Pub Date : 2025-02-20DOI: 10.1016/j.physa.2025.130448
Denis Michel
Large cosmological redshifts show that the expansion of the universe is accelerating, whereas a deceleration was expected under the influence of gravity. Since this discovery, the search for a repulsive force has gone in several directions. The main candidate is the postulated dark energy whose physical support is the subject of intense research, but alternative ideas such as a different physics of gravity on a large scale or the backreaction effect, are not ruled out. However, all of these lines of research fall within the same framework which was established by the pioneers of modern cosmology in the early 20th century. This note proposes to look back at an earlier view of the universe by Boltzmann. Based on his thermodynamic intuition, Boltzmann proposed that our visible universe could be part of a fluctuation within a global universe in equilibrium. This seemingly far-fetched vision is supported here by a minimalist Newtonian modeling which predicts that an acceleration of expansion would be initiated by a fluctuation in density, thus eliminating the objections to the Boltzmann universe regarding its size and maintenance. The strengths and weaknesses of this amusing hypothesis are discussed.
{"title":"Accelerated expansion is a built-in property of the Boltzmann universe","authors":"Denis Michel","doi":"10.1016/j.physa.2025.130448","DOIUrl":"10.1016/j.physa.2025.130448","url":null,"abstract":"<div><div>Large cosmological redshifts show that the expansion of the universe is accelerating, whereas a deceleration was expected under the influence of gravity. Since this discovery, the search for a repulsive force has gone in several directions. The main candidate is the postulated dark energy whose physical support is the subject of intense research, but alternative ideas such as a different physics of gravity on a large scale or the backreaction effect, are not ruled out. However, all of these lines of research fall within the same framework which was established by the pioneers of modern cosmology in the early 20th century. This note proposes to look back at an earlier view of the universe by Boltzmann. Based on his thermodynamic intuition, Boltzmann proposed that our visible universe could be part of a fluctuation within a global universe in equilibrium. This seemingly far-fetched vision is supported here by a minimalist Newtonian modeling which predicts that an acceleration of expansion would be initiated by a fluctuation in density, thus eliminating the objections to the Boltzmann universe regarding its size and maintenance. The strengths and weaknesses of this amusing hypothesis are discussed.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"664 ","pages":"Article 130448"},"PeriodicalIF":2.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143488263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-19DOI: 10.1016/j.physa.2025.130440
Peng Gang Sun, Jingqi Hu, Xunlian Wu, Han Zhang, Yining Quan, Qiguang Miao
Community detection is a fundamental task in complex network analysis, focusing on uncovering the underlying organizational structures of networks by analyzing relationships between nodes. While existing methods have shown significant success, they often struggle in networks with overlapping communities or intricate topologies, primarily due to their reliance on local information and limited ability to capture global structures. To overcome these limitations, we introduce the Graph Reconstruction Model for Enhanced Community Detection (GRMECD), a novel approach that integrates higher-order information with network reconstruction. Leveraging a Markov chain-based transfer probability matrix, GRMECD captures the global network structure, enabling effective pruning and reconstruction to enhance the performance of community detection. Experimental evaluations on synthetic and real-world datasets demonstrate that GRMECD consistently outperforms state-of-the-art methods, particularly in networks with complex or overlapping structures.
{"title":"Graph reconstruction model for enhanced community detection","authors":"Peng Gang Sun, Jingqi Hu, Xunlian Wu, Han Zhang, Yining Quan, Qiguang Miao","doi":"10.1016/j.physa.2025.130440","DOIUrl":"10.1016/j.physa.2025.130440","url":null,"abstract":"<div><div>Community detection is a fundamental task in complex network analysis, focusing on uncovering the underlying organizational structures of networks by analyzing relationships between nodes. While existing methods have shown significant success, they often struggle in networks with overlapping communities or intricate topologies, primarily due to their reliance on local information and limited ability to capture global structures. To overcome these limitations, we introduce the Graph Reconstruction Model for Enhanced Community Detection (GRMECD), a novel approach that integrates higher-order information with network reconstruction. Leveraging a Markov chain-based transfer probability matrix, GRMECD captures the global network structure, enabling effective pruning and reconstruction to enhance the performance of community detection. Experimental evaluations on synthetic and real-world datasets demonstrate that GRMECD consistently outperforms state-of-the-art methods, particularly in networks with complex or overlapping structures.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"664 ","pages":"Article 130440"},"PeriodicalIF":2.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143464884","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 : 2025-02-18DOI: 10.1016/j.physa.2025.130458
Ziyu Xing
The mechanical properties of slidable cross-links mediated dual cross-linked polymers present an improvement over those of standard single cross-linked polymers. Nonetheless, the specific role played by the two cross-links within the same condensed polymer state remains ambiguous, and the distinct characteristics and interconnected impacts of these two cross-links necessitate further investigation. The introduction of different cross-links can result in polymers displaying wholly disparate mechanical behaviors. In this study, a constitutive model is developed by integrating self-avoiding walk and scaling theory to examine the rubber elastic behavior of dual cross-linked polymers undergoing slidable cross-links mediation. Following the principles of rubber elasticity, the mechanism underlying the formation of dual cross-linked polymers is elucidated, encompassing stable cross-linked networks, slidable cross-linked networks, and their coupling effects, which correspond to molecular mechanisms, such as the Gent model, self-avoiding walk chains, and scaling theory, respectively. Moreover, based on the Kardar-Parisi-Zhang scaling, the stable cross-linked network entails boundary conditions, while the sliding chain experiences constrained self-avoiding walking to relax stress and dissipate energy. The study further offers insights into the free energy of slidable cross-links mediated dual cross-linked polymers to analyze their rubber elasticity and hysteresis (loading-unloading cycle) effects. Finally, the efficacy of the proposed constitutive models is affirmed through comparison with experimental results documented in the literature, shedding light on the exceptional mechanical properties of dual cross-linked polymers.
{"title":"A constitutive model for slidable cross-links mediated dual cross-linked polymers to understand coupling and hysteresis of dual cross-links","authors":"Ziyu Xing","doi":"10.1016/j.physa.2025.130458","DOIUrl":"10.1016/j.physa.2025.130458","url":null,"abstract":"<div><div>The mechanical properties of slidable cross-links mediated dual cross-linked polymers present an improvement over those of standard single cross-linked polymers. Nonetheless, the specific role played by the two cross-links within the same condensed polymer state remains ambiguous, and the distinct characteristics and interconnected impacts of these two cross-links necessitate further investigation. The introduction of different cross-links can result in polymers displaying wholly disparate mechanical behaviors. In this study, a constitutive model is developed by integrating self-avoiding walk and scaling theory to examine the rubber elastic behavior of dual cross-linked polymers undergoing slidable cross-links mediation. Following the principles of rubber elasticity, the mechanism underlying the formation of dual cross-linked polymers is elucidated, encompassing stable cross-linked networks, slidable cross-linked networks, and their coupling effects, which correspond to molecular mechanisms, such as the Gent model, self-avoiding walk chains, and scaling theory, respectively. Moreover, based on the Kardar-Parisi-Zhang scaling, the stable cross-linked network entails boundary conditions, while the sliding chain experiences constrained self-avoiding walking to relax stress and dissipate energy. The study further offers insights into the free energy of slidable cross-links mediated dual cross-linked polymers to analyze their rubber elasticity and hysteresis (loading-unloading cycle) effects. Finally, the efficacy of the proposed constitutive models is affirmed through comparison with experimental results documented in the literature, shedding light on the exceptional mechanical properties of dual cross-linked polymers.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130458"},"PeriodicalIF":2.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453364","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 : 2025-02-18DOI: 10.1016/j.physa.2025.130468
J.L.E. da Silva
This work brings applications of the Lambert-Tsallis Wq function in graph theory and quantum networks. Initially, the function Wq is used to represent the k colorings of certain classes of chromatic graphs and to describe the positive real root of certain modified orbital polynomials of simple graphs, as well as determining the lower limit for the k colorings of a random graph . Subsequently, we will present the disentropy and Renyi-based disentropy, functionals that use the Lambert-Tsallis function in their kernel, of a simple hypergraph in addition to showing the analytical relationship of the Renyi-based disentropy of this hypergraph with its spectral Zeta function. Finally, we will show that the function Wq can be used to quantify the quantum disentanglement of pure two-qubit states in random networks and in probability estimation in some networks with multipartite quantum entanglement percolation and optimal bit-flip correction.
{"title":"Applications of the Lambert-Tsallis Wq function in graph theory and quantum networks","authors":"J.L.E. da Silva","doi":"10.1016/j.physa.2025.130468","DOIUrl":"10.1016/j.physa.2025.130468","url":null,"abstract":"<div><div>This work brings applications of the Lambert-Tsallis <em>W</em><sub><em>q</em></sub> function in graph theory and quantum networks. Initially, the function <em>W</em><sub><em>q</em></sub> is used to represent the <em>k</em> colorings of certain classes of chromatic graphs and to describe the positive real root of certain modified orbital polynomials of simple graphs, as well as determining the lower limit for the <em>k</em> colorings of a random graph <span><math><mrow><mi>G</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></mrow></math></span>. Subsequently, we will present the disentropy and Renyi-based disentropy, functionals that use the Lambert-Tsallis function in their kernel, of a simple hypergraph in addition to showing the analytical relationship of the Renyi-based disentropy of this hypergraph with its spectral Zeta function. Finally, we will show that the function <em>W</em><sub><em>q</em></sub> can be used to quantify the quantum disentanglement of pure two-qubit states in random networks and in probability estimation in some networks with multipartite quantum entanglement percolation and optimal bit-flip correction.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"664 ","pages":"Article 130468"},"PeriodicalIF":2.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474542","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 : 2025-02-18DOI: 10.1016/j.physa.2025.130408
Yujiao Chen, Futao Zhang, Yongsheng Qian, Junwei Zeng, Xin Li
Based on the influence of the driver's driving visual angle and the gradient value on the car-following behavior, the two-way information feedback and time delay, a new car-following model considering dynamic reaction time and visual angle when the vehicle goes up and down the slope continuously is proposed, and the parameters are calibrated based on the actual vehicle driving data. On this basis, the linear stability condition of traffic flow is analyzed based on the long wave theory, and the evolution process of small disturbances of traffic flow and the emission rate fluctuation and total amount change of fuel consumption and CO2, NOX, PM10, and VOC are simulated and analyzed. Then, the driver is divided into aggressive type, conservative type, and neutral type, and the influence of driver characteristics and lane change behavior on stability and safety is studied by simulation. The results show that the model considering driving visual angle can give the vehicle better self-stabilizing. Bidirectional information feedback control has better stability control ability than unidirectional information feedback. The increased headway delay will aggravate the diffusion of minor disturbances, but the rise in velocity delay will help to enhance stability. The fluctuation trend of the instantaneous emission rate of fuel consumption and pollutant gas is consistent with the stability, but the total fuel consumption and the total emission of pollutant gas do not have a single correlation with the stability. Aggressive drivers contribute to improving stability but are not conducive to the safety of traffic flow. Lane-changing behavior will aggravate the speed difference, but it will help to improve safety. This study provides a new approach for constructing traffic flow-following models on mountainous roads. Further, it explores the correlation between stability, fuel consumption, and pollutant emissions, which is significant for formulating future traffic control strategies for mountainous roads and emission reduction strategies.
{"title":"A new car-following model considering the driver's dynamic reaction time and driving visual angle on the slope","authors":"Yujiao Chen, Futao Zhang, Yongsheng Qian, Junwei Zeng, Xin Li","doi":"10.1016/j.physa.2025.130408","DOIUrl":"10.1016/j.physa.2025.130408","url":null,"abstract":"<div><div>Based on the influence of the driver's driving visual angle and the gradient value on the car-following behavior, the two-way information feedback and time delay, a new car-following model considering dynamic reaction time and visual angle when the vehicle goes up and down the slope continuously is proposed, and the parameters are calibrated based on the actual vehicle driving data. On this basis, the linear stability condition of traffic flow is analyzed based on the long wave theory, and the evolution process of small disturbances of traffic flow and the emission rate fluctuation and total amount change of fuel consumption and CO2, NO<sub>X</sub>, PM10, and VOC are simulated and analyzed. Then, the driver is divided into aggressive type, conservative type, and neutral type, and the influence of driver characteristics and lane change behavior on stability and safety is studied by simulation. The results show that the model considering driving visual angle can give the vehicle better self-stabilizing. Bidirectional information feedback control has better stability control ability than unidirectional information feedback. The increased headway delay will aggravate the diffusion of minor disturbances, but the rise in velocity delay will help to enhance stability. The fluctuation trend of the instantaneous emission rate of fuel consumption and pollutant gas is consistent with the stability, but the total fuel consumption and the total emission of pollutant gas do not have a single correlation with the stability. Aggressive drivers contribute to improving stability but are not conducive to the safety of traffic flow. Lane-changing behavior will aggravate the speed difference, but it will help to improve safety. This study provides a new approach for constructing traffic flow-following models on mountainous roads. Further, it explores the correlation between stability, fuel consumption, and pollutant emissions, which is significant for formulating future traffic control strategies for mountainous roads and emission reduction strategies.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130408"},"PeriodicalIF":2.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453363","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 : 2025-02-18DOI: 10.1016/j.physa.2025.130456
Jianwei Du , Jialei Cui , Gang Ren , Russell G. Thompson , Lele Zhang
The growing complexity of urban road traffic networks (URTNs) has increased their vulnerability to cascading failures. As one of the fundamental sources of network dynamics, route choice behavior should be essential for the pattern of resilience against cascading failures, but the mechanism between behavioral uncertainty and resilience evolution remains understudied. This paper proposes a novel framework for analyzing URTN resilience under cascading failures, focusing on how behavioral uncertainty shapes failure process and resilience evolution. Specifically, we develop a link-based cascading failure model that integrates load redistribution processes with route choice behavior under uncertainty, incorporating dynamic capacity changes and event intensity effects. The model employs fuzzy cumulative prospect theory (FCPT) to capture travelers' decision-making characteristics, considering both risk preference and perception uncertainty. A multi-level resilience assessment indicator is introduced to evaluate network performance from both structural and operational perspectives. Using Shangyu's URTN as the case study, we find that: (1) the network exhibits moderately high resilience with failure propagation following distinct thresholds; (2) high-importance link failures trigger severe cascading effects, particularly during sustained area-wide disruptions and peak hours; (3) optimal network performance is achieved with a tolerance parameter of 0.2 and moderate risk preference combined with low-to-medium perception uncertainty; and (4) recovery strategies should prioritize directly attacked links to effectively mitigate cascade propagation. These findings provide valuable references for studying URTN resilience against unforeseen cascading failures.
{"title":"Cascading failures and resilience evolution in urban road traffic networks with bounded rational route choice","authors":"Jianwei Du , Jialei Cui , Gang Ren , Russell G. Thompson , Lele Zhang","doi":"10.1016/j.physa.2025.130456","DOIUrl":"10.1016/j.physa.2025.130456","url":null,"abstract":"<div><div>The growing complexity of urban road traffic networks (URTNs) has increased their vulnerability to cascading failures. As one of the fundamental sources of network dynamics, route choice behavior should be essential for the pattern of resilience against cascading failures, but the mechanism between behavioral uncertainty and resilience evolution remains understudied. This paper proposes a novel framework for analyzing URTN resilience under cascading failures, focusing on how behavioral uncertainty shapes failure process and resilience evolution. Specifically, we develop a link-based cascading failure model that integrates load redistribution processes with route choice behavior under uncertainty, incorporating dynamic capacity changes and event intensity effects. The model employs fuzzy cumulative prospect theory (FCPT) to capture travelers' decision-making characteristics, considering both risk preference and perception uncertainty. A multi-level resilience assessment indicator is introduced to evaluate network performance from both structural and operational perspectives. Using Shangyu's URTN as the case study, we find that: (1) the network exhibits moderately high resilience with failure propagation following distinct thresholds; (2) high-importance link failures trigger severe cascading effects, particularly during sustained area-wide disruptions and peak hours; (3) optimal network performance is achieved with a tolerance parameter of 0.2 and moderate risk preference combined with low-to-medium perception uncertainty; and (4) recovery strategies should prioritize directly attacked links to effectively mitigate cascade propagation. These findings provide valuable references for studying URTN resilience against unforeseen cascading failures.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"664 ","pages":"Article 130456"},"PeriodicalIF":2.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143518895","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 : 2025-02-17DOI: 10.1016/j.physa.2025.130436
Kosmas Kosmidis
DNA sequences have a complex structure that reflects their evolutionary history, such as functional elements, gene modifications, and repetitive segments. To study this structure, mathematical models like DNA walks can be used. DNA walks assign opposite movements to pyrimidines (C, T) and purines (A, G), allowing the application of nonlinear dynamics and complex systems theory. These methods can reveal long-range correlations and genome signatures that are useful for metagenomics. We combined DNA walks and visibility graphs to create DNA visibility graphs (Kosmidis and Hütt, 2023), which can capture correlations in DNA regions and artificial sequences.
We applied these methods to E. coli genes and found patterns that suggest gene grouping into classes. We also found that the degree distribution of visibility graphs in different organisms follows a power-law, indicating universal scaling. Importantly, we find that genes of the same organism i.e. E. coli exhibit vast differences in their visibility graph characteristics while complete-genome visibility graphs from different organisms have remarkable similarities. Our results offer new ways to visualize the relationship between DNA structure and function and have implications for genomics, bioinformatics, and systems biology.
{"title":"Applied DNA visibility graphs: Understanding DNA structure-function relationship in genomics","authors":"Kosmas Kosmidis","doi":"10.1016/j.physa.2025.130436","DOIUrl":"10.1016/j.physa.2025.130436","url":null,"abstract":"<div><div>DNA sequences have a complex structure that reflects their evolutionary history, such as functional elements, gene modifications, and repetitive segments. To study this structure, mathematical models like DNA walks can be used. DNA walks assign opposite movements to pyrimidines (C, T) and purines (A, G), allowing the application of nonlinear dynamics and complex systems theory. These methods can reveal long-range correlations and genome signatures that are useful for metagenomics. We combined DNA walks and visibility graphs to create DNA visibility graphs (Kosmidis and Hütt, 2023), which can capture correlations in DNA regions and artificial sequences.</div><div>We applied these methods to <em>E. coli</em> genes and found patterns that suggest gene grouping into classes. We also found that the degree distribution of visibility graphs in different organisms follows a power-law, indicating universal scaling. Importantly, we find that genes of the same organism i.e. <em>E. coli</em> exhibit vast differences in their visibility graph characteristics while complete-genome visibility graphs from different organisms have remarkable similarities. Our results offer new ways to visualize the relationship between DNA structure and function and have implications for genomics, bioinformatics, and systems biology.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130436"},"PeriodicalIF":2.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143463881","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 : 2025-02-16DOI: 10.1016/j.physa.2025.130434
Zhengrong Jin , Wanrong Zan , Shichao Ma , Wantao Jia
The Fokker–Planck–Kolmogorov (FPK) equation provides a deterministic framework for describing the evolution of probability density functions (PDF) and holds great significance in the field of stochastic dynamics. Physics-Informed Neural Networks (PINNs) development provides a new approach for solving the FPK equation. However, the vanilla PINNs method with uniform sampling faces challenges when dealing with FPK equations with strong nonlinear terms whose solutions have high frequency. In this study, we introduce PINNs with hybrid sampling specifically designed to solve the stationary FPK equation. The proposed hybrid sampling specifically introduces trajectory residual points and combines them with an adaptive sampling of residual points based on the residuals of the equation. In addition, the network incorporates a customized architecture and loss function tailored to address the challenges and specific requirements associated with solving the stationary FPK equation. We apply the proposed hybrid sampling method to three nonlinear systems, demonstrating its accuracy and efficiency by comparing it with Latin hypercube sampling (LHS), adaptive sampling, and trajectory sampling. The impact of the nonlinear parameters on the performance of different sampling methods is analyzed, emphasizing the superior accuracy achieved by hybrid sampling in cases involving significant nonlinearity. These experimental results demonstrate that incorporating trajectory residual points notably enhances computational performance and precision. Furthermore, we analyze the impact of different trajectory points and adaptive points on network training and examine the effect of the learning rate strategy on the performance of the proposed method.
{"title":"Physics-Informed Neural Networks with hybrid sampling for stationary Fokker–Planck–Kolmogorov Equation","authors":"Zhengrong Jin , Wanrong Zan , Shichao Ma , Wantao Jia","doi":"10.1016/j.physa.2025.130434","DOIUrl":"10.1016/j.physa.2025.130434","url":null,"abstract":"<div><div>The Fokker–Planck–Kolmogorov (FPK) equation provides a deterministic framework for describing the evolution of probability density functions (PDF) and holds great significance in the field of stochastic dynamics. Physics-Informed Neural Networks (PINNs) development provides a new approach for solving the FPK equation. However, the vanilla PINNs method with uniform sampling faces challenges when dealing with FPK equations with strong nonlinear terms whose solutions have high frequency. In this study, we introduce PINNs with hybrid sampling specifically designed to solve the stationary FPK equation. The proposed hybrid sampling specifically introduces trajectory residual points and combines them with an adaptive sampling of residual points based on the residuals of the equation. In addition, the network incorporates a customized architecture and loss function tailored to address the challenges and specific requirements associated with solving the stationary FPK equation. We apply the proposed hybrid sampling method to three nonlinear systems, demonstrating its accuracy and efficiency by comparing it with Latin hypercube sampling (LHS), adaptive sampling, and trajectory sampling. The impact of the nonlinear parameters on the performance of different sampling methods is analyzed, emphasizing the superior accuracy achieved by hybrid sampling in cases involving significant nonlinearity. These experimental results demonstrate that incorporating trajectory residual points notably enhances computational performance and precision. Furthermore, we analyze the impact of different trajectory points and adaptive points on network training and examine the effect of the learning rate strategy on the performance of the proposed method.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130434"},"PeriodicalIF":2.8,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445418","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 : 2025-02-15DOI: 10.1016/j.physa.2025.130447
Bo-wen Xiao, Si-yu Huang, Ying An, Wei Wang
MBene is a branch of the new two-dimensional (2D) material MXene. Due to its high stability, good electrical conductivity, and excellent electrocatalytic performance, MBene shows great potential in energy storage and electrocatalysis. In this work, we used Monte Carlo simulation to study an MBene-like material described by a mixed-spin (5/2, 2) Ising model. We discuss the effects on the dynamic magnetic characteristics of the system, including dynamic order parameters and hysteresis loops, caused by the crystal field and exchange coupling. We found that the system can exhibit the behavior of double compensation temperatures. Increasing the absolute values of the exchange coupling or decreasing the absolute values of the crystal field can increase the coercivity and the area of the dynamic hysteresis loop.
{"title":"Dynamic magnetic properties of the mixed-spin (5/2, 2) Ising model with an MBene-like structure","authors":"Bo-wen Xiao, Si-yu Huang, Ying An, Wei Wang","doi":"10.1016/j.physa.2025.130447","DOIUrl":"10.1016/j.physa.2025.130447","url":null,"abstract":"<div><div>MBene is a branch of the new two-dimensional (2D) material MXene. Due to its high stability, good electrical conductivity, and excellent electrocatalytic performance, MBene shows great potential in energy storage and electrocatalysis. In this work, we used Monte Carlo simulation to study an MBene-like material described by a mixed-spin (5/2, 2) Ising model. We discuss the effects on the dynamic magnetic characteristics of the system, including dynamic order parameters and hysteresis loops, caused by the crystal field and exchange coupling. We found that the system can exhibit the behavior of double compensation temperatures. Increasing the absolute values of the exchange coupling or decreasing the absolute values of the crystal field can increase the coercivity and the area of the dynamic hysteresis loop.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130447"},"PeriodicalIF":2.8,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445417","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 : 2025-02-15DOI: 10.1016/j.physa.2025.130431
Charles S. do Amaral
We study a percolation model with restrictions on the opening of sites on the square lattice. In this model, each site starts closed and an attempt to open it occurs at time , where is a sequence of independent random variables uniformly distributed on the interval . The site will open if the volume difference between the two largest clusters adjacent to it is greater than or equal to a constant or if it has at most one adjacent cluster. Through numerical analysis, we determine the critical threshold for various values of , verifying that is non-decreasing in and that there exists a critical value beyond which percolation does not occur. Additionally, we find that the correlation length exponent of this model is equal to that of the ordinary percolation model. For and , we estimate the averages of the density of open sites, the number of distinct cluster volumes, and the volume of the largest cluster.
{"title":"Constrained volume-difference site percolation model on the square lattice","authors":"Charles S. do Amaral","doi":"10.1016/j.physa.2025.130431","DOIUrl":"10.1016/j.physa.2025.130431","url":null,"abstract":"<div><div>We study a percolation model with restrictions on the opening of sites on the square lattice. In this model, each site <span><math><mrow><mi>s</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> starts closed and an attempt to open it occurs at time <span><math><mrow><mi>t</mi><mo>=</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></math></span>, where <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>s</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span> is a sequence of independent random variables uniformly distributed on the interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. The site will open if the volume difference between the two largest clusters adjacent to it is greater than or equal to a constant <span><math><mi>r</mi></math></span> or if it has at most one adjacent cluster. Through numerical analysis, we determine the critical threshold <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span> for various values of <span><math><mi>r</mi></math></span>, verifying that <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>c</mi></mrow></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span> is non-decreasing in <span><math><mi>r</mi></math></span> and that there exists a critical value <span><math><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>=</mo><mn>5</mn></mrow></math></span> beyond which percolation does not occur. Additionally, we find that the correlation length exponent of this model is equal to that of the ordinary percolation model. For <span><math><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mn>1</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mn>9</mn></mrow></math></span>, we estimate the averages of the density of open sites, the number of distinct cluster volumes, and the volume of the largest cluster.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"663 ","pages":"Article 130431"},"PeriodicalIF":2.8,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453365","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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