Pub Date : 2024-07-13DOI: 10.1007/s10955-024-03302-y
Kohei Hayashi
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and in physics. As a microscopic model, we consider multi-species interacting diffusion processes, whose dynamics is driven by a nonlinear potential which satisfies some regularity conditions. In particular, we study asymptotic behavior of fluctuation fields associated with the processes in the high temperature regime under equilibrium. As a main result, we show that when the characteristic speed of each species is the same, the family of the fluctuation fields seen in moving frame with this speed converges to the coupled KPZ equations. Our approach is based on a Taylor expansion argument which extracts the harmonic potential as a main part. This argument works without assuming a specific form of the potential and thereby the coupled KPZ equations are derived in a robust way.
{"title":"Derivation of Coupled KPZ Equations from Interacting Diffusions Driven by a Single-Site Potential","authors":"Kohei Hayashi","doi":"10.1007/s10955-024-03302-y","DOIUrl":"https://doi.org/10.1007/s10955-024-03302-y","url":null,"abstract":"<p>The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and in physics. As a microscopic model, we consider multi-species interacting diffusion processes, whose dynamics is driven by a nonlinear potential which satisfies some regularity conditions. In particular, we study asymptotic behavior of fluctuation fields associated with the processes in the high temperature regime under equilibrium. As a main result, we show that when the characteristic speed of each species is the same, the family of the fluctuation fields seen in moving frame with this speed converges to the coupled KPZ equations. Our approach is based on a Taylor expansion argument which extracts the harmonic potential as a main part. This argument works without assuming a specific form of the potential and thereby the coupled KPZ equations are derived in a robust way.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610658","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 : 2024-07-13DOI: 10.1007/s10955-024-03307-7
Amit Einav
Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called choose the Leader model.
{"title":"The Emergence of Order in Many Element Systems","authors":"Amit Einav","doi":"10.1007/s10955-024-03307-7","DOIUrl":"https://doi.org/10.1007/s10955-024-03307-7","url":null,"abstract":"<p>Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called choose the Leader model.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610659","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 : 2024-07-12DOI: 10.1007/s10955-024-03303-x
Junho Kim, Young Keon Gong, Yeongchae Park, Peter Jeong
This paper proposes an improved cumulant collision model for the pseudo-potential lattice Boltzmann method (LBM) to increase the stability of multiphase flow simulations involving low viscosities. This model is based on the work of Kharmiani et al. in (J Stat Phys 175: 47, 2019), which can be extended regardless of the collision model. The original cumulant collision model (Geier et al. in Comput Math Appl 70:507, 2015) causes a non-physical shape of droplets in pseudo-potential LBM because only the first-order central moments are considered in the forcing scheme. The improved cumulant collision model proposed in this paper applies the central moment forcing scheme to the original cumulant model to cover the high-order central moments. Several numerical simulations were carried out to validate the proposed model. First, the problem of a stationary liquid layer was solved, where the proposed model was demonstrated to be thermodynamically consistent. Second, the problem of a stationary droplet was solved, where the result agreed well with Laplace’s law. Third, the problem of a droplet impact on a liquid film was solved, where the crown radius agreed well with the analytical and numerical results available. Fourth, the simulation results carried out with the raw moment, central moment, and the proposed improved cumulant collision models were compared, as the liquid and vapor viscosities were gradually lowered. With all else being equal, only the lattice Boltzmann method with the proposed improved cumulant collision model was able to successfully simulate a density ratio of 720 and a Reynolds number of ({mathbf {8.7}}{mathbf {times 10}}^{{textbf{4}}}).
{"title":"Pseudo-potential Lattice Boltzmann Method with an Improved Forcing Scheme for the Cumulant Collision Model","authors":"Junho Kim, Young Keon Gong, Yeongchae Park, Peter Jeong","doi":"10.1007/s10955-024-03303-x","DOIUrl":"https://doi.org/10.1007/s10955-024-03303-x","url":null,"abstract":"<p>This paper proposes an improved cumulant collision model for the pseudo-potential lattice Boltzmann method (LBM) to increase the stability of multiphase flow simulations involving low viscosities. This model is based on the work of Kharmiani et al. in (J Stat Phys 175: 47, 2019), which can be extended regardless of the collision model. The original cumulant collision model (Geier et al. in Comput Math Appl 70:507, 2015) causes a non-physical shape of droplets in pseudo-potential LBM because only the first-order central moments are considered in the forcing scheme. The improved cumulant collision model proposed in this paper applies the central moment forcing scheme to the original cumulant model to cover the high-order central moments. Several numerical simulations were carried out to validate the proposed model. First, the problem of a stationary liquid layer was solved, where the proposed model was demonstrated to be thermodynamically consistent. Second, the problem of a stationary droplet was solved, where the result agreed well with Laplace’s law. Third, the problem of a droplet impact on a liquid film was solved, where the crown radius agreed well with the analytical and numerical results available. Fourth, the simulation results carried out with the raw moment, central moment, and the proposed improved cumulant collision models were compared, as the liquid and vapor viscosities were gradually lowered. With all else being equal, only the lattice Boltzmann method with the proposed improved cumulant collision model was able to successfully simulate a density ratio of <b>720</b> and a Reynolds number of <span>({mathbf {8.7}}{mathbf {times 10}}^{{textbf{4}}})</span>.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610660","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 : 2024-07-08DOI: 10.1007/s10955-024-03300-0
Muhammad Faisal Nadeem, Faiza Ishfaq, Ayesha Shabbir
Resistance distance in electrical circuits measures how much a component or an entire circuit resists the flow of electric current. When dealing with intricate circuits, this term explicitly denotes the total resistance observed between any two points, which varies based on the configuration and resistance values of the components within the circuit. The Kirchhoff index is a metric used to quantify the mean resistance distance across all pairs of nodes in an electrical network. In graph theory, these networks are depicted as graphs with nodes representing electrical components and edges symbolizing the connecting wires. The resistance distance between any two nodes is calculated as if the graph were an electrical circuit, with each edge functioning as a resistor. We focus on a particular type of graph known as a cacti graph, denoted by (mathcal {C}(n,s)), which features interconnected cycles that share a single common vertex, with n representing the total number of nodes and s the number of cycles. This paper explores cacti networks to establish the maximum possible values of the Kirchhoff index for these structures.
{"title":"On Resistance Distance and Kirchhoff Index of Cacti Networks","authors":"Muhammad Faisal Nadeem, Faiza Ishfaq, Ayesha Shabbir","doi":"10.1007/s10955-024-03300-0","DOIUrl":"https://doi.org/10.1007/s10955-024-03300-0","url":null,"abstract":"<p>Resistance distance in electrical circuits measures how much a component or an entire circuit resists the flow of electric current. When dealing with intricate circuits, this term explicitly denotes the total resistance observed between any two points, which varies based on the configuration and resistance values of the components within the circuit. The Kirchhoff index is a metric used to quantify the mean resistance distance across all pairs of nodes in an electrical network. In graph theory, these networks are depicted as graphs with nodes representing electrical components and edges symbolizing the connecting wires. The resistance distance between any two nodes is calculated as if the graph were an electrical circuit, with each edge functioning as a resistor. We focus on a particular type of graph known as a cacti graph, denoted by <span>(mathcal {C}(n,s))</span>, which features interconnected cycles that share a single common vertex, with <i>n</i> representing the total number of nodes and <i>s</i> the number of cycles. This paper explores cacti networks to establish the maximum possible values of the Kirchhoff index for these structures.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570862","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 : 2024-07-07DOI: 10.1007/s10955-024-03289-6
Naoto Shiraishi, Hal Tasaki
We show, without relying on any unproven assumptions, that a low-density free fermion chain exhibits thermalization in the following (restricted) sense. We choose the initial state as a pure state drawn randomly from the Hilbert space in which all particles are in half of the chain. This represents a nonequilibrium state such that the half chain containing all particles is in equilibrium at infinite temperature, and the other half chain is a vacuum. We let the system evolve according to the unitary time evolution determined by the Hamiltonian and, at a sufficiently large typical time, measure the particle number in an arbitrary macroscopic region in the chain. In this setup, it is proved that the measured number is close to the equilibrium value with probability very close to one. Our result establishes the presence of thermalization in a concrete model in a mathematically rigorous manner. The key for the proof is a new strategy to show that a randomly generated nonequilibrium initial state typically has a large enough effective dimension by using only mild verifiable assumptions. In the present work, we first give general proof of thermalization based on two assumptions, namely, the absence of degeneracy in energy eigenvalues and a property about the particle distribution in energy eigenstates. We then justify these assumptions in a concrete free-fermion model, where the absence of degeneracy is established by using number-theoretic results. This means that our general result also applies to any lattice gas models in which the above two assumptions are justified. To confirm the potential wide applicability of our theory, we discuss some other models for which the essential assumption about the particle distribution is easily verified, and some non-random initial states whose effective dimensions are sufficiently large.
{"title":"Nature Abhors a Vacuum: A Simple Rigorous Example of Thermalization in an Isolated Macroscopic Quantum System","authors":"Naoto Shiraishi, Hal Tasaki","doi":"10.1007/s10955-024-03289-6","DOIUrl":"https://doi.org/10.1007/s10955-024-03289-6","url":null,"abstract":"<p>We show, without relying on any unproven assumptions, that a low-density free fermion chain exhibits thermalization in the following (restricted) sense. We choose the initial state as a pure state drawn randomly from the Hilbert space in which all particles are in half of the chain. This represents a nonequilibrium state such that the half chain containing all particles is in equilibrium at infinite temperature, and the other half chain is a vacuum. We let the system evolve according to the unitary time evolution determined by the Hamiltonian and, at a sufficiently large typical time, measure the particle number in an arbitrary macroscopic region in the chain. In this setup, it is proved that the measured number is close to the equilibrium value with probability very close to one. Our result establishes the presence of thermalization in a concrete model in a mathematically rigorous manner. The key for the proof is a new strategy to show that a randomly generated nonequilibrium initial state typically has a large enough effective dimension by using only mild verifiable assumptions. In the present work, we first give general proof of thermalization based on two assumptions, namely, the absence of degeneracy in energy eigenvalues and a property about the particle distribution in energy eigenstates. We then justify these assumptions in a concrete free-fermion model, where the absence of degeneracy is established by using number-theoretic results. This means that our general result also applies to any lattice gas models in which the above two assumptions are justified. To confirm the potential wide applicability of our theory, we discuss some other models for which the essential assumption about the particle distribution is easily verified, and some non-random initial states whose effective dimensions are sufficiently large.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570863","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 : 2024-07-04DOI: 10.1007/s10955-024-03292-x
Yixiang Wang, Kainan Xiang, Shangjie Yang, Lang Zou
By the dimension reduction idea, overshoot for random walks, coupling and martingale arguments, we obtain a simpler and easily computable expression for the first-order correction constant between discrete harmonic measures for random walks with rotationally invariant step distribution in (mathbb {R}^d (dge 2)) and the corresponding continuous counterparts. This confirms and extends a conjecture in Jiang and Kennedy (J Theor Probab 30(4):1424–1444, 2017), and simplifies the related expression of Wang et al. (Bernoulli 25(3):2279–2300, 2019). Furthermore, we propose a universality conjecture on high-order corrections for error estimation between generalized discrete harmonic measures and their continuous counterparts, which generalizes the universality conjecture of the first-order correction in Kennedy (J Stat Phys 164(1):174–189, 2016); and we prove this conjecture heuristically for the rotationally invariant case, and also provide several examples of second-order error corrections to check the conjecture by a numerical simulation argument.
{"title":"The High-Order Corrections of Discrete Harmonic Measures and Their Correction Constants","authors":"Yixiang Wang, Kainan Xiang, Shangjie Yang, Lang Zou","doi":"10.1007/s10955-024-03292-x","DOIUrl":"https://doi.org/10.1007/s10955-024-03292-x","url":null,"abstract":"<p>By the dimension reduction idea, overshoot for random walks, coupling and martingale arguments, we obtain a simpler and easily computable expression for the first-order correction constant between discrete harmonic measures for random walks with rotationally invariant step distribution in <span>(mathbb {R}^d (dge 2))</span> and the corresponding continuous counterparts. This confirms and extends a conjecture in Jiang and Kennedy (J Theor Probab 30(4):1424–1444, 2017), and simplifies the related expression of Wang et al. (Bernoulli 25(3):2279–2300, 2019). Furthermore, we propose a universality conjecture on high-order corrections for error estimation between generalized discrete harmonic measures and their continuous counterparts, which generalizes the universality conjecture of the first-order correction in Kennedy (J Stat Phys 164(1):174–189, 2016); and we prove this conjecture heuristically for the rotationally invariant case, and also provide several examples of second-order error corrections to check the conjecture by a numerical simulation argument.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551990","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 : 2024-07-02DOI: 10.1007/s10955-024-03294-9
Loren Coquille, Aernout van Enter, Arnaud Le Ny, Wioletta M. Ruszel
We show that a modification of the proof of our paper Coquille et al. (J. Stat. Phys. 172(5), 1210–1222 (2018)), in the spirit of Fröhlich and Pfister (Commun. Math. Phys. 81, 277–298 (1981)), shows delocalisation in the long-range Discrete Gaussian Chain, and generalisations thereof, for any decay power (alpha >2) and at all temperatures. The argument proceeds by contradiction: any shift-invariant and localised measure (in the (L^1) sense), is a convex combination of ergodic localised measures. But the latter cannot exist: on one hand, by the ergodic theorem, the average of the field over growing boxes would be almost surely bounded ; on the other hand the measure would be absolutely continuous with respect to its height-shifted translates, as a simple relative entropy computation shows. This leads to a contradiction and answers, in a non-quantitative way, an open question stated in a recent paper of C. Garban (Invisibility of the integers for the discrete Gaussian Chain via a caffarelli-silvestre extension of the discrete fractional laplacian. Preprint arXiv:2312.04536v2, (2023)).
{"title":"Absence of Shift-Invariant Gibbs States (Delocalisation) for One-Dimensional $$pmb {mathbb {Z}}$$ -Valued Fields With Long-Range Interactions","authors":"Loren Coquille, Aernout van Enter, Arnaud Le Ny, Wioletta M. Ruszel","doi":"10.1007/s10955-024-03294-9","DOIUrl":"https://doi.org/10.1007/s10955-024-03294-9","url":null,"abstract":"<p>We show that a modification of the proof of our paper Coquille et al. (J. Stat. Phys. <b>172</b>(5), 1210–1222 (2018)), in the spirit of Fröhlich and Pfister (Commun. Math. Phys. <b>81</b>, 277–298 (1981)), shows delocalisation in the long-range Discrete Gaussian Chain, and generalisations thereof, for any decay power <span>(alpha >2)</span> and at all temperatures. The argument proceeds by contradiction: any shift-invariant and localised measure (in the <span>(L^1)</span> sense), is a convex combination of ergodic localised measures. But the latter cannot exist: on one hand, by the ergodic theorem, the average of the field over growing boxes would be almost surely bounded ; on the other hand the measure would be absolutely continuous with respect to its height-shifted translates, as a simple relative entropy computation shows. This leads to a contradiction and answers, in a non-quantitative way, an open question stated in a recent paper of C. Garban (Invisibility of the integers for the discrete Gaussian Chain <i>via</i> a caffarelli-silvestre extension of the discrete fractional laplacian. Preprint arXiv:2312.04536v2, (2023)).</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514560","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 : 2024-06-29DOI: 10.1007/s10955-024-03298-5
Nikhil Bhatia, Arvind K. Gupta
Inspired by different stochastic mechanisms, such as the two-sided motion of ribosomes seen during the initiation of mRNA translation, which is backed by their decay, we investigate a totally asymmetric simple exclusion process with open boundaries in a bidirectional setting where two oppositely charged species of particles move opposite to each other and locally reset to the respective entry site. The steady-state characteristics, such as density profiles and phase diagrams, are investigated theoretically under the mean-field framework. The introduction of resetting into the system produces non-trivial effects in the form of two novel asymmetric phases that appear in the phase diagram. The system possesses several different combinations of symmetric phases as well as asymmetric phases for different resetting rates. A rich behavior is observed in the system, emphasizing the occurrence of spontaneous symmetry-breaking phenomena even in the small resetting regime. Moreover, the significance of the resetting rate is analyzed on the domain wall, and it is found that one of the stationary phases with a localized domain wall vanishes for a substantial resetting rate. Due to the interaction of both species at the boundaries, the consequences of the resetting dynamics on the boundary densities are also investigated. All the findings, including finite-system size, are thoroughly validated by the Monte Carlo simulations.
{"title":"Local Resetting in a Bidirectional Transport System","authors":"Nikhil Bhatia, Arvind K. Gupta","doi":"10.1007/s10955-024-03298-5","DOIUrl":"https://doi.org/10.1007/s10955-024-03298-5","url":null,"abstract":"<p>Inspired by different stochastic mechanisms, such as the two-sided motion of ribosomes seen during the initiation of mRNA translation, which is backed by their decay, we investigate a totally asymmetric simple exclusion process with open boundaries in a bidirectional setting where two oppositely charged species of particles move opposite to each other and locally reset to the respective entry site. The steady-state characteristics, such as density profiles and phase diagrams, are investigated theoretically under the mean-field framework. The introduction of resetting into the system produces non-trivial effects in the form of two novel asymmetric phases that appear in the phase diagram. The system possesses several different combinations of symmetric phases as well as asymmetric phases for different resetting rates. A rich behavior is observed in the system, emphasizing the occurrence of spontaneous symmetry-breaking phenomena even in the small resetting regime. Moreover, the significance of the resetting rate is analyzed on the domain wall, and it is found that one of the stationary phases with a localized domain wall vanishes for a substantial resetting rate. Due to the interaction of both species at the boundaries, the consequences of the resetting dynamics on the boundary densities are also investigated. All the findings, including finite-system size, are thoroughly validated by the Monte Carlo simulations.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502805","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 : 2024-06-27DOI: 10.1007/s10955-024-03297-6
Lu Xu, Linjie Zhao
We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in Bardos et al (Commun Partial Differ Equ 4(9):1017–1034, https://doi.org/10.1080/03605307908820117, 1979) and Otto (C R Acad Sci Paris 322(1):729–734, 1996), discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme.
我们考虑的是有限晶格上的开放式相互作用粒子系统。粒子执行非对称简单排斥,在所有位置随机产生或摧毁,其速率在边界附近迅速增长。我们研究了双曲时空尺度下粒子密度的流体力学极限,并获得了带有源项的边界驱动准线性守恒定律的熵解。与 Bardos 等人 (Commun Partial Differ Equ 4(9):1017-1034, https://doi.org/10.1080/03605307908820117, 1979) 和 Otto (C R Acad Sci Paris 322(1):729-734, 1996) 中介绍的通常边界条件不同,由于采用了强弛豫方案,在边界处不会形成不连续性(边界层)。
{"title":"Hydrodynamics for Asymmetric Simple Exclusion on a Finite Segment with Glauber-Type Source","authors":"Lu Xu, Linjie Zhao","doi":"10.1007/s10955-024-03297-6","DOIUrl":"https://doi.org/10.1007/s10955-024-03297-6","url":null,"abstract":"<p>We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in Bardos et al (Commun Partial Differ Equ 4(9):1017–1034, https://doi.org/10.1080/03605307908820117, 1979) and Otto (C R Acad Sci Paris 322(1):729–734, 1996), discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502806","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 : 2024-06-24DOI: 10.1007/s10955-024-03295-8
Carlos Handrey A. Ferraz, José Luiz S. Lima
In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions. Quenched bond-diluted lattice disorder was introduced into the systems, allowing them to evolve over time. By employing percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the model for different bond-dilution rates (p). An examination of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was performed to ascertain the universality class of the model. The simulation results strongly indicate that the present model belongs to a new universality class distinct from that of 2D dynamical percolation, depending on the specific p value under consideration.
本文研究了键稀释无序对随机 SIR 模型临界行为的影响。我们使用具有第一和第二近邻相互作用的方晶格进行了蒙特卡罗模拟。在系统中引入了淬火键稀释晶格无序,使其随时间演变。通过采用渗流理论和有限尺寸缩放分析,我们估算出了该模型在不同键稀释率(p)下的临界阈值和领先临界指数比。为了确定该模型的普遍性,我们还考察了渗流簇的平均大小和恢复个体的非渗流簇的大小分布。模拟结果有力地表明,根据所考虑的特定 p 值,本模型属于一个新的普遍性类别,不同于二维动态渗滤的普遍性类别。
{"title":"Critical Behavior of the Stochastic SIR Model on Random Bond-Diluted Lattices","authors":"Carlos Handrey A. Ferraz, José Luiz S. Lima","doi":"10.1007/s10955-024-03295-8","DOIUrl":"https://doi.org/10.1007/s10955-024-03295-8","url":null,"abstract":"<p>In this paper, we investigate the impact of bond-dilution disorder on the critical behavior of the stochastic SIR model. Monte Carlo simulations were conducted using square lattices with first- and second-nearest neighbor interactions. Quenched bond-diluted lattice disorder was introduced into the systems, allowing them to evolve over time. By employing percolation theory and finite-size scaling analysis, we estimate both the critical threshold and leading critical exponent ratios of the model for different bond-dilution rates (<i>p</i>). An examination of the average size of the percolating cluster and the size distribution of non-percolating clusters of recovered individuals was performed to ascertain the universality class of the model. The simulation results strongly indicate that the present model belongs to a new universality class distinct from that of 2D dynamical percolation, depending on the specific <i>p</i> value under consideration.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502810","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}