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}
Pub Date : 2024-07-30DOI: 10.1103/physreve.110.015003
Abhijeet Melkani, Jayson Paulose
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual oscillators are well understood, those of systems of coupled oscillators remain challenging to characterize. Here we determine the parametric resonance conditions for time-modulated mechanical systems by exploiting the internal symmetries arising from the real-valued and symplectic nature of classical mechanics. We also determine how these conditions are further constrained when the system exhibits external symmetries. In particular, we analyze systems with space-time symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined space-time translation operator that provides more information about the dynamics of the system than the Floquet operator does and use it to derive conditions for one-way amplification of traveling waves. Our exact theoretical framework based on symmetries enables the design of exotic responses such as nonreciprocal transport and one-way amplification in dynamic mechanical metamaterials and is generalizable to all physical systems that obey space-time symmetry.
{"title":"Space-time symmetry and nonreciprocal parametric resonance in mechanical systems","authors":"Abhijeet Melkani, Jayson Paulose","doi":"10.1103/physreve.110.015003","DOIUrl":"https://doi.org/10.1103/physreve.110.015003","url":null,"abstract":"Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual oscillators are well understood, those of systems of coupled oscillators remain challenging to characterize. Here we determine the parametric resonance conditions for time-modulated mechanical systems by exploiting the internal symmetries arising from the real-valued and symplectic nature of classical mechanics. We also determine how these conditions are further constrained when the system exhibits external symmetries. In particular, we analyze systems with space-time symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined space-time translation operator that provides more information about the dynamics of the system than the Floquet operator does and use it to derive conditions for one-way amplification of traveling waves. Our exact theoretical framework based on symmetries enables the design of exotic responses such as nonreciprocal transport and one-way amplification in dynamic mechanical metamaterials and is generalizable to all physical systems that obey space-time symmetry.","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":"141862783","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.110.014215
Ming Zhong, Boris A. Malomed, Zhenya Yan
We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equation represents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment. The dispersion relation (DR) for lattice waves and the corresponding propagation band in the system's linear spectrum are found in an exact form for all values of LI. The DR is consistent with the continuum limit, differing in the range of wave numbers. Formation of single-site and two-site discrete solitons is explored, starting from the anticontinuum limit and continuing the analysis in the numerical form up to the existence boundary of the discrete solitons. Stability of the solitons is identified in terms of eigenvalues for small perturbations, and verified in direct simulations. Mobility of the discrete solitons is considered too, by means of an estimate of the system's Peierls-Nabarro potential barrier, and with the help of direct simulations. Collisions between persistently moving discrete solitons are also studied.
我们根据适当修改后的里兹分数导数定义，阐述了分数离散非线性薛定谔（FDNLS）方程，该方程的特征是其列维指数（LI）。该 FDNLS 方程代表了一种新型离散系统，其中近邻耦合与长程相互作用相结合，其衰减为晶格位点间距的反平方。该系统可以实现为由原子或小分子组成的平行准一维玻色-爱因斯坦凝聚体阵列，它们分别携带永久磁偶极矩或电偶极矩。我们以精确的形式找到了晶格波的色散关系（DR）和系统线性频谱中的相应传播带，适用于所有 LI 值。色散关系与连续极限一致，在波数范围内有所不同。从反连续极限开始，以数值形式继续分析直至离散孤子的存在边界，探讨了单位和双位离散孤子的形成。根据小扰动的特征值确定了孤子的稳定性，并通过直接模拟进行了验证。通过对系统的 Peierls-Nabarro 势垒进行估计，并在直接模拟的帮助下，离散孤子的移动性也得到了考虑。此外，还研究了持续运动的离散孤子之间的碰撞。
{"title":"Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative","authors":"Ming Zhong, Boris A. Malomed, Zhenya Yan","doi":"10.1103/physreve.110.014215","DOIUrl":"https://doi.org/10.1103/physreve.110.014215","url":null,"abstract":"We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equation represents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment. The dispersion relation (DR) for lattice waves and the corresponding propagation band in the system's linear spectrum are found in an exact form for all values of LI. The DR is consistent with the continuum limit, differing in the range of wave numbers. Formation of single-site and two-site discrete solitons is explored, starting from the anticontinuum limit and continuing the analysis in the numerical form up to the existence boundary of the discrete solitons. Stability of the solitons is identified in terms of eigenvalues for small perturbations, and verified in direct simulations. Mobility of the discrete solitons is considered too, by means of an estimate of the system's Peierls-Nabarro potential barrier, and with the help of direct simulations. Collisions between persistently moving discrete solitons are also studied.","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":"141862780","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}
With magnetic resonance imaging experiments, we study packings of granular spherocylinders with merely 2% asphericity. Evident structural anisotropies across all length scales are identified. Most interestingly, the global nematic order decreases with increasing packing fraction, while the local contact anisotropy shows an opposing trend. We attribute this counterintuitive phenomenon to a competition between gravity-driven ordering aided by frictional contacts and a geometric frustration effect at the marginally jammed state. It is also surprising to notice that such slight particle asphericity can trigger non-negligible correlations between contact-level and mesoscale structures, manifested in drastically different nonaffine structural rearrangements upon compaction from that of granular spheres. These observations can help improve statistical mechanical models for the orientational order transformation of nonspherical granular particle packings, which involves complex interplays between particle shape, frictional contacts, and external force field.
{"title":"Evident structural anisotropies arising from near-zero particle asphericity in granular spherocylinder packings","authors":"Yuwen Sun, Chenyang Wang, Jing Yang, Weijia Shi, Qifan Pang, Yujie Wang, Jianqi Li, Bingwen Hu, Chengjie Xia","doi":"10.1103/physreve.110.014903","DOIUrl":"https://doi.org/10.1103/physreve.110.014903","url":null,"abstract":"With magnetic resonance imaging experiments, we study packings of granular spherocylinders with merely 2% asphericity. Evident structural anisotropies across all length scales are identified. Most interestingly, the global nematic order decreases with increasing packing fraction, while the local contact anisotropy shows an opposing trend. We attribute this counterintuitive phenomenon to a competition between gravity-driven ordering aided by frictional contacts and a geometric frustration effect at the marginally jammed state. It is also surprising to notice that such slight particle asphericity can trigger non-negligible correlations between contact-level and mesoscale structures, manifested in drastically different nonaffine structural rearrangements upon compaction from that of granular spheres. These observations can help improve statistical mechanical models for the orientational order transformation of nonspherical granular particle packings, which involves complex interplays between particle shape, frictional contacts, and external force field.","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":"141862781","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.110.015209
G. Lehmann, K. H. Spatschek
To avoid damage in high-power laser systems, a chirped plasma-based grating is proposed for compressing laser pulses that have been previously stretched and amplified. This chirped grating is generated through the interaction of chirped pump laser pulses in a plasma slab. Particle-in-cell (PIC) simulations demonstrate that the grating exists for a duration sufficient to be utilized in the final chirped pulse amplification (CPA) stage. The generation of the grating is quite flexible, as several parameters can be adjusted, such as plasma density, chirp, length, and intensity of the pump laser. To begin, the structure of the grating is analyzed in terms of ponderomotive effects of the pump laser pulses. The primary application of the chirped plasma-based grating lies in compressing laser pulses to large amplitudes and short durations after they have been stretched and amplified beforehand. The compression factor is explored in connection with potential grating parameters. Reflectivity and effective bandwidth of chirped plasma gratings are parameters to be optimized. However, the grating spectral bandwidth can only be increased at the expense of reflectivity. The PIC results are made understandable through model calculations based on coupled mode equations.
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Pub Date : 2024-07-30DOI: 10.1103/physreve.110.014609
Ladislav Šamaj, Emmanuel Trizac, Martin Trulsson
We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia et al., J. Phys. Chem. B126, 3143 (2022)], we developed an effective-field theory for symmetric plates, stemming from the ground-state description that holds at infinite couplings. Here, we generalize the approach to the asymmetric case, where the plates bear charges of the same sign, but of different values. In the symmetric situation, the mobile ions, which are localized in the vicinity of the two plates, share equally between both of them. Here, the sharing is nontrivial, depending both on the coupling parameter and the distance between the plates. We thus introduce a counterion occupation parameter that is determined variationally to ensure minimum of the free energy. The analytical results for the pressure as a function of the plate-plate distance agree well with our Monte Carlo data, in a large interval of strong and intermediate coupling constants . We show in particular that within this description there exists a range of large distances at which the attractive pressure features a behavior.
我们有兴趣对带电体（如一对胶体）之间在强耦合机制下的同类电荷吸引力现象进行合理解释。这两个胶体被模拟成均匀带电的平行板，由移动反离子中和。在早先的研究中[Palaia 等人，J. Phys. Chem. B 126, 3143 (2022)]，我们从无限耦合条件下的基态描述出发，建立了对称板的有效场理论。在此，我们将这一方法推广到非对称情况，即板上的电荷符号相同，但电荷值不同。在对称情况下，移动离子位于两板附近，在两板之间平均分享。在这种情况下，移动离子在两块板之间的分担是非对等的，取决于耦合参数和两块板之间的距离。因此，我们引入了一个可变的反离子占据参数，以确保自由能最小。在强耦合常数 Ξ 和中间耦合常数 Ξ 的较大范围内，压力随板间距 d 变化的分析结果与蒙特卡罗数据非常吻合。我们特别表明，在这一描述范围内，存在一个大距离范围，在该距离范围内，吸引力压力的特征是 1/d2 行为。
{"title":"Strong-coupling effective-field theory for asymmetrically charged plates with counterions only","authors":"Ladislav Šamaj, Emmanuel Trizac, Martin Trulsson","doi":"10.1103/physreve.110.014609","DOIUrl":"https://doi.org/10.1103/physreve.110.014609","url":null,"abstract":"We are interested in rationalizing the phenomenon of like-charge attraction between charged bodies, such as a pair of colloids, in the strong coupling regime. The two colloids are modelled as uniformly charged parallel plates, neutralized by mobile counterions. In an earlier work [Palaia <i>et al.</i>, <span>J. Phys. Chem. B</span> <b>126</b>, 3143 (2022)], we developed an effective-field theory for symmetric plates, stemming from the ground-state description that holds at infinite couplings. Here, we generalize the approach to the asymmetric case, where the plates bear charges of the same sign, but of different values. In the symmetric situation, the mobile ions, which are localized in the vicinity of the two plates, share equally between both of them. Here, the sharing is nontrivial, depending both on the coupling parameter and the distance between the plates. We thus introduce a counterion occupation parameter that is determined variationally to ensure minimum of the free energy. The analytical results for the pressure as a function of the plate-plate distance <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi></math> agree well with our Monte Carlo data, in a large interval of strong and intermediate coupling constants <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">Ξ</mi></math>. We show in particular that within this description there exists a range of large distances at which the attractive pressure features a <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><mo>/</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></math> behavior.","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":"141862779","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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