Pub Date : 2024-08-08DOI: 10.1103/physreve.110.024116
Raz Halifa Levi, Yacov Kantor
We consider a -dimensional correlated percolation problem of sites not visited by a random walk on a hypercubic lattice for , 4, and 5. The length of the random walk is . Close to the critical value , many geometrical properties of the problem can be described as powers (critical exponents) of , such as , which controls the strength of the spanning cluster, and , which characterizes the behavior of the mean finite cluster size . We show that at the ratio between the mean mass of the largest cluster and the mass of the second largest cluster is independent of and can be used to find . We calculate from the dependence of and , and from the finite size scaling of . The resulting exponent remains close to 1 in all dimensions. The exponent decreases from in to in
我们考虑一个 d 维的相关渗滤问题，即在 d=3、4 和 5 的超立方晶格 Ld 上，随机行走未访问的点的渗滤问题。随机行走的长度为 N=uLd。在临界值 u=uc 附近，问题的许多几何特性都可以用 uc-u 的幂次（临界指数）来描述，如控制跨簇强度的 β 和描述平均有限簇大小 S 行为的 γ。我们证明，在 uc 时，最大簇 M1 的平均质量与第二大簇 M2 的质量之比与 L 无关，可以用来求出 uc。我们根据 M1 和 M2 与 L 的关系计算出 β，并根据 S 的有限大小缩放计算出 γ。指数γ从 d=3 时的≈3.9 下降到 d=4 时的≈1.9 和 d=5 时的≈1.3，最终在 d=6 时达到预期的 γ=1，接近 γ=4/（d-2）。
{"title":"Critical exponents of correlated percolation of sites not visited by a random walk","authors":"Raz Halifa Levi, Yacov Kantor","doi":"10.1103/physreve.110.024116","DOIUrl":"https://doi.org/10.1103/physreve.110.024116","url":null,"abstract":"We consider a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math>-dimensional correlated percolation problem of sites <i>not</i> visited by a random walk on a hypercubic lattice <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>L</mi><mi>d</mi></msup></math> for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math>, 4, and 5. The length of the random walk is <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"script\">N</mi><mo>=</mo><mi>u</mi><msup><mi>L</mi><mi>d</mi></msup></mrow></math>. Close to the critical value <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>u</mi><mo>=</mo><msub><mi>u</mi><mi>c</mi></msub></mrow></math>, many geometrical properties of the problem can be described as powers (critical exponents) of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>u</mi><mi>c</mi></msub><mo>−</mo><mi>u</mi></mrow></math>, such as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math>, which controls the strength of the spanning cluster, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math>, which characterizes the behavior of the mean finite cluster size <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>S</mi></math>. We show that at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>u</mi><mi>c</mi></msub></math> the ratio between the mean mass of the largest cluster <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>1</mn></msub></math> and the mass of the second largest cluster <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>2</mn></msub></math> is independent of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> and can be used to find <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>u</mi><mi>c</mi></msub></math>. We calculate <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math> from the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> dependence of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>1</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>M</mi><mn>2</mn></msub></math>, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> from the finite size scaling of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>S</mi></math>. The resulting exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>β</mi></math> remains close to 1 in all dimensions. The exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> decreases from <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≈</mo><mn>3.9</mn></mrow></math> in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>3</mn></mrow></math> to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≈</mo><mn>1.9</mn></mrow></math> in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>d</mi><mo>=</mo><mn>4</mn","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938708","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 : 2024-08-08DOI: 10.1103/physreve.110.l022601
Ana M. Montero, Andrés Santos
This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.
{"title":"Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids: Exact results","authors":"Ana M. Montero, Andrés Santos","doi":"10.1103/physreve.110.l022601","DOIUrl":"https://doi.org/10.1103/physreve.110.l022601","url":null,"abstract":"This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969158","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 : 2024-08-07DOI: 10.1103/physreve.110.024113
Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, Justin H. Wilson
The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic -adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.
{"title":"Statistical mechanics of stochastic quantum control: d-adic Rényi circuits","authors":"Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, Justin H. Wilson","doi":"10.1103/physreve.110.024113","DOIUrl":"https://doi.org/10.1103/physreve.110.024113","url":null,"abstract":"The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math>-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938793","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 : 2024-08-07DOI: 10.1103/physreve.110.024114
Johannes Schmidt, Andreas Schadschneider
The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings, we demonstrate scale invariance at different times and heights using large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.
{"title":"Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class","authors":"Johannes Schmidt, Andreas Schadschneider","doi":"10.1103/physreve.110.024114","DOIUrl":"https://doi.org/10.1103/physreve.110.024114","url":null,"abstract":"The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings, we demonstrate scale invariance at different times and heights using large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process, which belongs to the KPZ universality class. Here we focus on current (or height) fluctuations in the steady-state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial-state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by superdiffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938796","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 : 2024-08-07DOI: 10.1103/physreve.110.025303
Leheng Chen, Chuang Zhang, Jin Zhao
Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.
{"title":"Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method","authors":"Leheng Chen, Chuang Zhang, Jin Zhao","doi":"10.1103/physreve.110.025303","DOIUrl":"https://doi.org/10.1103/physreve.110.025303","url":null,"abstract":"Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938795","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 : 2024-08-07DOI: 10.1103/physreve.110.024115
Peter Werner, Alexander K. Hartmann, Satya N. Majumdar
A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature and subject to an external force , which couples to the free length of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature and force , the full distribution of free lengths in the thermodynamic limit and show that it is qualitatively very different for , and . Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained already allows us to derive an analytical expression for the work distribution in the zipped phase for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as with numerical simulations performed by applying sophisticated large-deviation algorithms.
我们引入了一个简单的拉链模型，以简化的方式表示折叠的 DNA 双螺旋或 RNA 中的发夹结构。双链发夹连接到温度为 T 的热浴中，并受到外力 f 的作用，该外力与未拉链序列的自由长度 L 相耦合。最左边的拉链位置可以看作是一个随机漫步者在一个特殊外场中的位置。在一个非常大的链的热力学极限中，增加力会导致在临界力 fc(T) 处出现拉链-解拉链的一阶相变。作为温度 T 和力 f 的函数，我们分析计算了热力学极限下自由长度的全分布 P(L)，并表明在 f<fc、f=fc 和 f>fc 时，自由长度的全分布有很大不同。接下来，我们将考虑力按照线性协议递增的准静态功过程。得到 P(L) 后，我们就可以推导出长链在拉链阶段 f<fc 的功分布 P(W) 的分析表达式。我们明确计算了工作量分布的大偏差尾部。该分布可解释为类似振荡模型的功分布。我们对功分布的分析结果与应用复杂的大偏差算法进行的数值模拟结果进行了比较。
{"title":"Work distribution for unzipping processes","authors":"Peter Werner, Alexander K. Hartmann, Satya N. Majumdar","doi":"10.1103/physreve.110.024115","DOIUrl":"https://doi.org/10.1103/physreve.110.024115","url":null,"abstract":"A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> and subject to an external force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math>, which couples to the free length <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>L</mi></math> of the unzipped sequence. The leftmost zipped position can be seen as the position of a random walker in a special external field. Increasing the force leads to a zipping-unzipping first-order phase transition at a critical force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>f</mi><mi>c</mi></msub><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math> in the thermodynamic limit of a very large chain. We compute analytically, as a function of temperature <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>T</mi></math> and force <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math>, the full distribution <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> of free lengths in the thermodynamic limit and show that it is qualitatively very different for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow><mo>,</mo><mo> </mo><mrow><mi>f</mi><mo>=</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo>></mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math>. Next we consider quasistatic work processes where the force is incremented according to a linear protocol. Having obtained <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>L</mi><mo>)</mo></mrow></math> already allows us to derive an analytical expression for the work distribution <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mo>(</mo><mi>W</mi><mo>)</mo></mrow></math> in the zipped phase <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>f</mi><mo><</mo><msub><mi>f</mi><mi>c</mi></msub></mrow></math> for a long chain. We compute the large-deviation tails of the work distribution explicitly. This distribution can be interpreted as work distribution for an oscillatorylike model. Our analytical result for the work distribution is compared over a large range of the support down to probabilities as small as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mn>10</mn><mrow><mo>−</mo><mn>200</mn></mrow></msup></math> with numerical simulations performed by applying sophisticated large-deviation algorithms.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141938794","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.110.025002
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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