Pub Date : 2025-12-13DOI: 10.1016/j.physa.2025.131182
Hang Liu, Chaoyang Shi, Fei Liu, Jiafeng Xie, Zhonglang Yao, Zhiyun Zou
<div><div>Under the vehicle following scenario that do not involve the lane changings in a relatively saturated traffic flow operating state, the driver’s driving behavior decision-makings mainly involve the compliant behavior of maintaining the existing following time and the illegal behavior of reducing the following time regardless of the risks. For the purpose of releasing the time pressure, the drivers will often choose the illegal behavior, which causes a sharp decline in the safety and the stability of the traffic flow operations. A method that can guide the drivers to actively choose the compliant behavior needs to be proposed urgently to improve the overall safety and gradually alleviate the efficiency crisis during the more orderly driving process, which is defined as the cooperative guidance. However, the cooperative guidance is not easy to establish because the underlying mechanism of the driving behavior decision-making is difficult to quantify. Based on this background, this paper proposes a cooperative guidance method that acts on the driver’s behavior based on the quantitative analysis of the driving behavior decision-making, which can improve the safety and the efficiency of the traffic flow operations by guiding the driver’s behavior to become more compliant and orderly during the vehicle following processes. In order to better utilize the safety improvement effect of the established cooperative guidance method, this paper sets the vehicle following scenario into a mixed traffic flow composed of the human-driven vehicles (HDVs) and the connected autonomous vehicles (CAVs). At the same time, in order to further exert the safety guarantee and auxiliary guidance role of the CAVs, this paper creates a mixing pattern that makes the CAVs into the CAV platoons (CPs) and the HDVs into the HDV platoons (HPs). By constructing a measuring architecture for different types of the following time in this mixing pattern, this paper proposes a decision-making quantification paradigm based on the comprehensive benefit that can consider both the safety as well as the time saving, and establishes a decision-making model based on the comprehensive benefit (CBDM) to quantitatively simulate the drivers’ benefit-oriented driving behavior decision-makings. Then, an intelligent transportation points system (ITPS) based on the Elo rating algorithm is involved to adjust the comprehensive benefit that can be obtained from different driving behaviors described by the CBDM. Finally, a mixed traffic flow micro-indicator system (M-TFMS) is proposed to update the traffic flow indicators of the constructed scenario and assess the safety improvement effect by using the cooperative guidance under the action of the CBDM and the ITPS. When the cooperative guidance comes into play, the overall safety level when the drivers choose the compliant behavior is up to 4.016% higher than when they choose illegal behavior. At the same time, on the premise of ensuring safety, d
{"title":"Improvement for vehicle following safety in mixed traffic flow: A cooperative guidance method for driving behavior decision-making","authors":"Hang Liu, Chaoyang Shi, Fei Liu, Jiafeng Xie, Zhonglang Yao, Zhiyun Zou","doi":"10.1016/j.physa.2025.131182","DOIUrl":"10.1016/j.physa.2025.131182","url":null,"abstract":"<div><div>Under the vehicle following scenario that do not involve the lane changings in a relatively saturated traffic flow operating state, the driver’s driving behavior decision-makings mainly involve the compliant behavior of maintaining the existing following time and the illegal behavior of reducing the following time regardless of the risks. For the purpose of releasing the time pressure, the drivers will often choose the illegal behavior, which causes a sharp decline in the safety and the stability of the traffic flow operations. A method that can guide the drivers to actively choose the compliant behavior needs to be proposed urgently to improve the overall safety and gradually alleviate the efficiency crisis during the more orderly driving process, which is defined as the cooperative guidance. However, the cooperative guidance is not easy to establish because the underlying mechanism of the driving behavior decision-making is difficult to quantify. Based on this background, this paper proposes a cooperative guidance method that acts on the driver’s behavior based on the quantitative analysis of the driving behavior decision-making, which can improve the safety and the efficiency of the traffic flow operations by guiding the driver’s behavior to become more compliant and orderly during the vehicle following processes. In order to better utilize the safety improvement effect of the established cooperative guidance method, this paper sets the vehicle following scenario into a mixed traffic flow composed of the human-driven vehicles (HDVs) and the connected autonomous vehicles (CAVs). At the same time, in order to further exert the safety guarantee and auxiliary guidance role of the CAVs, this paper creates a mixing pattern that makes the CAVs into the CAV platoons (CPs) and the HDVs into the HDV platoons (HPs). By constructing a measuring architecture for different types of the following time in this mixing pattern, this paper proposes a decision-making quantification paradigm based on the comprehensive benefit that can consider both the safety as well as the time saving, and establishes a decision-making model based on the comprehensive benefit (CBDM) to quantitatively simulate the drivers’ benefit-oriented driving behavior decision-makings. Then, an intelligent transportation points system (ITPS) based on the Elo rating algorithm is involved to adjust the comprehensive benefit that can be obtained from different driving behaviors described by the CBDM. Finally, a mixed traffic flow micro-indicator system (M-TFMS) is proposed to update the traffic flow indicators of the constructed scenario and assess the safety improvement effect by using the cooperative guidance under the action of the CBDM and the ITPS. When the cooperative guidance comes into play, the overall safety level when the drivers choose the compliant behavior is up to 4.016% higher than when they choose illegal behavior. At the same time, on the premise of ensuring safety, d","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"683 ","pages":"Article 131182"},"PeriodicalIF":3.1,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145750311","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 : 2025-12-13DOI: 10.1016/j.physa.2025.131208
J.F. Silva Neto , D.S.M. Alencar , L.T. Brito , G.A. Alves , F.W.S. Lima , A. Macedo-Filho , R.S. Ferreira , T.F.A. Alves
We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For supervised learning, dense neural networks are trained on spin configuration data generated via the kinetic Monte Carlo method. Using independently simulated configuration data, the neural network accurately identifies the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and enables estimation of critical exponents, typically obtained via Monte Carlo importance sampling. Furthermore, deep unsupervised learning is performed using variational autoencoders, which reconstruct input spin configurations and generate artificial outputs. The autoencoders detect the phase transition through the loss function, quantifying the preservation of essential data features. We define a correlation function between the real and reconstructed data, and find that this correlation function is universal at the critical point. Variational autoencoders also serve as generative models, producing artificial spin configurations.
{"title":"Supervised and unsupervised deep learning applied to the majority vote model","authors":"J.F. Silva Neto , D.S.M. Alencar , L.T. Brito , G.A. Alves , F.W.S. Lima , A. Macedo-Filho , R.S. Ferreira , T.F.A. Alves","doi":"10.1016/j.physa.2025.131208","DOIUrl":"10.1016/j.physa.2025.131208","url":null,"abstract":"<div><div>We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For supervised learning, dense neural networks are trained on spin configuration data generated via the kinetic Monte Carlo method. Using independently simulated configuration data, the neural network accurately identifies the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and enables estimation of critical exponents, typically obtained via Monte Carlo importance sampling. Furthermore, deep unsupervised learning is performed using variational autoencoders, which reconstruct input spin configurations and generate artificial outputs. The autoencoders detect the phase transition through the loss function, quantifying the preservation of essential data features. We define a correlation function between the real and reconstructed data, and find that this correlation function is universal at the critical point. Variational autoencoders also serve as generative models, producing artificial spin configurations.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"683 ","pages":"Article 131208"},"PeriodicalIF":3.1,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145750312","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 : 2025-12-11DOI: 10.1016/j.physa.2025.131205
Sajal Debnath, Santimoy Kundu
The electrical, physical, structural and chemical characteristics of neurons combine to develop very complex dynamical systems. A valuable approach for addressing such high levels of complexity is the investigation of brain spatiotemporal patterns. In this work, two neural systems connected by a nonlinear synapse initiate to manage the stability of synchronization and mode transition in neurons that are in phase lock. In order to activate two neural systems via nonlinear coupling, chaotic signals are encoded to represent separated waves with a restricted frequency range. We have particularly concentrated on the spiral spatiotemporal pattern for the purpose of our investigation. A substantial influence of spirals is made to certain brain functions. We investigate the different dynamical characteristics for the coupled neuronal model, considering the flux coupling constant and coupling coefficients for account as control factors. The results demonstrated that nonlinear coupling through certain components prevents bursting between neurons generated by filtered chaotic inputs and is useful in the creation of nonlinear synapses. In the end, we will examine the impact of amplitude and frequency of an external force on the dynamics of a spiral wave inside a neural network for controlling the wave.
{"title":"Spiral wave analysis in bidirectional Hindmarsh–Rose neurons with nonlinear coupling and dynamical control through external magnetic induction","authors":"Sajal Debnath, Santimoy Kundu","doi":"10.1016/j.physa.2025.131205","DOIUrl":"10.1016/j.physa.2025.131205","url":null,"abstract":"<div><div>The electrical, physical, structural and chemical characteristics of neurons combine to develop very complex dynamical systems. A valuable approach for addressing such high levels of complexity is the investigation of brain spatiotemporal patterns. In this work, two neural systems connected by a nonlinear synapse initiate to manage the stability of synchronization and mode transition in neurons that are in phase lock. In order to activate two neural systems via nonlinear coupling, chaotic signals are encoded to represent separated waves with a restricted frequency range. We have particularly concentrated on the spiral spatiotemporal pattern for the purpose of our investigation. A substantial influence of spirals is made to certain brain functions. We investigate the different dynamical characteristics for the coupled neuronal model, considering the flux coupling constant and coupling coefficients for account as control factors. The results demonstrated that nonlinear coupling through certain components prevents bursting between neurons generated by filtered chaotic inputs and is useful in the creation of nonlinear synapses. In the end, we will examine the impact of amplitude and frequency of an external force on the dynamics of a spiral wave inside a neural network for controlling the wave.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"683 ","pages":"Article 131205"},"PeriodicalIF":3.1,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145718917","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 : 2025-12-09DOI: 10.1016/j.physa.2025.131188
S. Sakhi
We analyze the O(N) theory near the upper critical dimension dc= 8/3, where the octic interaction is marginal. For we find a Wilson–Fisher–type non-Gaussian infrared fixed point associated with a tetracritical O(N) universality class and extract its exponents. At d = 8/3 the interacting fixed point merges with Gaussian, leading to mean-field scaling. Using a large-N expansion and a modified minimal subtraction scheme, we compute the effective potential and renormalization group functions up to next-to-next-to-leading order (NNLO). The renormalized potential remains bounded from below without constraints on the coupling constant, in contrast to similar models in three dimensions. At the identified nontrivial fixed points, we determine the critical exponents of the tetracritical O(N) universality class. Our results extend the Wilson–Fisher framework to marginal higher-order interactions in non-integer dimensions, with relevance to systems exhibiting fractal or disordered structure.
{"title":"Large-N analysis of critical behavior and effective potential in an O(N) model with octic interaction in fractional dimension d = 8/3","authors":"S. Sakhi","doi":"10.1016/j.physa.2025.131188","DOIUrl":"10.1016/j.physa.2025.131188","url":null,"abstract":"<div><div>We analyze the O(N) theory near the upper critical dimension d<sub>c</sub>= 8/3, where the octic interaction <span><math><msup><mrow><mo>(</mo><mi>ϕ</mi><mo>⋅</mo><mi>ϕ</mi><mo>)</mo></mrow><mn>4</mn></msup></math></span> is marginal. For <span><math><mrow><mi>d</mi><mo>=</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>−</mo><mn>2</mn><mi>ε</mi></mrow></math></span> we find a Wilson–Fisher–type non-Gaussian infrared fixed point associated with a tetracritical O(N) universality class and extract its exponents. At d = 8/3 the interacting fixed point merges with Gaussian, leading to mean-field scaling. Using a large-N expansion and a modified minimal subtraction scheme, we compute the effective potential and renormalization group functions up to next-to-next-to-leading order (NNLO). The renormalized potential remains bounded from below without constraints on the coupling constant, in contrast to similar models in three dimensions. At the identified nontrivial fixed points, we determine the critical exponents of the tetracritical O(N) universality class. Our results extend the Wilson–Fisher framework to marginal higher-order interactions in non-integer dimensions, with relevance to systems exhibiting fractal or disordered structure.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"683 ","pages":"Article 131188"},"PeriodicalIF":3.1,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145750313","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 : 2025-12-08DOI: 10.1016/j.physa.2025.131194
Anton A. Kutsenko
We consider a simplified mass redistribution scheme, with and without permutations, that simulates stochastic compression under high and low disorder. For this case, surprisingly, the limit density distributions can be computed explicitly, and neat formulas are provided. As the dimension of space increases, the distinction between structured and turbulent compression becomes less pronounced. Already in dimension two, the density distributions are barely distinguishable.
{"title":"Stochastic compression with and without permutations","authors":"Anton A. Kutsenko","doi":"10.1016/j.physa.2025.131194","DOIUrl":"10.1016/j.physa.2025.131194","url":null,"abstract":"<div><div>We consider a simplified mass redistribution scheme, with and without permutations, that simulates stochastic compression under high and low disorder. For this case, surprisingly, the limit density distributions can be computed explicitly, and neat formulas are provided. As the dimension of space increases, the distinction between structured and turbulent compression becomes less pronounced. Already in dimension two, the density distributions are barely distinguishable.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"683 ","pages":"Article 131194"},"PeriodicalIF":3.1,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145718889","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}
The kappa distribution of velocities is frequently found instead of the Maxwellian distribution in collisionless plasmas present in Earth’s magnetosphere, the solar wind among other contexts where particles do not reach thermal equilibrium. Although the origin of these distributions is sometimes explained by means of non-extensive statistics, they can also be recovered using alternative frameworks such as superstatistics, providing a closer connection with probability theory. In this work we take this approach and derive the multi-particle and single-particle kappa distributions from superstatistics while taking into account the scale invariance property of the superstatistical temperature distribution. The formalism presented here emphasizes the usefulness of superstatistics in the computation of expectation values under kappa distributions. Some consequences of a superstatistical interpretation of kappa distributions are also discussed, such as the connection between correlations and temperature uncertainty, the meaning of the superstatistical temperature and the entropy of kappa-distributed plasmas.
{"title":"Kappa distributions in the framework of superstatistics","authors":"Sergio Davis, Biswajit Bora, Cristian Pavez, Leopoldo Soto","doi":"10.1016/j.physa.2025.131191","DOIUrl":"10.1016/j.physa.2025.131191","url":null,"abstract":"<div><div>The kappa distribution of velocities is frequently found instead of the Maxwellian distribution in collisionless plasmas present in Earth’s magnetosphere, the solar wind among other contexts where particles do not reach thermal equilibrium. Although the origin of these distributions is sometimes explained by means of non-extensive statistics, they can also be recovered using alternative frameworks such as superstatistics, providing a closer connection with probability theory. In this work we take this approach and derive the multi-particle and single-particle kappa distributions from superstatistics while taking into account the scale invariance property of the superstatistical temperature distribution. The formalism presented here emphasizes the usefulness of superstatistics in the computation of expectation values under kappa distributions. Some consequences of a superstatistical interpretation of kappa distributions are also discussed, such as the connection between correlations and temperature uncertainty, the meaning of the superstatistical temperature and the entropy of kappa-distributed plasmas.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"682 ","pages":"Article 131191"},"PeriodicalIF":3.1,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736557","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 : 2025-12-08DOI: 10.1016/j.physa.2025.131190
W. Lebrecht D-P
An alternative model is presented to study site percolation and frustration when monomers and dimers are deposited on square and triangular lattices. To this end, 77 square cell configurations and 82 triangular cell configurations are considered. The configurations allow the determination of a distribution function whose maximum corresponds to the site percolation threshold using a semi-analytical technique. Next, frustration is induced in the cells through interactions of nearest neighbors, using the formal definition of frustrated plaquettes. New distributions are established to determine the level of frustration of the configurations, which leads to the identification of similarities with spin glass properties. In this sense, the work proposes a semi-analytical extension of the site percolation model that incorporates magnetic frustration and establishes a link with spin-glass-like systems.
{"title":"Distribution functions in site percolation and magnetic frustration","authors":"W. Lebrecht D-P","doi":"10.1016/j.physa.2025.131190","DOIUrl":"10.1016/j.physa.2025.131190","url":null,"abstract":"<div><div>An alternative model is presented to study site percolation and frustration when monomers and dimers are deposited on square and triangular lattices. To this end, 77 square cell configurations and 82 triangular cell configurations are considered. The configurations allow the determination of a distribution function whose maximum corresponds to the site percolation threshold using a semi-analytical technique. Next, frustration is induced in the cells through <span><math><mrow><mo>±</mo><mi>J</mi></mrow></math></span> interactions of nearest neighbors, using the formal definition of frustrated plaquettes. New distributions are established to determine the level of frustration of the configurations, which leads to the identification of similarities with spin glass properties. In this sense, the work proposes a semi-analytical extension of the site percolation model that incorporates magnetic frustration and establishes a link with spin-glass-like systems.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"682 ","pages":"Article 131190"},"PeriodicalIF":3.1,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736555","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 : 2025-12-08DOI: 10.1016/j.physa.2025.131202
D.G. Hodonou , E. Albayrak , R. Houenou , R.A.A. Yessoufou , T.D. Oke , A. Kpadonou
In this work, we investigate the magnetic and critical properties of a diatomic molecular model in which each molecule is composed of two atoms with spin . The system is simulated on the Bethe lattice (BL) with coordination number using the Exacts Recursion Relations (ERR) method. To explore antiferromagnetic (AFM) behavior, all exchange interactions are chosen to be negative (). The thermal variations of the sublattice magnetizations reveal the existence of several ordered phases, including five antiferromagnetic, one ferrimagnetic, and one mixed (partially ordered) phase. These phases are separated by both first- and second-order phase transition lines, giving rise to different types of critical points such as tricritical points (TCP), critical end points (CEP), and quadruple points (QP). The corresponding phase diagrams in the and planes exhibit rich topological structures resulting from the competition between the exchange interactions, the crystal field , and the external magnetic field . The results obtained provide a deeper understanding of the complex magnetic ordering phenomena in molecular-based spin systems on recursive lattices.
{"title":"The simulation of diatomic molecule of spin-3/2 Blume–Capel model with full antiferromagnetic interactions: Exacts recursion relations approach","authors":"D.G. Hodonou , E. Albayrak , R. Houenou , R.A.A. Yessoufou , T.D. Oke , A. Kpadonou","doi":"10.1016/j.physa.2025.131202","DOIUrl":"10.1016/j.physa.2025.131202","url":null,"abstract":"<div><div>In this work, we investigate the magnetic and critical properties of a diatomic molecular model in which each molecule is composed of two atoms with spin <span><math><mrow><mi>σ</mi><mo>=</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math></span>. The system is simulated on the Bethe lattice (BL) with coordination number <span><math><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow></math></span> using the Exacts Recursion Relations (ERR) method. To explore antiferromagnetic (AFM) behavior, all exchange interactions are chosen to be negative (<span><math><mrow><mi>J</mi><mo>=</mo><msup><mrow><mi>J</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><msub><mrow><mi>J</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></math></span>). The thermal variations of the sublattice magnetizations reveal the existence of several ordered phases, including five antiferromagnetic, one ferrimagnetic, and one mixed (partially ordered) phase. These phases are separated by both first- and second-order phase transition lines, giving rise to different types of critical points such as tricritical points (TCP), critical end points (CEP), and quadruple points (QP). The corresponding phase diagrams in the <span><math><mrow><mo>(</mo><mi>D</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math></span> planes exhibit rich topological structures resulting from the competition between the exchange interactions, the crystal field <span><math><mi>D</mi></math></span>, and the external magnetic field <span><math><mi>H</mi></math></span>. The results obtained provide a deeper understanding of the complex magnetic ordering phenomena in molecular-based spin systems on recursive lattices.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"682 ","pages":"Article 131202"},"PeriodicalIF":3.1,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736553","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 : 2025-12-08DOI: 10.1016/j.physa.2025.131201
Tianxin Zhang, Dazhi Zhang, Yi Ran, Zhichang Guo, Shengzhu Shi
Optimal control problems constrained by partial differential equations (PDEs) are widely studied in science and engineering, with physics-informed neural networks emerging as a powerful tool for solving such problems. However, existing methods often encounter difficulties when dealing with complex problem structures and show sensitivity to varying regularization parameters. To address these challenges, we propose ASNN, an adversarial and scale-adjusted neural network. ASNN is formulated within the Karush–Kuhn–Tucker framework and utilizes two independent neural networks to approximate the state, adjoint, and control variables. By incorporating adversarial attacks, ASNN enhances the accuracy of the solution, while the scale adjustment strategy improves numerical stability under different regularization settings. Extensive numerical experiments on benchmark PDE-constrained optimal control problems, including those governed by the Poisson’s equation, semilinear equation, control-constrained equation, and Navier–Stokes and Burgers’ equations, demonstrate the effectiveness and robustness of the proposed method and highlight its advantages over existing approaches.
{"title":"Enhanced physics-informed neural networks for PDE-constrained optimal control: A synergistic approach with adversarial attack and scale adjustment","authors":"Tianxin Zhang, Dazhi Zhang, Yi Ran, Zhichang Guo, Shengzhu Shi","doi":"10.1016/j.physa.2025.131201","DOIUrl":"10.1016/j.physa.2025.131201","url":null,"abstract":"<div><div>Optimal control problems constrained by partial differential equations (PDEs) are widely studied in science and engineering, with physics-informed neural networks emerging as a powerful tool for solving such problems. However, existing methods often encounter difficulties when dealing with complex problem structures and show sensitivity to varying regularization parameters. To address these challenges, we propose ASNN, an adversarial and scale-adjusted neural network. ASNN is formulated within the Karush–Kuhn–Tucker framework and utilizes two independent neural networks to approximate the state, adjoint, and control variables. By incorporating adversarial attacks, ASNN enhances the accuracy of the solution, while the scale adjustment strategy improves numerical stability under different regularization settings. Extensive numerical experiments on benchmark PDE-constrained optimal control problems, including those governed by the Poisson’s equation, semilinear equation, control-constrained equation, and Navier–Stokes and Burgers’ equations, demonstrate the effectiveness and robustness of the proposed method and highlight its advantages over existing approaches.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"682 ","pages":"Article 131201"},"PeriodicalIF":3.1,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737156","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 : 2025-12-06DOI: 10.1016/j.physa.2025.131192
Yan Li , Zhihong Ren
Achieving robust and high-precision quantum measurement is the ultimate goal in quantum metrology. Here, we employ the quantum Fisher information (QFI) as a tool to explore the potential of maximal superposition of symmetric Dicke (SSD) states in this aspect. The research in noninteracting environment shows that the metrological power of maximal SSD state is better than state (a special kind of SSD state) but with a limitation of the number of qubits, . We then present the optimal strategies for achieving the precision limit and study the decoherence effects. In the interacting Ising model, the metrological performance is universally enhanced and as the interacting strength increases it exhibits an interesting reversal behavior that the large-qubit maximal SSD state performs better than state and GHZ state in strong interaction, and vice versa. Additionally, we find that the effect of decay probability on the precision limit is largely decreased in the amplitude damping channel, especially in the strong interaction, which may shed some new light on the noisy quantum metrology. Our results provide insights into the interaction-enhanced quantum metrology.
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