非线性科学
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- [1] arXiv:2508.06502 [中文pdf, pdf, html, 其他]
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标题： 增强相位滞后的多层网络中的集群同步标题： Enhancing cluster synchronization in phase-lagged multilayer networks主题： 混沌动力学 (nlin.CD) ; 计算物理 (physics.comp-ph)
多层相位振子网络中的集群同步由于延迟相互作用的不稳定效应而面临重大挑战。 利用Sakaguchi-Kuramoto模型，本研究通过系统地探索自然频率分布对在高相位滞后条件下维持集群同步的作用，解决了这些挑战。 我们关注四种分布：均匀分布（uni-uni）、部分度相关（deg-uni，uni-deg）和完全度相关（deg-deg），其中振子的固有频率与其网络连通性一致。 通过数值和分析研究，我们证明了deg-deg分布，即两层都采用度匹配频率，显著增强了同步稳定性，优于其他配置。 我们分析了两种不同的网络架构：一种完全由非平凡簇组成，另一种结合了平凡和非平凡簇。 结果表明，编码在deg-deg耦合中的结构异质性抵消了相位滞后引起的去同步化，即使在大相位滞后值下也能实现稳健的集群同步。 通过横向Lyapunov指数（TLEs）严格验证了稳定性，结果表明deg-deg网络相比均匀或部分相关系统表现出更宽的同步区域。 这些发现为拓扑异质性和动态鲁棒性之间的相互作用提供了关键见解，为从容忍延迟的电力网格到自适应生物网络等需要相位滞后下同步的设计提供了框架。
Cluster synchronization in multilayer networks of phase oscillators with phase-lag poses significant challenges due to the destabilizing effects of delayed interactions. Leveraging the Sakaguchi-Kuramoto model, this study addresses these challenges by systematically exploring the role of natural frequency distributions in sustaining cluster synchronization under high phase-lag conditions. We focus on four distributions: uniform (uni-uni), partially degree-correlated (deg-uni, uni-deg), and fully degree-correlated (deg-deg), where oscillators' intrinsic frequencies align with their network connectivity. Through numerical and analytical investigations, we demonstrate that the deg-deg distribution, where both layers employ degree-matched frequencies, remarkably enhances synchronization stability, outperforming other configurations. We analyze two distinct network architectures: one composed entirely of nontrivial clusters and another combining trivial and nontrivial clusters. Results reveal that structural heterogeneity encoded in the deg-deg coupling counteracts phase-lag-induced desynchronization, enabling robust cluster synchronization even at large phase-lag values. Stability is rigorously validated via transverse Lyapunov exponents (TLEs), which confirm that deg-deg networks exhibit broader synchronization regimes compared to uniform or partially correlated systems. These findings provide critical insights into the interplay between topological heterogeneity and dynamical resilience, offering a framework for designing robust multilayer systems from delay-tolerant power grids to adaptive biological networks, where synchronization under phase-lag is paramount.
- [2] arXiv:2508.06833 [中文pdf, pdf, html, 其他]
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标题： 用于空间模式形成的降阶建模的高效数据驱动回归标题： Efficient data-driven regression for reduced-order modeling of spatial pattern formation主题： 模式形成与孤子 (nlin.PS) ; 数值分析 (math.NA)
我们提出了一种高效的数据驱动回归方法，用于构建表现出模式形成的反应扩散系统的降阶模型（ROMs）。 ROMs 是通过从物理准确的数值模拟可用训练数据中非侵入性地学习得到的。 该方法可以通过使用多项式模型形式应用于一般非线性系统，而无需了解底层物理模型、控制方程或数值求解器。 学习 ROMs 的过程被表述为在通过本征正交分解（POD）识别的降阶子空间中的低成本最小二乘问题。 对经典模式形成系统——包括 Schnakenberg 模型和 Mimura-Tsujikawa 模型——进行的数值实验表明，高阶代理模型显著提高了预测精度，同时保持了低计算成本。 所提出的方法提供了一个灵活的非侵入式模型降阶框架，非常适合复杂时空模式形成现象的分析。
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically accurate numerical simulations. The method can be applied to general nonlinear systems through the use of polynomial model form, while not requiring knowledge of the underlying physical model, governing equations, or numerical solvers. The process of learning ROMs is posed as a low-cost least-squares problem in a reduced-order subspace identified via Proper Orthogonal Decomposition (POD). Numerical experiments on classical pattern-forming systems--including the Schnakenberg and Mimura--Tsujikawa models--demonstrate that higher-order surrogate models significantly improve prediction accuracy while maintaining low computational cost. The proposed method provides a flexible, non-intrusive model reduction framework, well suited for the analysis of complex spatio-temporal pattern formation phenomena.
- [3] arXiv:2508.06881 [中文pdf, pdf, html, 其他]
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标题： 暗孤子的量子化索尔思泵浦标题： Quantized Thouless Pumping of Dark Solitons评论： 6+6页，3+6图主题： 模式形成与孤子 (nlin.PS) ; 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 量子气体 (cond-mat.quant-gas) ; 光学 (physics.optics)
非线性使得局域波如孤子的出现成为可能，这些孤子在传播过程中保持其形状。 孤子广泛分为亮孤子和暗孤子。 亮孤子表现出密度峰值，而暗孤子则在连续波背景上表现为缺陷。 暗孤子的一个显著特征是其波函数中的突然相位变化，这可以在拓扑费米超流体中容纳马约拉纳零模。 最近的研究表明，亮孤子可以通过索利斯泵浦实现量子化输运，其中亮孤子作为瓦尼尔函数起作用。 然而，尚不清楚索利斯泵浦是否也能在本质上与亮孤子不同的暗孤子中发生。 在这里，我们理论上展示了在光学晶格下的连续模型和紧束缚模型中，暗孤子均可发生整数和分数的索利斯泵浦。 具体而言，我们发现当系统参数在一个周期内缓慢变化时，暗孤子通过一个或半个晶格单元被输运，其运动遵循瓦尼尔函数的质心位置。 我们的工作为探索具有相位变化的缺陷（如暗孤子、涡旋孤子、环形暗孤子和涡旋）的索利斯泵浦开辟了新的途径。
Nonlinearity enables the emergence of localized waves such as solitons that maintain their shapes during propagation. Solitons are broadly classified into bright and dark solitons. While a bright soliton exhibits a density peak, a dark soliton presents as a defect on a continuous wave background. A distinctive feature of dark solitons is the abrupt phase change in their wave function, which can host Majorana zero modes in topological fermionic superfluids. Recent studies have shown that bright solitons can undergo quantized transport through Thouless pumping, where the bright soliton functions as a Wannier function. However, it remains unclear whether Thouless pumping can also occur for dark solitons, which fundamentally differ from bright solitons. Here, we theoretically demonstrate the occurrence of both integer and fractional Thouless pumping for dark solitons within both a continuous model under optical lattices and a tight-binding model. Specifically, we find that a dark soliton is transported by one or half a unit cell, following the center-of-mass position of a Wannier function, as a system parameter is slowly varied over one cycle. Our work opens new avenues for exploring Thouless pumping for defects with phase changes, such as dark solitons, vortex solitons, ring dark solitons, and vortices.
- [4] arXiv:2508.07350 [中文pdf, pdf, html, 其他]
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标题： 两组分离散KP层次标题： The two--component discrete KP hierarchy评论： 25页主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph)
离散KP层次也被称为$(l-l')$阶修正KP层次。 在本文中，我们考虑相应的两组分推广，称为两组分离散KP（2dKP）层次。 首先，从2dKP层次的双线性方程出发，我们通过Shiota方法推导出相应的Lax方程，这是使用涉及两个差分算子$\Lambda_1$和$\Lambda_2$的标量Lax算子。 然后，从2dKP Lax方程出发，我们得到相应的双线性方程，包括tau函数的存在性。 从上述讨论中，我们可以确定在2dKP Lax表述中哪些是关键的。 最后，我们讨论对应于环代数$\widehat{sl}_{M+N}=sl_{M+N}[\lambda,\lambda^{-1}]\oplus\mathbb{C}c \ (M,N\geq1)$的2dKP层次的约化。
The discrete KP hierarchy is also known as the $(l-l')$--th modified KP hierarchy. Here in this paper, we consider the corresponding two--component generalization, called the two--component discrete KP (2dKP) hierarchy. Firstly, starting from the bilinear equation of the 2dKP hierarchy, we derive the corresponding Lax equation by the Shiota method, this is using scalar Lax operators involving two difference operators $\Lambda_1$ and $\Lambda_2$. Then starting from the 2dKP Lax equation, we obtain the corresponding bilinear equation, including the existence of the tau function. From above discussions, we can determine which are essential in the 2dKP Lax formulation. Finally, we discuss the reduction of the 2dKP hierarchy corresponding to the loop algebra $\widehat{sl}_{M+N}=sl_{M+N}[\lambda,\lambda^{-1}]\oplus\mathbb{C}c \ (M,N\geq1)$.
- [5] arXiv:2508.08047 [中文pdf, pdf, html, 其他]
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标题： 重新思考自我复制：在异常细胞自动机中检测分布式自我意识标题： Rethinking Self-Replication: Detecting Distributed Selfhood in the Outlier Cellular Automaton主题： 细胞自动机与格子气体 (nlin.CG) ; 人工智能 (cs.AI)
细胞自动机中的自发自我复制长期以来被认为很少见，大多数已知的例子需要精心设计或人工初始化。 在本文中，我们提供了正式的因果证据，表明这种复制可以无需辅助而出现——并且可以以分布式、多组件的形式出现。 基于之前工作对异常规则中复杂动态的识别，我们引入了一个数据驱动的框架，该框架重建确定性细胞自动机中模式的完整因果谱系。 这使我们能够通过显式的因果谱系严格识别自我复制结构。 我们的结果明确表明，在异常CA中的自我复制体不仅是自发和稳健的，而且通常由多个不相交的簇协同工作组成，这引发了对人工生命系统中个体性和复制的一些传统概念的质疑。
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can emerge unassisted -- and that it can do so in a distributed, multi-component form. Building on prior work identifying complex dynamics in the Outlier rule, we introduce a data-driven framework that reconstructs the full causal ancestry of patterns in a deterministic cellular automaton. This allows us to rigorously identify self-replicating structures via explicit causal lineages. Our results show definitively that self-replicators in the Outlier CA are not only spontaneous and robust, but are also often composed of multiple disjoint clusters working in coordination, raising questions about some conventional notions of individuality and replication in artificial life systems.
新提交 (展示 5 之 5 条目 )
- [6] arXiv:2508.06685 (交叉列表自 physics.soc-ph) [中文pdf, pdf, html, 其他]
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标题： 角色间互惠性在正方形格子上的进化信任博弈中的研究标题： Inter-role reciprocity in evolutionary trust game on square lattices评论： 10页，7图期刊参考： 混沌 35，083117 (2025)主题： 物理与社会 (physics.soc-ph) ; 计算机科学与博弈论 (cs.GT) ; 细胞自动机与格子气体 (nlin.CG)
模拟双人游戏，如信任游戏，在单一种群中由于缺乏自然区分角色的方法，因此并不直接。方形格子拓扑结构通过交替信任者和受信者提供了一个简单而优雅的解决方案。对于偶数格子尺寸，它为策略学习创建了两个不相交的对角子格子，而游戏互动可以在原始格子上进行。这种设置确保了一个最小的空间结构，允许跨角色的互动以及角色内的学习。通过在此设置上的模拟，我们检测到一种跨角色的空间互惠机制，通过该机制可以产生信任。特别是，适度的回报率使得投资的信任者和值得信赖的受信者能够形成跨角色的聚类，从而保存信任。如果回报过高，会损害受信者的生存；如果过低，则会损害信任者的生存。所提出的模拟框架也适用于任何双人游戏，以揭示各种情景下的潜在跨角色空间机制。
Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating trustors and trustees. For even lattice sizes, it creates two disjoint diagonal sub-lattices for strategy learning, while game interactions can take place on the original lattice. This setup ensures a minimal spatial structure that allows interactions across roles and learning within roles. By simulations on this setup, we detect an inter-role spatial reciprocity mechanism, through which trust can emerge. In particular, a moderate return ratio allows investing trustors and trustworthy trustees to form inter-role clusters and thus save trust. If the return is too high, it harms the survival of trustees; if too low, it harms trustors. The proposed simulation framework is also applicable to any bipartite game to uncover potential inter-role spatial mechanisms across various scenarios.
- [7] arXiv:2508.07459 (交叉列表自 cond-mat.quant-gas) [中文pdf, pdf, html, 其他]
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标题： 谐振阱中一维玻色气体缺乏碰撞流体力学标题： Lack of collisional hydrodynamics in a harmonically trapped one-dimensional Bose gas评论： 正文：8页，2图，1表；附录：2页，2图，1表主题： 量子气体 (cond-mat.quant-gas) ; 超导性 (cond-mat.supr-con) ; 精确可解与可积系统 (nlin.SI) ; 核理论 (nucl-th)
使用广义流体力学理论，我们研究了从弱到强排斥相互作用的过渡中，一个一维玻色气体在谐波势中的偶极压缩集体振荡。在均匀极限下，系统由可积的Lieb-Liniger模型描述，而势阱的存在破坏了可积性。与基于经典流体动力学变分假设的先前预测不同——该假设得出单一频率的偶极压缩模式——我们在所有气体的参数范围内观察到了包含两个频率的拍频信号。此外，我们发现较高频率随着温度升高从低温声子流体动力学区域过渡到无碰撞极限——而不会在之前预测的高温碰撞流体动力学区域的特征值处饱和。这种过渡发生在所谓的空穴诱导异常温度附近，在此温度以上，激发的准粒子图像不再适用。这解释了碰撞流体动力学区域的缺失，并解决了在弱约束几乎破坏可积性的系统中，该区域在高温下的有效性这一长期悬而未决的问题。我们的发现揭示了激发、热力学、关联、动力学和粒子间碰撞之间的复杂联系，并可能对其他表现出类似异常或热第二类相变的原子、核、固态、电子和自旋系统具有相关性。
Using the theory of generalized hydrodynamics, we study the dipole compression collective oscillations of a harmonically trapped one-dimensional Bose gas in the crossover from weak to strong repulsive interactions. In the uniform limit, the system is described by the integrable Lieb-Liniger model, while the presence of the trap breaks integrability. In contrast to previous predictions based on the classical hydrodynamic variational ansatz -- which yields a single-frequency dipole compression mode -- we observe a beating signal comprising two frequencies across all regimes of the gas. Furthermore, we find that the higher frequency crosses over from the low-temperature phononic hydrodynamic regime to the collisionless limit as the temperature increases -- without saturating at the previously predicted value characteristic of the high-temperature collisional hydrodynamic regime. This crossover occurs around the so-called hole-induced anomaly temperature, above which the quasiparticle picture of excitations no longer applies. This explains the absence of the collisional hydrodynamic regime and resolves a long-standing open question about its validity at high temperatures in systems where integrability is nearly broken by weak confinement. Our findings reveal intricate connections between excitations, thermodynamics, correlations, dynamics, and interparticle collisions, and may prove relevant to other atomic, nuclear, solid-state, electronic, and spin systems that exhibit similar anomalies or thermal second-order phase transitions.
- [8] arXiv:2508.07862 (交叉列表自 hep-th) [中文pdf, pdf, html, 其他]
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标题： 量子化箭形流形和量子自旋Ruijsenaars-Schneider模型标题： Quantized Quiver Varieties and the Quantum Spin Ruijsenaars-Schneider Model评论： 31页主题： 高能物理 - 理论 (hep-th) ; 数学物理 (math-ph) ; 精确可解与可积系统 (nlin.SI)
本文解决了源自Krichever和Zabrodin工作的有理自旋Ruijsenaars--Schneider模型的量化这一长期问题。我们利用量子哈密顿约化技术，构建了一个与带框架的Jordan箭图相关的量化箭图空间$\mathfrak{A}_{N,\ell}$。这个量化箭图空间同时是$N$个粒子具有$\ell$个自旋极化的有理自旋Ruijsenaars--Schneider模型的量子可观测量代数。在这个代数中，我们发现了一个环代数和$\mathfrak{gl}_\ell$的Yangian，并猜想在粒子数量无限大的极限下，代数$\mathfrak{A}_{N,\ell}$将变为一个平移仿射Yangian。我们还展示了一个最低哈密顿量本征态的差分方程，当$\ell=1$时该方程退化为无自旋情况。
This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars--Schneider model originating in the work of Krichever and Zabrodin. We make use of the technique of quantum Hamiltonian reduction to construct a quantized quiver variety $\mathfrak{A}_{N,\ell}$ associated to the framed Jordan quiver. This quantized quiver variety is simultaneously the algebra of quantum observables of the rational spin Ruijsenaars--Schneider model of $N$ particles with $\ell$ spin polarizations. Inside this algebra, we find a loop algebra and Yangian of $\mathfrak{gl}_\ell$ and conjecture that in the limit of infinitely many particles, the algebra $\mathfrak{A}_{N,\ell}$ becomes a shifted affine Yangian. We also exhibit a difference equation for eigenstates of the lowest Hamiltonian that reduces to the spinless case when $\ell=1$.
- [9] arXiv:2508.07949 (交叉列表自 math-ph) [中文pdf, pdf, html, 其他]
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标题： 代数方法处理具有 so($d+1)$ )对称性的$d$维矩阵哈密顿量标题： Algebraic approach to a $d$-dimensional matrix Hamiltonian with so($d+1)$ symmetry评论： 19页，无图主题： 数学物理 (math-ph) ; 精确可解与可积系统 (nlin.SI) ; 量子物理 (quant-ph)
一种新的自旋扩展的so($d+1$,1)代数被引入，并显示为讨论具有自旋1/2和so($d+1$)对称性的$d$维矩阵哈密顿量性质的一个有趣框架。 通过一些额外的$d+2$算符，它们构成一个so($d+1$,1)不可约表示的基，so($d+1$,1)生成元为在Sturm表示中推导矩阵哈密顿量的运动积分提供了一种非常简便的方法。 然后将这些运动积分转换为Schrödinger表示中的矩阵哈密顿量的运动积分，包括带有自旋的Laplace-Runge-Lenz矢量。 这导致在更扩展的代数框架中推导出后者及其性质。
A novel spin-extended so($d+1$,1) algebra is introduced and shown to provide an interesting framework for discussing the properties of a $d$-dimensional matrix Hamiltonian with spin 1/2 and so($d+1$) symmetry. With some $d+2$ additional operators, spanning a basis of an so($d+1$,1) irreducible representation, the so($d+1$,1) generators provide a very easy way for deriving the integrals of motion of the matrix Hamiltonian in Sturm representation. Such integrals of motion are then transformed into those of the matrix Hamiltonian in Schr\"odinger representation, including a Laplace-Runge-Lenz vector with spin. This leads to a derivation of the latter, as well as its properties in a more extended algebraic framework.
交叉提交 (展示 4 之 4 条目 )
- [10] arXiv:2311.06506 (替换) [中文pdf, pdf, html, 其他]
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标题： 从Toda层级到KP层级标题： From Toda Hierarchy to KP Hierarchy期刊参考： SIGMA 21 (2025), 068, 25页主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph) ; 代数几何 (math.AG)
使用矩阵求解方法和第二作者关于 KP tau 函数的$n$-点函数的公式，我们证明了 Toda 格式层次任意解的 tau 函数是一个 KP tau 函数。 然后我们通过为扩展 Toda 层次 (ETH) 开发矩阵求解方法，将这一结果推广到 ETH 的 tau 函数。 作为例子，Gromov-Witten 不变量的分划函数是 KP tau 函数，并得到了对称群不可约表示的一个应用。
Using the matrix-resolvent method and a formula of the second-named author on the $n$-point function for a KP tau-function, we show that the tau-function of an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We then generalize this result to tau-functions for the extended Toda hierarchy (ETH) by developing the matrix-resolvent method for the ETH. As an example the partition function of Gromov-Witten invariants of the complex projective line is a KP tau-function, and an application on irreducible representations of the symmetric group is obtained.
- [11] arXiv:2403.19297 (替换) [中文pdf, pdf, html, 其他]
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标题： 量子振荡系统从Koopman算子观点的量子渐近幅值标题： Quantum asymptotic amplitude for quantum oscillatory systems from the Koopman operator viewpoint评论： 31页，6图。更新版本。减少与arXiv:2302.05584的文本重叠主题： 适应性与自组织系统 (nlin.AO) ; 量子物理 (quant-ph)
我们最近提出了一个完全量子力学的渐近相位定义，适用于量子非线性振子，并且在强量子 regime 中也适用 [Kato 和 Nakao 2022 Chaos 32 063133]。 在本研究中，我们提出了量子振荡系统中的量子渐近振幅定义，该定义基于 Koopman 算子理论，自然地扩展了经典非线性振子的渐近振幅。 我们通过使用与最大非零实特征值相关的反向 Liouville 算子的本征算符，引入了量子振荡系统的渐近振幅。 通过量子 van der Pol 振子结合量子 Kerr 效应的例子，该振子表现出量子极限环振荡，以及量子 van der Pol 模型结合量子压缩和简并参量振荡器与非线性阻尼的例子，这些表现出量子噪声诱导的振荡，我们证明所提出的量子渐近振幅产生的是稳定振幅值，其以恒定速率指数衰减。 此外，利用量子渐近振幅，我们为量子极限环振荡和量子噪声诱导振荡引入了有效的量子周期轨道。
We have recently proposed a fully quantum-mechanical definition of the asymptotic phase for quantum nonlinear oscillators, which is also applicable in the strong quantum regime [Kato and Nakao 2022 Chaos 32 063133]. In this study, we propose a definition of the quantum asymptotic amplitude for quantum oscillatory systems, which naturally extends the asymptotic amplitude for classical nonlinear oscillators on the basis of the Koopman operator theory. We introduce the asymptotic amplitude for quantum oscillatory systems by using the eigenoperator of the backward Liouville operator associated with the largest non-zero real eigenvalue. Using examples of the quantum van der Pol oscillator with the quantum Kerr effect, which exhibits quantum limit-cycle oscillations, and the quantum van der Pol model with the quantum squeezing and degenerate parametric oscillator with nonlinear damping, which exhibit quantum noise-induced oscillations, we demonstrate that the proposed quantum asymptotic amplitude yields isostable amplitude values that decay exponentially with a constant rate. Furthermore, using the quantum asymptotic amplitude, we introduce effective quantum periodic orbits for quantum limit-cycle oscillations and quantum noise-induced oscillations.
- [12] arXiv:2508.03200 (替换) [中文pdf, pdf, html, 其他]
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标题： 定点陀螺仪运动问题的Hess-Sretensky情况中Liouvillian解的存在性标题： Existence of Liouvillian solutions in the Hess-Sretensky case of the problem of motion of a gyrostat with a fixed point评论： arXiv管理员注释：与arXiv:2011.14183有大量文本重叠主题： 精确可解与可积系统 (nlin.SI) ; 动力系统 (math.DS)
1890年，W. Hess发现了刚体绕固定点运动的欧拉-泊松方程可积性的新特殊情况。1963年，L.N. Sretensky证明了类似于Hess情况的可积特殊情况也存在于重陀螺仪的运动问题中——即包含一个旋转均匀转子的重刚体绕固定点的运动。此后提出了许多经典的Hess情况的推广，这些推广在刚体和陀螺仪在各种力场中绕固定点运动时都成立。几乎在发现该情况的同时，首次提供了对重刚体在可积Hess情况下运动的定性描述的研究成果。1892年，P.A. Nekrasov证明，在Hess情况下，重刚体绕固定点运动问题的解可以归结为具有变系数的二阶线性齐次微分方程的积分。Sretensky给出了关于Hess-Sretensky情况下重陀螺仪运动问题的类似结果。在本文中，我们推导出相应的二阶线性微分方程，并将该方程的系数化为有理函数的形式。然后，使用Kovacic算法研究了相应二阶线性微分方程的Liouvillian解的存在性问题。我们得到了问题参数的条件，使得相应线性微分方程的Liouvillian解存在。在这些条件下，Hess-Sretensky情况下绕固定点运动的重陀螺仪的运动方程可以通过求积法进行积分。
In 1890 W. Hess found the new special case of integrability of the Euler - Poisson equations of motion of a heavy rigid body with a fixed point. In 1963 L.N. Sretensky proved that the special case of integrability, similar to the Hess case, also exists in the problem of the motion of a heavy gyrostat - a heavy rigid body with a fixed point, which contains a rotating homogeneous rotor. Further numerous generalizations of the classical Hess case were proposed, which take place during the motion of a heavy rigid body and a gyrostat with a fixed point in various force fields. The first studies that provided a qualitative description of the motion of a heavy rigid body in the integrable Hess case were published almost immediately after this case was found. In 1892 P.A. Nekrasov proved, that the solution of the problem of motion of a heavy rigid body with a fixed point in the Hess case is reduced to the integration the second order linear homogeneous differential equation with variable coefficients. A similar result regarding the problem of the motion of a heavy gyrostat in the Hess - Sretensky case was presented by Sretensky. In this paper we present the derivation of the corresponding second order linear differential equation and reduce the coefficients of this equation to the form of rational functions. Then, using the Kovacic algorithm we study the problem of the existence of liouvillian solutions of the corresponding second order linear differential equation. We obtain the conditions for the parameters of the problem, under which the liouvillian solutions of the corresponding linear differential equation exist. Under these conditions equations of motion of a heavy gyrostat with a fixed point in the Hess - Sretensky case can be integrated in quadratures.
- [13] arXiv:2505.01847 (替换) [中文pdf, pdf, html, 其他]
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标题： 受限手性活性物质中的编织混合标题： Braided mixing in confined chiral active matter评论： 10页，9图主题： 软凝聚态物理 (cond-mat.soft) ; 混沌动力学 (nlin.CD)
高效混合流体在许多实际应用中对于实现均匀性至关重要。 然而，在微观系统中，由于雷诺数较低，扩散和湍流都是无效的方法来实现混沌混合，因此通常采用主动搅拌或通过几何边界效应诱导湍流。 在这里，我们研究了一个修改后的手性维斯克模型，其中主动微泳体作为移动的杆，搅拌周围的基质。 我们研究了由限制、手性运动和对齐相互作用之间的相互作用形成的图案中的混合程度。 这种混合是通过考虑粒子时空轨迹的纠缠来计算的，这形成了一种辫子。 然后优化这种辫子的有限时间辫子指数，得到一组系统的组成参数，表明由局部稳定涡旋液滴和有序振荡相组成的图案实现了最高的混合程度。
Efficient mixing of fluids is essential in many practical applications to achieve homogeneity. For microscopic systems, however, both diffusion and turbulence are ineffective methods to achieve chaotic mixing due to the low Reynolds number, hence either active stirring or inducing turbulence through geometric boundary effects are generally implemented. Here, we study a modified chiral Vicsek model, where active microswimmers act as moving rods, stirring the surrounding substrate. We study the degree of mixing in the patterns formed by interplay between confinement, chiral motion and alignment interactions. This mixing is computed by considering the entanglement of spacetime trajectories of the particles, which forms a braid. Optimising the finite-time braiding exponent of this braid then yields a set of constituent parameters of the system, showing that a pattern consisting of a local stable vortex droplet and an ordered oscillating phase achieves the highest degree of mixing.