Pub Date : 2024-04-17DOI: 10.1088/1742-5468/ad319c
Zhonghao Zhan, Weiguo Song, Jun Zhang
We propose a new model of boundary-constrained intersecting pedestrian flow based on the collision-free velocity model, named the collision-aware deflection model (CADM). The movement of pedestrians in the new model depends on the positions and velocities of other pedestrians ahead. A pedestrian walks in the desired direction at a free speed until an obstacle appears in the desired direction. When there is an obstacle in the desired direction, pedestrians tend to choose the direction with the smallest deflection angle. When the decision of a pedestrian conflicts with the movement of the nearest neighbor in front, the pedestrian stops moving. Comparing CADM with other models, the evacuation time of CADM during the simulation is very close to the time in the experiment. CADM also successfully reproduced the stripe phenomenon in boundary-constrained intersecting pedestrian streams, which was difficult to accomplish with the compared model. CADM also inherits several advantages of the original model, in that it can reproduce the corresponding self-organization phenomena in straight corridors and bottlenecks.
{"title":"Collision-aware deflection model for boundary-constrained intersecting pedestrian streams","authors":"Zhonghao Zhan, Weiguo Song, Jun Zhang","doi":"10.1088/1742-5468/ad319c","DOIUrl":"https://doi.org/10.1088/1742-5468/ad319c","url":null,"abstract":"We propose a new model of boundary-constrained intersecting pedestrian flow based on the collision-free velocity model, named the collision-aware deflection model (CADM). The movement of pedestrians in the new model depends on the positions and velocities of other pedestrians ahead. A pedestrian walks in the desired direction at a free speed until an obstacle appears in the desired direction. When there is an obstacle in the desired direction, pedestrians tend to choose the direction with the smallest deflection angle. When the decision of a pedestrian conflicts with the movement of the nearest neighbor in front, the pedestrian stops moving. Comparing CADM with other models, the evacuation time of CADM during the simulation is very close to the time in the experiment. CADM also successfully reproduced the stripe phenomenon in boundary-constrained intersecting pedestrian streams, which was difficult to accomplish with the compared model. CADM also inherits several advantages of the original model, in that it can reproduce the corresponding self-organization phenomena in straight corridors and bottlenecks.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"59 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611625","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 : 2024-04-17DOI: 10.1088/1742-5468/ad363e
S Zhou
We investigated the effective interaction potential (EIP) between charged surfaces in solvent comprised of dipole dimer molecules added with a certain amount of ionic liquid. Using classical density functional theory, the EIP is calculated and decoupled into entropic and energy terms. Unlike the traditional Asakura–Oosawa (AO) depletion model, the present entropic term can be positive or negative, depending on the entropy change associated with solvent molecule migration from bulk into slit pore. This is determined by pore congestion and disruption of the bulk dipole network. The energy term is determined by the free energy associated with hard-core repulsion and electrostatic interactions between surface charges, ion charges, and polarized charges carried by the dipole dimer molecules. The calculations in this article clearly demonstrate the variability of the entropy term, which contrasts sharply with the traditional AO depletion model, and the corrective effects of electrostatic and spatial hindrance interactions on the total EIP; we revealed several non-monotonic behaviors of the EIP and its entropic and energy terms concerning solvent bulk concentration and solvent molecule dipole moment; additionally, we demonstrated the promoting effect of dipolar solvent on the emergence of like-charge attraction, even in 1:1 electrolyte solutions. The microscopic origin of the aforementioned phenomena was analyzed to be due to the non-monotonic change of dipolar solvent adsorption with dipole moment under conditions of low solution dielectric constant. The present findings offer novel approaches and molecular-level guidance for regulating the EIP. This insight has implications for understanding fundamental processes in various fields, including biomolecule-ligand binding, activation energy barriers, ion tunneling transport, as well as the formation of hierarchical structures, such as mesophases, micro-, and nanostructures, and beyond.
{"title":"Variability of entropy force and its coupling with electrostatic and steric hindrance interactions","authors":"S Zhou","doi":"10.1088/1742-5468/ad363e","DOIUrl":"https://doi.org/10.1088/1742-5468/ad363e","url":null,"abstract":"We investigated the effective interaction potential (EIP) between charged surfaces in solvent comprised of dipole dimer molecules added with a certain amount of ionic liquid. Using classical density functional theory, the EIP is calculated and decoupled into entropic and energy terms. Unlike the traditional Asakura–Oosawa (AO) depletion model, the present entropic term can be positive or negative, depending on the entropy change associated with solvent molecule migration from bulk into slit pore. This is determined by pore congestion and disruption of the bulk dipole network. The energy term is determined by the free energy associated with hard-core repulsion and electrostatic interactions between surface charges, ion charges, and polarized charges carried by the dipole dimer molecules. The calculations in this article clearly demonstrate the variability of the entropy term, which contrasts sharply with the traditional AO depletion model, and the corrective effects of electrostatic and spatial hindrance interactions on the total EIP; we revealed several non-monotonic behaviors of the EIP and its entropic and energy terms concerning solvent bulk concentration and solvent molecule dipole moment; additionally, we demonstrated the promoting effect of dipolar solvent on the emergence of like-charge attraction, even in 1:1 electrolyte solutions. The microscopic origin of the aforementioned phenomena was analyzed to be due to the non-monotonic change of dipolar solvent adsorption with dipole moment under conditions of low solution dielectric constant. The present findings offer novel approaches and molecular-level guidance for regulating the EIP. This insight has implications for understanding fundamental processes in various fields, including biomolecule-ligand binding, activation energy barriers, ion tunneling transport, as well as the formation of hierarchical structures, such as mesophases, micro-, and nanostructures, and beyond.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"72 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611542","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}
This study investigates the behavioral patterns of children during emergency evacuations through a dual approach comprising controlled experimental evacuations within a classroom and computational modeling via a cellular automaton (CA) model. Observations from the experiments reveal several characteristic behaviors among children, including preferences for destinations, the impact of obstacles on their movement, as well as patterns of exit utilization, running and pushing during the evacuation process. Drawing upon these empirical findings, a CA model is developed to encapsulate these observed behaviors. A novel algorithm is introduced within this model to simulate the pushing behavior of children during emergency evacuations. Numerical simulations are conducted to validate the capability of the model to replicate the observed behaviors. The simulation results confirm that the model accurately reproduces the child behavior during evacuations. Furthermore, the results indicate that the total evacuation time is directly influenced by both the proportion of children exhibiting pushing behavior and the strength of the pushing force. These insights advance our understanding of child behavior in emergency situations and have significant implications for enhancing public safety.
本研究采用双重方法研究儿童在紧急疏散过程中的行为模式，包括在教室内进行受控疏散实验和通过蜂窝自动机（CA）模型进行计算建模。实验观察发现了儿童的一些特征行为，包括对目的地的偏好、障碍物对其移动的影响，以及疏散过程中出口的利用、奔跑和推挤模式。根据这些实证研究结果，我们开发了一个 CA 模型来概括这些观察到的行为。在该模型中引入了一种新算法，用于模拟紧急疏散过程中儿童的推挤行为。为了验证模型复制观察到的行为的能力，我们进行了数值模拟。模拟结果证实，该模型准确地再现了疏散过程中的儿童行为。此外，模拟结果表明，总疏散时间直接受表现出推挤行为的儿童比例和推挤力强度的影响。这些见解加深了我们对紧急情况下儿童行为的理解，对提高公共安全具有重要意义。
{"title":"Behavioral patterns of children during emergency evacuations: a comparative analysis of experimental observations and simulation results","authors":"Liang Chen, Chen Qiao, Jian Zhang, Chuan-Zhi (Thomas) Xie, Tie-Qiao Tang, Yanyan Chen","doi":"10.1088/1742-5468/ad363b","DOIUrl":"https://doi.org/10.1088/1742-5468/ad363b","url":null,"abstract":"This study investigates the behavioral patterns of children during emergency evacuations through a dual approach comprising controlled experimental evacuations within a classroom and computational modeling via a cellular automaton (CA) model. Observations from the experiments reveal several characteristic behaviors among children, including preferences for destinations, the impact of obstacles on their movement, as well as patterns of exit utilization, running and pushing during the evacuation process. Drawing upon these empirical findings, a CA model is developed to encapsulate these observed behaviors. A novel algorithm is introduced within this model to simulate the pushing behavior of children during emergency evacuations. Numerical simulations are conducted to validate the capability of the model to replicate the observed behaviors. The simulation results confirm that the model accurately reproduces the child behavior during evacuations. Furthermore, the results indicate that the total evacuation time is directly influenced by both the proportion of children exhibiting pushing behavior and the strength of the pushing force. These insights advance our understanding of child behavior in emergency situations and have significant implications for enhancing public safety.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"44 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611624","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 : 2024-04-09DOI: 10.1088/1742-5468/ad343a
Marius Lemm
The von Neumann entropy of a k-body-reduced density matrix γk quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1⩽k⩽N and non-decreasing until the midpoint k⩽⌊N/2⌋. The results hold for indistinguishable quantum particles and are independent of the statistics.
一个 k 体还原密度矩阵 γk 的冯-诺依曼熵量化了 k 个量子粒子与其余粒子之间的纠缠。在本文中，我们严格证明了这种纠缠熵作为 k 的函数的一般性质；它对所有 1⩽k⩽N 都是凹的，并且在中点 k⩽⌊N/2⌋ 之前是不递减的。这些结果适用于不可区分的量子粒子，并且与统计量无关。
{"title":"Entropic relations for indistinguishable quantum particles","authors":"Marius Lemm","doi":"10.1088/1742-5468/ad343a","DOIUrl":"https://doi.org/10.1088/1742-5468/ad343a","url":null,"abstract":"The von Neumann entropy of a <italic toggle=\"yes\">k</italic>-body-reduced density matrix <italic toggle=\"yes\">γ</italic>\u0000<sub>\u0000<italic toggle=\"yes\">k</italic>\u0000</sub> quantifies the entanglement between <italic toggle=\"yes\">k</italic> quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of <italic toggle=\"yes\">k</italic>; it is concave for all <inline-formula>\u0000<tex-math><?CDATA $1unicode{x2A7D} kunicode{x2A7D} N$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mtext>⩽</mml:mtext><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mi>N</mml:mi></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad343aieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and non-decreasing until the midpoint <inline-formula>\u0000<tex-math><?CDATA $kunicode{x2A7D} lfloor{N/2} rfloor$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mo fence=\"false\" stretchy=\"false\">⌊</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⌋</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad343aieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. The results hold for indistinguishable quantum particles and are independent of the statistics.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"61 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611546","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 : 2024-04-08DOI: 10.1088/1742-5468/ad363f
Naftali R Smith
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps Δx, Δt in space and time, respectively. By applying large-deviation theory on the discretized dynamics, we analyze the numerical errors due to the discretization, and find that the (relative) errors are especially large in regions of space where the concentration of particles is very small. We find that the choice Δt=Δx2/(6D), where D is the diffusion coefficient, gives optimal accuracy compared to any other choice (including, in particular, the limit Δt→0), thus reproducing the known result that may be obtained using truncation error analysis. In addition, we give quantitative estimates for the dynamical lengthscale that describes the size of the spatial region in which the numerical solution is accurate, and study its dependence on the discretization parameters. We then turn to study the advection–diffusion equation, and obtain explicit expressions for the optimal Δt and other parameters of the finite-differences scheme, in terms of Δx, D and the advection velocity. We apply these results to study large deviations of the area swept by a diffusing particle in one dimension, trapped by an external potential ∼|x|. We extend our analysis to higher dimensions by combining our results from the one dimensional case with the locally one-dimension method.
{"title":"Optimal finite-differences discretization for the diffusion equation from the perspective of large-deviation theory","authors":"Naftali R Smith","doi":"10.1088/1742-5468/ad363f","DOIUrl":"https://doi.org/10.1088/1742-5468/ad363f","url":null,"abstract":"When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps Δ<italic toggle=\"yes\">x</italic>, Δ<italic toggle=\"yes\">t</italic> in space and time, respectively. By applying large-deviation theory on the discretized dynamics, we analyze the numerical errors due to the discretization, and find that the (relative) errors are especially large in regions of space where the concentration of particles is very small. We find that the choice <inline-formula>\u0000<tex-math><?CDATA $Delta t = {Delta x}^2 / (6D)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mn>6</mml:mn><mml:mi>D</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad363fieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, where <italic toggle=\"yes\">D</italic> is the diffusion coefficient, gives optimal accuracy compared to any other choice (including, in particular, the limit <inline-formula>\u0000<tex-math><?CDATA $Delta t to 0$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"normal\">Δ</mml:mi><mml:mi>t</mml:mi><mml:mo accent=\"false\" stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad363fieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>), thus reproducing the known result that may be obtained using truncation error analysis. In addition, we give quantitative estimates for the dynamical lengthscale that describes the size of the spatial region in which the numerical solution is accurate, and study its dependence on the discretization parameters. We then turn to study the advection–diffusion equation, and obtain explicit expressions for the optimal Δ<italic toggle=\"yes\">t</italic> and other parameters of the finite-differences scheme, in terms of Δ<italic toggle=\"yes\">x</italic>, <italic toggle=\"yes\">D</italic> and the advection velocity. We apply these results to study large deviations of the area swept by a diffusing particle in one dimension, trapped by an external potential <inline-formula>\u0000<tex-math><?CDATA ${sim}|x|$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mo>∼</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow><mml:mi>x</mml:mi><mml:mo stretchy=\"false\">|</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad363fieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. We extend our analysis to higher dimensions by combining our results from the one dimensional case with the locally one-dimension method.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"176 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140611543","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 : 2024-04-03DOI: 10.1088/1742-5468/ad3197
Joachim Krug, Daniel Oros
Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here, we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length L becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotypes, which can be explicitly computed for large classes of genotype graphs. The behaviour of uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.
生物进化可以被概念化为在基因序列空间中的搜索过程，而搜索过程是由适应度景观（Fitness landscape）引导的，这种映射为每种基因型赋予了一定的繁殖价值。在这里，我们讨论了适应度景观的概率模型，重点是其进化的可及性，如果在适应度景观中遇到的适应度值沿路径单调增加，则称该路径为可及性路径。对于具有独立且同分布适配值的非相关（随机）景观，在初始基因型和最终基因型之间的适配值差异达到一个非微不足道的临界值时，在距离与序列长度 L 成线性关系的基因型之间存在可访问路径的概率将变为非零，而这个临界值可以明确地计算出大类基因型图谱。无相关随机景观的行为与景观模型形成了鲜明对比，后者显示出更多生物结构特征。特别是，通过对环境极端适应性的权衡而定义的景观被发现显示了大量通向所有局部适应性最大值的组合路径。我们证明了这一特性是满足特定全局约束条件的一大类模型的特征，并提供了该类模型的更多实例。
{"title":"Evolutionary accessibility of random and structured fitness landscapes","authors":"Joachim Krug, Daniel Oros","doi":"10.1088/1742-5468/ad3197","DOIUrl":"https://doi.org/10.1088/1742-5468/ad3197","url":null,"abstract":"Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here, we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length <italic toggle=\"yes\">L</italic> becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotypes, which can be explicitly computed for large classes of genotype graphs. The behaviour of uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"59 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592953","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 : 2024-04-03DOI: 10.1088/1742-5468/ad2dda
Ethan Levien
The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the log offspring sizes have stretched exponential tails. Such offspring distributions are motivated by biology, where they emerge from a toy model of growth in a heterogeneous environment, but also from mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have received considerable attention due to their appearance in the partition function of Derrida’s random energy model (REM). We find that the limit coalescent is a β-coalescent—a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the connection to previous results on the REM.
金曼（Kingman）提出了在固定环境下中性演化种群系谱的经典模型。金曼的凝聚过程产生了一棵二叉树，它普遍存在于后代数量方差有限的许多微观模型中。据了解，具有无限方差的幂律后代分布会导致一种非常不同的凝聚结构，即两个以上的品系合并。在这里，我们将研究子代分布方差有限但与种群数量相当的情况。这是通过研究后代大小对数具有拉伸指数尾部的模型来实现的。这种后代分布的动机不仅来自于生物学，即在异质环境中生长的玩具模型，还来自于数学和统计物理学，其中随机指数和的极限定理和相变因出现在德里达的随机能量模型（REM）的分区函数中而受到广泛关注。我们发现，极限凝聚是一种 β 凝聚--这是以前研究过的具有重尾后代分布的进化动力学模型中出现的模型。我们还讨论了与之前关于 REM 结果的联系。
{"title":"Coalescent processes emerging from large deviations","authors":"Ethan Levien","doi":"10.1088/1742-5468/ad2dda","DOIUrl":"https://doi.org/10.1088/1742-5468/ad2dda","url":null,"abstract":"The classical model for the genealogies of a neutrally evolving population in a fixed environment is due to Kingman. Kingman’s coalescent process, which produces a binary tree, emerges universally from many microscopic models in which the variance in the number of offspring is finite. It is understood that power-law offsprings distributions with infinite variance can result in a very different type of coalescent structure with merging of more than two lineages. Here, we investigate the regime where the variance of the offspring distribution is finite but comparable to the population size. This is achieved by studying a model in which the log offspring sizes have stretched exponential tails. Such offspring distributions are motivated by biology, where they emerge from a toy model of growth in a heterogeneous environment, but also from mathematics and statistical physics, where limit theorems and phase transitions for sums over random exponentials have received considerable attention due to their appearance in the partition function of Derrida’s random energy model (REM). We find that the limit coalescent is a <italic toggle=\"yes\">β</italic>-coalescent—a previously studied model emerging from evolutionary dynamics models with heavy-tailed offspring distributions. We also discuss the connection to previous results on the REM.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"50 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593409","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 : 2024-03-27DOI: 10.1088/1742-5468/ad2ddb
Jacopo Romano, Benoît Mahault, Ramin Golestanian
We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the +1/2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.
我们在最近开发的框架（Romano et al 2023 J. Stat. Mech.）我们展示了如何用一个统一的数学框架来理解点缺陷、域壁、分离线和任何其他奇异点的运动方程。对于离散线，这也使我们能够研究内部线张力和与其他线的相互作用之间的相互作用。这种相互作用是非对称的，它允许缺陷环由于外部相互作用而膨胀，而不是收缩。我们还利用这一框架对点缺陷运动中两个长期存在的问题进行了分析描述，即缺陷迁移率的尺度依赖性和弹性各向异性在液晶中缺陷运动中的作用。对于前者，我们证明了有效的缺陷迁移率与问题密切相关，但对于一对湮灭的缺陷，它可以被高精度地计算出来。对于后者，我们的研究表明，在微扰理论的一阶，各向异性会导致非径向力，使湮没缺陷的运动轨迹偏离直线。在更高的阶次，各向异性还会引起迁移率的修正，对于 +1/2 缺陷来说，迁移率变得非各向异性。我们认为，由于其通用性，我们的方法有助于揭示许多不同系统中奇点的运动，包括驱动和活动非平衡理论。
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Pub Date : 2024-03-27DOI: 10.1088/1742-5468/ad319a
Kristian Stølevik Olsen, Hartmut Löwen
We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable via correlations. We derive the Fourier–Laplace transforms of the observable variable’s propagator and provide a recursive relation for all the moments, facilitating a comprehensive examination of the process. We apply this framework to inertial transport processes where we observe the particle position while the velocity is hidden and is being reset at a constant rate. We show that velocity resetting results in a linearly growing spatial mean squared displacement at later times, independently of reset-free dynamics, due to resetting-induced tempering of velocity correlations. General expressions for the effective diffusion and drift coefficients are derived as a function of the resetting rate. A non-trivial dependence on the rate may appear due to multiple timescales and crossovers in the reset-free dynamics. An extension that incorporates refractory periods after each reset is considered, where post-resetting pauses can lead to anomalous diffusive behavior. Our results are of relevance to a wide range of systems, such as inertial transport where the mechanical momentum is lost in collisions with the environment or the behavior of living organisms where stop-and-go locomotion with inertia is ubiquitous. Numerical simulations for underdamped Brownian motion and the random acceleration process confirm our findings.
{"title":"Dynamics of inertial particles under velocity resetting","authors":"Kristian Stølevik Olsen, Hartmut Löwen","doi":"10.1088/1742-5468/ad319a","DOIUrl":"https://doi.org/10.1088/1742-5468/ad319a","url":null,"abstract":"We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable via correlations. We derive the Fourier–Laplace transforms of the observable variable’s propagator and provide a recursive relation for all the moments, facilitating a comprehensive examination of the process. We apply this framework to inertial transport processes where we observe the particle position while the velocity is hidden and is being reset at a constant rate. We show that velocity resetting results in a linearly growing spatial mean squared displacement at later times, independently of reset-free dynamics, due to resetting-induced tempering of velocity correlations. General expressions for the effective diffusion and drift coefficients are derived as a function of the resetting rate. A non-trivial dependence on the rate may appear due to multiple timescales and crossovers in the reset-free dynamics. An extension that incorporates refractory periods after each reset is considered, where post-resetting pauses can lead to anomalous diffusive behavior. Our results are of relevance to a wide range of systems, such as inertial transport where the mechanical momentum is lost in collisions with the environment or the behavior of living organisms where stop-and-go locomotion with inertia is ubiquitous. Numerical simulations for underdamped Brownian motion and the random acceleration process confirm our findings.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"141 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315723","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 : 2024-03-27DOI: 10.1088/1742-5468/ad2dd7
Xin Jiang, Quanyi Liang
The phenomenon of epidemic spread has received continuous attention due to its profound applications in a wide range of social and economic activities. In this paper we propose a partially overlapped multi-layer network model and illustrate the influence of multi-layer structure on outbreaks. Combined with the classic SIS model, we propose a set of discrete Markov equations and make first-order approximation on the threshold of epidemic outbreak. In comparison with independent simplex networks, we find that a multi-layer structure promotes epidemic spread and leads to a smaller critical threshold. In addition, we also find that the epidemic process on partially overlapped multi-layer networks is dominated by the layer with the largest main eigenvalue. Through Monte Carlo simulations, we find that the role of the dominant layer is irrelevant with its size, which means a small set of nodes can exhibit a disproportionate impact on the epidemics of a large network. Our research sheds light on the epidemic process on partially overlapped multi-layer complex systems, and provides a theoretical explanation of unexpected real-world outbreaks.
{"title":"Epidemic process on partially overlapped multi-layer networks","authors":"Xin Jiang, Quanyi Liang","doi":"10.1088/1742-5468/ad2dd7","DOIUrl":"https://doi.org/10.1088/1742-5468/ad2dd7","url":null,"abstract":"The phenomenon of epidemic spread has received continuous attention due to its profound applications in a wide range of social and economic activities. In this paper we propose a partially overlapped multi-layer network model and illustrate the influence of multi-layer structure on outbreaks. Combined with the classic SIS model, we propose a set of discrete Markov equations and make first-order approximation on the threshold of epidemic outbreak. In comparison with independent simplex networks, we find that a multi-layer structure promotes epidemic spread and leads to a smaller critical threshold. In addition, we also find that the epidemic process on partially overlapped multi-layer networks is dominated by the layer with the largest main eigenvalue. Through Monte Carlo simulations, we find that the role of the dominant layer is irrelevant with its size, which means a small set of nodes can exhibit a disproportionate impact on the epidemics of a large network. Our research sheds light on the epidemic process on partially overlapped multi-layer complex systems, and provides a theoretical explanation of unexpected real-world outbreaks.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"55 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315722","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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