Wei-Liang Qian, Kai Lin, Rui-Hong Yue, Yogiro Hama, Takeshi Kodama
Although partition temperature derived using the Darwin–Fowler method is exact for simple scenarios, the derivation for complex systems might reside in specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed-form expressions can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore, it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase-space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed.
{"title":"On the Partition Temperature of Massless Particles in High-Energy Collisions","authors":"Wei-Liang Qian, Kai Lin, Rui-Hong Yue, Yogiro Hama, Takeshi Kodama","doi":"10.3390/sym15112035","DOIUrl":"https://doi.org/10.3390/sym15112035","url":null,"abstract":"Although partition temperature derived using the Darwin–Fowler method is exact for simple scenarios, the derivation for complex systems might reside in specific approximations whose viability is not ensured if the thermodynamic limit is not attained. This work elaborates on a related problem relevant to relativistic high-energy collisions. On the one hand, it is simple enough that closed-form expressions can be obtained precisely for the one-particle distribution function. On the other hand, the resulting expression is not an exponential form, and therefore, it is not straightforward that the notion of partition function could be implied. Specifically, we derive the one-particle distribution function for massless particles where the phase-space integration is performed exactly for the underlying canonical ensemble consisting of a given number of particles. We discuss the viability of the partition temperature in this case. Possible implications of the obtained results regarding the observed Tsallis distribution in transverse momentum spectra in high-energy collisions are also addressed.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"324 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kun Shi, Miaohan Zhang, Zhaolei He, Shi Yin, Zhen Ai, Nan Pan
Automated guided vehicles (AGVs) are one of the core technologies for building unmanned autonomous integrated automated electric meter verification workshops in metrology centers. However, complex obstacles on the verification lines, frequent AGV charging, and multi-AGV collaboration make the scheduling problem more complicated. Aiming at the characteristics and constraints of AGV transportation scheduling for metrology verification, a multi-AGV scheduling model was established to minimize the maximum completion time and charging cost, integrating collision-avoidance constraints. An improved snake optimization algorithm was proposed that first assigns and sorts tasks based on AGV-order-address three-level mapping encoding and decoding, then searches optimal paths using an improved A* algorithm solves multi-AGV path conflicts, and finally finds the minimum-charging-cost schedule through large neighborhood search. We conducted simulations using real data, and the calculated results reduced the objective function value by 16.4% compared to the traditional first-in-first-out (FIFO) method. It also reduced the number of charges by 60.3%. In addition, the proposed algorithm is compared with a variety of cutting-edge algorithms and the results show that the objective function value is reduced by 8.7–11.2%, which verifies the superiority of the proposed algorithm and the feasibility of the model.
{"title":"Scheduling of Multi-AGV Systems in Automated Electricity Meter Verification Workshops Based on an Improved Snake Optimization Algorithm","authors":"Kun Shi, Miaohan Zhang, Zhaolei He, Shi Yin, Zhen Ai, Nan Pan","doi":"10.3390/sym15112034","DOIUrl":"https://doi.org/10.3390/sym15112034","url":null,"abstract":"Automated guided vehicles (AGVs) are one of the core technologies for building unmanned autonomous integrated automated electric meter verification workshops in metrology centers. However, complex obstacles on the verification lines, frequent AGV charging, and multi-AGV collaboration make the scheduling problem more complicated. Aiming at the characteristics and constraints of AGV transportation scheduling for metrology verification, a multi-AGV scheduling model was established to minimize the maximum completion time and charging cost, integrating collision-avoidance constraints. An improved snake optimization algorithm was proposed that first assigns and sorts tasks based on AGV-order-address three-level mapping encoding and decoding, then searches optimal paths using an improved A* algorithm solves multi-AGV path conflicts, and finally finds the minimum-charging-cost schedule through large neighborhood search. We conducted simulations using real data, and the calculated results reduced the objective function value by 16.4% compared to the traditional first-in-first-out (FIFO) method. It also reduced the number of charges by 60.3%. In addition, the proposed algorithm is compared with a variety of cutting-edge algorithms and the results show that the objective function value is reduced by 8.7–11.2%, which verifies the superiority of the proposed algorithm and the feasibility of the model.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"325 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The time–energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows the grasping of peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam–Tamm method, TEUR has recently been derived for neutrino oscillations by connecting the uncertainty in neutrino energy with the characteristic timescale of oscillations. Interestingly, the suggested interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects were later discussed in semiclassical gravity theory, by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations.
{"title":"Time–Energy Uncertainty Relation for Neutrino Oscillations: Historical Development, Applications, and Future Prospects","authors":"Giuseppe Gaetano Luciano, Luca Smaldone","doi":"10.3390/sym15112032","DOIUrl":"https://doi.org/10.3390/sym15112032","url":null,"abstract":"The time–energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows the grasping of peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam–Tamm method, TEUR has recently been derived for neutrino oscillations by connecting the uncertainty in neutrino energy with the characteristic timescale of oscillations. Interestingly, the suggested interpretation of neutrinos as unstable-like particles has proved to naturally emerge in this context. Further aspects were later discussed in semiclassical gravity theory, by computing corrections to the neutrino energy uncertainty in a generic stationary curved spacetime, and in quantum field theory, where the clock observable turns out to be identified with the non-conserved flavor charge operator. In the present work, we give an overview on the above achievements. In particular, we analyze the implications of TEUR and explore the impact of gravitational and non-relativistic effects on the standard condition for neutrino oscillations.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"329 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.
{"title":"An Optimal Control Perspective on Classical and Quantum Physical Systems","authors":"Mauricio Contreras G., Marcelo Villena","doi":"10.3390/sym15112033","DOIUrl":"https://doi.org/10.3390/sym15112033","url":null,"abstract":"This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":" 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. The exploitation of the rotating wave approximation allows for the identification of a constant of motion, which simplifies both the analytical and the numerical treatment, which allows for evaluating the total unitary evolution of the system and bath. The efficiency of the population transfer process is investigated in several regimes, including the weak and strong coupling with the environment and the off-resonance. The formation of appropriate Zeno subspaces explains the lowering of the efficiency in the strong damping regime.
{"title":"Adiabatic Manipulation of a System Interacting with a Spin Bath","authors":"Benedetto Militello, Anna Napoli","doi":"10.3390/sym15112028","DOIUrl":"https://doi.org/10.3390/sym15112028","url":null,"abstract":"The Stimulated Raman Adiabatic Passage, a very efficient technique for manipulating a quantum system based on the adiabatic theorem, is analyzed in the case where the manipulated physical system is interacting with a spin bath. The exploitation of the rotating wave approximation allows for the identification of a constant of motion, which simplifies both the analytical and the numerical treatment, which allows for evaluating the total unitary evolution of the system and bath. The efficiency of the population transfer process is investigated in several regimes, including the weak and strong coupling with the environment and the off-resonance. The formation of appropriate Zeno subspaces explains the lowering of the efficiency in the strong damping regime.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"133 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Omar El Moutea, Nadia Nakbi, Abdeslam El Akkad, Ahmed Elkhalfi, Lahcen El Ouadefli, Sorin Vlase, Maria Luminita Scutaru
In this paper, we present a numerical scheme for addressing the unsteady asymmetric flows governed by the incompressible Navier–Stokes equations under a general boundary condition. We utilized the Finite Element Method (FEM) for spatial discretization and the fully implicit Euler scheme for time discretization. In addition to the theoretical analysis of the error in our numerical scheme, we introduced two types of a posteriori error indicators: one for time discretization and another for spatial discretization, aimed at effectively controlling the error. We established the equivalence between these estimators and the actual error. Furthermore, we conducted numerical simulations in two dimensions to assess the accuracy and effectiveness of our scheme.
{"title":"A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition","authors":"Omar El Moutea, Nadia Nakbi, Abdeslam El Akkad, Ahmed Elkhalfi, Lahcen El Ouadefli, Sorin Vlase, Maria Luminita Scutaru","doi":"10.3390/sym15112031","DOIUrl":"https://doi.org/10.3390/sym15112031","url":null,"abstract":"In this paper, we present a numerical scheme for addressing the unsteady asymmetric flows governed by the incompressible Navier–Stokes equations under a general boundary condition. We utilized the Finite Element Method (FEM) for spatial discretization and the fully implicit Euler scheme for time discretization. In addition to the theoretical analysis of the error in our numerical scheme, we introduced two types of a posteriori error indicators: one for time discretization and another for spatial discretization, aimed at effectively controlling the error. We established the equivalence between these estimators and the actual error. Furthermore, we conducted numerical simulations in two dimensions to assess the accuracy and effectiveness of our scheme.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"47 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Q-multi cubic Pythagorean fuzzy sets (Q-mCPFSs) are influential, effective and symmetrical for representing uncertain and imprecise information in decision making processes. Q-mCPFSs extend the concept of Q-multi fuzzy sets by introducing the notion of cubic Pythagorean membership functions, which provide a more flexible and accurate representation of uncertainty. First, we will introduce the concepts of Q-mPFSs and Q-mIVPFSs. With the combination of Q-mPFSs and Q-mIVPFSs, we will present the concept of Q-mCPFSs. Then, we propose two correlation coefficients for Q-mCPFSs. Furthermore, multi-criteria GDM methods using Q-mCPFSs will be discussed, highlighting their advantages in handling uncertain and imprecise information. Finally, we will provide an illustrative example, to demonstrate the effectiveness of Q-mCPFSs in decision making processes.The main contributions of the Q-mCPFS information expression, correlation coefficients and GDM methods in the Q-mCPFS setting of both uncertainty and certainty are thus highlighted in this study. These contributions provide valuable insights into the application of Q-mCPFSs in decision making processes, allowing decision makers to make more informed and effective choices. Additionally, the illustrative example serves as a practical demonstration of how these methods can be applied in real-world scenarios, further emphasizing their effectiveness and relevance.
{"title":"Q-Multi Cubic Pythagorean Fuzzy Sets and Their Correlation Coefficients for Multi-Criteria Group Decision Making","authors":"Safa Hussain Almasabi, Kholood Mohammad Alsager","doi":"10.3390/sym15112026","DOIUrl":"https://doi.org/10.3390/sym15112026","url":null,"abstract":"Q-multi cubic Pythagorean fuzzy sets (Q-mCPFSs) are influential, effective and symmetrical for representing uncertain and imprecise information in decision making processes. Q-mCPFSs extend the concept of Q-multi fuzzy sets by introducing the notion of cubic Pythagorean membership functions, which provide a more flexible and accurate representation of uncertainty. First, we will introduce the concepts of Q-mPFSs and Q-mIVPFSs. With the combination of Q-mPFSs and Q-mIVPFSs, we will present the concept of Q-mCPFSs. Then, we propose two correlation coefficients for Q-mCPFSs. Furthermore, multi-criteria GDM methods using Q-mCPFSs will be discussed, highlighting their advantages in handling uncertain and imprecise information. Finally, we will provide an illustrative example, to demonstrate the effectiveness of Q-mCPFSs in decision making processes.The main contributions of the Q-mCPFS information expression, correlation coefficients and GDM methods in the Q-mCPFS setting of both uncertainty and certainty are thus highlighted in this study. These contributions provide valuable insights into the application of Q-mCPFSs in decision making processes, allowing decision makers to make more informed and effective choices. Additionally, the illustrative example serves as a practical demonstration of how these methods can be applied in real-world scenarios, further emphasizing their effectiveness and relevance.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"15 1‐2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.
{"title":"Toward Enhanced Geological Analysis: A Novel Approach Based on Transmuted Semicircular Distribution","authors":"Phani Yedlapalli, Gajula Naveen Venkata Kishore, Wadii Boulila, Anis Koubaa, Nabil Mlaiki","doi":"10.3390/sym15112030","DOIUrl":"https://doi.org/10.3390/sym15112030","url":null,"abstract":"This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"329 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Obtaining a suitable chemical composition for high-entropy alloys (HEAs) with superior mechanical properties and good biocompatibility is still a formidable challenge through conventional trial-and-error methods. Here, based on a large amount of experimental data, a machine learning technique may be used to establish the relationship between the composition and the mechanical properties of the biocompatible HEAs. Subsequently, first-principles calculations are performed to verify the accuracy of the prediction results from the machine learning model. The predicted Young’s modulus and yield strength of HEAs performed very well in the previous experiments. In addition, the effect on the mechanical properties of alloying an element is investigated in the selected Ti-Zr-Hf-Nb-Ta HEA with the high crystal symmetry. Finally, the Ti8-Zr20-Hf16-Nb35-Ta21 HEA predicted by the machine learning model exhibits a good combination of biocompatibility and mechanical performance, attributed to a significant electron flow and charge recombination. This work reveals the importance of these strategies, combined with machine learning and first-principles calculations, on the development of advanced biocompatible HEAs.
{"title":"Chemical Composition Optimization of Biocompatible Non-Equiatomic High-Entropy Alloys Using Machine Learning and First-Principles Calculations","authors":"Gengzhu Zhou, Zili Zhang, Renyao Feng, Wenjie Zhao, Shenyou Peng, Jia Li, Feifei Fan, Qihong Fang","doi":"10.3390/sym15112029","DOIUrl":"https://doi.org/10.3390/sym15112029","url":null,"abstract":"Obtaining a suitable chemical composition for high-entropy alloys (HEAs) with superior mechanical properties and good biocompatibility is still a formidable challenge through conventional trial-and-error methods. Here, based on a large amount of experimental data, a machine learning technique may be used to establish the relationship between the composition and the mechanical properties of the biocompatible HEAs. Subsequently, first-principles calculations are performed to verify the accuracy of the prediction results from the machine learning model. The predicted Young’s modulus and yield strength of HEAs performed very well in the previous experiments. In addition, the effect on the mechanical properties of alloying an element is investigated in the selected Ti-Zr-Hf-Nb-Ta HEA with the high crystal symmetry. Finally, the Ti8-Zr20-Hf16-Nb35-Ta21 HEA predicted by the machine learning model exhibits a good combination of biocompatibility and mechanical performance, attributed to a significant electron flow and charge recombination. This work reveals the importance of these strategies, combined with machine learning and first-principles calculations, on the development of advanced biocompatible HEAs.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"28 32","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135390947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.
{"title":"Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology","authors":"Vasyl’ Davydovych, Vasyl’ Dutka, Roman Cherniha","doi":"10.3390/sym15112025","DOIUrl":"https://doi.org/10.3390/sym15112025","url":null,"abstract":"The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.","PeriodicalId":48874,"journal":{"name":"Symmetry-Basel","volume":"126 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135539313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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