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Search Results (963)

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Keywords = kinetic theory

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15 pages, 2173 KiB  
Article
Crystallization Kinetics of Tacrolimus Monohydrate in an Ethanol–Water System
by Suoqing Zhang, Jixiang Zhao, Ming Kong, Jiahui Li, Mingxuan Li, Miao Ma, Li Tong, Tao Li and Mingyang Chen
Crystals 2024, 14(10), 849; https://doi.org/10.3390/cryst14100849 - 28 Sep 2024
Viewed by 334
Abstract
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in [...] Read more.
Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in an ethanol–water system (1:1, v/v) and examines its crystallization kinetics using batch crystallization experiments. Initially, the solubility of FK506 was measured, and classical nucleation theory was employed to analyze the induction period to determine interfacial free energy (γ) and other nucleation parameters, including the critical nucleus radius (r*), critical free energy (G*), and the molecular count of the critical nucleus (i*). Crystallization kinetics under seeded conditions were also measured, and the parameters of the kinetic model were analyzed to understand the effects of process states such as temperature on the crystallization process. The results suggested that increasing temperature and supersaturation promotes nucleation. The surface entropy factor (f) indicates that the tacrolimus crystal growth mechanism is a two-dimensional nucleation growth. The growth process follows the particle size-independent growth law proposed by McCabe. The estimated kinetic parameters reveal the effects of supersaturation, temperature, and suspension density on the nucleation and growth rates. Full article
(This article belongs to the Special Issue Crystallization Process and Simulation Calculation, Third Edition)
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Figure 1

Figure 1
<p>Solubility of tacrolimus monohydrate in an ethanol–water system.</p>
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<p>The variation in transmittance over time.</p>
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<p>Relationship between induction time and supersaturation.</p>
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<p>Relationship between and <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>n</mi> <msub> <mrow> <mi>t</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msup> <mrow> <mn>1</mn> <mo>/</mo> <mfenced separators="|"> <mrow> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">n</mi> <mi>S</mi> </mrow> </mfenced> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>Relationships between nucleation parameters and supersaturation: (<b>a</b>) the radius of the critical nucleus, (<b>b</b>) the critical free energy of the nucleus, (<b>c</b>) primary nucleation rate, and (<b>d</b>) the molecular number of the critical nucleus.</p>
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<p>Relationship between particle density and particle size.</p>
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<p>Relationship between suspension density and nucleation rate.</p>
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<p>Relationships between supersaturation and nucleation (growth).</p>
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<p>Comparison between experimental and theoretical kinetics rate for FK506 crystallization: (<b>a</b>) nucleation rate and (<b>b</b>) growth rate.</p>
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11 pages, 9936 KiB  
Article
Modeling and Experimental Validation of Cell Morphology in Microcellular-Foamed Polycaprolactone
by Donghwan Lim, Sanghyun Lee, Seungho Jung, Kwanhoon Kim, Jin Hong and Sung Woon Cha
Polymers 2024, 16(19), 2723; https://doi.org/10.3390/polym16192723 - 26 Sep 2024
Viewed by 327
Abstract
This study investigates the modeling and experimental validation of cell morphology in microcellular-foamed polycaprolactone (PCL) using supercritical carbon dioxide (scCO2) as the blowing agent. The microcellular foaming process (MCP) was conducted using a solid-state batch foaming process, where PCL was saturated [...] Read more.
This study investigates the modeling and experimental validation of cell morphology in microcellular-foamed polycaprolactone (PCL) using supercritical carbon dioxide (scCO2) as the blowing agent. The microcellular foaming process (MCP) was conducted using a solid-state batch foaming process, where PCL was saturated with scCO2 at 6 to 9 MPa and 313 K, followed by depressurization at a rate of −0.3 and −1 MPa/s. This study utilized the Sanchez–Lacombe equation of state and the Peng–Robinson–Stryjek–Vera equation of state to model the solubility and density of the PCL-CO2 mixture. Classical nucleation theory was modified and combined with numerical analysis to predict cell density, incorporating factors such as gas absorption kinetics, the role of scCO2 in promoting nucleation, and the impact of depressurization rate and saturation pressure on cell growth. The validity of the model was confirmed by comparing the theoretical predictions with experimental and reference data, with the cell density determined through field-emission scanning electron microscopy analysis of foamed PCL samples. This study proposes a method for predicting cell density that can be applied to various polymers, with the potential for wide-ranging applications in biomaterials and industrial settings. This research also introduces a Python-based numerical analysis tool that allows for easy calculation of solubility and cell density based on the material properties of polymers and penetrant gases, offering a practical solution for optimizing MCP conditions in different contexts. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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Figure 1
<p>Optical image of 3D-printed PCL specimen and size.</p>
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<p>Overall process of microcellular foaming process (created with BioRender.com).</p>
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<p>(<b>a</b>) CO<sub>2</sub> density as a function of pressure at 313 K. Physical parameters to calculate cell density at 313 K: (<b>b</b>) CO<sub>2</sub> solubility, (<b>c</b>) interfacial surface tension, and (<b>d</b>) cell nucleation energy barrier.</p>
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<p>SEM images of PCL samples at 313 K under varying saturation pressures and depressurization rates. (<b>a</b>) 6 MPa, −0.3 MPa/s, ×300, (<b>b</b>) 7 MPa, −0.3 MPa/s, ×300, (<b>c</b>) 8 MPa, −0.3 MPa/s, ×500, (<b>d</b>) 9 MPa, −0.3 MPa/s, ×1000, and (<b>e</b>) 8 MPa, −1 MPa/s, ×500.</p>
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<p>Theoretical cell density at 313 K predicted by SL-EOS and CNT, compared with experimentally measured cell density at 6, 7, 8, and 9 MPa, 313 K, −0.3, MPa/s and 8 MPa, 313 K, −1 MPa/s.</p>
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20 pages, 5563 KiB  
Article
Performance Enhancement of Polyurethane Acrylate Resin by Urushiol: Rheological and Kinetic Studies
by Yuchi Zhang, Run Fang, Hanyu Xue, Yuansong Ye, Li Chen and Jianrong Xia
Polymers 2024, 16(19), 2716; https://doi.org/10.3390/polym16192716 - 25 Sep 2024
Viewed by 438
Abstract
A natural extract, i.e., urushiol, was employed to effectively cross-link and modify commercial wet-cured polyurethane acrylic resin. Comprehensive characterization of the paint film was performed using techniques such as FTIR, SEM, and TGA. The results indicated that the incorporation of urushiol significantly increased [...] Read more.
A natural extract, i.e., urushiol, was employed to effectively cross-link and modify commercial wet-cured polyurethane acrylic resin. Comprehensive characterization of the paint film was performed using techniques such as FTIR, SEM, and TGA. The results indicated that the incorporation of urushiol significantly increased the cross-linking density of the resin, which in turn enhanced the film-forming properties, mechanical strength, and thermal stability of the paint film. Additionally, the study discovered that under isothermal conditions, the dynamic moduli (G′ and G″) of the paint film are related to the gel point frequency by a power law, aligning with the predictions of percolation theory. The application of the autocatalytic model has provided a novel approach to studying non-isothermal kinetic reactions, offering valuable insights for process optimization and further development of urushiol-based polyurethane. Full article
(This article belongs to the Special Issue Additive Agents for Polymer Functionalization Modification)
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<p>Chemical structure and composition of urushiol.</p>
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<p>FTIR spectra of the PUA and PUA-U25 coating films.</p>
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<p>FTIR spectra of NCO changes over time in PUA-U25 coatings.</p>
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<p>TG curves of PUA with variation in urushiol content.</p>
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<p>SEM images of the PUA surface (<b>a</b>), the PUA-U25 surface (<b>b</b>), the PUA cross-sectional morphology (<b>c</b>), the PUA-U25 cross-sectional morphology (<b>d</b>).</p>
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<p>The time-dependent isothermal viscosity curve |η*| (color-coded mark) of the PUA-U25 system in the thermal range of 40–80 °C.</p>
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<p>Variation of the dynamic moduli (G′ and G″, color-coded mark) with the reaction time of the PUA-U25 system during curing at different temperatures: (<b>a</b>–<b>e</b>) represent 40 °C to 80 °C, respectively, and (<b>f</b>) represents the Arrhenius expression of t<sub>c</sub> as a reciprocal temperature function (the gel point at t<sub>c</sub> was determined at the G′ and G″ crossover).</p>
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<p>Viscoelastic properties (G′, G″, and tanδ) versus reaction time of the PUA-U25 system in multi-frequency mode at 70 °C. The gel point, t<sub>gel</sub>, is determined from the intersection point.</p>
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<p>Variation of G′ as a function of angular frequency (<b>a</b>) of the PUA-U25 system; the change in G″ with angular frequency (<b>b</b>) of the PUA-U25 system; time dependence of exponents n′ and n′′ obtained from the data of G′ and G″ at 70 °C (<b>c</b>). The arrow indicates the gel time, t<sub>gel</sub>.</p>
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<p>Storage modulus (G′) and loss modulus (G″) versus temperature at various heating rates of the PUA-U25 system.</p>
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<p>The non-isothermal rheological curve of the PUA-U25 system.</p>
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<p>The law of conversion rate changes with temperature during the curing process of the PUA-U25 system.</p>
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<p>Non-isothermal autocatalytic simulation data and experimental data comparison of the PUA-U25 system.</p>
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<p>Ln (β/T<sup>2</sup>) versus 1/T of the PUA-U25 system.</p>
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<p>The evolution of <span class="html-italic">E<sub>α</sub></span> with the conversion rate during the curing process of the PUA-U25 system.</p>
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16 pages, 3242 KiB  
Article
Unveiling the Photodegradation Mechanism of Monochlorinated Naphthalenes under UV-C Irradiation: Affecting Factors Analysis, the Roles of Hydroxyl Radicals, and DFT Calculation
by Yingtan Yu, Mengdi Liu, Shimeng Wang, Chaoxing Zhang, Xue Zhang, Li Liu and Shuang Xue
Molecules 2024, 29(19), 4535; https://doi.org/10.3390/molecules29194535 - 24 Sep 2024
Viewed by 279
Abstract
Polychlorinated naphthalenes (PCNs) are a new type of persistent organic pollutant (POP) characterized by persistence, bioaccumulation, dioxin-like toxicity, and long-range atmospheric transport. Focusing on one type of PCN, monochlorinated naphthalenes (CN-1, CN-2), this study aimed to examine their photodegradation in the environment. In [...] Read more.
Polychlorinated naphthalenes (PCNs) are a new type of persistent organic pollutant (POP) characterized by persistence, bioaccumulation, dioxin-like toxicity, and long-range atmospheric transport. Focusing on one type of PCN, monochlorinated naphthalenes (CN-1, CN-2), this study aimed to examine their photodegradation in the environment. In this work, CN-1 and CN-2 were employed as the model pollutants to investigate their photodegradation process under UV-C irradiation. Factors like the pH, initial concentrations of CN-1, and inorganic anions were investigated. Next, the roles of hydroxyl radicals (OH), superoxide anion radicals (O2•−), and singlet oxygen (1O2) in the photodegradation process were discussed and proposed via theory computation. The results show that the photodegradation of CN-1 and CN-2 follows pseudo-first-order kinetics. Acidic conditions promote the photodegradation of CN-1, while the effects of pH on the photodegradation of CN-2 are not remarkable. Cl, NO3, and SO32− accelerate the photodegradation of CN-1, whereas the effect of SO42− and CO32− is not significant. Additionally, the contributions of OH and O2•− to the photodegradation of CN-1 are 20.47% and 38.80%, while, for CN-2, the contribution is 16.40% and 16.80%, respectively. Moreover, the contribution of 1O2 is 15.7%. Based on DFT calculations, C4 and C6 of the CN-1 benzene ring are prioritized attack sites for OH, while C2 and C9 of CN-2 are prioritized attack sites. Full article
(This article belongs to the Section Cross-Field Chemistry)
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Graphical abstract

Graphical abstract
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<p>(<b>a</b>) Comparison of light and dark reactions between CN-1 and CN-2; (<b>b</b>) effect of initial concentration of CN-1 on photodegradation rate. Conditions: [CN-1]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, [CN-2]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, 20 °C.</p>
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<p>Effect of different pH on photodegradation of (<b>a</b>) CN-1, (<b>b</b>) CN-2. Conditions: [CN-1]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, [CN-2]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, 20 °C.</p>
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<p>Effects of IPA on photodegradation of (<b>a</b>) CN-1, (<b>b</b>) CN-2; effects of H<sub>2</sub>O<sub>2</sub> on photodegradation reaction of (<b>c</b>) CN-1, (<b>d</b>) CN-2; effects of CCl<sub>4</sub> on photodegradation of (<b>e</b>) CN-1, (<b>f</b>) CN-2; conditions: [CN-1]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, [CN-2]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, 20 °C.</p>
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<p>EPR spectra for different systems with (<b>a</b>) DMPO-<sup>•</sup>OH; (<b>b</b>) DMPO-O<sub>2</sub><sup>•−</sup>.</p>
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<p>Effect of different substances on the photodegradation of CN–. (<b>a</b>) NaCl; (<b>b</b>) Na<sub>2</sub>CO<sub>3</sub>; (<b>c</b>) NaSO<sub>4</sub>; (<b>d</b>) NaNO<sub>3</sub>; (<b>e</b>) Na<sub>2</sub>SO<sub>3</sub>; (<b>f</b>) effects of TBA and EtOH on the photodegradation of CN-1 with Na<sub>2</sub>SO<sub>3</sub>. Conditions: [CN-1]<sub>0</sub> = 0.615 μmol L<sup>−1</sup>, 20 °C.</p>
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<p>Calculated reaction barriers (ΔrG) for the <sup>•</sup>OH; (<b>a</b>) CN-1; (<b>b</b>) CN-2.</p>
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16 pages, 3558 KiB  
Article
Experimental and Theoretical Studies on the Adsorption of Bromocresol Green from Aqueous Solution Using Cucumber Straw Biochar
by Chenxi Zhang, Lingbin Meng, Zhihao Fang, Youxin Xu, Yue Zhou, Hongsen Guo, Jinyu Wang, Xiaotian Zhao, Shuyan Zang and Hailin Shen
Molecules 2024, 29(19), 4517; https://doi.org/10.3390/molecules29194517 - 24 Sep 2024
Viewed by 509
Abstract
Biochar prepared from crop straw is an economical method for adsorbing bromocresol green (BCG) from textile industrial wastewater. However, there is limited research on the adsorption mechanism of biochar for the removal of BCG. This study utilized cucumber straw as raw material to [...] Read more.
Biochar prepared from crop straw is an economical method for adsorbing bromocresol green (BCG) from textile industrial wastewater. However, there is limited research on the adsorption mechanism of biochar for the removal of BCG. This study utilized cucumber straw as raw material to prepare biochar with good adsorption potential and characterized its physicochemical properties. Through adsorption experiments, the effects of solution pH, biochar dosage, and initial dye concentration on adsorption performance were examined. The adsorption mechanism of cucumber straw biochar (CBC) for BCG was elucidated at the molecular level using adsorption kinetics, adsorption isotherm models, and density functional theory (DFT) calculations. Results show that the specific surface area of the CBC is 101.58 m2/g, and it has a high degree of carbonization, similar to the structure of graphite crystals. The presence of aromatic rings, –OH groups, and –COOH groups in CBC provides abundant adsorption sites for BCG. The adsorption process of CBC for BCG is influenced by both physical and chemical adsorption, and can be described by the Langmuir isotherm model, indicating a monolayer adsorption process. The theoretical maximum monolayer adsorption capacity (qm) of BCG at 298 K was calculated to be 99.18 mg/g. DFT calculations reveal interactions between BCG and CBC involving electrostatic interactions, van der Waals forces, halogen–π interactions, π–π interactions, and hydrogen bonds. Additionally, the interaction of hydrogen bonds between BCG and the –COOH group of biochar is stronger than that between BCG and the –OH group. These findings provide valuable insights into the preparation and application of efficient organic dye adsorbents. Full article
(This article belongs to the Section Green Chemistry)
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Figure 1
<p>(<b>a</b>) SEM image, and (<b>b</b>) the N<sub>2</sub> adsorption–desorption isotherms of CBC.</p>
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<p>XRD patterns of CBC.</p>
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<p>(<b>a</b>) The FT-IR spectra of CBC before and after the adsorption of BCG, (<b>b</b>) XPS spectra of CBC, (<b>c</b>) XPS core spectrum C 1s before adsorption, (<b>d</b>) XPS core spectrum C 1s after adsorption, (<b>e</b>) XPS core spectrum O 1s before adsorption, and (<b>f</b>) XPS core spectrum O 1s after adsorption.</p>
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<p>Effects of (<b>a</b>) pH, (<b>b</b>) temperature, and (<b>c</b>) dosage on the removal of BCG.</p>
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<p>(<b>a</b>) Sorption kinetics of BCG onto CBC, and (<b>b</b>) sorption isotherms of BCG onto CBC.</p>
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<p>The ESP of (<b>a</b>) BC, (<b>b</b>) BCG, (<b>c</b>) BC–COOH and (<b>d</b>) BC–OH.</p>
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<p>Optimal adsorption configuration and calculated adsorption energies for BCG adsorbed on BC.</p>
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<p>Optimal adsorption configuration and calculated adsorption energies for BCG adsorbed on BC–COOH and BC–OH.</p>
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<p>Removal rate at different cycle numbers.</p>
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27 pages, 2408 KiB  
Article
Study of the Thermomechanical Behavior of Single-Crystal and Polycrystal Copper
by Sudip Kunda, Noah J. Schmelzer, Akhilesh Pedgaonkar, Jack E. Rees, Samuel D. Dunham, Charles K. C. Lieou, Justin C. M. Langbaum and Curt A. Bronkhorst
Metals 2024, 14(9), 1086; https://doi.org/10.3390/met14091086 - 22 Sep 2024
Viewed by 615
Abstract
This research paper presents an experimental, theoretical, and numerical study of the thermomechanical behavior of single-crystal and polycrystal copper under uniaxial stress compression loading at varying rates of deformation. The thermomechanical theory is based on a thermodynamically consistent framework for single-crystal face-centered cubic [...] Read more.
This research paper presents an experimental, theoretical, and numerical study of the thermomechanical behavior of single-crystal and polycrystal copper under uniaxial stress compression loading at varying rates of deformation. The thermomechanical theory is based on a thermodynamically consistent framework for single-crystal face-centered cubic metals, and assumes that all plastic power is partitioned between stored energy due to dislocation structure evolution (configurational) and thermal (kinetic vibrational) energy. An expression for the Taylor–Quinney factor is proposed, which is a simple function of effective temperature and is allowed by second-law restrictions. This single-crystal model is used for the study of single- and polycrystal copper. New polycrystal thermomechanical experimental results are presented at varying strain rates. The temperature evolution on the surface of the polycrystal samples is measured using mounted thermocouples. Thermomechanical numerical single- and polycrystal simulations were performed for all experimental conditions ranging between 103 and 5 × 103 s1. A Taylor homogenization model is used to represent polycrystal behavior. The numerical simulations of all conditions compare reasonable well with experimental results for both stress and temperature evolution. Given our lack of understanding of the mechanisms responsible for the coupling of dislocation glide and atomic vibration, this implies that the proposed theory is a reasonably accurate approximation of the single-crystal thermomechanics. Full article
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Figure 1
<p>Meshes representing initial configurations: (<b>a</b>) single-crystal, sample size of 6mm diameter and 6 mm length; (<b>b</b>) axisymmetric and half-length thermomechanical polycrystal mesh (sample size of 12.7 mm diameter and 19.05 mm length), where the left edge is the axis of symmetry, the top edge is the sample’s center, the bottom (tan) region corresponds to steel platens (9.34 mm height, 6.35 mm width), the top (green) region corresponds to copper (9.525 mm height), and a thin (0.0127 mm) PTFE layer is between the steel and copper; (<b>c</b>) axisymmetric and half-length thermal transient model.</p>
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<p>Temperature transient results used to determine a numerical film coefficient for the air–solid interface of 0.18 W/m<sup>2</sup>-K. The temperature measured by the thermocouples and simulated temperature are taken from the center surface node.</p>
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<p>Comparison of experiment and simulation for single-crystal copper. Solid lines represent experiments and dashed lines represent simulations. Plastic work densities are calculated as the area under the stress–strain curve. The simulation temperature change was taken from the center surface node. (<b>a</b>) Single crystal stress–strain; (<b>b</b>) 0.1 <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> and 2.0 <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> temperature change; (<b>c</b>) 3000 <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> temperature change; (<b>d</b>) 4000 <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> and 5800 <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> temperature changes.</p>
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<p>Comparison of polycrystal experiment and simulation results: (<b>a</b>) stress-strain curve for polycrystal copper and (<b>b</b>) temperature evolution for polycrystal copper. The experimental temperature was measured by thermocouples, while the simulated temperature was taken from the center surface node.</p>
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<p>Deformed shapes of single-crystal simulations, showing the von Mises stress for different strain rates: (<b>a</b>), <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>3000</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>4800</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. All images were taken at an axial compressive strain of 0.35. The von Mises stress, also known as equivalent stress, is defined as <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>V</mi> <mi>M</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> <msup> <munder> <mi mathvariant="bold">T</mi> <mo>̲</mo> </munder> <mo>′</mo> </msup> <mo>:</mo> <msup> <munder> <mi mathvariant="bold">T</mi> <mo>̲</mo> </munder> <mo>′</mo> </msup> </mrow> </msqrt> </mrow> </semantics></math>.</p>
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<p>Deformed shapes of single-crystal simulations showing the temperature for different strain rates: (<b>a</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>3000</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>ϵ</mi> <mo>˙</mo> </mover> <mo>=</mo> <mn>4800</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msup> <mi mathvariant="normal">s</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math>. The initial temperature for all simulations was 295 K. All images were taken at an axial compressive strain of 0.35.</p>
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<p>Evolution of Taylor-Quinney state variables for single and polycrystal simulations: (<b>a</b>) single-crystal Taylor-Quinney factor; (<b>b</b>) polycrystal Taylor-Quinney factor; (<b>c</b>) polycrystal effective temperature; (<b>d</b>) polycrystal steady-state effective temperature.</p>
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22 pages, 2742 KiB  
Article
Simulation of Shock Waves in Methane: A Self-Consistent Continuum Approach Enhanced Using Machine Learning
by Zarina Maksudova, Liia Shakurova and Elena Kustova
Mathematics 2024, 12(18), 2924; https://doi.org/10.3390/math12182924 - 20 Sep 2024
Viewed by 521
Abstract
This study presents a self-consistent one-temperature approach for modeling shock waves in single-component methane. The rigorous mathematical model takes into account the complex structure of CH4 molecules with multiple vibrational modes and incorporates exact kinetic theory-based transport coefficients, including bulk viscosity. The [...] Read more.
This study presents a self-consistent one-temperature approach for modeling shock waves in single-component methane. The rigorous mathematical model takes into account the complex structure of CH4 molecules with multiple vibrational modes and incorporates exact kinetic theory-based transport coefficients, including bulk viscosity. The effects of the bulk viscosity on gas-dynamic variables and transport terms are investigated in detail under varying degree of gas rarefaction. It is demonstrated that neglecting bulk viscosity significantly alters the shock front width and peak values of normal stress and heat flux, with the effect being more evident in denser gases. The study also evaluates limitations in the use of a constant specific heat ratio, revealing that this approach fails to accurately predict post-shock parameters in polyatomic gases, even at moderate Mach numbers. To enhance computational efficiency, a simplified approach based on a reduced vibrational spectrum is assessed. The results indicate that considering only the ground state leads to substantial errors in the fluid-dynamic variables across the shock front. Another approach explored involves the application of machine learning techniques to calculate vibrational energy and specific heat. Among the methods tested, the Feedforward Neural Network (FNN) proves to be the most effective, offering significant acceleration in calculations and providing one of the lowest errors. When integrated into the fluid-dynamic solver, the FNN approach yields nearly a three-fold increase in speed in numerical simulations of the shock wave structure. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning, 2nd Edition)
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Figure 1

Figure 1
<p>Vibrational modes of methane. 1–4 correspond to symmetrical, twisting, antisymmetrical, and scissoring modes (see <a href="#mathematics-12-02924-t001" class="html-table">Table 1</a>).</p>
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<p>Specific heat capacity (<b>left</b>) and thermal conductivity coefficient (<b>right</b>) as functions of <span class="html-italic">T</span>. Comparison with reference data [<a href="#B48-mathematics-12-02924" class="html-bibr">48</a>].</p>
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<p>Shear viscosity coefficient (<b>left</b>) and ratio of bulk and shear viscosity coefficients (<b>right</b>) as functions of <span class="html-italic">T</span>. Comparison with reference data [<a href="#B48-mathematics-12-02924" class="html-bibr">48</a>,<a href="#B58-mathematics-12-02924" class="html-bibr">58</a>].</p>
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<p>Density (<b>left</b>) and temperature (<b>right</b>) profiles as functions of the normalized distance <span class="html-italic">x</span> under different modeling scenarios, <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> Pa.</p>
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<p>Viscous stress (<b>left</b>), <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>−</mo> <mi>p</mi> </mrow> </semantics></math>, and heat flux (<b>right</b>) as functions of the normalized distance <span class="html-italic">x</span> under different modeling scenarios, <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> Pa.</p>
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<p>Temperature profiles as functions of the distance <span class="html-italic">x</span> for different free-stream pressures. Effect of bulk viscosity.</p>
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<p>Viscous stress (<b>left</b>), <math display="inline"><semantics> <mrow> <mi>P</mi> <mo>−</mo> <mi>p</mi> </mrow> </semantics></math>, and heat flux (<b>right</b>) as functions of the distance <span class="html-italic">x</span> for different free-stream pressures. Effect of bulk viscosity.</p>
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<p>Specific heat ratio as a function of the normalized distance <span class="html-italic">x</span> for different Mach numbers.</p>
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<p>Percentage error in <math display="inline"><semantics> <msub> <mi>E</mi> <mi>vibr</mi> </msub> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <msub> <mi>c</mi> <mi>vibr</mi> </msub> </semantics></math> (<b>right</b>) predicted using the FNN with respect to the general theoretical model as a function of <span class="html-italic">T</span>.</p>
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<p>Comparison of density (<b>left</b>) and temperature (<b>right</b>) profiles across the shock calculated using the general model and FNN.</p>
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27 pages, 9433 KiB  
Article
Pyrolysis and Physicochemical, Thermokinetic and Thermodynamic Analyses of Ceiba aesculifolia (Kunth) Britt and Baker Waste to Evaluate Its Bioenergy Potential
by José Juan Alvarado Flores, Luis Fernando Pintor Ibarra, Fernando Daniel Mendez Zetina, José Guadalupe Rutiaga Quiñones, Jorge Víctor Alcaraz Vera and María Liliana Ávalos Rodríguez
Molecules 2024, 29(18), 4388; https://doi.org/10.3390/molecules29184388 - 15 Sep 2024
Viewed by 776
Abstract
Ceiba aesculifolia is an important species in Mexico that generates significant amounts of biomass waste during its exploitation, which can be utilized to produce energy. This study presents the characterization of this waste based on chemical (proximal and elemental) and thermal analyses (TGA-DTG) [...] Read more.
Ceiba aesculifolia is an important species in Mexico that generates significant amounts of biomass waste during its exploitation, which can be utilized to produce energy. This study presents the characterization of this waste based on chemical (proximal and elemental) and thermal analyses (TGA-DTG) at different heating rates (β = 10–30 °C/min (283–303 K/min)) in the presence of nitrogen and in a temperature range of 25–900 °C. Kinetic parameters were calculated and analyzed as well. Activation energy (Ea) and the pre-exponential factor (A) were determined using the Friedman (132.03 kJ/mol, 8.11E + 10 s −1), FWO (121.65 kJ/mol, 4.30E + 09), KAS (118.14 kJ/mol, 2.41E + 09), and Kissinger (155.85 kJ/mol, 3.47E + 11) kinetic methods. Variation in the reaction order, n (0.3937–0.6141), was obtained by Avrami’s theory. We also calculated the thermodynamic parameters (ΔH, ΔG, ΔS) for each kinetic method applied. The results for Ea, A, n, ΔH, ΔG, and ΔS show that this biomass waste is apt for use in pyrolysis. Moreover, the moisture (<10%), ash (<2%), volatile material (>80%), and HHV (>19%) contents of C. aesculifolia allowed us to predict acceptable performance in generating energy and fuels. Finally, infrared spectroscopy analysis (FT-IR) allowed us to identify important functional groups, including one that belongs to the family of the aliphatic hydrocarbons. Full article
(This article belongs to the Special Issue Lignocellulosic Biomass III)
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Figure 1

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<p>Generation of high-value-added products from biomass.</p>
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<p>Basic chemical composition of <span class="html-italic">C. aesculifolia</span> wood.</p>
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<p>TGA-DTG test of <span class="html-italic">C. aesculifolia</span> for five heating rates.</p>
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<p>Regression lines to apparent activation energy proposed by Friedman (<b>a</b>), Flynn–Wall–Ozawa (FWO) (<b>b</b>), Kissinger–Akahira–Sunose (KAS) (<b>c</b>), and Kissinger (<b>d</b>) method free plots at the different heating rates for <span class="html-italic">C. aesculifolia</span> biomass.</p>
Full article ">Figure 4 Cont.
<p>Regression lines to apparent activation energy proposed by Friedman (<b>a</b>), Flynn–Wall–Ozawa (FWO) (<b>b</b>), Kissinger–Akahira–Sunose (KAS) (<b>c</b>), and Kissinger (<b>d</b>) method free plots at the different heating rates for <span class="html-italic">C. aesculifolia</span> biomass.</p>
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<p>Regression lines to reaction order (<span class="html-italic">n</span>) proposed by Avrami’s theory.</p>
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<p>FT-IR spectra of <span class="html-italic">C. aesculifolia</span>.</p>
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<p>Geographic location of <span class="html-italic">C. aesculifolia</span>.</p>
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<p>Equipment for thermogravimetric analysis (<b>a</b>), nitrogen tanks used in the experiment (<b>b</b>) and heating ramp used (<b>c</b>).</p>
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<p>General biomass pyrolysis process.</p>
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<p>Mathematical method to determine the kinetic parameters of <span class="html-italic">C. aesculifolia</span>.</p>
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<p>Equations for the determination of thermodynamic parameters, where <span class="html-italic">E<sub>a</sub></span> is the activation energy, <span class="html-italic">R</span> is the ideal gas constant, <span class="html-italic">T<sub>α</sub></span> is the temperature according to the degree of conversion, <span class="html-italic">T<sub>m</sub></span> is the temperature at the maximum peak of the DTG, <span class="html-italic">K<sub>B</sub></span> is the Boltzmann constant (1.381E-23 J/K), <span class="html-italic">h</span> is Planck’s constant (6.626E-34 J.s), and β is the heating rate (15 °C/min).</p>
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14 pages, 2373 KiB  
Article
Reaction Rate Rules of Intramolecular H-Migration Reaction Class for RIORIIOO·Radicals in Ether Combustion
by Xiaohui Sun and Zerong Li
Molecules 2024, 29(18), 4387; https://doi.org/10.3390/molecules29184387 - 15 Sep 2024
Viewed by 395
Abstract
The intramolecular H-migration reaction of RIORIIOO· radicals constitute a key class of reactions in the low-temperature combustion mechanism of ethers. Despite this, there is a dearth of direct computations regarding the potential energy surface and rate constants specific to [...] Read more.
The intramolecular H-migration reaction of RIORIIOO· radicals constitute a key class of reactions in the low-temperature combustion mechanism of ethers. Despite this, there is a dearth of direct computations regarding the potential energy surface and rate constants specific to ethers, especially when considering large molecular systems and intricate branched-chain structures. Furthermore, combustion kinetic models for large molecular ethers generally utilize rate constants derived from those of structurally similar alcohols or alkane fuels. Consequently, chemical kinetic studies involve the calculation of energy barriers and rate rules for the intramolecular H-migration reaction class of RIORIIOO· radicals, which are systematically conducted using the isodesmic reaction method (IRM). The geometries of the species participating in these reactions are optimized, and frequency calculations are executed using the M06–X method in tandem with the 6–31+G(d,p) basis set by the Gaussian 16 program. Moreover, the M06–2X/6–31+G(d,p) method acts as the low-level ab initio method, while the CBS–QB3 method is utilized as the high-level ab initio method for calculating single-point energies. Rate constants at the high-pressure-limit are computed based on the reaction class transition state theory (RC-TST) by ChemRate program, incorporating asymmetric Eckart tunneling corrections for intramolecular H-migration reactions across a temperature range of 500 to 2000 K. It was found that the isodesmic reaction method gives accurate energy barriers and rate constants, and the rate constants of the H-migration reaction for RIORIIOO· radicals diverge from those of comparable reactions in alkanes and alcohol fuels. There are significant disparities in energy barriers and rate constants across the entire reaction classes of the H-migration reaction for RIORIIOO· radicals, necessitating the subdivision of the H-migration reaction into subclasses. Rate rules are established by averaging the rate constants of representative reactions for each subclass, which is pivotal for the advancement of accurate low-temperature combustion reaction mechanisms for ethers. Full article
(This article belongs to the Section Physical Chemistry)
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Figure 1
<p>Comparison of the energy barriers between the CCSD(T)/cc-PVTZ and CBS–QB3 method.</p>
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<p>Comparison of the rate constants between the CBS–QB3 method and isodesmic reaction method at 500 K, 1000 K, and 1500 K.</p>
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<p>Comparison of average rate constants for 1,6 H–migration reaction of different peroxy radicals [<a href="#B30-molecules-29-04387" class="html-bibr">30</a>,<a href="#B34-molecules-29-04387" class="html-bibr">34</a>]. (<b>a</b>) 1,6-H(p) (<b>b</b>) 1,6-H(s) (<b>c</b>) 1,6-H(t).</p>
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<p>Rate constants of 1,6 H–migration reaction (1200 K) as a function of the type of carbon atoms of different peroxy radicals.</p>
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<p>Reaction path for ethers at low temperature [<a href="#B3-molecules-29-04387" class="html-bibr">3</a>].</p>
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<p>The geometry structure of transition states (TSs) for different reaction classes. (<b>a</b>)1,3–H migration (<b>b</b>) 1,5–H migration (<b>c</b>)1,6-H migration (<b>d</b>)1,7–H migration.</p>
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12 pages, 2847 KiB  
Article
Computational Insights into the Radical Scavenging Activity and Xanthine Oxidase Inhibition of the Five Anthocyanins Derived from Grape Skin
by Xiao-Qin Lu, Jindong Li, Bin Wang and Shu Qin
Antioxidants 2024, 13(9), 1117; https://doi.org/10.3390/antiox13091117 - 15 Sep 2024
Viewed by 458
Abstract
Anthocyanins, typical polyphenol compounds in grape skin, have attracted increasing interest due to their health-promoting properties. In this body of work, five representative anthocyanins (Cy-3-O-glc, Dp-3-O-glc, Pn-3-O-glc, Mv-3-O-glc, and Pt-3-O-glc) were studied using [...] Read more.
Anthocyanins, typical polyphenol compounds in grape skin, have attracted increasing interest due to their health-promoting properties. In this body of work, five representative anthocyanins (Cy-3-O-glc, Dp-3-O-glc, Pn-3-O-glc, Mv-3-O-glc, and Pt-3-O-glc) were studied using the density functional theory (DFT) to elucidate structure–radical scavenging activity in the relationship and the reaction path underlying the radical-trapping process. Based on thermodynamic parameters involved in HAT, SET-PT, and SPLET mechanisms, along with the structural attributes, it was found that the C4′ hydroxyl group mainly contributes to the radical scavenging activities of the investigated compounds. Pt-3-O-glc exhibits a good antioxidant capacity among the five compounds. The preferred radical scavenging mechanisms vary in different phases. For the Pt-3-O-glc compound, the calculations indicate the thermodynamically favoured product is benzodioxole, rather than o-quinone, displaying considerably reduced energy in double HAT mechanisms. Additionally, the thermodynamic and kinetic calculations indicate that the reaction of OH into the 4′-OH site of Pt-3-O-glc has a lower energy barrier (7.6 kcal/mol), a higher rate constant (5.72 × 109 M−1 s−1), and exhibits potent OH radical scavenging properties. Molecular docking results have shown the strong affinity of the studied anthocyanins with the pro-oxidant enzyme xanthine oxidase, displaying their significant role in inhibiting ROS formation. Full article
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Figure 1
<p>Basis structure and atom numbering sites of anthocyanin and chemical structures of five anthocyanins derived from grape skin.</p>
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<p>Double HAT mechanism of Pt-3-<span class="html-italic">O</span>-glc in the gas phase and solvents (unit: kcal/mol).</p>
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<p>The PESs of reaction between Pt-3-<span class="html-italic">O</span>-glc and <sup>•</sup>OH via HAT pathway in the gas phase. The distances are shown in blue (unit: Å). The gray, red, and white balls represent the elements C, O, and H, respectively.</p>
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<p>The 3D and 2D interactions of the Pt-3-<span class="html-italic">O</span>-glc with XO, along with the corresponding binding poses.</p>
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14 pages, 2392 KiB  
Article
Quantitative Assessment of Rock Burst Risk in Roadway Tunneling Considering Variation of Coal Mass Parameters
by Yu Yang and Ning Li
Appl. Sci. 2024, 14(18), 8211; https://doi.org/10.3390/app14188211 - 12 Sep 2024
Viewed by 292
Abstract
To investigate the influence of varied mechanical parameters of coal mass on rock burst occurrence during deep roadway tunneling, the surrounding coal and rock mass of a deep roadway were taken as the research objects. A geometric model of roadway tunneling was developed [...] Read more.
To investigate the influence of varied mechanical parameters of coal mass on rock burst occurrence during deep roadway tunneling, the surrounding coal and rock mass of a deep roadway were taken as the research objects. A geometric model of roadway tunneling was developed using 3DEC numerical simulation software, and the failure characteristics of the coal mass in the roadway side were analyzed based on the rock burst mechanism and stress difference gradient theory for deep mining. The risk of rock burst during roadway tunneling was quantitatively assessed using the change rate of the stress difference gradient (Dgc), thereby elucidating the burst failure patterns of the deep roadway under the influence of varied mechanical parameters. The findings indicate that the coal mass in the roadway side zone is more prone to burst failure due to stress disturbances during deep excavation compared to the coal and rock mass in the roof and floor zones, and that the released kinetic energy and the risk of burst failure are positively correlated with the magnitude of the ground stress. The variation of the mechanical properties of coal mass has a significant effect on the rock burst risk during roadway tunneling. The variation of both internal friction angle and cohesion significantly affects rock burst, with cohesion exerting a greater influence. Conversely, the elastic modulus does not significantly impact the risk. The tendency of bursting in the coal mass is positively correlated with the coefficient of variation (COV) in cohesion and negatively correlated with the COV in internal friction angle. These research findings offer valuable insights for the quantitative assessment of rock burst risk during roadway tunneling. Full article
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<p>Rock strata and block delineation in the model.</p>
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<p>Schematic locations of monitoring points.</p>
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<p>Plot of displacements at monitoring points versus time steps.</p>
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<p>Plot of velocities at monitoring points versus time steps.</p>
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<p>Plot of displacements on the tunnel roadway side versus time steps of different coal mass parameters.</p>
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<p>Plots of coal mass kinetic energy versus time steps for ten groups of parameters.</p>
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<p>Plots of coal mass kinetic energy versus time steps under different ground stresses.</p>
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<p>Histogram of three-way difference gradient and rate of change for coal mass under different ground stresses.</p>
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<p>Plot of gradient of stress differences and change rates for 10 groups of parameters.</p>
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<p>Plots of <span class="html-italic">D<sub>gc</sub></span> curves under different COVs for coal mass mechanical parameters.</p>
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16 pages, 3327 KiB  
Article
Computational Exploration of the Mechanism of Action of a Sorafenib-Containing Ruthenium Complex as an Anticancer Agent for Photoactivated Chemotherapy
by Pierraffaele Barretta, Fortuna Ponte, Daniel Escudero and Gloria Mazzone
Molecules 2024, 29(18), 4298; https://doi.org/10.3390/molecules29184298 - 11 Sep 2024
Viewed by 418
Abstract
Ruthenium(II) polypyridyl complexes are being tested as potential anticancer agents in different therapies, which include conventional chemotherapy and light-activated approaches. A mechanistic study on a recently synthesized dual-action Ru(II) complex [Ru(bpy)2(sora)Cl]+ is described here. It is characterized by two mono-dentate [...] Read more.
Ruthenium(II) polypyridyl complexes are being tested as potential anticancer agents in different therapies, which include conventional chemotherapy and light-activated approaches. A mechanistic study on a recently synthesized dual-action Ru(II) complex [Ru(bpy)2(sora)Cl]+ is described here. It is characterized by two mono-dentate leaving ligands, namely, chloride and sorafenib ligands, which make it possible to form a di-aquo complex able to bind DNA. At the same time, while the released sorafenib can induce ferroptosis, the complex is also able to act as a photosensitizer according to type II photodynamic therapy processes, thus generating one of the most harmful cytotoxic species, 1O2. In order to clarify the mechanism of action of the drug, computational strategies based on density functional theory are exploited. The photophysical properties of the complex, which include the absorption spectrum, the kinetics of ISC, and the character of all the excited states potentially involved in 1O2 generation, as well as the pathway providing the di-aquo complex, are fully explored. Interestingly, the outcomes show that light is needed to form the mono–aquo complex, after releasing both chloride and sorafenib ligands, while the second solvent molecule enters the coordination sphere of the metal once the system has come back to the ground-state potential energy surface. In order to simulate the interaction with canonical DNA, the di-aquo complex interaction with a guanine nucleobase as a model has also been studied. The whole study aims to elucidate the intricate details of the photodissociation process, which could help with designing tailored metal complexes as potential anticancer agents. Full article
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Figure 1
<p>Optimized structures of the (<b>a</b>) synthesized <b>Ru-Sora</b> complex and the models (<b>b</b>) <b>RuS</b> and (<b>c</b>) <b>Ru</b>. Selected bond lengths and valence angles are reported in Å and degrees, respectively.</p>
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<p>(<b>a</b>) Absorption spectra of the synthesized complex <b>Ru-Sora</b> [<a href="#B21-molecules-29-04298" class="html-bibr">21</a>] and the models <b>RuS</b> and <b>Ru</b>. (<b>b</b>) NTOs of the lowest-lying singlet state (λ<sub>max</sub>).</p>
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<p>(<b>a</b>) Absorption spectra of <b>RuS</b> complex in which the main vertical electronic transitions (those with an oscillator strength (a.u.) greater than 0.01), together with the main character of the two bands, are reported; (<b>b</b>) percentage of metal-centered (MC), ligand-centered (LC), metal-to-ligand (MLCT), ligand-to-metal (LMCT) and ligand-to-ligand (LLCT) charge transfers character for each vertical transition; (<b>c</b>) oscillator strength (a.u.) for the first thirty electronic transitions.</p>
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<p>Computed spin density isosurfaces (accomplished with an isovalue of 1 × 10<sup>−3</sup> a.u., envy and purple colors stand for positive and negative parts) of the intercepted TDA–PBE0 triplet states. The spin density of the metal center and adiabatic energy gap ΔE with respect to the GS are also provided.</p>
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<p>Jablonski-like diagram representing the mechanism of action of the <b>RuS</b> complex. The kinetic constant of the most probable ISC process starting from the lowest-lying singlet state (S<sub>1</sub>) is reported above the dashed red arrow in s<sup>−1</sup>.</p>
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<p>Calculated B3LYP-D3 free energy profile describing the activation mechanisms of <b>Ru</b> complex. Energies are in kcal mol<sup>−1</sup> and relative to separated reactants, which are <b>Ru</b> complex and two water molecules.</p>
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<p>Reaction mechanism found for the substitution reaction of a water molecule with the guanine purine base. Relative Gibbs free energies (kcal mol<sup>−1</sup>) are reported in bold. The optimized structure of the intercepted transition states is reported above the arrows. For the sake of clarity in the sketched minima structures, the species around the metal complex, either guanine or water, are omitted.</p>
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<p>Schematic mechanism of action of the <b>Ru-Sora</b> complex, where ISC stands for intersystem crossing and EnT for energy transfer.</p>
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<p>Proposed activation mechanism of <b>Ru-Sora</b> complex.</p>
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4 pages, 693 KiB  
Proceeding Paper
Hybrid Chemical and Data-Driven Model for Stiff Chemical Kinetics Using a Physics-Informed Neural Network
by Matthew Frankel, Mario De Florio, Enrico Schiassi and Lina Sela
Eng. Proc. 2024, 69(1), 40; https://doi.org/10.3390/engproc2024069040 - 3 Sep 2024
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Abstract
Models of chemical kinetic processes, comprising systems of stiff ordinary differential equations (ODEs), are essential for modeling important chemical reactions relevant to drinking water chemistry, such as disinfectant decay and disinfection byproduct formation. However, the accuracy of these models can be inhibited by [...] Read more.
Models of chemical kinetic processes, comprising systems of stiff ordinary differential equations (ODEs), are essential for modeling important chemical reactions relevant to drinking water chemistry, such as disinfectant decay and disinfection byproduct formation. However, the accuracy of these models can be inhibited by (1) the challenge of fully describing the chemical reaction system, and (2) additional chemical reactions occurring in actual environmental settings that were not accounted for in the laboratory conditions used to develop and calibrate the models. This study proposes the use of a Physics-Informed Neural Network framework, utilizing the eXtreme Theory of Functional Connections (X-TFC) technique to create a hybrid chemical- and data-driven model that incorporates data and the underlying system of ODEs into the trained model in order to increase the accuracy of the predicted chemical concentrations. Full article
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<p>X-TFC model results using training data for TOTNH and TOTCl.</p>
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25 pages, 10275 KiB  
Article
Production of Low-Cost Adsorbents within a Circular Economy Approach: Use of Spruce Sawdust Pretreated with Desalination Brine to Adsorb Methylene Blue
by Dorothea Politi, Elias Sakellis and Dimitrios Sidiras
Materials 2024, 17(17), 4317; https://doi.org/10.3390/ma17174317 - 30 Aug 2024
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Abstract
A sustainable low-cost activated carbon substitute was produced based on pretreated lignocellulosic biomass, especially spruce sawdust. A harmful liquid waste, desalination brine, was used for the treatment of a solid wood industry waste, spruce sawdust. This approach is in the circular economy theory [...] Read more.
A sustainable low-cost activated carbon substitute was produced based on pretreated lignocellulosic biomass, especially spruce sawdust. A harmful liquid waste, desalination brine, was used for the treatment of a solid wood industry waste, spruce sawdust. This approach is in the circular economy theory and aims at the decarbonization of the economy. Pretreated sawdust was tested as an adsorbent appropriate for the removal of a commonly used pollutant, methylene blue, from industrial wastewater. The adsorption capacity of the pretreated material was found to have increased four times compared to the untreated one in the case that the Freundlich equation was fitted to the isotherms’ data, i.e., the one with the best fit to the isotherm’s experimental data of the three isotherm models used herein. The treatment experimental conditions with desalination brine that gave maximum adsorption capacity correspond to a 1.97 combined severity factor in logarithmic form value. Moreover, a kinetic experiment was carried out with regard to the methylene blue adsorption process. The desalination brine-pretreated sawdust adsorption capacity increased approximately two times compared to the untreated one, in the case when the second-order kinetic equation was used, which had the best fit of the kinetic data of the three kinetic models used herein. In this case, the pretreatment experimental conditions that gave maximum adsorption capacity correspond to −1.049 combined severity factor in logarithmic form. Industrial scale applications can be based on the kinetic data findings, i.e., spruce sawdust optimal pretreatment conditions at 200 °C, for 25 min, with brine solution containing 98.12 g L−1 NaCl, as they are related to a much shorter adsorption period compared to the isotherm data. Full article
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<p>Brine pretreatment process was performed in a 4-L PARR batch reactor (autoclave).</p>
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<p>Temperature vs. time of the spruce sawdust desalination brine pretreatment experiments using a 4-L autoclave for 160, 200, and 240 °C ending temperatures.</p>
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<p>Autoclave pressure profile vs. time of the spruce sawdust desalination brine pretreatment experiments at 160, 200, and 240 °C ending temperatures.</p>
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<p>Spruce brine pretreatment’s liquid phase pH vs. the combined severity factor logarithm.</p>
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<p>Spruce sawdust desalination brine pretreatment experiments solid residue yield (SRY) vs. the combined severity factor logarithm.</p>
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<p>Spruce sawdust desalination brine pretreatment experiments solid residue BET values vs. the combined severity factor logarithm.</p>
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<p>Freundlich isotherm model for methylene blue adsorption on pretreated (240 °C, 25 min, 178.71 mg/L NaCl) and untreated spruce sawdust (<b>a</b>) logq vs. logCe and (<b>b</b>) q vs. Ce. Brine concentrated seven times compared to the simulated seawater.</p>
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<p>Langmuir isotherm equation for methylene blue adsorption on pretreated (240 °C, 25 min, 178.71 mg/L NaCl) and untreated spruce sawdust (<b>a</b>) 1/q vs. 1/C<sub>e</sub> and (<b>b</b>) q vs. C<sub>e</sub>. Brine concentrated seven times compared to the simulated seawater.</p>
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<p>Sips isotherm model for methylene blue adsorption on pretreated (240 °C, 25 min, 178.71 mg/L NaCl) and untreated spruce sawdust, q vs. C<sub>e</sub>. Brine concentrated seven times compared to the simulated seawater.</p>
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<p>(<b>a</b>) Freundlich capacity <span class="html-italic">K<sub>F</sub></span> and (<b>b</b>) Langmuir capacity <span class="html-italic">q<sub>m</sub></span> parameters of the isotherm models vs. combined severity factor logarithm.</p>
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<p>(<b>a</b>) Freundlich intensity <span class="html-italic">n</span> and (<b>b</b>) Langmuir intensity <span class="html-italic">K<sub>L</sub></span> of the isotherm models vs. combined severity factor logarithm.</p>
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<p>The Lagergren (first-order) kinetics of methylene blue adsorption on pretreated (200 °C, 25 min, 98.12 mg/L NaCl) and untreated spruce sawdust. Adsorption temperature 23 °C, initial methylene blue concentration C<sub>0</sub> = 12 mg L<sup>−1</sup>, m/V = 1 g L<sup>−1</sup>.</p>
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<p>(<b>a</b>) Lagergren (first-order) and (<b>b</b>) second-order adsorption kinetic rate parameter for methylene blue adsorption on pretreated and untreated spruce vs. the logarithm of the combined severity factor.</p>
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<p>(<b>a</b>) Lagergren (first-order) and (<b>b</b>) second-order adsorption capacity parameter for methylene blue adsorption on pretreated and untreated spruce vs. the logarithm of the combined severity factor.</p>
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<p>Second-order kinetics of methylene blue adsorption on pretreated (200 °C, 25 min, 98.12 mg/L NaCl), untreated, and spruce sawdust. Adsorption temperature 23 °C, methylene blue initial concentration Co = 12 mg L<sup>−1</sup>, m/V = 1 gL<sup>−1</sup>.</p>
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<p>Intraparticle kinetics of methylene blue adsorption on untreated and brine-treated (200 °C, 25 min, 98.12 NaCl) spruce sawdust (<b>a</b>) <span class="html-italic">q<sub>t</sub></span> vs. <span class="html-italic">t</span><sup>0.5</sup> and (<b>b</b>) <span class="html-italic">q<sub>t</sub></span> vs. <span class="html-italic">t</span>. Adsorption temperature 23 °C, MB initial concentration C<sub>0</sub> = 12 mg L<sup>−1</sup>, m/V = 1 gL<sup>−1</sup>.</p>
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<p>SEM of untreated spruce sawdust with magnification (<b>a</b>) 750×, (<b>b</b>) 7500×, and (<b>c</b>) 30,000×.</p>
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<p>SEM of pretreated spruce sawdust. The pretreatment was using desalination brine (containing 178.71 g L<sup>−1</sup> NaCl and other contents) at 200 °C for 50 min. The magnification was (<b>a</b>) 750×, (<b>b</b>) 7500×, and (<b>c</b>) 30,000×.</p>
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<p>FTIR spectra of (<b>a</b>) untreated and (<b>b</b>) desalination brine-pretreated spruce sawdust.</p>
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<p>XRD patterns of desalination brine-pretreated and untreated spruce sawdust. The pretreatment was using desalination brine (containing 178.71 g L<sup>−1</sup> NaCl and other contents) at 200 °C for 50 min.</p>
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<p>Crystallinity index (CrI) of desalination brine-pretreated spruce sawdust vs. the logarithm of the combined severity factor (log<span class="html-italic">R</span><sub>0</sub>*).</p>
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20 pages, 17123 KiB  
Article
A Physics-Informed Neural Network Based on the Boltzmann Equation with Multiple-Relaxation-Time Collision Operators
by Zhixiang Liu, Chenkai Zhang, Wenhao Zhu and Dongmei Huang
Axioms 2024, 13(9), 588; https://doi.org/10.3390/axioms13090588 - 29 Aug 2024
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Abstract
The Boltzmann equation with multiple-relaxation-time (MRT) collision operators has been widely employed in kinetic theory to describe the behavior of gases and liquids at the macro-level. Given the successful development of deep learning and the availability of data analytic tools, it is a [...] Read more.
The Boltzmann equation with multiple-relaxation-time (MRT) collision operators has been widely employed in kinetic theory to describe the behavior of gases and liquids at the macro-level. Given the successful development of deep learning and the availability of data analytic tools, it is a feasible idea to try to solve the Boltzmann-MRT equation using a neural network-based method. Based on the canonical polyadic decomposition, a new physics-informed neural network describing the Boltzmann-MRT equation, named the network for MRT collision (NMRT), is proposed in this paper for solving the Boltzmann-MRT equation. The method of tensor decomposition in the Boltzmann-MRT equation is utilized to combine the collision matrix with discrete distribution functions within the moment space. Multiscale modeling is adopted to accelerate the convergence of high frequencies for the equations. The micro–macro decomposition method is applied to improve learning efficiency. The problem-dependent loss function is proposed to balance the weight of the function for different conditions at different velocities. These strategies will greatly improve the accuracy of the network. The numerical experiments are tested, including the advection–diffusion problem and the wave propagation problem. The results of the numerical simulation show that the network-based method can obtain a measure of accuracy at O103. Full article
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<p>Network architecture. <math display="inline"><semantics> <mi mathvariant="bold">x</mi> </semantics></math> is spatial space and t is time, which all are the inputs of the network. The Monte Carlo method is used to create a dataset. Multiscale modeling and canonical polyadic decomposition are adopted in the neural network.</p>
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<p>Compositions of the loss function. <math display="inline"><semantics> <mi mathvariant="bold">x</mi> </semantics></math> is spatial space and t is time, which are inputs to the network. The Monte Carlo method is used to create a dataset. The loss function is made up of three parts: IC loss, BC loss, and PDE loss. The problem-dependent weights for the three loss parts are adopted.</p>
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<p>Numerical solution of advection–diffusion problem using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.01</mn> <mo>,</mo> <mn>0.1</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math>. The numerical solution of NMRT is the solid line, and the reference solution is the dashed line. (<b>a</b>) s = 0.01, t = 0; (<b>b</b>) s = 0.01, t = 0.1; (<b>c</b>) s = 0.1, t = 0; (<b>d</b>) s = 0.1, t = 0.1; (<b>e</b>) s = 1.0, t = 0; (<b>f</b>) s = 1.0, t = 0.1.</p>
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<p>Numerical solution of advection–diffusion problem using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.01</mn> <mo>,</mo> <mn>0.1</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math>. The numerical solution of NMRT is the solid line, and the reference solution is the dashed line. (<b>a</b>) s = 0.01, t = 0; (<b>b</b>) s = 0.01, t = 0.1; (<b>c</b>) s = 0.1, t = 0; (<b>d</b>) s = 0.1, t = 0.1; (<b>e</b>) s = 1.0, t = 0; (<b>f</b>) s = 1.0, t = 0.1.</p>
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<p>Numerical solution of wave propagation problem using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.01</mn> <mo>,</mo> <mn>0.1</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math>. The numerical solution of NMRT is the solid line, and the reference solution is the dashed line. (<b>a</b>) s = 0.01, t = 0; (<b>b</b>) s = 0.01, t = 0.1; (<b>c</b>) s = 0.1, t = 0; (<b>d</b>) s = 0.1, t = 0.1; (<b>e</b>) s = 1.0, t = 0; (<b>f</b>) s = 1.0, t = 0.1.</p>
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<p>Numerical solution of the wave propagation problem in two-dimensional scenarios using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>. The first row corresponds to the density <math display="inline"><semantics> <mi>ρ</mi> </semantics></math>, the second column corresponds to the macroscopic velocity <span class="html-italic">u</span>, and the last column corresponds to the temperature <span class="html-italic">T</span>. The numerical solution of NMRT is the solid line, and the result of FSM is the dashed line. (<b>a</b>) <span class="html-italic">s</span> = 0.01, <span class="html-italic">t</span> = 0.1; (<b>b</b>) <span class="html-italic">s</span> = 0.01, <span class="html-italic">t</span> = 0.1; (<b>c</b>) <span class="html-italic">s</span> = 0.01, <span class="html-italic">t</span> = 0.1.</p>
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<p>Numerical solution of wave propagation problem in two-dimensional scenarios using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>. The first row corresponds to the density <math display="inline"><semantics> <mi>ρ</mi> </semantics></math>, the second column corresponds to the macroscopic velocity <span class="html-italic">u</span>, and the last column corresponds to the temperature <span class="html-italic">T</span>. The numerical solution of NMRT is the solid line, and the result of FSM is the dashed line. (<b>a</b>) <span class="html-italic">s</span> = 0.1, <span class="html-italic">t</span> = 0.1; (<b>b</b>) <span class="html-italic">s</span> = 0.1, <span class="html-italic">t</span> = 0.1; (<b>c</b>) <span class="html-italic">s</span> = 0.1, <span class="html-italic">t</span> = 0.1.</p>
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<p>Numerical solution of the wave propagation problem in two-dimensional scenarios using NMRT for <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>. The first row corresponds to the density <math display="inline"><semantics> <mi>ρ</mi> </semantics></math>, the second column corresponds to the macroscopic velocity <span class="html-italic">u</span>, and the last column corresponds to the temperature <span class="html-italic">T</span>. The numerical solution of NMRT is the solid line, and the result of FSM is the dashed line. (<b>a</b>) <span class="html-italic">s</span> = 1.0, <span class="html-italic">t</span> = 0.1; (<b>b</b>) <span class="html-italic">s</span> = 1.0, <span class="html-italic">t</span> = 0.1; (<b>c</b>) <span class="html-italic">s</span> = 1.0, <span class="html-italic">t</span> = 0.1.</p>
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