in the absence of dark matter in the CCC+TL scenario. It requires reconsidering alternatives to dark matter to explain observations on gravitationally bound structures. Incidentally, since the CCC models inherently have no dark energy, it has no coincidence problem. The model’s consistency with the CMB power spectrum, BBN element abundances, and other critical observations is yet to be established. Full article
(This article belongs to the Special Issue Dark Energy and Dark Matter)
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<p>Variation of <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> <mo>/</mo> <mrow> <mn>2</mn> </mrow> </mrow> </mrow> </msup> <msup> <mrow> <mi>f</mi> </mrow> <mrow> <mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> <mo>/</mo> <mrow> <mn>2</mn> </mrow> </mrow> </mrow> </msup> </mrow> </semantics></math> with measured redshift <math display="inline"><semantics> <mrow> <mi>z</mi> </mrow> </semantics></math>.</p>
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<p>Free fall time ratio for the CTL and ΛCDM models.</p>
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<p>The age advantage in the CTL model over the ΛCDM model.</p>
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<p>The ratio <math display="inline"><semantics> <mrow> <mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mrow> <mi>z</mi> </mrow> <mrow> <mi>c</mi> </mrow> <mrow> <mo>′</mo> </mrow> </msubsup> <mo>)</mo> </mrow> </mrow> </mrow> </semantics></math> as discussed in the text.</p>
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<p>The ratio of cooling time in the CTL and ΛCDM models.</p>
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<p>Aging rate comparison in three models shown with supernovae data.</p>
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15 pages, 2571 KiB  
Article
Nitrogen-Related High-Spin Vacancy Defects in Bulk (SiC) and 2D (hBN) Crystals: Comparative Magnetic Resonance (EPR and ENDOR) Study
by Larisa Latypova, Fadis Murzakhanov, George Mamin, Margarita Sadovnikova, Hans Jurgen von Bardeleben and Marat Gafurov
Quantum Rep. 2024, 6(2), 263-277; https://doi.org/10.3390/quantum6020019 - 14 Jun 2024
Viewed by 1498
Abstract
The distinct spin, optical, and coherence characteristics of solid-state spin defects in semiconductors have positioned them as potential qubits for quantum technologies. Both bulk and two-dimensional materials, with varying structural properties, can serve as crystalline hosts for color centers. In this study, we [...] Read more.
The distinct spin, optical, and coherence characteristics of solid-state spin defects in semiconductors have positioned them as potential qubits for quantum technologies. Both bulk and two-dimensional materials, with varying structural properties, can serve as crystalline hosts for color centers. In this study, we conduct a comparative analysis of the spin–optical, electron–nuclear, and relaxation properties of nitrogen-bound vacancy defects using electron paramagnetic resonance (EPR) and electron–nuclear double resonance (ENDOR) techniques. We examine key parameters of the spin Hamiltonian for the nitrogen vacancy (NV) center in 4H-SiC: D = 1.3 GHz, Azz = 1.1 MHz, and CQ = 2.53 MHz, as well as for the boron vacancy (VB) in hBN: D = 3.6 GHz, Azz = 85 MHz, and CQ = 2.11 MHz, and their dependence on the material matrix. The spin–spin relaxation times T2 (NV center: 50 µs and VB: 15 µs) are influenced by the local nuclear environment and spin diffusion while Rabi oscillation damping times depend on crystal size and the spatial distribution of microwave excitation. The ENDOR absorption width varies significantly among color centers due to differences in crystal structures. These findings underscore the importance of selecting an appropriate material platform for developing quantum registers based on high-spin color centers in quantum information systems. Full article
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<p>(<b>a</b>) hBN crystals mounted on an aluminum substrate before electron irradiation. The distance between the black horizontal lines on the right is 5 mm; (<b>b</b>) Samples under study prepared for high-frequency part of the spectrometer. The characteristic dimensions of the samples and capillaries correspond to the internal diameter of the resonator to achieve the highest filling factor; (<b>c</b>) Bulk crystal (0.42 × 0.67 × 1.22 mm<sup>3</sup>) of silicon carbide under an optical microscope during the preparation of samples for experiments; (<b>d</b>) Bruker Elexsys E680 spectrometer operating at 94 GHz (W-band) equipped with helium flow cryostat; (<b>e</b>) Measurement setup diagram including the main blocks of the spectrometer for the photoinduced EPR and ENDOR.</p>
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<p>(<b>a</b>) ESE-EPR spectra for an <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>N</mi> <mi>V</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> </semantics></math> center in 4H-SiC (top half, red line) and a <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>V</mi> </mrow> <mrow> <mi>B</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> in hBN (bottom half, green line—experiment; blue solid line—simulation). The two insets at top show the detailed recorded low- and high-field components (red solid lines at 532 nm and navy color—“dark” mode) for structurally nonequivalent centers along with the corresponding simulation (blue dashed line). Yellow arrows indicate splittings between the components of the “zero-field splitting”; an asterisk (hBN) and a dot (SiC) indicate optically neutral signals both with spin = 1/2 from ionic compensators and interstitial defects, respectively, and are outside the scope of our study. (<b>b</b>) Schematic of spin polarization of color centers under optical excitation, where GS is a ground state, ES is an excited state, and MS is a metastable state. <span class="html-italic">D</span> denotes zero-field splitting.</p>
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<p>Dynamic characteristics of color centers obtained at <span class="html-italic">Temp.</span> = 10 K and optical excitation with λ = 532 nm. The upper part shows the curves of Rabi oscillations (blue dots) and transverse relaxation time (red solid line in the inset) for <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>N</mi> <mi>V</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> </semantics></math> centers in SiC, and for <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>V</mi> </mrow> <mrow> <mi>B</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> in hBN (Rabi oscillations are shown as green dots, transverse relaxations are shown as a solid dark green line). Red dashed lines for each center show decay traces of Rabi oscillations with characteristic damping time <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>τ</mi> </mrow> <mrow> <mi mathvariant="normal">R</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) EPR spectra of color centers at <span class="html-italic">Temp.</span> = 297 K, where the green solid line is a <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>V</mi> </mrow> <mrow> <mi>B</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> in hBN, the red line in the inset is an <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>N</mi> <mi>V</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> </semantics></math> center in SiC. The middle peak marked by a violet asterisk on the inset refers to an interstitial defect with electron spin <span class="html-italic">S</span> = ½. This spin center is independent of optical excitation of any wavelength (260–980 nm) and is beyond the scope of our study. (<b>b</b>) Spin–spin (<span class="html-italic">T</span><sub>2</sub>) or transverse relaxation and spin–lattice (<span class="html-italic">T</span><sub>1</sub>) or longitudinal relaxation (inset) curves for both color centers, where green is the <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>V</mi> </mrow> <mrow> <mi>B</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> in hBN, red is the <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>N</mi> <mi>V</mi> </mrow> <mrow> <mo>−</mo> </mrow> </msup> </mrow> </semantics></math> center in SiC.</p>
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<p>ENDOR spectra for SiC and hBN irradiated crystals. Hyperfine and quadrupole splitting values of the spin Hamiltonian (1) are shown in <a href="#quantumrep-06-00019-t004" class="html-table">Table 4</a>. The top inset shows individual NMR absorption lines for <sup>14</sup>N nuclei in the hBN and SiC crystal with significantly different line widths Δν.</p>
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16 pages, 386 KiB  
Article
Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations
by Mingxuan Ma, Yanting Li, Michel Godefroid, Gediminas Gaigalas, Jiguang Li, Jacek Bieroń, Chongyang Chen, Jianguo Wang and Per Jönsson
Atoms 2024, 12(6), 30; https://doi.org/10.3390/atoms12060030 - 29 May 2024
Cited by 1 | Viewed by 1361
Abstract
Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron [...] Read more.
Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the 1s and 2s core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the 2s22p23s configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations. Full article
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Figure 1

Figure 1
<p>Convergence of hyperfine constants <span class="html-italic">A</span> for the (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msup> <mi>p</mi> <mn>3</mn> </msup> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">b</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>p</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>4</mn> <mi>p</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> </mrow> </semantics></math> odd states and the (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>s</mi> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">e</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>4</mn> <mi>s</mi> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">f</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>d</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>D</mi> <mrow> <mn>5</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> even states from energy-driven LBL calculations (blue dots + orange lines) and from calculations with merged polarization orbitals (blue crosses). The orbital sets are the ones from <a href="#atoms-12-00030-t001" class="html-table">Table 1</a> and <a href="#atoms-12-00030-t002" class="html-table">Table 2</a>.</p>
Full article ">Figure 1 Cont.
<p>Convergence of hyperfine constants <span class="html-italic">A</span> for the (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msup> <mi>p</mi> <mn>3</mn> </msup> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">b</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>p</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">c</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>4</mn> <mi>p</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msubsup> <mi>S</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <mi>o</mi> </msubsup> </mrow> </semantics></math> odd states and the (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>s</mi> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">e</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>4</mn> <mi>s</mi> <msup> <mo> </mo> <mn>4</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>P</mi> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mrow> <mo>(</mo> <mi mathvariant="bold">f</mi> <mo>)</mo> </mrow> <mspace width="3.33333pt"/> <mn>2</mn> <msup> <mi>p</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>d</mi> <msup> <mo> </mo> <mn>2</mn> </msup> <mspace width="-0.166667em"/> <msub> <mi>D</mi> <mrow> <mn>5</mn> <mo>/</mo> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> even states from energy-driven LBL calculations (blue dots + orange lines) and from calculations with merged polarization orbitals (blue crosses). The orbital sets are the ones from <a href="#atoms-12-00030-t001" class="html-table">Table 1</a> and <a href="#atoms-12-00030-t002" class="html-table">Table 2</a>.</p>
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