Pub Date : 2024-08-01DOI: 10.1103/physreve.110.l022101
Katja Klobas, Cecilia De Fazio, Juan P. Garrahan
We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical “Floquet-East” model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the “energy-entropy” crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of “hydrophobic collapse.”
{"title":"Exact pretransition effects in kinetically constrained circuits: Dynamical fluctuations in the Floquet-East model","authors":"Katja Klobas, Cecilia De Fazio, Juan P. Garrahan","doi":"10.1103/physreve.110.l022101","DOIUrl":"https://doi.org/10.1103/physreve.110.l022101","url":null,"abstract":"We study the dynamics of a classical circuit corresponding to a discrete-time version of the kinetically constrained East model. We show that this classical “Floquet-East” model displays pre-transition behavior which is a dynamical equivalent of the hydrophobic effect in water. For the deterministic version of the model, we prove exactly (i) a change in scaling with size in the probability of inactive space-time regions (akin to the “energy-entropy” crossover of the solvation free energy in water), (ii) a first-order phase transition in the dynamical large deviations, (iii) the existence of the optimal geometry for local phase separation to accommodate space-time solutes, and (iv) a dynamical analog of “hydrophobic collapse.”","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872795","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 : 2024-08-01DOI: 10.1103/physreve.110.024301
Elena Agliari, Francesco Alemanno, Adriano Barra, Michele Castellana, Daniele Lotito, Matthieu Piel
Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counterexamples, as in leukocyte coordination (where signaling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signaling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.
{"title":"Inverse modeling of time-delayed interactions via the dynamic-entropy formalism","authors":"Elena Agliari, Francesco Alemanno, Adriano Barra, Michele Castellana, Daniele Lotito, Matthieu Piel","doi":"10.1103/physreve.110.024301","DOIUrl":"https://doi.org/10.1103/physreve.110.024301","url":null,"abstract":"Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counterexamples, as in leukocyte coordination (where signaling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signaling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873426","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 : 2024-08-01DOI: 10.1103/physreve.110.l022102
Fábio D. A. Aarão Reis, Vaughan R. Voller
Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on and with diffusion exponents that depend on the dimensions of matrix and fractal as . This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.
{"title":"Universal superdiffusion of random walks in media with embedded fractal networks of low diffusivity","authors":"Fábio D. A. Aarão Reis, Vaughan R. Voller","doi":"10.1103/physreve.110.l022102","DOIUrl":"https://doi.org/10.1103/physreve.110.l022102","url":null,"abstract":"Diffusion in composite media with high contrasts between diffusion coefficients in fractal sets of inclusions and in their embedding matrices is modeled by lattice random walks (RWs) with probabilities <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>p</mi><mo><</mo><mn>1</mn></mrow></math> of hops from fractal sites and 1 from matrix sites. Superdiffusion is predicted in time intervals that depend on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math> and with diffusion exponents that depend on the dimensions of matrix <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><mi>E</mi><mo>)</mo></math> and fractal <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi>D</mi><mi>F</mi></msub><mo>)</mo></math> as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>ν</mi><mo>=</mo><mn>1</mn><mo>/</mo><mo>(</mo><mn>2</mn><mo>+</mo><msub><mi>D</mi><mi>F</mi></msub><mo>−</mo><mi>E</mi><mo>)</mo></mrow></math>. This contrasts with the nonuniversal subdiffusion of RWs confined to fractal media. Simulations with four fractals show the anomaly at several time decades for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>p</mi><mo>≲</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> and the crossover to the asymptotic normal diffusion. These results show that superdiffusion can be observed in isotropic RWs with finite moments of hop length distributions and allow the estimation of the dimension of the inclusion set from the diffusion exponent. However, displacements within single trajectories have normal scaling, which shows transient ergodicity breaking.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872655","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 : 2024-08-01DOI: 10.1103/physreve.110.024401
Felipe Serafim, Tawan T. A. Carvalho, Mauro Copelli, Pedro V. Carelli
An important working hypothesis to investigate brain activity is whether it operates in a critical regime. Recently, maximum-entropy phenomenological models have emerged as an alternative way of identifying critical behavior in neuronal data sets. In the present paper, we investigate the signatures of criticality from a firing rate-based maximum-entropy approach on data sets generated by computational models, and we compare them to experimental results. We found that the maximum entropy approach consistently identifies critical behavior around the phase transition in models and rules out criticality in models without phase transition. The maximum-entropy-model results are compatible with results for cortical data from urethane-anesthetized rats data, providing further support for criticality in the brain.
{"title":"Maximum-entropy-based metrics for quantifying critical dynamics in spiking neuron data","authors":"Felipe Serafim, Tawan T. A. Carvalho, Mauro Copelli, Pedro V. Carelli","doi":"10.1103/physreve.110.024401","DOIUrl":"https://doi.org/10.1103/physreve.110.024401","url":null,"abstract":"An important working hypothesis to investigate brain activity is whether it operates in a critical regime. Recently, maximum-entropy phenomenological models have emerged as an alternative way of identifying critical behavior in neuronal data sets. In the present paper, we investigate the signatures of criticality from a firing rate-based maximum-entropy approach on data sets generated by computational models, and we compare them to experimental results. We found that the maximum entropy approach consistently identifies critical behavior around the phase transition in models and rules out criticality in models without phase transition. The maximum-entropy-model results are compatible with results for cortical data from urethane-anesthetized rats data, providing further support for criticality in the brain.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862775","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 : 2024-08-01DOI: 10.1103/physreve.110.l023101
J. S. Hansen
In this Letter, the single-element Maxwell model is generalized with respect to the wave vector and extended with a correction function that measures the reduced viscous response. This model has only two free parameters and avoids the attenuation-frequency locking present in the original model. Through molecular simulations it is shown that the model satisfactory predicts the transverse dynamics of the binary Lennard-Jones system at different temperatures, as well as water and toluene at ambient conditions. The correction function shows that the viscous response is significantly reduced compared to the predictions of the original Maxwell model and that there exists a characteristic length scale of minimum dissipation.
{"title":"Modified and generalized single-element Maxwell viscoelastic model","authors":"J. S. Hansen","doi":"10.1103/physreve.110.l023101","DOIUrl":"https://doi.org/10.1103/physreve.110.l023101","url":null,"abstract":"In this Letter, the single-element Maxwell model is generalized with respect to the wave vector and extended with a correction function that measures the reduced viscous response. This model has only two free parameters and avoids the attenuation-frequency locking present in the original model. Through molecular simulations it is shown that the model satisfactory predicts the transverse dynamics of the binary Lennard-Jones system at different temperatures, as well as water and toluene at ambient conditions. The correction function shows that the viscous response is significantly reduced compared to the predictions of the original Maxwell model and that there exists a characteristic length scale of minimum dissipation.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862776","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}
Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, thus overcoming a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes: the weighted triangulated torus and the weighted waffle. We completely characterize their higher-order spectral properties and demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices.
{"title":"Global topological synchronization of weighted simplicial complexes","authors":"Runyue Wang, Riccardo Muolo, Timoteo Carletti, Ginestra Bianconi","doi":"10.1103/physreve.110.014307","DOIUrl":"https://doi.org/10.1103/physreve.110.014307","url":null,"abstract":"Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, thus overcoming a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes: the weighted triangulated torus and the weighted waffle. We completely characterize their higher-order spectral properties and demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-31DOI: 10.1103/physreve.110.015106
Anna L. Herring, Ruotong Huang (黄若橦), Adrian Sheppard
Diffusive transport has implications for the long-term status of underground storage of hydrogen fuel and carbon dioxide , technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, and will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport (“Ostwald ripening”). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved and driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for and at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For , even geothermal gradients less than (far less than typical gradients of ) are sufficient to induce downwards diffusion at depths relevant to storage. Diff
扩散输运对氢气（H2）燃料和二氧化碳（CO2）地下储存的长期状况具有影响，而这些技术正被用于减缓气候变化和推动能源转型。一旦注入地下，二氧化碳和氢气将存在于多相流体-水-岩石系统中。部分可溶的注入流体可以以连接的羽流形式流经多孔岩石，也可以断开连接并作为被地下水包围的神经节被困在储藏岩孔隙空间中，还可以溶解并在溶解后通过水相迁移。最近的分析主要集中在流体节间不同的毛细管压力所引起的浓度梯度，这种梯度可以推动扩散迁移（"奥斯特瓦尔德熟化"）。然而，这些研究忽视或过度简化了一些重要因素，即地质条件下气体的非理想性、由溶解溶质的部分摩尔密度驱动的溶解 CO2 和 H2 的对立平衡状态，以及地热梯度产生的熵效应和热扩散效应。我们根据热力学第一原理进行了分析，并以此为基础对地下储层相关条件下的 CO2 和 H2 进行了数值估算。我们的研究表明，正如之前的分析所表明的那样，虽然这两种气体在等温系统中的扩散输运都是向上的，但自由能的熵贡献是如此之大，以至于在有地热梯度的系统中会导致扩散输运方向的逆转。对于 CO2 来说，即使地热梯度小于 10∘C/km（远小于 25∘C/km 的典型梯度），也足以在与封存有关的深度引起向下扩散。H2 的扩散输运受到的影响较小，但在典型梯度下（例如在 1000 米深处为 30∘C/km）仍然会发生方向逆转。这种逆转的发生与溶质在水溶液中的疏热性或亲热性无关。在存在地热梯度的地方，熵贡献也会改变通量的大小，尽管 H2 的扩散系数较高，但估计 CO2 在 30∘C/km 梯度下的扩散通量最大。我们发现，在 30∘C/km 的情况下，二氧化碳的最大通量约为 10-13 摩尔/（平方厘米）；明显低于文献中对中高渗透率地层中最大对流通量的估计。与之前的研究相反，我们发现扩散和对流可能会协同作用--在各自储层的代表性条件下，扩散和对流都会向下驱动 CO2，向上驱动 H2。
{"title":"Directionality of gravitational and thermal diffusive transport in geologic fluid storage","authors":"Anna L. Herring, Ruotong Huang (黄若橦), Adrian Sheppard","doi":"10.1103/physreve.110.015106","DOIUrl":"https://doi.org/10.1103/physreve.110.015106","url":null,"abstract":"Diffusive transport has implications for the long-term status of underground storage of hydrogen <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub><mo>)</mo></math> fuel and carbon dioxide <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>(</mo><msub><mi>CO</mi><mn>2</mn></msub><mo>)</mo></math>, technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport (“Ostwald ripening”). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">H</mi><mn>2</mn></msub></math> at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>CO</mi><mn>2</mn></msub></math>, even geothermal gradients less than <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>10</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math> (far less than typical gradients of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>25</mn><msup><mspace width=\"0.16em\"></mspace><mo>∘</mo></msup><mi mathvariant=\"normal\">C</mi><mo>/</mo><mi>km</mi></mrow></math>) are sufficient to induce downwards diffusion at depths relevant to storage. Diff","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.1103/physreve.110.015311
Kaiyu Shi, Guanqing Wang, Jiangrong Xu, Lu Wang
In this paper, we extend the improved discrete unified gas-kinetic scheme (DUGKS) from solving the hydrodynamic equations to addressing the phase field equations, building upon our prior work [Wang et al., Phys. Fluids35, 017106 (2023)]. The conservative Allen-Cahn equation and its modified form are presented first, followed by the construction of two improved DUGKS methods for interface capturing, based on the corresponding kinetic equations. The improved DUGKS for interface capturing utilizes the node distribution function instead of the interface center distribution function for evaluating the interface flux. The improved DUGKS enhances the numerical stability of the original DUGKS, and the good stability allows the calculations to be performed using large time steps, reducing the cumulative error from which more accurate predictions can be obtained. To verify the validity of the scheme, a series of numerical experiments were further carried out, including the diagonal translation, Zalesak's disk rotation, reversed single vortex, and deformation field. The comparison with the benchmark data shows that the improved DUGKS can simply and effectively capture the sharp interface and complex deformation interface of the two-phase flow interface.
{"title":"Improved discrete unified gas-kinetic scheme for interface capturing","authors":"Kaiyu Shi, Guanqing Wang, Jiangrong Xu, Lu Wang","doi":"10.1103/physreve.110.015311","DOIUrl":"https://doi.org/10.1103/physreve.110.015311","url":null,"abstract":"In this paper, we extend the improved discrete unified gas-kinetic scheme (DUGKS) from solving the hydrodynamic equations to addressing the phase field equations, building upon our prior work [Wang <i>et al.</i>, <span>Phys. Fluids</span> <b>35</b>, 017106 (2023)]. The conservative Allen-Cahn equation and its modified form are presented first, followed by the construction of two improved DUGKS methods for interface capturing, based on the corresponding kinetic equations. The improved DUGKS for interface capturing utilizes the node distribution function instead of the interface center distribution function for evaluating the interface flux. The improved DUGKS enhances the numerical stability of the original DUGKS, and the good stability allows the calculations to be performed using large time steps, reducing the cumulative error from which more accurate predictions can be obtained. To verify the validity of the scheme, a series of numerical experiments were further carried out, including the diagonal translation, Zalesak's disk rotation, reversed single vortex, and deformation field. The comparison with the benchmark data shows that the improved DUGKS can simply and effectively capture the sharp interface and complex deformation interface of the two-phase flow interface.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.1103/physreve.110.015310
Abram Rodgers, Daniele Venturi
Functional differential equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations), and statistical physics. Despite their significance, computing solutions to FDEs remains a longstanding challenge in mathematical physics. In this paper we address this challenge by introducing approximation theory and high-performance computational algorithms designed for solving FDEs on tensor manifolds. Our approach involves approximating FDEs using high-dimensional partial differential equations (PDEs), and then solving such high-dimensional PDEs on a low-rank tensor manifold leveraging high-performance (parallel) tensor algorithms. The effectiveness of the proposed approach is demonstrated through its application to the Burgers-Hopf FDE, which governs the characteristic functional of the stochastic solution to the Burgers equation evolving from a random initial state.
{"title":"Tensor approximation of functional differential equations","authors":"Abram Rodgers, Daniele Venturi","doi":"10.1103/physreve.110.015310","DOIUrl":"https://doi.org/10.1103/physreve.110.015310","url":null,"abstract":"Functional differential equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations), and statistical physics. Despite their significance, computing solutions to FDEs remains a longstanding challenge in mathematical physics. In this paper we address this challenge by introducing approximation theory and high-performance computational algorithms designed for solving FDEs on tensor manifolds. Our approach involves approximating FDEs using high-dimensional partial differential equations (PDEs), and then solving such high-dimensional PDEs on a low-rank tensor manifold leveraging high-performance (parallel) tensor algorithms. The effectiveness of the proposed approach is demonstrated through its application to the Burgers-Hopf FDE, which governs the characteristic functional of the stochastic solution to the Burgers equation evolving from a random initial state.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.1103/physreve.110.014214
Koki Yoshida, Keiji Konishi
Delayed feedback control is a commonly used control method for stabilizing unstable periodic orbits and unstable steady states. The present paper proposes an adaptive tuning delay time rule for delayed feedback control focused on stabilizing unstable steady states. The rule is designed to slowly vary the delay time, increasing the difference between the past and current states of dynamical systems, which induces the delay time to automatically fall into the stability region. We numerically confirm that the tuning rule works well for the Stuart–Landau oscillator, FitzHugh–Nagumo model, and Lorenz system.
{"title":"Adaptive delayed feedback control for stabilizing unstable steady states","authors":"Koki Yoshida, Keiji Konishi","doi":"10.1103/physreve.110.014214","DOIUrl":"https://doi.org/10.1103/physreve.110.014214","url":null,"abstract":"Delayed feedback control is a commonly used control method for stabilizing unstable periodic orbits and unstable steady states. The present paper proposes an adaptive tuning delay time rule for delayed feedback control focused on stabilizing unstable steady states. The rule is designed to slowly vary the delay time, increasing the difference between the past and current states of dynamical systems, which induces the delay time to automatically fall into the stability region. We numerically confirm that the tuning rule works well for the Stuart–Landau oscillator, FitzHugh–Nagumo model, and Lorenz system.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872656","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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