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Search Results (4,095)

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22 pages, 1193 KiB  
Article
Do High School Students Learn More or Shift Their Beliefs and Attitudes Toward Learning Physics with the Social Constructivism of Problem-Based Learning?
by Amangul Sagatbek, Temitayo Kehinde Oni, Emily Adah Miller, Gulmira Gabdullina and Nuri Balta
Educ. Sci. 2024, 14(12), 1280; https://doi.org/10.3390/educsci14121280 - 22 Nov 2024
Viewed by 191
Abstract
Rooted in social constructivist learning theory, problem-based learning (PBL) is a tool that deepens students’ learning of complex subjects and improves students’ attitudes and beliefs towards learning. Physics is a subject that students themselves view as challenging. When taking physics, students develop negative [...] Read more.
Rooted in social constructivist learning theory, problem-based learning (PBL) is a tool that deepens students’ learning of complex subjects and improves students’ attitudes and beliefs towards learning. Physics is a subject that students themselves view as challenging. When taking physics, students develop negative beliefs about their own learning of the subject. There is a call for more innovation in the subject area of physics. This study addresses the following: (1) What is the effect of PBL on the achievement of 10th-grade students in mechanics when compared to traditional instruction? (2) How do students’ beliefs and attitudes towards physics change before and after the intervention, and how might these beliefs and attitudes relate to their competency outcomes? The sample of this study comprised 63 students in the 10th grade in a public (non-elite) school distributed across four classes, where the teacher used PBL with the experimental group and traditional teaching with the control group. The physics teacher who implemented PBL has 13 years of teaching experience. The two instruments used were the Force Concept Inventory and the Colorado Learning Attitudes About Science Survey. The result of this study revealed that, although students’ knowledge of physics increased when their teachers adopted the PBL approach, there were no significant changes in their attitudes and beliefs towards learning physics. The implications suggest that there is potential for PBL to be taken up by high school science teachers to improve their students’ physics knowledge, but may this not impact their attitudes and beliefs, which presents questions to investigate further. Full article
(This article belongs to the Section STEM Education)
13 pages, 4985 KiB  
Article
Unveiling the Photocatalytic Potential of BiAgOS Solid Solution for Hydrogen Evolution Reaction
by Oumaima Ben Abdelhadi, Majid El Kassaoui, Hajar Moatassim, Ahmed Kotbi, Mohamed Balli, Omar Mounkachi and Mustapha Jouiad
Nanomaterials 2024, 14(23), 1869; https://doi.org/10.3390/nano14231869 - 22 Nov 2024
Viewed by 399
Abstract
The growing emphasis on green energy has spurred momentum in research and development within the field of photocatalytic materials, particularly for green hydrogen production. Among the most abundant oxides on Earth, oxychalcogenides stand out for their cost-effectiveness and ease of synthesis. In this [...] Read more.
The growing emphasis on green energy has spurred momentum in research and development within the field of photocatalytic materials, particularly for green hydrogen production. Among the most abundant oxides on Earth, oxychalcogenides stand out for their cost-effectiveness and ease of synthesis. In this context, we present an investigation of the potential use of BiAgOS as an efficient photocatalyst for hydrogen generation. Utilizing density functional theory and ab initio molecular dynamics (AIMD) simulations, we computed its physical properties and assessed its photocatalytic performance. Specifically, using Heyd–Scuseria–Ernzerhof corrections, our calculations yielded an appropriate electronic gap of ~1.47 eV necessary for driving the water-splitting reaction. Additionally, we obtained a very high optical absorption coefficient of ~5 × 105/cm–1 and an estimation of hydrogen generation yield of ~289.56 µmol∙g–1. These findings suggest that BiAgOS holds promise for enabling the development of cheap, reliable, and highly efficient photocatalysts for hydrogen production. Full article
(This article belongs to the Special Issue Advanced Nanomaterials for Photocatalysis)
Show Figures

Figure 1

Figure 1
<p>(<b>a</b>) Top/side view of BiAgOS crystal after relaxation, (<b>b</b>) top snapshot with the corresponding variation of the total energy between 0 and 7 ps during the AIMD simulations at 300 K, (<b>c</b>) the phonon spectra and PhDOS, (<b>d</b>) variation of entropy S, heat capacity C<sub>V</sub>, and enthalpy H as a function of temperature, and (<b>e</b>) variation of Gibbs free energy as a function of temperature.</p>
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<p>DFT computed band structures of BiAgOS using (<b>a</b>) PBE approximation and (<b>b</b>) HSE approximation.</p>
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<p>DFT computed the total and partial DOS of BiAgOS using (<b>a</b>) PBE approximation and (<b>b</b>) HSE approximation. The Fermi energy level (<span class="html-italic">E<sub>f</sub></span>) is set to 0 eV.</p>
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<p>Computed optical properties of BiAgOS: (<b>a</b>) absorption as a function of energy, (<b>b</b>) absorption coefficient, and (<b>c</b>) reflectivity.</p>
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<p>Computed thermoelectric properties of BiAGOS: (<b>a</b>) electrical conductivity, (<b>b</b>) thermal conductivity, (<b>c</b>) electronic specific heat, and (<b>d</b>) Seebeck coefficient as a function of temperature.</p>
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<p>Variation in conduction band energy (blue) and valence band energy (red) as a function of pH.</p>
Full article ">
18 pages, 616 KiB  
Article
Differences in Water-Saving Behaviors Among College Students: Research Based on the Theory of Planned Behavior
by Xiaosheng Wang, Zhaoxing Liu and Yanping Zhang
Sustainability 2024, 16(23), 10182; https://doi.org/10.3390/su162310182 - 21 Nov 2024
Viewed by 262
Abstract
The implementation of water-saving methods has become imperative in college water management to facilitate the promotion of the sustainable growth of water resources within educational institutions. This research aimed to identify differences in water-saving behaviors (WSBs) among college students due to different environmental [...] Read more.
The implementation of water-saving methods has become imperative in college water management to facilitate the promotion of the sustainable growth of water resources within educational institutions. This research aimed to identify differences in water-saving behaviors (WSBs) among college students due to different environmental education in their schools and to determine the corresponding driving factors. The specific steps were as follows: Firstly, specific factors based on the theory of planned behavior (TPB) and specific WSBs were selected for conducting a questionnaire. Then, 347 college students from HUE’s School of Water Conservancy and Hydroelectric Power (S1) and School of Mathematics and Physics (S2) were surveyed. Finally, factor analysis and gray relational analysis were utilized to analyze the data. The results show that the college students from S1 scored better in regard to three WSBs than the students from S2. This can be attributed to the better environmental education offered by S1, which improved the students’ understanding of the importance of water saving. This paper highlights the differences in WSBs among college students and suggests ways for college administrators in departments concerned with course offerings, such as the Ministry of Education and the Office of Academic Affairs, to improve these behaviors. Full article
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Figure 1
<p>A flowchart of the adopted methodology.</p>
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<p>The specific process of the TPB and the theoretical model. (<b>a</b>) The specific process of the TPB. (<b>b</b>) The theoretical model of this research.</p>
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<p>Plot of variable percentage pile area. (<b>a</b>) Variables that differed between schools. (<b>b</b>) Variables that were the same between schools.</p>
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24 pages, 9885 KiB  
Article
General Three-Body Problem in Conformal-Euclidean Space: New Properties of a Low-Dimensional Dynamical System
by Ashot S. Gevorkyan, Aleksander V. Bogdanov and Vladimir V. Mareev
Particles 2024, 7(4), 1038-1061; https://doi.org/10.3390/particles7040063 - 20 Nov 2024
Viewed by 267
Abstract
Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, [...] Read more.
Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynamical systems. In addition, one often has to answer the cognitive question: is irreversibility fundamental for the description of the classical world? To answer this question, we considered a reference classical dynamical system, the general three-body problem, formulating it in conformal Euclidean space and rigorously proving its equivalence to the Newtonian three-body problem. It has been proven that a curved configuration space with a local coordinate system reveals new hidden symmetries of the internal motion of a dynamical system, which makes it possible to reduce the problem to a sixth-order system instead of the eighth order. An important consequence of the developed representation is that the chronologizing parameter of the motion of a system of bodies, which we call internal time, differs significantly from ordinary time in its properties. In particular, it more accurately describes the irreversible nature of multichannel scattering in a three-body system and other chaotic properties of a dynamical system. The paper derives an equation describing the evolution of the flow of geodesic trajectories, with the help of which the entropy of the system is constructed. New criteria for assessing the complexity of a low-dimensional dynamical system and the dimension of stochastic fractal structures arising in three-dimensional space are obtained. An effective mathematical algorithm is developed for the numerical simulation of the general three-body problem, which is traditionally a difficult-to-solve system of stiff ordinary differential equations. Full article
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Figure 1

Figure 1
<p>The problem of multichannel scattering in a classical three-body system can be represented in the most general form, as shown in the diagram, where 1, 2 and 3 denote interacting particles, brackets (<math display="inline"><semantics> <mrow> <mo>⋯</mo> </mrow> </semantics></math>) denote a coupled system of two bodies, and <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <mo>⋯</mo> <mo>)</mo> </mrow> <mo>∗</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mrow> <mo>(</mo> <mo>⋯</mo> <mo>)</mo> </mrow> <mrow> <mo>∗</mo> <mo>∗</mo> </mrow> </msup> </semantics></math> denote accordingly some short-lived coupled three-body system.</p>
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<p>In the Cartesian coordinate system <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo>,</mo> <mi>Z</mi> <mo>)</mo> </mrow> </semantics></math>, the Jacobi coordinates <math display="inline"><semantics> <mrow> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>ρ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> are shown, where the colored circles indicate bodies 1, 2 and 3, and the colorless circle respectively indicates the center of mass of bodies 2 and 3.</p>
Full article ">Figure 3
<p>The set of smooth curves <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>=</mo> <mo>(</mo> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>3</mn> </msub> <mo>,</mo> <mspace width="0.166667em"/> <msub> <mi mathvariant="fraktur">s</mi> <mn>4</mn> </msub> <mo>)</mo> </mrow> </semantics></math> connecting the asymptotic subspace <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>i</mi> <mi>n</mi> <mo>)</mo> </mrow> </semantics></math>, in which the three-body system <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </semantics></math> is grouped, with other asymptotic subspaces <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>o</mi> <mi>u</mi> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, where the particles are grouped as follows: <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> <mo>+</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> <mo>+</mo> <mn>2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> </mrow> </semantics></math>. The distance between particles “<span class="html-italic">i</span>” and “<span class="html-italic">j</span>” in the Cartesian coordinate system is given by the expression <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mspace width="0.166667em"/> <mi>i</mi> <mo>≠</mo> <mi>j</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <msubsup> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mn>0</mn> </msubsup> </semantics></math> - the average distance between particles in the corresponding pairs. During the scattering process, the three-dimensional internal time <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </semantics></math>, which has an arrow, selects a specific asymptotic subspace for transition, which in some conditions may be random.</p>
Full article ">Figure 4
<p>Energy surface of interaction particles for three different scattering angles. Recall that <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>3</mn> </msub> </semantics></math> in Jacobi coordinates determines the scattering angle, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>3</mn> </msub> <mo>=</mo> <mi>ϑ</mi> </mrow> </semantics></math> (see <a href="#particles-07-00063-f002" class="html-fig">Figure 2</a>).</p>
Full article ">Figure 5
<p>A manifold of the family <math display="inline"><semantics> <mi mathvariant="script">A</mi> </semantics></math>, which has the form <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (sphere) and two additional manifolds surrounding it from left to right <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math>. Combining these manifolds by a direct product, we obtain a complete member of the family <math display="inline"><semantics> <mi mathvariant="script">A</mi> </semantics></math>, which can be represented in the following form <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="script">R</mi> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>A manifold of the family <math display="inline"><semantics> <mi mathvariant="script">B</mi> </semantics></math>, which has the form <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> (two three-dimensional pyramids fastened together) and two additional manifolds surrounding it from left to right <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math> and <math display="inline"><semantics> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </semantics></math>. Combining these manifolds by a direct product, we obtain a complete member of the family <math display="inline"><semantics> <mi mathvariant="script">B</mi> </semantics></math>, which can be represented in the following form <math display="inline"><semantics> <mrow> <msubsup> <mi mathvariant="script">R</mi> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>×</mo> <msubsup> <mi mathvariant="script">R</mi> <mrow> <mo>(</mo> <msub> <mi>α</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Internal time of three particles for three different initial data on two different complete terms of the manifolds <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math>. On the plots, blue and red colors indicate internal times that were calculated on the manifolds <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math>, respectively. Each point of internal time, if projected onto the coordinate axes, determines the configuration of three particles at a given moment.</p>
Full article ">Figure 8
<p>On the left are plots of two internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve), which were obtained by calculating on the <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> manifold with initial conditions differing by <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math>. On the right is a plot of the Lyapunov exponent versus time. As can be clearly seen from the plot, the Lyapunov exponent very slowly tends to zero.</p>
Full article ">Figure 9
<p>On the left are plots of two internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve), which were obtained by calculating on the <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math> manifold with initial conditions differing by <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math>. On the right is a plot of the Lyapunov exponent versus time.</p>
Full article ">Figure 10
<p>On the left in the first figure, internal times <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(red curve) and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="fraktur">s</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mo>}</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>-(blue curve) are shown that were calculated on the manifolds’ families <math display="inline"><semantics> <msub> <mi mathvariant="script">A</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="script">B</mi> <mn>1</mn> </msub> </semantics></math> for the same initial data using the third line of <a href="#particles-07-00063-t002" class="html-table">Table 2</a>. The second plot from the left shows the internal time <math display="inline"><semantics> <mrow> <mi mathvariant="fraktur">s</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> depending the ordinary time “<span class="html-italic">t</span>” for the two marked families of manifolds. As can be seen from the graph, internal time can be either positive or negative. The third figure from the left shows the dimensionality of the structures formed by internal times in three-dimensional space.</p>
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20 pages, 298 KiB  
Review
Career Choices Among Individuals with Disabilities in the Gulf Region: Cultural, Religious, Policy, and Socio-Economic Influences: A Literature Review
by Maha Al-Hendawi, Esraa Hussein and Fathia Ismail
Societies 2024, 14(11), 243; https://doi.org/10.3390/soc14110243 - 20 Nov 2024
Viewed by 260
Abstract
This study explores the multifaceted factors influencing career decisions among individuals with disabilities (IWDs) in the Gulf region, emphasizing the interplay between health and cultural/religious contexts. To examine these complex influences, this review adopts Bronfenbrenner’s Ecological Systems Theory as a guiding framework. This [...] Read more.
This study explores the multifaceted factors influencing career decisions among individuals with disabilities (IWDs) in the Gulf region, emphasizing the interplay between health and cultural/religious contexts. To examine these complex influences, this review adopts Bronfenbrenner’s Ecological Systems Theory as a guiding framework. This theoretical lens facilitates an in-depth analysis of how personal attributes, religious and cultural beliefs, disability-specific challenges, systemic and environmental barriers, gender-related issues, social networks, transition and teachers’ attitudes, work environment, and government policies interact across multiple levels to shape career choices for IWDs in the Gulf region. Cultural and religious beliefs critically shape both the perceptions and opportunities available to IWDs, reflecting the broader macrosystem influences. By applying this multi-layered approach, this review highlights the need to integrate religious and spiritual considerations into support frameworks to enhance the mental and physical well-being of IWDs as they navigate their career paths. The findings suggest actionable implications for policymakers and practitioners dedicated to improving inclusion and equity in the workforce for individuals with disabilities. Full article
26 pages, 7129 KiB  
Article
Multiscale Modeling of Nanoparticle Precipitation in Oxide Dispersion-Strengthened Steels Produced by Laser Powder Bed Fusion
by Zhengming Wang, Seongun Yang, Stephanie B. Lawson, Cheng-Hsiao Tsai, V. Vinay K. Doddapaneni, Marc Albert, Benjamin Sutton, Chih-Hung Chang, Somayeh Pasebani and Donghua Xu
Materials 2024, 17(22), 5661; https://doi.org/10.3390/ma17225661 - 20 Nov 2024
Viewed by 467
Abstract
Laser Powder Bed Fusion (LPBF) enables the efficient production of near-net-shape oxide dispersion-strengthened (ODS) alloys, which possess superior mechanical properties due to oxide nanoparticles (e.g., yttrium oxide, Y-O, and yttrium-titanium oxide, Y-Ti-O) embedded in the alloy matrix. To better understand the precipitation mechanisms [...] Read more.
Laser Powder Bed Fusion (LPBF) enables the efficient production of near-net-shape oxide dispersion-strengthened (ODS) alloys, which possess superior mechanical properties due to oxide nanoparticles (e.g., yttrium oxide, Y-O, and yttrium-titanium oxide, Y-Ti-O) embedded in the alloy matrix. To better understand the precipitation mechanisms of the oxide nanoparticles and predict their size distribution under LPBF conditions, we developed an innovative physics-based multiscale modeling strategy that incorporates multiple computational approaches. These include a finite volume method model (Flow3D) to analyze the temperature field and cooling rate of the melt pool during the LPBF process, a density functional theory model to calculate the binding energy of Y-O particles and the temperature-dependent diffusivities of Y and O in molten 316L stainless steel (SS), and a cluster dynamics model to evaluate the kinetic evolution and size distribution of Y-O nanoparticles in as-fabricated 316L SS ODS alloys. The model-predicted particle sizes exhibit good agreement with experimental measurements across various LPBF process parameters, i.e., laser power (110–220 W) and scanning speed (150–900 mm/s), demonstrating the reliability and predictive power of the modeling approach. The multiscale approach can be used to guide the future design of experimental process parameters to control oxide nanoparticle characteristics in LPBF-manufactured ODS alloys. Additionally, our approach introduces a novel strategy for understanding and modeling the thermodynamics and kinetics of precipitation in high-temperature systems, particularly molten alloys. Full article
(This article belongs to the Special Issue High-Performance Alloys and Steels)
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Graphical abstract

Graphical abstract
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<p>Scanning electron microscopy (SEM) images of (<b>a</b>) pre-mixing 316L and yttria nanoparticles (the inset) and (<b>b</b>) the light ball milled mixture of 316L + 0.8 wt.% of yttria powder, and the EDX spectrum (<b>c</b>) from the mixed powder after the light ball milling.</p>
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<p>Schematic of the multiscale thermodynamic and kinetic model framework.</p>
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<p>Flow chart of the cluster dynamics model to predict the oxide nanoparticle precipitation during LPBF. <math display="inline"><semantics> <mrow> <mi>C</mi> </mrow> </semantics></math> is concentration, D (<span class="html-italic">T</span>) is temperature dependent diffusivity for Y and O monomers, and <span class="html-italic">E<sub>b</sub></span> is the binding energy of Y-O clusters.</p>
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<p>Geometry configuration of the LPBF model with a mesh size of 5 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>.</p>
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<p>Molten state exemplary atomic configurations in the AIMD model for diffusivity calculations: (<b>a</b>) a <math display="inline"><semantics> <mrow> <mn>128</mn> <mo> </mo> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> supercell of molten 316L SS (containing one Y, one O, and one Ti atoms) after training the MLFF, and (<b>b</b>) a 432-atom supercell of molten 316L SS (containing one O atom) after a 20 ps diffusion simulation at 2200 K.</p>
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<p>AIMD model for the total energy calculation, the 316L SS matrix with a <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <msub> <mrow> <mi>O</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> embedded: (<b>a</b>) at the assembled solid state, and (<b>b</b>) after relaxation at the 2200 K liquid state.</p>
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<p>SEM micrographs and corresponding PSD histograms of Y-O nanoparticles (white spheres) in all LPBF fabricated 316L SS ODS alloys. LPBF processing parameters for S1–S8 are listed in <a href="#materials-17-05661-t002" class="html-table">Table 2</a>.</p>
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<p>(<b>a</b>) Top view of the single track printed in FLOW-3D, (<b>b</b>) 3D view of the sample during steady printing and the isolated melt pool in the insert figure, (<b>c</b>) the temperature profile for a unit cell with a peak temperature of ~2600 K, (<b>d</b>) peak temperatures vs. cooling rates for all unit cells in the melt pool, and (<b>e</b>) an SEM micrograph of the cross section of the S2 sample with multiple tracks.</p>
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<p>Total energies of the systems containing Y−O clusters with various numbers of Y and O atoms, calculated by pure AIMD in the VASP (red surface) and the fitted equation (multi-colored surface).</p>
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<p>(<b>a</b>) Cluster evolution in a 1000 × 1500 Y−O composition matrix during the first 1 K drop, and (<b>b</b>) corresponding PSD histograms of Y-O clusters.</p>
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<p>Y−O cluster evolution during solidification (<b>a</b>) from 2400 K to 2200 K (plotted for marked temperatures), and (<b>b</b>) from 2600 K to 2555 K (plotted every 5 K drops in temperature). The blue arrows indicate the nanoparticle evolution during the cooling process, and the yellow arrow indicates that the nanoparticle evolution has reached the composition boundary.</p>
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<p>(<b>a</b>) Predicted PSD curves for different representative points (peak temperatures) in the melt pool of sample S2 after solidification, (<b>b</b>) statistics of peak temperatures in the melt pool, (<b>c</b>) the combined PSD, and (<b>d</b>) the comparison of the predicted and experimentally measured PSD for sample S2.</p>
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<p>PSD (histograms) after CD simulations from 2600 K to 2570 K with initial concentrations of (<b>a</b>) 0.4 wt.% and (<b>b</b>) 0.8 wt.% of yttria powder.</p>
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31 pages, 1408 KiB  
Article
Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
by Maria Margarida Lima and Cláudio Gomes
Universe 2024, 10(11), 433; https://doi.org/10.3390/universe10110433 - 20 Nov 2024
Viewed by 238
Abstract
Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which [...] Read more.
Schwarzschild and Reissner–Nordstrøm black hole solutions are found in the context of a non-minimal matter–curvature coupling with Weyl connection both in vacuum and in the presence of a cosmological constant-like matter content. This model has the advantage of an extra force term which can mimic dark matter and dark energy, and simultaneously following Weyl’s idea of unifying gravity and electromagnetism. In fact, vacuum Schwarzschild solutions differ from the ones in a constant curvature scenario in f(R) theories, with the appearance of a coefficient in the term that is linear in r and a corrected “cosmological constant”. Non-vacuum Schwarzschild solutions formally have the same solutions as in the previous case, with the exception being the physical interpretation of a cosmological constant as the source of the matter Lagrangian and not a simple reparameterization of the f(R) description. Reissner–Nordstrøm solutions cannot be found in a vacuum, only in the presence of matter fields, with the result that the solutions also differ from the constant curvature scenario in f(R) theories by the term being linear in r, the corrected/dressed charge, and the cosmological constant. These results have bearings on future numerical simulations for black holes and gravitational waves in next-generation wavelet templates. Full article
(This article belongs to the Section Gravitation)
Show Figures

Figure 1

Figure 1
<p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
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<p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≫</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
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<p>Geodesic representation of the Schwarzschild-like black hole (30), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≪</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mi>H</mi> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
Full article ">Figure 6
<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
Full article ">Figure 7
<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <msub> <mi>r</mi> <mi>H</mi> </msub> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
Full article ">Figure 8
<p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≫</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Geodesic representation of the Schwarzschild-like black hole (36), considering <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>≪</mo> <mi>M</mi> </mrow> </semantics></math>, for the parameters <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>. For the representation, the initial radius is denoted by <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math>, with initial time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>.</p>
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<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>H</mi> <mo>,</mo> <mi>ext</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
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<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <mi>ω</mi> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
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<p>Behavior of <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mi>H</mi> <mo>,</mo> <mi>ext</mi> </mrow> </msub> </semantics></math> compared to <math display="inline"><semantics> <msub> <mi>r</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>crit</mi> </mrow> </msub> </semantics></math>, considering three different black hole masses: <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, represented by the colors purple, red, and blue, respectively. To capture all global behavior, 35 different values were considered for the <math display="inline"><semantics> <mi>ω</mi> </semantics></math> parameter. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>3</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>4</mn> </msup> </semantics></math>. For <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> </mrow> </semantics></math>, values were between <math display="inline"><semantics> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>10</mn> <mn>5</mn> </msup> </semantics></math>.</p>
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<p>Global behavior of the scalar curvature <math display="inline"><semantics> <mover accent="true"> <mi>R</mi> <mo>¯</mo> </mover> </semantics></math> as a function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Global behavior of the standard Ricci scalar (built from the Levi–Civita part of the connection) as a function of the distance, assuming <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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20 pages, 4002 KiB  
Article
Valsartan/2-Aminopyridine Co-Amorphous System: Preparation, Characterization, and Supramolecular Structure Simulation by Density Functional Theory Calculation
by Linjie Wang, Chunan Du, Yang Yang, Pengtu Zhang and Shiling Yuan
Molecules 2024, 29(22), 5467; https://doi.org/10.3390/molecules29225467 - 20 Nov 2024
Viewed by 266
Abstract
The objective of this work was to improve the solubility and discover a stable co-amorphous form of valsartan (VAL), a BCS class-II drug, by utilizing small molecule 2-Aminopyridine (2-AP) in varying molar ratios (2:1, 1:1, and 1:2), employing a solvent evaporation technique. Additionally, [...] Read more.
The objective of this work was to improve the solubility and discover a stable co-amorphous form of valsartan (VAL), a BCS class-II drug, by utilizing small molecule 2-Aminopyridine (2-AP) in varying molar ratios (2:1, 1:1, and 1:2), employing a solvent evaporation technique. Additionally, by way of a density functional theory (DFT)-based computational method with commercially available software, a new approach for determining the intermolecular connectivity of multi-molecular hydrogen bonding systems was proposed. The binary systems’ features were characterized by PXRD, DSC, FTIR, and Raman spectroscopy, while the equilibrium solubility and dissolution was determined in 0.1 N HCL and water conditions to investigate the dissolution advantage of the prepared co-amorphous systems. The results demonstrated that the co-amorphous system was successfully prepared in VAL/2-AP with a 1:2 molar ratio following solvent evaporation, whereby the hydrogen bonding sites of VAL were fully occupied. Physical stability studies were carried out under dry conditions at room temperature for 6 months. Furthermore, four possible ternary systems were constructed, and their vibrational modes were simulated by DFT calculations. The calculated infrared spectra of the four configurations varied widely, with trimer 1 showing the most resemblance to the experimental spectrum of the co-amorphous 1:2 system. Additionally, co-amorphous VAL/2-AP displayed significant improvement in the solubility and dissolution study. Notably, in the 1:2 ratio, there was almost a 4.5-fold and 15.6-fold increase in VAL’s solubility in 0.1 N HCL and water environments, respectively. In conclusion, our findings highlight the potential of co-amorphous systems as a feasible approach to improving the properties and bioavailabilities of insoluble drugs. The proposed simulation method provides valuable insights into determining the supramolecular structure of multi-molecular hydrogen bonding systems, offering a novel perspective for investigating such systems. Full article
(This article belongs to the Special Issue Molecular Simulation in Interface and Surfactant—2nd Edition)
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<p>Molecular structure and atom numbering scheme of VAL and 2-AP.</p>
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<p>PXRD patterns of 2-AP (a), (b) VAL, (c) VAL-2-AP 2:1 CA, (d) VAL-2-AP 1:1 CA, (e) VAL-2-AP 1:2 CA, and (f) VAL-2-AP 1:3 CA.</p>
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<p>FT-IR spectra of (a) VAL, (b) 2-AP, (c) VAL-2-AP 2:1 CA, (d) VAL-2-AP 1:1 CA, (e) VAL-2-AP 1:2 CA, and (f) VAL-2-AP 1:3 CA.</p>
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<p>Raman spectra and contour plots of the isolated compounds and their interactions. (<b>α</b>) Raman spectra, (<b>β</b>) contour plots; (a): plain VAL, (b): 2-AP, (c): VAL-2-AP CA (2:1), (d): VAL-2-AP CA (1:1), (e): VAL-2-AP CA (1:2), and (f): VAL-2-AP CA (1:3).</p>
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<p>DSC thermogram of (a): plain VAL, (b): 2-AP, (c): VAL-2-AP CA (2:1), (d): VAL-2-AP CA (1:1), (e): VAL-2-AP CA (1:2), and (f): VAL-2-AP CA (1:3).</p>
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<p>Equilibrium solubility of VAL, VAL/2-AP 1:2 physical mixture (PM), and VAL-2-AP co-amorphous systems in various media (<span class="html-italic">n</span> = 3, ±sd).</p>
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<p>Dissolution profiles of raw drug and VAL-2-AP co-amorphous samples in pH 1.2 (<b>A</b>) and water (<b>B</b>) dissolution media.</p>
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<p>PXRD pattens of VAL-2-AP co-amorphous systems stored under dry condition at room temperature for 8 months compared to the new prepared samples.</p>
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<p>The possible configurations of the co-amorphous ternary systems after optimized by GGA/PW91.</p>
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<p>The comparison of calculated and the experimental vibrational spectrums. The red dashed line showed the position comparison of the calculated infrared spectra of different trimers relative to some diffraction peaks of the experimental spectra.</p>
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21 pages, 2991 KiB  
Article
Gypsum: From the Equilibrium to the Growth Shapes—Theory and Experiments
by Dino Aquilano, Marco Bruno and Stefano Ghignone
Minerals 2024, 14(11), 1175; https://doi.org/10.3390/min14111175 - 19 Nov 2024
Viewed by 364
Abstract
The gypsum crystals (CaSO4·2H2O) crystallizes in a low symmetry system (monoclinic) and shows a marked layered structure along with a perfect cleavage parallel to the {010} faces. Owing to its widespread occurrence, as a single or twinned crystal, here [...] Read more.
The gypsum crystals (CaSO4·2H2O) crystallizes in a low symmetry system (monoclinic) and shows a marked layered structure along with a perfect cleavage parallel to the {010} faces. Owing to its widespread occurrence, as a single or twinned crystal, here the gypsum equilibrium (E.S.) and growth shapes (G.S.) have been re-visited. In making the distinction among E.S. and G.S., in the present work, the basic difference between epitaxy and homo-taxy is clearly evidenced. Gypsum has also been a fruitful occasion to recollect the general rules concerning either contact or penetration twins, for free growing and for twinned crystals nucleating onto pre-existing substrates. Both geometric and crystal growth aspects have been considered as well, by unifying theory and experiments of crystallography and crystal growth through the intervention of βadh, the physical quantity representing the specific adhesion energy between gypsum and other phases. Hence, the adhesion energy allowed us to systematically use the Dupré’s formula. In the final part of the paper, peculiar attention has been paid to sediments (or solution growth) where the crystal size is very small, in order to offer a new simple way to afford classical (CNT) and non-classical nucleation (NCNT) theories, both ruling two quantities commonly used in the industrial crystallization: the total induction times (tindtotal) and crystal size distribution (CSD). Full article
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Figure 1

Figure 1
<p>The separation work W<sub>AB</sub> comes from the balance of two works: (i) that for separating each of the two phases (W<sub>A</sub>, W<sub>B</sub>) and (ii) the work recovered (−2E<sub>AB</sub>) by coupling the two phases. To achieve the sense of “specific”, all works must be divided by 2S. <a href="#minerals-14-01175-t001" class="html-table">Table 1</a> is for twinning.</p>
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<p>The drawing refers to Equation (1). Furthermore, it comments that the E.S. of a crystal embryo is able to make a twin. Case (a): <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">γ</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math> = 2<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">γ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>, for two separated crystals. Case (c): 0 &lt; <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mi>t</mi> <mi>w</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> &lt; 2<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>, for a non-perfect adhesion between P and T. Case (b): <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">γ</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math> = 0, when one cannot distinguish P from T.</p>
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<p>The Gibbs–Wulff–Kaischew theorem. In the Figure, the O point, called the Wulff’s point [<a href="#B19-minerals-14-01175" class="html-bibr">19</a>], represents the completely random origin.</p>
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<p>Twinned crystal: the free i-faces are not interested with the original contact plane (OCP- dashed line), and then can grow “homothetically”. Instead, the j-faces adjacent to the OCP, will have an extension depending on the twin energy. The OCP has the constant (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>c</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>) related to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> its specific surface energy, as in <a href="#minerals-14-01175-f003" class="html-fig">Figure 3</a>.</p>
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<p>(<b>a</b>) The activation energy for twin nucleation ΔG*<sub>twin</sub> is always higher than that needed to nucleate a normal crystal (Δϕ = 0) and lower than that due for two normal crystals; (<b>b</b>) The J<sub>3D</sub> function: twins can be observed only at higher supersaturation values (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="sans-serif">β</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">w</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">n</mi> </mrow> <mi mathvariant="normal">*</mi> </msubsup> </mrow> </semantics></math>) with respect to β* = <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="sans-serif">β</mi> </mrow> <mrow> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> <mrow> <mi mathvariant="normal">*</mi> </mrow> </msubsup> </mrow> </semantics></math> needed to nucleate normal crystals; (<b>c</b>) The value (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">J</mi> </mrow> <mrow> <mi mathvariant="normal">T</mi> </mrow> </msub> </mrow> </semantics></math>/<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">J</mi> </mrow> <mrow> <mi mathvariant="normal">N</mi> </mrow> </msub> </mrow> </semantics></math>) = 100% is reached only when: ΔG*<sub>twin</sub> = ΔG*.</p>
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<p>The homemade drawing, representing the gypsum projected along its [001] direction, is a strict application of the HP method [<a href="#B22-minerals-14-01175" class="html-bibr">22</a>]. Ca-atoms (blue) are located on the tetrahedra tops (and bottom), while <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> </mrow> <mrow> <mn>4</mn> </mrow> <mrow> <mn>2</mn> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> ions are square-shaped. Each <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> </mrow> <mrow> <mn>4</mn> </mrow> <mrow> <mn>2</mn> <mo>−</mo> </mrow> </msubsup> </mrow> </semantics></math> ion is only linked to its two water molecules. The limits of the d<sub>020</sub> spacing are located in between the water molecules. The screw 2<sub>1</sub> axes, parallel to [010], lie in between A and B layers of thickness d<sub>200</sub>. The d <sub>040</sub> thickness is also indicated as a private communication by L. Pastero.</p>
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<p>Scheme of an observed growth spiral along with the nanometric interstep distances and step directions. The measured step height is ∼7.5 Å, which is the thickness d<sub>020</sub> = ½ b<sub>0</sub>. Working data: pure gypsum–water solutions; T<sub>cryst.</sub> = 80 °C; very low supersaturation: β = 1.062. Modified from [<a href="#B31-minerals-14-01175" class="html-bibr">31</a>].</p>
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<p>Historical gypsum twins, inspired by [<a href="#B4-minerals-14-01175" class="html-bibr">4</a>]. The twin percent (ordinate axis) is a function of both the twin laws and σ<sub>v</sub>, the exceeding supersaturation. On the abscissa axis, one has: σ<sub>v</sub> = β − 1 = (C − C<sub>eq</sub>)/C<sub>eq</sub>, where C<sub>eq</sub> is here related to T = 20 °C.</p>
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20 pages, 691 KiB  
Article
DiscHAR: A Discrete Approach to Enhance Human Activity Recognition in Cyber Physical Systems: Smart Homes
by Ishrat Fatima, Asma Ahmad Farhan, Maria Tamoor, Shafiq ur Rehman, Hisham Abdulrahman Alhulayyil and Fawaz Tariq
Computers 2024, 13(11), 300; https://doi.org/10.3390/computers13110300 - 19 Nov 2024
Viewed by 330
Abstract
The main challenges in smart home systems and cyber-physical systems come from not having enough data and unclear interpretation; thus, there is still a lot to be done in this field. In this work, we propose a practical approach called Discrete Human Activity [...] Read more.
The main challenges in smart home systems and cyber-physical systems come from not having enough data and unclear interpretation; thus, there is still a lot to be done in this field. In this work, we propose a practical approach called Discrete Human Activity Recognition (DiscHAR) based on prior research to enhance Human Activity Recognition (HAR). Our goal is to generate diverse data to build better models for activity classification. To tackle overfitting, which often occurs with small datasets, we generate data and convert them into discrete forms, improving classification accuracy. Our methodology includes advanced techniques like the R-Frame method for sampling and the Mixed-up approach for data generation. We apply K-means vector quantization to categorize the data, and through the elbow method, we determine the optimal number of clusters. The discrete sequences are converted into one-hot encoded vectors and fed into a CNN model to ensure precise recognition of human activities. Evaluations on the OPP79, PAMAP2, and WISDM datasets show that our approach outperforms existing models, achieving 89% accuracy for OPP79, 93.24% for PAMAP2, and 100% for WISDM. These results demonstrate the model’s effectiveness in identifying complex activities captured by wearable devices. Our work combines theory and practice to address ongoing challenges in this field, aiming to improve the reliability and performance of activity recognition systems in dynamic environments. Full article
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<p>High-level architecture of DiscHAR.</p>
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<p>Elbow method to determine clusters within each activity class, where the x axis shows the number of clusters and the y axis represents distortion.</p>
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<p>Detailed overview of the CNN model used in DiscHAR.</p>
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<p>F1 score for the OPP79 [<a href="#B34-computers-13-00300" class="html-bibr">34</a>] dataset, where the x axis shows epochs and the y axis represents the F1 score.</p>
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<p>Loss curve for the OPP79 [<a href="#B34-computers-13-00300" class="html-bibr">34</a>] dataset, where the x axis shows epochs and the y axis represents the loss curve.</p>
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<p>F1 score for the PAMAP2 [<a href="#B30-computers-13-00300" class="html-bibr">30</a>] dataset, where the x axis shows epochs and the y axis represents the F1 score.</p>
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<p>Loss curve for the PAMAP2 [<a href="#B30-computers-13-00300" class="html-bibr">30</a>] dataset, where the x axis shows epochs and the y axis represents the loss curve.</p>
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<p>Accuracy for the WISDM [<a href="#B38-computers-13-00300" class="html-bibr">38</a>] dataset, where the x axis shows epochs and the y axis represents the accuracy for different learning rates.</p>
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<p>Loss curve for the WISDM [<a href="#B38-computers-13-00300" class="html-bibr">38</a>] dataset, where the x axis shows epochs and the y axis represents the loss curve for different learning rates.</p>
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17 pages, 356 KiB  
Article
Accelerating Charge: Add-Ons to Rest Mass and Field Energy
by Elizabeth P. Tito and Vadim I. Pavlov
Physics 2024, 6(4), 1264-1280; https://doi.org/10.3390/physics6040078 - 19 Nov 2024
Viewed by 231
Abstract
We present—in the framework of classical theory—a self-consistent derivation scheme which produces equations for the calculation of add-ons to the full field energy and to the effective mass of a charge moving with acceleration, which may be practically used for analyses in various [...] Read more.
We present—in the framework of classical theory—a self-consistent derivation scheme which produces equations for the calculation of add-ons to the full field energy and to the effective mass of a charge moving with acceleration, which may be practically used for analyses in various scenarios. The charge is treated as a quasi-point-like charge; this helps to resolve the complications of the “infinite” electromagnetic energy, which are avoided by the procedure of slightly “spreading” the charge. As a result, the concept of the size of the particle takes a straightforward physical interpretation. Indeed, it is within the charge spread, at scales smaller than Compton’s length, where the quantum-field-mechanics approach to be applied. Beyond this region, no “infinite” tails of quantities accumulate. The seeming divergences of the integrals at the upper limits are not physical if one takes into account that the charge moves with acceleration only for a finite duration of time; every real physical process has its beginning and its end. The key focus of this paper is on the methodological aspects of the calculations. Full article
(This article belongs to the Section Classical Physics)
20 pages, 6607 KiB  
Article
Investigating the Dynamics of a Unidirectional Wave Model: Soliton Solutions, Bifurcation, and Chaos Analysis
by Tariq Alraqad, Muntasir Suhail, Hicham Saber, Khaled Aldwoah, Nidal Eljaneid, Amer Alsulami and Blgys Muflh
Fractal Fract. 2024, 8(11), 672; https://doi.org/10.3390/fractalfract8110672 - 18 Nov 2024
Viewed by 357
Abstract
The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-equation method, not yet explored in the literature, to [...] Read more.
The current work investigates a recently introduced unidirectional wave model, applicable in science and engineering to understand complex systems and phenomena. This investigation has two primary aims. First, it employs a novel modified Sardar sub-equation method, not yet explored in the literature, to derive new solutions for the governing model. Second, it analyzes the complex dynamical structure of the governing model using bifurcation, chaos, and sensitivity analyses. To provide a more accurate depiction of the underlying dynamics, they use quantum mechanics to explain the intricate behavior of the system. To illustrate the physical behavior of the obtained solutions, 2D and 3D plots, along with a phase plane analysis, are presented using appropriate parameter values. These results validate the effectiveness of the employed method, providing thorough and consistent solutions with significant computational efficiency. The investigated soliton solutions will be valuable in understanding complex physical structures in various scientific fields, including ferromagnetic dynamics, nonlinear optics, soliton wave theory, and fiber optics. This approach proves highly effective in handling the complexities inherent in engineering and mathematical problems, especially those involving fractional-order systems. Full article
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Figure 1

Figure 1
<p>Visualization of phase diagrams of the introduced system of ODEs’ bifurcations for different conditions on <math display="inline"><semantics> <msub> <mi mathvariant="script">G</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="script">G</mi> <mn>2</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <msub> <mi mathvariant="script">G</mi> <mn>3</mn> </msub> </semantics></math> by utilizing different parameter values. (<b>a</b>) Bifurcation for <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>b</b>) Bifurcation for <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>0</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math>, <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mo>−</mo> <mn>5.39333</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math> and <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>0.593326</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math>. (<b>c</b>) Bifurcation for <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>0</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math>, <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mo>−</mo> <mn>0.593326</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>5.39333</mn> <mo>)</mo> </mrow> </semantics></math>. (<b>d</b>) Bifurcation for non-complex real stationary point <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>0</mn> <mo>,</mo> <mn>0</mn> </mfenced> </semantics></math>. (<b>e</b>) Bifurcation for <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0.593326</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>5.39333</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
Full article ">Figure 2
<p>Chaotic visual representations of a suggested equation, with parameters taken into consideration as <math display="inline"><semantics> <mrow> <mi mathvariant="normal">a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">b</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>β</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. In subplots (<b>a</b>,<b>b</b>), we take <math display="inline"><semantics> <mrow> <mi>Ω</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>φ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. In subplots (<b>c</b>,<b>d</b>), we take <math display="inline"><semantics> <mrow> <mi>Ω</mi> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>φ</mi> <mo>=</mo> <mn>3.2</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>Chaotic visual representations of a suggested equation, with parameters taken into consideration as <math display="inline"><semantics> <mrow> <mi mathvariant="normal">a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">b</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>β</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. In subplots (<b>a</b>,<b>b</b>), we take <math display="inline"><semantics> <mrow> <mi>Ω</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>φ</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. In subplots (<b>c</b>,<b>d</b>), we take <math display="inline"><semantics> <mrow> <mi>Ω</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>φ</mi> <mo>=</mo> <mn>5.1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Effects of parameters <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <math display="inline"><semantics> <msub> <mi>Υ</mi> <mn>4</mn> </msub> </semantics></math> on the behavior of the chaos in the governed system with other parameters supposed as <math display="inline"><semantics> <mrow> <mi mathvariant="normal">a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">b</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>Ω</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>φ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Numerical demonstrations of the state variables vs. <span class="html-italic">t</span> with parameters considered as <math display="inline"><semantics> <mrow> <mi mathvariant="normal">a</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">b</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi mathvariant="normal">c</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>β</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, with various initial values considered as <math display="inline"><semantics> <mrow> <mo>[</mo> <mi>b</mi> <mi>l</mi> <mi>u</mi> <mi>e</mi> <mo>,</mo> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>S</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0.1</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>,</mo> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mrow> <mo>[</mo> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mi>n</mi> <mo>,</mo> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>S</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0.3</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>]</mo> </mrow> <mo>,</mo> <mrow> <mo>[</mo> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mo>,</mo> <mrow> <mo>(</mo> <msub> <mi>S</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>S</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0.6</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>]</mo> </mrow> </mrow> </semantics></math>. (<b>a</b>) 2D graph for <math display="inline"><semantics> <msub> <mi mathvariant="script">S</mi> <mn>1</mn> </msub> </semantics></math> vs <span class="html-italic">t</span>. (<b>b</b>) 2D graph for <math display="inline"><semantics> <msub> <mi mathvariant="script">S</mi> <mn>2</mn> </msub> </semantics></math> vs <span class="html-italic">t</span>.</p>
Full article ">Figure 6
<p>Physical structure of kink soliton solution of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">U</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>6</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> under suitable parametric values of <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>y</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 7
<p>Physical structure of singular soliton solution of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">U</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>7</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> under suitable parametric values of <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>y</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 8
<p>Physical structure of anti-kink solution of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">U</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>8</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> under suitable parametric values of <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>y</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 9
<p>Physical structure of bright soliton solution of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">U</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>19</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> under suitable parametric values of <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>y</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 10
<p>Physical structure of dark soliton solution of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">U</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mrow> </semantics></math> under suitable parametric values of <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>w</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mi>Υ</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>z</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>y</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> </mrow> </semantics></math></p>
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17 pages, 1304 KiB  
Article
Enhancing Distributed Energy Markets in Smart Grids Through Game Theory and Reinforcement Learning
by Ameni Boumaiza and Kenza Maher
Energies 2024, 17(22), 5765; https://doi.org/10.3390/en17225765 - 18 Nov 2024
Viewed by 325
Abstract
The rapid growth of distributed energy resources (DERs) in smart grids has necessitated innovative strategies to manage and optimize energy markets. This paper introduces an architectural framework that leverages game theory and reinforcement learning (RL) as foundational methodologies to enhance the efficiency and [...] Read more.
The rapid growth of distributed energy resources (DERs) in smart grids has necessitated innovative strategies to manage and optimize energy markets. This paper introduces an architectural framework that leverages game theory and reinforcement learning (RL) as foundational methodologies to enhance the efficiency and robustness of distributed energy markets. Through simulations and case studies, we demonstrate how these approaches can facilitate improved decision-making among market participants, leading to better energy distribution and consumption. This exploratory approach is intended to lay the groundwork for more complex implementations that account for physical and regulatory constraints. Our preliminary results indicate a 25% reduction in energy costs and a 30% improvement in energy distribution efficiency compared to traditional methods. Full article
(This article belongs to the Section A1: Smart Grids and Microgrids)
Show Figures

Figure 1

Figure 1
<p>Enhanced analytical comparison of proposed approach vs. existing models. This figure illustrates profitability, energy utilization efficiency, market stability, agent learning rate, and demand–supply balance with constraints, comparing the proposed ABM approach with existing models over a daily timescale.</p>
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<p>Advanced analytical comparison over extended timescales. This figure shows cumulative performance metrics (e.g., profitability and efficiency) over daily and weekly periods, highlighting the adaptability and robustness of the proposed ABM model under different operational conditions.</p>
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<p>Net energy balance over time. This plot shows the difference between energy supply and demand over a 24 h period, with the system aiming to maintain a near-zero balance to ensure stability.</p>
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<p>Demand response dynamics to price changes over time.</p>
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<p>Cost efficiency and imbalance penalty over time. This plot illustrates the total energy cost based on demand and unit price, along with an imbalance penalty applied when demand deviates significantly from supply.</p>
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<p>Scalability with Market Volatility.</p>
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<p>Web-enabled distributed energy platform analytics.</p>
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46 pages, 15416 KiB  
Review
Mathematical Modeling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model
by Marian Kupczynski
Entropy 2024, 26(11), 991; https://doi.org/10.3390/e26110991 - 18 Nov 2024
Viewed by 432
Abstract
In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and [...] Read more.
In physics, we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands of years ago, and I discuss some challenges and open questions in quantum foundations and in the Standard Model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes, many believe that when we reconcile general relativity with quantum theory we will have the correct theory of everything. Perhaps we should be much humbler. Our perceptions of reality are biased by our senses and by our brain, bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite, we can use a concept of a material point, but the point-like approximation breaks completely when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear and elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist. Full article
Show Figures

Figure 1

Figure 1
<p>Hieroglyphics from Egyptian numerals. Complex numbers were formed by addition. For example, writing from right to left, 23 was depicted as <math display="inline"><semantics> <mrow> <mn>111</mn> <mo>∩</mo> <mo>∩</mo> </mrow> </semantics></math>.</p>
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<p>Glyphs copied from a decorated mace head, which depicts a ceremony where captives and other gifts are presented to Pharaoh Narmer, c. 3100 BC, who is enthroned beneath a canopy on a stepped platform.</p>
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<p>The fraction 1/2 was represented by a glyph that may have depicted a piece of linen folded in two. The fraction 2/3 was represented by the glyph for a mouth with 2 (different-sized) strokes. The rest of the fractions were always represented by a mouth superimposed over a number.</p>
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<p>The first six triangular numbers.</p>
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<p>We easily notice that 3<sup>2</sup> + 2 × 3 + 1 = 4<sup>2</sup>, etc. The number 2<span class="html-italic">n</span> + 1 was called gnomon.</p>
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<p>Greeks’ numbers represented by letters.</p>
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<p>The incomplete diagram of the model of the universe proposed by Philolaus of Croton. We see only Central Fire, Sun Moon, Earth and CE (Anticthon–Counter Earth. Five more distant, known planets and the celestial sphere of stars are missing. The existence of Anticthon helped explain the diurnal cycle [<a href="#B22-entropy-26-00991" class="html-bibr">22</a>]. At midnight CE is blocking completely the light coming from the Sun.</p>
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<p>Early printed version of Ptolemaic system (Christian Aristotelian cosmos. From Peter Apian, Cosmographia, 1524. Earth is in the center and Sun (Solis) is in between Venus and Mars.</p>
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<p>God the Geometer—Gothic frontispiece of the Bible moralized, representing God’s act of Creation. France, mid-13th century.</p>
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<p>Six families of periodic orbits discovered recently by two Chinese scientists.</p>
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<p>Two examples of periodic orbits for equal masses.</p>
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<p>The relatively periodic BHH satellites orbit the three-body system with various masses in a rotating frame of reference. Blue line: body-1; red line: body-2; black line: body-3.</p>
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<p>Lorentz strange attractor and the butterfly effect.</p>
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<p>First 4 iterations of the algorithm constructing the Koch snowflake curve.</p>
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<p>(<b>a</b>) Snowflake dendrite [<a href="#B53-entropy-26-00991" class="html-bibr">53</a>]; (<b>b</b>) the first and the fourth iteration of the Sierpinski gasket [<a href="#B54-entropy-26-00991" class="html-bibr">54</a>].</p>
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<p>Three examples of fractal structures in nature.</p>
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<p>Fractal art inspired by nature. Colors at different points depend on how these points are transformed in successive iterations. Of course, the final choice is motivated by the artistic effect one wants obtain [<a href="#B51-entropy-26-00991" class="html-bibr">51</a>,<a href="#B52-entropy-26-00991" class="html-bibr">52</a>].</p>
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<p>Mandelbrot set. A system in a black initial point remains inside the set. Colors indicate how fast a system in these points escapes to infinity.</p>
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<p>Details of the Mandelbrot set.</p>
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<p>Connected and disconnected Julia sets.</p>
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<p>One mole of carbon C-12.</p>
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<p>Phosphorus electronic stricture, Lewis’ diagram and a tetrahedral P<sub>4</sub> molecule.</p>
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<p>Periodic tables in 1869 and the modern table in which atomic number instead of mass is used.</p>
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<p>The visible solar spectrum, ranging from the shortest visible wavelengths (violet light, at 400 nm) to the longest (red light, at 700 nm). Shown in the diagram are prominent Fraunhofer lines, representing wavelengths at which light is absorbed by elements present in the atmosphere of the Sun.</p>
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<p>Balmer series of hydrogen visible spectral lines.</p>
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<p>Full hydrogen spectrum including infrared and ultraviolet.</p>
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<p>Bohr model of an atom. Maximum number of electrons: 2 in the first shell, 8 in the second shell and 18 in the third shell.</p>
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<p>Feynman graphs as mnemonic tools to account for the important mathematical terms to be included in the calculations in QED.</p>
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<p>The bubble chamber photography shows many events after a high-energy collision of <math display="inline"><semantics> <mrow> <msup> <mi>π</mi> <mo>−</mo> </msup> </mrow> </semantics></math> with a proton (12); the insert is a drawing of identified tracks [<a href="#B85-entropy-26-00991" class="html-bibr">85</a>].</p>
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<p>Histogram of invariant mass proving the existence of elementary particle <math display="inline"><semantics> <mrow> <msup> <mi mathvariant="sans-serif">Δ</mi> <mo>+</mo> </msup> </mrow> </semantics></math> [<a href="#B85-entropy-26-00991" class="html-bibr">85</a>].</p>
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<p>Building blocks of matter according to the Standard Model.</p>
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<p>Meson nonets, baryon octet and decuplet.</p>
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<p>Interactions in the Standard Model. All Feynman diagrams in the model are built from combinations of these vertices; q is any quark, g is a gluon, X is any charged particle, γ is a photon, f is any fermion, m<sub>B</sub> is any boson with mass. In diagrams with multiple particle labels separated by /, one particle label is chosen. In diagrams with particle labels separated by |, the labels must be chosen in the same order. For example, in the four boson electroweak case, the valid diagrams are WWWW, WWZZ, WWγγ, WWZγ. The conjugate of each listed vertex (reversing the direction of arrows) is also allowed [<a href="#B90-entropy-26-00991" class="html-bibr">90</a>].</p>
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<p>Simulation showing the production of the Higgs boson in the collision of two protons at the Large Hadron Collider. The Higgs boson quickly decays into four muons, which are a type of heavy electron that is not absorbed by the detector. The tracks of the muons are shown in yellow. (Image credit: Lucas Taylor/CMS).</p>
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<p>The Kanizsa triangle: the Pac-Man-like shapes give the impression of a triangle in our minds. It seems like a triangle, because we are used to seeing triangles.</p>
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<p>We see a horse’s head or a seal depending on our previous life experiences.</p>
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<p>In reality, the Crocs are pink, the pixels in the strawberries are only gray and cyan. <span class="html-italic">Courtesy of Pascal Wallisch</span>.</p>
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<p>Epistemological cycle, using theoretical model CTM, observables are chosen and an experiment is designed and performed. Regularities in experimental data are discovered and the observational model OM is postulated and tested. An improved CTM is constructed, additional observables are defined and new experiments are designed and performed.</p>
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<p>A simple pendulum with one degree of freedom and one generalized coordinate θ.</p>
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<p>Action S is greater on path 2, in comparison with the path chosen by a material point in the gravitational field on the Earth.</p>
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39 pages, 416 KiB  
Article
“In Mathematical Language”: On Mathematical Foundations of Quantum Foundations
by Arkady Plotnitsky
Entropy 2024, 26(11), 989; https://doi.org/10.3390/e26110989 - 18 Nov 2024
Viewed by 351
Abstract
The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the [...] Read more.
The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle. Full article
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