Pub Date : 2024-08-06DOI: 10.1103/physreve.110.025002
Jason W. Rocks, Pankaj Mehta
The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees of freedom, the theorem relates the emergence of rigidity to constraint counting arguments. However, the Maxwell-Calladine paradigm is significantly limited—its exclusive reliance on the geometric relationships between constraints and degrees of freedom completely neglects the actual energetic costs of deforming individual components. To address this limitation, we derive a generalization of the Maxwell-Calladine index theorem based on susceptibilities that naturally incorporate local energetic properties such as stiffness and prestress. Using this extended framework, we investigate how local energetics modify the classical constraint counting picture to capture the relationship between deformations and external forces. We then combine this formalism with group representation theory to design mechanical metamaterials where differences in symmetry between local energy costs and structural geometry are exploited to control responses to external forces.
{"title":"Integrating local energetics into Maxwell-Calladine constraint counting to design mechanical metamaterials","authors":"Jason W. Rocks, Pankaj Mehta","doi":"10.1103/physreve.110.025002","DOIUrl":"https://doi.org/10.1103/physreve.110.025002","url":null,"abstract":"The Maxwell-Calladine index theorem plays a central role in our current understanding of the mechanical rigidity of discrete materials. By considering the geometric constraints each material component imposes on a set of underlying degrees of freedom, the theorem relates the emergence of rigidity to constraint counting arguments. However, the Maxwell-Calladine paradigm is significantly limited—its exclusive reliance on the geometric relationships between constraints and degrees of freedom completely neglects the actual energetic costs of deforming individual components. To address this limitation, we derive a generalization of the Maxwell-Calladine index theorem based on susceptibilities that naturally incorporate local energetic properties such as stiffness and prestress. Using this extended framework, we investigate how local energetics modify the classical constraint counting picture to capture the relationship between deformations and external forces. We then combine this formalism with group representation theory to design mechanical metamaterials where differences in symmetry between local energy costs and structural geometry are exploited to control responses to external forces.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"40 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modeling the nonequilibrium process between ions and electrons is of great importance in laboratory fusion ignition, laser-plasma interaction, and astrophysics. For hot and dense plasmas, theoretical descriptions of Coulomb collisions remain complicated due to quantum effect at short distances and screening effect at long distances. In this paper, we propose an analytical screened quantum statistical potential that takes into account both the short-range quantum diffraction effect and the long-range screening effect. By implementing the newly developed potential into the binary scattering framework, the electron-proton temperature relaxation in hot-dense hydrogen plasmas is investigated. In both the classical and quantum limits, analytical expressions for the Coulomb logarithm have been obtained, which are generally embedded in an asymptotic matching formula. Quantitative comparisons with molecular dynamics simulations and recent OMEGA experiments demonstrate that the present modeling is well suited to describe the temperature relaxation process between electrons and ions in hot-dense plasmas.
{"title":"Electron-proton relaxation in hot-dense plasmas with a screened quantum statistical potential","authors":"Zhengfeng Fan, Chengxin Yu, Cong-Zhang Gao, Xuefeng Xu, Cunbo Zhang, Binbing Wu, Jie Liu, Pei Wang, Shaoping Zhu","doi":"10.1103/physreve.110.025202","DOIUrl":"https://doi.org/10.1103/physreve.110.025202","url":null,"abstract":"Modeling the nonequilibrium process between ions and electrons is of great importance in laboratory fusion ignition, laser-plasma interaction, and astrophysics. For hot and dense plasmas, theoretical descriptions of Coulomb collisions remain complicated due to quantum effect at short distances and screening effect at long distances. In this paper, we propose an analytical screened quantum statistical potential that takes into account both the short-range quantum diffraction effect and the long-range screening effect. By implementing the newly developed potential into the binary scattering framework, the electron-proton temperature relaxation in hot-dense hydrogen plasmas is investigated. In both the classical and quantum limits, analytical expressions for the Coulomb logarithm have been obtained, which are generally embedded in an asymptotic matching formula. Quantitative comparisons with molecular dynamics simulations and recent OMEGA experiments demonstrate that the present modeling is well suited to describe the temperature relaxation process between electrons and ions in hot-dense plasmas.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-06DOI: 10.1103/physreve.110.024304
Ruiwu Niu, Yin-Chi Chan, Eric W. M. Wong, Michaël Antonie van Wyk, Simin Liu
We present a susceptible-infected-recovered model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions. However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdős-Rényi) networks compared to small-scale (Barabási-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest nonzero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.
{"title":"Dynamics of a susceptible-infected-recovered model on complex networks with interregional migration","authors":"Ruiwu Niu, Yin-Chi Chan, Eric W. M. Wong, Michaël Antonie van Wyk, Simin Liu","doi":"10.1103/physreve.110.024304","DOIUrl":"https://doi.org/10.1103/physreve.110.024304","url":null,"abstract":"We present a susceptible-infected-recovered model based on a dynamic flow network that describes the epidemic process on complex metapopulation networks. This model views population regions as interconnected nodes and describes the evolution of each region using a system of differential equations. The next-generation matrix method is used to derive the global basic reproduction number for three cases: a general network with homogeneous infection rates in all regions, a fully connected network, and a star network with heterogeneous infection and recovery rates. For the homogeneous case, we show that this global basic reproduction number is independent of the migration rates between regions. However, the rate of convergence of each region to an equilibrium state exhibits a much larger variance in random (Erdős-Rényi) networks compared to small-scale (Barabási-Albert) networks. For the general heterogeneous case, we report interesting results, namely that the global basic reproduction number decays exponentially with respect to the smallest nonzero Laplacian eigenvalue (algebraic connectivity). Furthermore, we demonstrate both analytically and numerically that as the network's algebraic connectivity increases, either by increasing the average node degree of each region or the global migration rate, the global basic reproduction number decreases and converges to the ratio of the average local infection rate to the average local recovery rate, meaning that the lower bound of the global basic reproduction rate does not equal the mean of local basic reproduction rates.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"93 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.
{"title":"Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor","authors":"Kenta Kato, Hiroyuki Hashiba, Jun Nagao, Hiroshi Gotoda, Yusuke Nabae, Ryoichi Kurose","doi":"10.1103/physreve.110.024204","DOIUrl":"https://doi.org/10.1103/physreve.110.024204","url":null,"abstract":"We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"58 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-06DOI: 10.1103/physreve.110.024112
Matthew Golden, Joseph P. Straley
In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary can be related by a conformal transformation to the conductance from one point to another in an unbounded network. We verify that this works at the percolation threshold for the square.
{"title":"Spatial dependence of microscopic percolation conduction","authors":"Matthew Golden, Joseph P. Straley","doi":"10.1103/physreve.110.024112","DOIUrl":"https://doi.org/10.1103/physreve.110.024112","url":null,"abstract":"In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary can be related by a conformal transformation to the conductance from one point to another in an unbounded network. We verify that this works at the percolation threshold for the square.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"51 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-06DOI: 10.1103/physreve.110.024801
Pavel Iliev, Nina Pesheva, Stanimir Iliev
We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with an ultrahydrophobic surface with randomly distributed microsized pillars or holes in the Cassie's wetting regime. We study the Wilhelmy plate system in the framework of the full capillary model to obtain these angles using the heterogeneous surface approximation model for a broad interval of values of pillar or hole concentration and for both square and circular shapes of the pillars or holes cross-section. Three types of random placing of defects on the plate are investigated, i.e., two with restrictions: (1) with maximum and (2) with minimum distance between the defects (in these cases the defects are isolated), and (3) without restrictions (the defects can overlap). The results show that the type of defect distribution and also the type of the defects shape (circular or square) does not affect the magnitude of the two angles. The results of the numerical simulations showed that the retention force for a plate with randomly located defects is not greater, and for larger concentrations of pillars or holes, it is smaller than that for periodically spaced ones. Comparisons with experimental results for the receding contact angle on surfaces with pillars and with the advancing contact angle on surfaces with periodically arranged holes is carried out.
{"title":"Contact angle hysteresis on nonwetting microstructured surfaces: Effect of randomly distributed pillars or holes","authors":"Pavel Iliev, Nina Pesheva, Stanimir Iliev","doi":"10.1103/physreve.110.024801","DOIUrl":"https://doi.org/10.1103/physreve.110.024801","url":null,"abstract":"We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with an ultrahydrophobic surface with randomly distributed microsized pillars or holes in the Cassie's wetting regime. We study the Wilhelmy plate system in the framework of the full capillary model to obtain these angles using the heterogeneous surface approximation model for a broad interval of values of pillar or hole concentration and for both square and circular shapes of the pillars or holes cross-section. Three types of random placing of defects on the plate are investigated, i.e., two with restrictions: (1) with maximum and (2) with minimum distance between the defects (in these cases the defects are isolated), and (3) without restrictions (the defects can overlap). The results show that the type of defect distribution and also the type of the defects shape (circular or square) does not affect the magnitude of the two angles. The results of the numerical simulations showed that the retention force for a plate with randomly located defects is not greater, and for larger concentrations of pillars or holes, it is smaller than that for periodically spaced ones. Comparisons with experimental results for the receding contact angle on surfaces with pillars and with the advancing contact angle on surfaces with periodically arranged holes is carried out.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"79 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-06DOI: 10.1103/physreve.110.025302
Jaemin Seo
Reconstructing the past of observed fluids has been known as an ill-posed problem due to both numerical and physical challenges, especially when observations are distorted by inevitable noise, resolution limits, or unknown factors. When employing traditional differencing schemes to reconstruct the past, the computation often becomes highly unstable or diverges within a few backward time steps from the distorted and noisy observation. Although several techniques have been recently developed for inverse problems, such as adjoint solvers and supervised learning, they are also unrobust against errors in observation when there is time-reversed simulation. Here we present that by using physics-informed neural computing, robust time-reversed fluid simulation is possible. By seeking a solution that closely satisfies the given physics and observations while allowing for errors, it reconstructs the most probable past from noisy observations. Our work showcases time rewinding in extreme fluid scenarios such as shock, instability, blast, and magnetohydrodynamic vortex. Potentially, this can be applied to trace back the interstellar evolution and determining the origin of fusion plasma instabilities.
{"title":"Past rewinding of fluid dynamics from noisy observation via physics-informed neural computing","authors":"Jaemin Seo","doi":"10.1103/physreve.110.025302","DOIUrl":"https://doi.org/10.1103/physreve.110.025302","url":null,"abstract":"Reconstructing the past of observed fluids has been known as an ill-posed problem due to both numerical and physical challenges, especially when observations are distorted by inevitable noise, resolution limits, or unknown factors. When employing traditional differencing schemes to reconstruct the past, the computation often becomes highly unstable or diverges within a few backward time steps from the distorted and noisy observation. Although several techniques have been recently developed for inverse problems, such as adjoint solvers and supervised learning, they are also unrobust against errors in observation when there is time-reversed simulation. Here we present that by using physics-informed neural computing, robust time-reversed fluid simulation is possible. By seeking a solution that closely satisfies the given physics and observations while allowing for errors, it reconstructs the most probable past from noisy observations. Our work showcases time rewinding in extreme fluid scenarios such as shock, instability, blast, and magnetohydrodynamic vortex. Potentially, this can be applied to trace back the interstellar evolution and determining the origin of fusion plasma instabilities.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"58 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-05DOI: 10.1103/physreve.110.024111
Chang Liu, Jia-Qi Dong, Lian-Chun Yu, Liang Huang
The percolation phase transition of a continuum adaptive neuron system with homeostasis is investigated. In order to maintain their average activity at a particular level, each neuron (represented by a disk) varies its connection radius until the sum of overlapping areas with neighboring neurons (representing the overall connection strength in the network) has reached a fixed target area for each neuron. Tuning the two key parameters in the model, i.e., the density defined as the number of neurons (disks) per unit area and the sum of the overlapping area of each disk with its adjacent disks, can drive the system into the critical percolating state. These two parameters are inversely proportional to each other at the critical state, and the critical filling factors are fixed about 0.7157, which is much less than the case of the continuum percolation with uniform disks. It is also confirmed that the critical exponents in this model are the same as the two-dimensional standard lattice percolation. Although the critical state is relatively more sensitive and exhibits long-range spatial correlation, local fluctuations do not propagate in a long-range manner through the system by the adaptive dynamics, which renders the system overall robust against perturbations.
{"title":"Continuum percolation of two-dimensional adaptive dynamics systems","authors":"Chang Liu, Jia-Qi Dong, Lian-Chun Yu, Liang Huang","doi":"10.1103/physreve.110.024111","DOIUrl":"https://doi.org/10.1103/physreve.110.024111","url":null,"abstract":"The percolation phase transition of a continuum adaptive neuron system with homeostasis is investigated. In order to maintain their average activity at a particular level, each neuron (represented by a disk) varies its connection radius until the sum of overlapping areas with neighboring neurons (representing the overall connection strength in the network) has reached a fixed target area for each neuron. Tuning the two key parameters in the model, i.e., the density defined as the number of neurons (disks) per unit area and the sum of the overlapping area of each disk with its adjacent disks, can drive the system into the critical percolating state. These two parameters are inversely proportional to each other at the critical state, and the critical filling factors are fixed about 0.7157, which is much less than the case of the continuum percolation with uniform disks. It is also confirmed that the critical exponents in this model are the same as the two-dimensional standard lattice percolation. Although the critical state is relatively more sensitive and exhibits long-range spatial correlation, local fluctuations do not propagate in a long-range manner through the system by the adaptive dynamics, which renders the system overall robust against perturbations.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"22 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-05DOI: 10.1103/physreve.110.024106
Florian Kischel, Stefan Wessel
We derive an exact formula for the corner free-energy contribution of weakly anisotropic two-dimensional critical systems in the Ising universality class on rectangular domains, expressed in terms of quantities that specify the anisotropic fluctuations. The resulting expression agrees with numerical exact calculations that we perform for the anisotropic triangular Ising model and quantifies the nonuniversality of the corner term for anisotropic critical two-dimensional systems. Our generic formula is expected to apply also to other weakly-anisotropic critical two-dimensional systems that allow for a conformal field theory description in the isotropic limit. We consider the three-states and four-states Potts models as further specific examples.
{"title":"Quantifying nonuniversal corner free-energy contributions in weakly anisotropic two-dimensional critical systems","authors":"Florian Kischel, Stefan Wessel","doi":"10.1103/physreve.110.024106","DOIUrl":"https://doi.org/10.1103/physreve.110.024106","url":null,"abstract":"We derive an exact formula for the corner free-energy contribution of weakly anisotropic two-dimensional critical systems in the Ising universality class on rectangular domains, expressed in terms of quantities that specify the anisotropic fluctuations. The resulting expression agrees with numerical exact calculations that we perform for the anisotropic triangular Ising model and quantifies the nonuniversality of the corner term for anisotropic critical two-dimensional systems. Our generic formula is expected to apply also to other weakly-anisotropic critical two-dimensional systems that allow for a conformal field theory description in the isotropic limit. We consider the three-states and four-states Potts models as further specific examples.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"15 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-05DOI: 10.1103/physreve.110.025301
Zheng Dai (代铮), Zhongyi Wang (王忠义), Junhao Zhu (朱俊豪), Xiaohu Chen (陈小虎), Qing Li (李庆), Zongrui Jin (金宗睿)
Based on the mesoscopic scale, the lattice Boltzmann method (LBM) with an enthalpy-based model represented in the form of distribution functions is widely used in the liquid-solid phase transition process of energy storage materials due to its direct and relatively accurate characterization of the presence of latent heat of solidification. However, since the enthalpy distribution function itself contains the physical properties of the material, these properties are transferred along with the enthalpy distribution function during the streaming process. This leads to deviations between the enthalpy-based model when simulating the phase transition process of different materials mixed and the actual process. To address this issue, in this paper, we construct an enthalpy-based model for different types of materials. For multiple materials, various forms of enthalpy distribution functions are employed. This method still uses the form of enthalpy distribution functions for collisions and streaming processes among the same type of substance, while for heat transfer between different materials, it avoids the direct transfer of enthalpy distribution functions and instead applies a source term to the enthalpy distribution functions, characterizing the heat transfer between different materials through the energy change before and after mixing based on the temperature. To verify the accuracy of the method proposed in this paper, a detailed solidification model for two different materials is constructed using the example of water droplets solidifying in air, and the results are compared with experimental outcomes. The results of the simulation show that the model constructed in this paper is largely in line with the actual process.
{"title":"Three-dimensional solidification modeling of various materials using the lattice Boltzmann method with an explicit enthalpy equation","authors":"Zheng Dai (代铮), Zhongyi Wang (王忠义), Junhao Zhu (朱俊豪), Xiaohu Chen (陈小虎), Qing Li (李庆), Zongrui Jin (金宗睿)","doi":"10.1103/physreve.110.025301","DOIUrl":"https://doi.org/10.1103/physreve.110.025301","url":null,"abstract":"Based on the mesoscopic scale, the lattice Boltzmann method (LBM) with an enthalpy-based model represented in the form of distribution functions is widely used in the liquid-solid phase transition process of energy storage materials due to its direct and relatively accurate characterization of the presence of latent heat of solidification. However, since the enthalpy distribution function itself contains the physical properties of the material, these properties are transferred along with the enthalpy distribution function during the streaming process. This leads to deviations between the enthalpy-based model when simulating the phase transition process of different materials mixed and the actual process. To address this issue, in this paper, we construct an enthalpy-based model for different types of materials. For multiple materials, various forms of enthalpy distribution functions are employed. This method still uses the form of enthalpy distribution functions for collisions and streaming processes among the same type of substance, while for heat transfer between different materials, it avoids the direct transfer of enthalpy distribution functions and instead applies a source term to the enthalpy distribution functions, characterizing the heat transfer between different materials through the energy change before and after mixing based on the temperature. To verify the accuracy of the method proposed in this paper, a detailed solidification model for two different materials is constructed using the example of water droplets solidifying in air, and the results are compared with experimental outcomes. The results of the simulation show that the model constructed in this paper is largely in line with the actual process.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"33 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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