非线性科学

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[1] arXiv:2508.01500 [中文pdf, pdf, html, 其他]

标题： 激进分子在语言特征传播中的作用 显示英文标题

标题： The role of zealots in the spread of linguistic traits

Vivian Dornelas, Celia Anteneodo, Renan Nunes, Els Heinsalu, Marco Patriarca

评论： 13页，10图

主题： 适应性与自组织系统 (nlin.AO) ; 物理与社会 (physics.soc-ph)

我们研究在一个完全连接的网络上语言创新的扩散，以理解语言多样性的出现。 我们采用基于Axelrod模型的基于代理的动力学，其中代理之间的相互作用由相似性和社会影响驱动，不同之处在于我们假设所有代理共享一些共同特征，确保成对相互作用的有限概率。 我们从一个同质的人口开始，并引入狂热者，这些狂热者像传播语言创新的代理一样行动，但不受其他代理的影响。 我们分析不同的因素，如凝聚力程度和不同语言状态中的狂热者数量，如何决定人口可以采用的语言配置，并促进多语言社区的可能出现。 结果与在平均场近似下得出的结果进行比较。 显示英文摘要

We investigate the diffusion of linguistic innovations on a fully connected network in order to understand the emergence of linguistic diversity. We employ an agent-based dynamics based on the Axelrod model, where interactions between agents are driven by homophily and social influence, with the difference that we assume that all agents share a number of common features that ensure a finite probability of pairwise interaction. We start from a homogeneous population and introduce zealots that act like agents spreading linguistic innovations, without being influenced by other agents. We analyze how different factors, such as the degree of cohesion and number of zealots in different linguistic states, determine the linguistic configurations that populations can adopt and contribute to the possible emergence of a multi-linguistic community. The results are compared with those derived within the mean-field approximation.

[2] arXiv:2508.01619 [中文pdf, pdf, html, 其他]

标题： 对“聚焦非线性薛定谔方程中双周期背景上的 rogue 波”的评论 显示英文标题

标题： Comment on "Rogue waves on the double-periodic background in the focusing nonlinear Schrödinger equation"

Hans Werner Schuermann, Valery Serov

评论： 对arXiv: 1909.08165v1（2019）的评论

主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph)

几年前，陈、佩林斯基和怀特声称发现了非线性薛定谔方程的某些解，用于模拟 rogue waves [arXiv: 1909.08165v1 (2019)]。本文的目的是指出这一声明是错误的。-- 所提出的解不满足非线性薛定谔方程。 显示英文摘要

Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is faulty. -- The solutions presented do not satisfy the nonlinear Schr\"odinger equation.

[3] arXiv:2508.01801 [中文pdf, pdf, html, 其他]

标题： 非线性科学中的主题简介 显示英文标题

标题： Introduction to Focus Issue: Topics in Nonlinear Science

Elizabeth Bradley, Adilson E. Motter, Louis M. Pecora

评论： 特别专辑：非线性科学专题：献给大卫·K·坎贝尔80岁生日

期刊参考： 混沌 35，070402 (2025)

主题： 适应性与自组织系统 (nlin.AO) ; 无序系统与神经网络 (cond-mat.dis-nn)

非线性科学在《Chaos》期刊创刊以来的35年里取得了显著发展。 本期专题，献给其创刊主编David K. Campbell80岁生日，汇集了关于有影响力主题的精选贡献，其中许多主题得到了Campbell自身研究计划和领导角色的推动。 这些主题包括网络动力学、机器学习、量子和材料系统、混沌与分形、局域态以及生命系统中的新现象和方法发展，文献综述、原创贡献和未来研究的展望之间有着良好的平衡。 显示英文摘要

Nonlinear science has evolved significantly over the 35 years since the launch of the journal Chaos. This Focus Issue, dedicated to the 80th Birthday of its founding editor-in-chief, David K. Campbell, brings together a selection of contributions on influential topics, many of which were advanced by Campbell's own research program and leadership role. The topics include new phenomena and method development in the realms of network dynamics, machine learning, quantum and material systems, chaos and fractals, localized states, and living systems, with a good balance of literature review, original contributions, and perspectives for future research.

[4] arXiv:2508.02311 [中文pdf, pdf, 其他]

标题： 由表面模局域化和带非互易性介导的孤子跃迁 显示英文标题

标题： Soliton Transitions Mediated by Skin-Mode Localization and Band Nonreciprocity

Shanyue Li, Mengying Hu, Jing Lin, Chen Fang, Zhensheng Tao, Kun Ding

评论： 21页，6图

主题： 模式形成与孤子 (nlin.PS) ; 其他凝聚态物理 (cond-mat.other) ; 光学 (physics.optics)

孤子通常源于带宽色散与非线性之间的竞争，在具有非厄米皮肤效应的晶格中，随着非线性的增加而出现，伴随着从线性皮肤模态到孤子的局域化转变。 然而，局域化无法将皮肤模态在孤子形成中的作用与带宽色散的作用区分开来。 在此类晶格中，我们揭示了两种不同的孤子相，即皮肤模态辅助的孤子（SMASs）和非互易性修饰的孤子（NRDSs）。 基于根本不同的机制，SMASs起源于皮肤效应，而NRDSs则源于带非互易性，各自表现出独特的空间轮廓。 使用一种堆叠的类似Su-Schrieffer-Heeger模型作为原型，我们描绘了SMASs和NRDSs的相图，每个都有清晰的相边界。 为了解释它们，我们提出了一个基于Wannier函数的非线性哈密顿量，表明孤子的形成关键取决于皮肤模态局域化和带非互易性如何抑制或增强波的色散。 对于SMASs，皮肤模态局域化减少了局域化位置的波扩散，从而降低了形成阈值。 这种孤子相可以从边缘动力学中观察到，并且在从线性皮肤模态过渡时伴随动态稳定性重新出现。 相比之下，NRDSs及其阈值起源于体带非互易性，并在周期性边界条件下持续存在。 我们的框架为表征和工程实验上可实现的非厄米系统中的孤子提供了预测工具，涵盖了光学到力学领域。 显示英文摘要

Solitons, typically resulting from a competition between band dispersion and nonlinearity, occur in lattices featuring the non-Hermitian skin effect as nonlinearity increases, accompanied by a transition in localization from linear skin modes to solitons. However, localization does not disentangle the role of skin modes in the soliton formation from that of band dispersion. Here, in such lattices, we uncover two distinct soliton phases, skin-mode-assisted solitons (SMASs) and nonreciprocity-dressed solitons (NRDSs). Rooted in fundamentally different mechanisms, SMASs originate from skin effect, while NRDSs stem from band nonreciprocity, each exhibiting unique spatial profiles. Using a stacked Su-Schrieffer-Heeger-like model as a prototype, we delineate the phase diagram of SMASs and NRDSs, each having clear phase boundaries. To interpret them, we formulate a Wannier-function-based nonlinear Hamiltonian, showing that soliton formation depends critically on how skin-mode localization and band nonreciprocity suppress or enhance wave dispersion. For SMASs, skin-mode localization reduces wave broadening at the localization sites, thereby lowering the formation threshold. This soliton phase is observable from edge dynamics and accompanied by a dynamical stability reentrance when transitioning from linear skin modes. In contrast, NRDSs, as well as their thresholds, originate from bulk band nonreciprocity and persist under periodic boundary conditions. Our framework offers predictive tools for characterizing and engineering solitons in experimentally realizable non-Hermitian systems, spanning optics to mechanics.

交叉提交 (展示 6 之 6 条目 )

[5] arXiv:2508.01097 (交叉列表自 cs.AI) [中文pdf, pdf, html, 其他]

标题： AI临界点与幻觉的多自旋物理 显示英文标题

标题： Multispin Physics of AI Tipping Points and Hallucinations

Neil F. Johnson, Frank Yingjie Huo

主题： 人工智能 (cs.AI) ; 适应性与自组织系统 (nlin.AO) ; 计算物理 (physics.comp-ph)

生成式人工智能（如ChatGPT）的输出可能是重复的和有偏见的。但更令人担忧的是，这种输出可能会在响应过程中神秘地从良好（正确）变为糟糕（误导或错误），而用户却未察觉。仅在2024年，据报道就造成了670亿美元的损失和数起死亡事件。我们建立了一个到多自旋热系统的数学映射，揭示了人工智能“原子”（基本注意力头）尺度下的隐藏临界不稳定性。我们推导出一个简单但本质上精确的临界点公式，该公式直接显示了用户提示选择和人工智能训练偏见的影响。然后我们展示了输出临界性如何被人工智能的多层架构放大。除了有助于提高人工智能的透明度、可解释性和性能外，我们的结果还开辟了一条量化用户AI风险和法律责任的路径。 显示英文摘要

Output from generative AI such as ChatGPT, can be repetitive and biased. But more worrying is that this output can mysteriously tip mid-response from good (correct) to bad (misleading or wrong) without the user noticing. In 2024 alone, this reportedly caused $67 billion in losses and several deaths. Establishing a mathematical mapping to a multispin thermal system, we reveal a hidden tipping instability at the scale of the AI's 'atom' (basic Attention head). We derive a simple but essentially exact formula for this tipping point which shows directly the impact of a user's prompt choice and the AI's training bias. We then show how the output tipping can get amplified by the AI's multilayer architecture. As well as helping improve AI transparency, explainability and performance, our results open a path to quantifying users' AI risk and legal liabilities.

[6] arXiv:2508.01288 (交叉列表自 cond-mat.soft) [中文pdf, pdf, html, 其他]

标题： 链式珠子中的级联裂纹 显示英文标题

标题： Cascade Crack in Chain of Beads

Meysam Bagheri, Thorsten Pöschel

评论： 5页，5图

主题： 软凝聚态物理 (cond-mat.soft) ; 模式形成与孤子 (nlin.PS)

我们考虑一个由液体桥在张力下连接的均质球链。 单个液体桥的断裂会导致碎片级联，这是由毛细力与球体距离之间的反比关系驱动的。 液体桥的初始长度决定了碎片的数量和大小以及碎片前缘的速度。 显示英文摘要

We consider a homogeneous chain of spheres linked by liquid bridges under tension. The rupture of a single liquid bridge leads to a fragmentation cascade driven by the inverse relation between the capillary force and the sphere distances. The initial length of the liquid bridges determines the number and size of the fragments and the velocity of the fragmentation front.

[7] arXiv:2508.01398 (交叉列表自 cs.SI) [中文pdf, pdf, 其他]

标题： 在线疫苗之战及其长期韧性 显示英文标题

标题： Long-term resilience of online battle over vaccines and beyond

Lucia Illari, Nicholas J. Restrepo, Neil F. Johnson

主题： 社会与信息网络 (cs.SI) ; 一般经济学 (econ.GN) ; 适应性与自组织系统 (nlin.AO) ; 物理与社会 (physics.soc-ph)

从新冠疫情前到现在的大量时间、努力和资金投入在推广疫苗科学方面产生了什么影响？ 我们通过一种独特的在线竞争地图，对约1亿名Facebook页面成员之间的支持疫苗和反对疫苗的观点进行了分析，追踪了通过平台干预的1356个相互关联的社区。 值得注意的是，该网络的基本架构没有变化：既定专业知识的隔离以及反疫苗和主流中立社区的共生关系仍然存在。 这意味着即使继续投入相同的时间、努力和资金，很可能不会发生改变。 这种韧性的原因在于“本地化”进化：社区将多个主题融合，并在邻里层面到国际层面之间建立联系，创造出超越分类目标的冗余路径。 前进的解决方案是关注系统的网络。 我们展示了网络工程方法如何在不删除内容的情况下实现观点管理，这代表了一种从压制向结构干预的范式转变。 显示英文摘要

What has been the impact of the enormous amounts of time, effort and money spent promoting pro-vaccine science from pre-COVID-19 to now? We answer this using a unique mapping of online competition between pro- and anti-vaccination views among ~100M Facebook Page members, tracking 1,356 interconnected communities through platform interventions. Remarkably, the network's fundamental architecture shows no change: the isolation of established expertise and the symbiosis of anti and mainstream neutral communities persist. This means that even if the same time, effort and money continue to be spent, nothing will likely change. The reason for this resilience lies in "glocal" evolution: Communities blend multiple topics while bridging neighborhood-level to international scales, creating redundant pathways that transcend categorical targeting. The solution going forward is to focus on the system's network. We show how network engineering approaches can achieve opinion moderation without content removal, representing a paradigm shift from suppression towards structural interventions.

[8] arXiv:2508.01654 (交叉列表自 cond-mat.quant-gas) [中文pdf, pdf, html, 其他]

标题： 集体激发的参数对产生在玻色-爱因斯坦凝聚体中 显示英文标题

标题： Parametric pair production of collective excitations in a Bose-Einstein condensate

Victor Gondret, Rui Dias, Clothilde Lamirault, Léa Camier, Amaury Micheli, Charlie Leprince, Quentin Marolleau, Scott Robertson, Denis Boiron, Christoph I. Westbrook

评论： 5+5页，本文献献给雷诺·帕伦坦

主题： 量子气体 (cond-mat.quant-gas) ; 广义相对论与量子宇宙学 (gr-qc) ; 模式形成与孤子 (nlin.PS) ; 量子物理 (quant-ph)

通过激发伸长的玻色-爱因斯坦凝聚体的横向呼吸模式，我们以成对的方式参数地产生纵向集体激发。 这一过程也被称为法拉第波生成，可以看作是宇宙学粒子生成的类比。 在单粒子检测的基础上，我们研究了指数增长的早期时间动力学，并将我们的观察结果与布洛赫诺夫描述进行比较。 我们实验观察到的增长率与理论预测非常吻合，证明了布洛赫诺夫描述的有效性，从而确认了这种伸长气体中准粒子相互作用的微小性。 我们还讨论了原子数中的振荡现象，这些振荡是由于成对关联以及相互作用被关闭的速度引起的。 显示英文摘要

By exciting the transverse breathing mode of an elongated Bose-Einstein condensate, we parametrically produce longitudinal collective excitations in a pairwise manner. This process also referred to as Faraday wave generation, can be seen as an analog to cosmological particle production. Building upon single particle detection, we investigate the early time dynamics of the exponential growth and compare our observation with a Bogoliubov description. The growth rate we observe experimentally is in very good agreement with theoretical predictions, demonstrating the validity of the Bogoliubov description and thereby confirming the smallness of quasiparticle interactions in such an elongated gas. We also discuss the presence of oscillations in the atom number, which are due to pair correlations and to the rate at which interactions are switched off.

[9] arXiv:2508.01729 (交叉列表自 cond-mat.quant-gas) [中文pdf, pdf, html, 其他]

标题： 精确对角化研究在谐波约束下的相互作用玻色子的能量级统计特性 显示英文标题

标题： Exact diagonalization study of energy level statistics in harmonically confined interacting bosons

Mohd Talib, M. A. H. Ahsan

评论： 13页，8图

主题： 量子气体 (cond-mat.quant-gas) ; 混沌动力学 (nlin.CD) ; 量子物理 (quant-ph)

我们对在准二维平面上通过排斥高斯势相互作用的玻色子的谱特性进行了精确对角化研究。 我们考虑了系统中$100$个最低能量级别，对于$N=12, 16$和$20$个玻色子，在非旋转（$L_{z}=0$）和旋转单涡旋态（$L_{z}=N$）下的中等和强相互作用 regimes。 对于更高的角动量，$L_{z}=2N$和$L_{z}=3N$，仅考虑强相互作用 regime。 虽然最近邻间距分布（NNSD）$P(s)$和连续能级间距分布的比值$P(r)$用于研究短程相关性，而 Dyson-Mehta$\Delta_3$统计量和能级数方差$\Sigma^2(L)$用于检查长程相关性。 在中等相互作用区域，当相互作用能量相对于陷阱能量较小时，非旋转系统表现出泊松分布，这是规则能谱的特征。 在强相互作用区域，当相互作用能量与陷阱能量相当的时候，非旋转系统表现出由 GOE 分布表示的混沌行为。 此外，在中等相互作用区域的单涡旋态（$L_{z} = N$）的旋转情况下，系统表现出弱混沌的特征，在能级谱中有一些规律性。 然而，在旋转情况下强相互作用区域对于$L_{z} = N$，$2N$和$3N$，系统表现出强烈的混沌行为。 发现旋转在中等和强相互作用区域都对系统混沌行为的增强有贡献。 我们的NNSD分析结果得到了连续能级间距分布比值$P(r)$的分析的支持。 显示英文摘要

We present an exact diagonalization study of the spectral properties of bosons harmonically confined in a quasi-2D plane and interacting via repulsive Gaussian potential. We consider the lowest $100$ energy levels for systems of $N=12, 16$ and $20$ bosons both for the moderate and strong interaction regimes for the non-rotating ($L_{z}=0$) and the rotating single-vortex state ($L_{z}=N$). For higher angular momenta, $L_{z}=2N$ and $L_{z}=3N$, only the strong interaction regime is considered. While the nearest-neighbor spacing distribution (NNSD) $P(s)$ and the ratios of consecutive level spacings distribution $P(r)$ are used to study the short-range correlations, the Dyson-Mehta $\Delta_3$ statistic and the level number variance $\Sigma^2(L)$ are used to examine the long-range correlations. In the moderate interaction regime when the interaction energy is small compared to the trap energy, the non-rotating system exhibits a Poisson distribution, characteristic of the regular energy spectra. In the strong interaction regime when the interaction energy is comparable to the trap energy, the non-rotating system exhibits chaotic behavior signified by GOE distribution. Furthermore, in the rotating case for the single-vortex state ($L_{z} = N$) in the moderate interaction regime, the system exhibits signatures of weak chaos with some degree of regularity in the energy-level spectra. However, in the strong interaction regime for the rotating case with $L_{z} = N$, $2N$ and $3N$, the system exhibits strong chaotic behavior. The rotation is found to contribute to an enhancement of chaotic behavior in the system for both the moderate and the strong interaction regimes. Our results of NNSD analysis are supported by the analysis of the ratios of consecutive level spacings distribution $P(r)$.

[10] arXiv:2508.01877 (交叉列表自 cond-mat.stat-mech) [中文pdf, pdf, html, 其他]

标题： 自组织——基本原理和一般模型 显示英文标题

标题： Self-organisation -- the underlying principle and a general model

Raphael Blumenfeld

评论： 6页，已提交

主题： 统计力学 (cond-mat.stat-mech) ; 适应性与自组织系统 (nlin.AO)

最近对颗粒系统中应力和结构协调自组织（SO）的观察提供了对该现象基本原理的见解。 这里首先认为，当一组配置比其余配置更加稳定时，SO就会出现，因此它们能比其他配置更长时间地经受系统中的噪声而被观察到。 这一原理比最近提出的能量考虑更为深入。 在这一原理的指导下，随后为这些系统中的SO提出了一个统计力学模型，并概述了其在三维空间中的扩展。 该原理不仅适用于颗粒系统，接下来该模型被扩展以描述更一般系统中SO的出现。 该模型的应用通过车道形成的具体例子进行了说明。 该建模方法与传统统计力学的类比提供了有用的见解，应有助于在其他非平衡系统中对SO进行建模。 显示英文摘要

Recent observations of coordinated self-organisation (SO) of stress and structure in granular systems provide insight into the fundamental principle underlying this phenomenon. It is first argued here that SO emerges when a minute subset of configurations are significantly more stable than the rest and therefore survive the noise in the system much longer to be observed. This principle goes deeper than recently proposed energy considerations. Guided by this principle, a statistical mechanics model is formulated then for SO in these systems and its extension to three dimensions is outlined. The principle holds beyond granular systems and the model is extended next to describe emergence of SO in more general systems. The application of the model is illustrated for the specific example of laning. Parallels of the modelling approach to traditional statistical mechanics provide useful insight that should assist in modelling SO in other out-of-equilibrium systems.

替换提交 (展示 8 之 8 条目 )

[11] arXiv:2409.15668 (替换) [中文pdf, pdf, html, 其他]

标题： 为什么集体行为会自组织到临界性：信息理论和热力学效用度量的基础知识 显示英文标题

标题： Why collective behaviours self-organise to criticality: A primer on information-theoretic and thermodynamic utility measures

Qianyang Chen, Mikhail Prokopenko

评论： 30页，23图

期刊参考： R. Soc. 开放科学，12(6):241655，2025

主题： 适应性与自组织系统 (nlin.AO) ; 统计力学 (cond-mat.stat-mech)

集体行为经常被观察到会自我组织到临界状态。 现有的解释这些现象的提议分散在不同学科中，只部分回答了这个问题。 本简明教程比较了可能解释接近临界状态的集体行为自我组织的基本内在效用。 我们关注信息驱动的方法（预测信息、赋权和主动推断），以及结合信息论和热力学的方法（热力学效率）。 通过将伊辛模型解释为感知-行动回路，我们比较了不同内在效用如何塑造集体行为，并分析了当每个效用被优化时出现的不同特征。 特别是，我们强调热力学效率——衡量系统获得的可预测性与其能量成本的比率——在临界区域达到最大值。 最后，我们提出了超效率原理，表明集体行为自我组织到临界区域，在该区域相对于热力学成本的熵减少实现了最优效率。 显示英文摘要

Collective behaviours are frequently observed to self-organise to criticality. Existing proposals to explain these phenomena are fragmented across disciplines and only partially answer the question. This primer compares the underlying, intrinsic, utilities that may explain the self-organisation of collective behaviours near criticality. We focus on information-driven approaches (predictive information, empowerment, and active inference), as well as an approach incorporating both information theory and thermodynamics (thermodynamic efficiency). By interpreting the Ising model as a perception-action loop, we compare how different intrinsic utilities shape collective behaviour and analyse the distinct characteristics that arise when each is optimised. In particular, we highlight that thermodynamic efficiency -- measuring the ratio of predictability gained by the system to its energy costs -- reaches its maximum at the critical regime. Finally, we propose the Principle of Super-efficiency, suggesting that collective behaviours self-organise to the critical regime where optimal efficiency is achieved with respect to the entropy reduction relative to the thermodynamic costs.

[12] arXiv:2507.19179 (替换) [中文pdf, pdf, html, 其他]

标题： 代数几何积分 Boussinesq 层级 显示英文标题

标题： Algebro-geometric integration of the Boussinesq hierarchy

Julia Bernatska, Taras Skrypnyk

评论： 22页，2图

主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph)

我们使用Holod-Flashka-Newell-Ratiu的李代数方法构造了Boussinesq方程的可积层次结构。 我们证明该层次结构中的有限间隙哈密顿系统出现在$\mathfrak{sl}(3)$环代数的共轭轨道上，并且具有来自$(3,3N\,{+}\,1)$曲线族的谱曲线，$N\,{\in}\, \Natural$。 变量分离导致在所述曲线上出现雅可比逆问题，该问题通过相应的多重周期函数求解。 获得了Boussinesq方程的一个精确有限间隙解，并提出了关于实条件的猜想。 对几种谱曲线计算了所得解，并以图形方式进行了说明。 显示英文摘要

We construct an integrable hierarchy of the Boussinesq equation using the Lie-algebraic approach of Holod-Flashka-Newell-Ratiu. We show that finite-gap hamiltonian systems of the hierarchy arise on coadjoint orbits in the loop algebra of $\mathfrak{sl}(3)$, and possess spectral curves from the family of $(3,3N\,{+}\,1)$-curves, $N\,{\in}\, \Natural$. Separation of variables leads to the Jacobi inversion problem on the mentioned curves, which is solved in terms of the corresponding multiply periodic functions. An exact finite-gap solution of the Boussinesq equation is obtained explicitly, and a conjecture on the reality conditions is made. The obtained solutions are computed for several spectral curves, and illustrated graphically.

[13] arXiv:2507.23406 (替换) [中文pdf, pdf, html, 其他]

标题： 拉曼效应在光纤中引起的色散冲击波理论 显示英文标题

标题： Theory of dispersive shock waves induced by the Raman effect in optical fibers

D.V. Shaykin, A.M. Kamchatnov

评论： 8页，4图

主题： 模式形成与孤子 (nlin.PS) ; 光学 (physics.optics)

我们发展了光学纤维中色散冲击波的理论，当光脉冲长距离传播时，微小的拉曼效应稳定了冲击波的轮廓。 Whitham调制方程被推导为Gurevich-Pitaevskii方法的基础，用于这种冲击波的解析理论。 我们表明，冲击波两侧的波变量由类似于从Whitham方程的守恒定律得出的Rankine-Hugoniot条件的关系所联系。 Whitham方程的解给出了与广义非线性薛定谔方程的精确数值解对于光脉冲传播结果非常吻合的波变量轮廓。 显示英文摘要

We develop the theory of dispersive shock waves in optical fibers for the case of long-distance propagation of optical pulses, when the small Raman effect stabilizes the profile of the shock. The Whitham modulation equations are derived as the basis for the Gurevich-Pitaevskii approach to the analytical theory of such shocks. We show that the wave variables at both sides of the shock are related by the analogue of the Rankine-Hugoniot condition that follows from the conservation laws of the Whitham equations. Solutions of the Whitham equations yield the profiles of the wave variables that agree very well with the exact numerical solution of the generalized nonlinear Schroedinger equation for propagation of optical pulses.

[14] arXiv:2011.06778 (替换) [中文pdf, pdf, html, 其他]

标题： 最可能的零售集聚模式：空间均衡的潜力最大化与随机稳定性 显示英文标题

标题： Most likely retail agglomeration patterns: Potential maximization and stochastic stability of spatial equilibria

Minoru Osawa, Takashi Akamatsu, Yosuke Kogure

评论： 30页，10图

主题： 理论经济学 (econ.TH) ; 一般经济学 (econ.GN) ; 动力系统 (math.DS) ; 模式形成与孤子 (nlin.PS)

我们研究了一个零售集聚模型，其中消费者更可能前往商店集中度较高的区域。这种集聚效应使拥有众多零售商的区域更具吸引力。在均衡状态下，零售商的空间分布是内生地根据购物需求的空间模式确定的。在这种情况下，可能会出现多个局部稳定的均衡，结果可能取决于店铺的初始分布。为了解决这个问题，我们应用了进化博弈论的一种方法，选择最大化代表零售商激励潜力函数的均衡。我们在二维空间设置中演示了该方法。与基于渐进、短视调整的局部稳定性相比，这种全局最大化导致了一个唯一且更稳健的预测。正如预期的那样，当不动消费者购物成本下降或更大零售集中区的吸引力增加时，零售集群的数量都会减少。 显示英文摘要

We study a model of retail agglomeration where consumers are more likely to visit zones with a higher concentration of shops. This agglomerative effect makes zones with many retailers more attractive. The spatial distribution of retailers in equilibrium is endogenously determined in response to the spatial pattern of shopping demand. In such a setting, multiple locally stable equilibria may arise, and the outcome can depend on the initial distribution of shops. To address this issue, we apply an approach from evolutionary game theory, selecting the equilibrium that maximizes a potential function representing the incentives of retailers. We demonstrate the method in a two-dimensional spatial setting. Compared to local stability based on gradual, myopic adjustments, this global maximization leads to a unique and more robust prediction. As expected, the number of retail clusters decreases either when shopping costs for immobile consumers fall or when the attractiveness of larger retail concentrations increases.

[15] arXiv:2410.20929 (替换) [中文pdf, pdf, html, 其他]

标题： 双自旋子对热汤克斯-吉拉多气体的影响 显示英文标题

标题： Two-spinon effects on the thermal Tonks-Girardeau gas

Felipe Taha Sant'Ana, Hui Liu

评论： 19页，4图

主题： 量子气体 (cond-mat.quant-gas) ; 统计力学 (cond-mat.stat-mech) ; 精确可解与可积系统 (nlin.SI)

我们研究了双自旋子激发对Tonks-Girardeau气体场-场关联函数的影响。 虽然这些激发在系统的基态中已被先前研究，但它们在有限温度下的作用仍未被探索。 在此，我们将分析扩展到一维相互作用玻色气体在热平衡状态下的情况，重点关注无限排斥的Lieb-Liniger模型的一体关联函数。 我们证明，由快速度分布中的两个空穴表征的双自旋子激发，在低温下构成了场-场关联函数的主要贡献。 此外，我们通过分析表明，包括额外的粒子-空穴激发会减少它们的贡献，突显了双自旋子框架在捕捉系统基本物理特性方面的有效性。 对来自双自旋子程序的弗雷德霍姆行列式和谱级数进行数值评估，并加入粒子-空穴激发后，显示在低温下趋于收敛。 显示英文摘要

We study the effects of the two-spinon excitations on the field-field correlator of the Tonks-Girardeau gas. While these excitations have been previously examined in the ground state of the system, their role at finite temperatures remains unexplored. Here, we extend the analysis to the one-dimensional interacting Bose gas at thermal equilibrium, focusing on the one-body correlation function of the infinitely repulsive Lieb-Liniger model. We demonstrate that two-spinon excitations, characterized by two holes within the rapidity distribution, constitute the dominant contribution to the field-field correlator at low temperatures. Furthermore, we analytically show that incorporating additional particle-hole excitations diminishes their contribution, highlighting the efficacy of the two-spinon framework in capturing the essential physics of the system. Numerical evaluations of both the Fredholm determinant and the spectral sum stemming from the two-spinon program, with the addition of particle-hole excitations, reveal convergence at low temperatures.

[16] arXiv:2502.21077 (替换) [中文pdf, pdf, html, 其他]

标题： 通过复值表示和Kuramoto同步动力学增强深度神经网络 显示英文标题

标题： Enhancing deep neural networks through complex-valued representations and Kuramoto synchronization dynamics

Sabine Muzellec, Andrea Alamia, Thomas Serre, Rufin VanRullen

主题： 计算机视觉与模式识别 (cs.CV) ; 人工智能 (cs.AI) ; 适应性与自组织系统 (nlin.AO) ; 神经与认知 (q-bio.NC)

神经同步被认为在大脑如何将视觉场景组织成结构化表示中起着关键作用，从而实现场景中多个对象的鲁棒编码。 然而，当前的深度学习模型在对象绑定方面常常遇到困难，限制了它们有效表示多个对象的能力。 受神经科学的启发，我们研究同步机制是否可以增强用于视觉分类的人工模型中的对象编码。 具体而言，我们将复数表示与Kuramoto动力学相结合，以促进相位对齐，从而促进属于同一对象的特征分组。 我们评估了两种采用同步性的架构：一种是前馈模型，另一种是具有反馈连接的循环模型，利用自上而下的信息来优化相位同步。 在涉及多对象图像的任务中，如重叠的手写数字、噪声输入和分布外变换，这两种模型都优于其实数对应模型以及没有Kuramoto同步的复数模型。 我们的研究结果突显了同步驱动机制在增强深度学习模型方面的潜力，提高了它们在复杂视觉分类任务中的性能、鲁棒性和泛化能力。 显示英文摘要

Neural synchrony is hypothesized to play a crucial role in how the brain organizes visual scenes into structured representations, enabling the robust encoding of multiple objects within a scene. However, current deep learning models often struggle with object binding, limiting their ability to represent multiple objects effectively. Inspired by neuroscience, we investigate whether synchrony-based mechanisms can enhance object encoding in artificial models trained for visual categorization. Specifically, we combine complex-valued representations with Kuramoto dynamics to promote phase alignment, facilitating the grouping of features belonging to the same object. We evaluate two architectures employing synchrony: a feedforward model and a recurrent model with feedback connections to refine phase synchronization using top-down information. Both models outperform their real-valued counterparts and complex-valued models without Kuramoto synchronization on tasks involving multi-object images, such as overlapping handwritten digits, noisy inputs, and out-of-distribution transformations. Our findings highlight the potential of synchrony-driven mechanisms to enhance deep learning models, improving their performance, robustness, and generalization in complex visual categorization tasks.

[17] arXiv:2504.19921 (替换) [中文pdf, pdf, html, 其他]

标题： 强活动干扰对建筑能量的影响 显示英文标题

标题： The impact of strong activity disruption on building energetics

Yu-Hsuan Hsu, Sara Beery, Christopher P. Kempes, Mingzhen Lu, Serguei Saavedra

评论： 简要通信。10页，2图

主题： 物理与社会 (physics.soc-ph) ; 适应性与自组织系统 (nlin.AO) ; 应用 (stat.AP)

证据表明，生物有机体在单位体积上倾向于更加节能。 这些在生物有机体中观察到的尺度模式也出现在城市能源需求中。 然而，在能量干预更容易管理的较低组织层次，例如建筑，由于收集细粒度数据的困难，这种分析仍然较为模糊。 在此，我们使用麻省理工学院（MIT）从2009年到2024年的建筑维护能耗数据，分析单个建筑规模的能量趋势及其对强烈外部扰动的敏感性。 我们发现，类似于生物有机体的基础代谢，大型建筑平均比小型建筑每单位体积更节能$24\%$。 由于如何更好地衡量建筑效率已成为有争议的问题，这种尺度模式自然为建筑建立了一个基准效率，其中偏离均值的建筑根据体积将意味着比基准更高效或更低效。 这种相对效率逐步增加到$34\%$直到2020年。 然而，由新冠疫情造成的大规模活动中断起到了主要冲击作用，消除了这一趋势，并导致恢复到预期的$24\%$基准水平。 这表明能量适应取决于相对稳定的条件。 显示英文摘要

Evidence shows that biological organisms tend to be more energetically efficient per unit size. These scaling patterns observed in biological organisms have also been observed in the energetic requirements of cities. However, at lower levels of organization where energetic interventions can be more manageable, such as buildings, this analysis has remained more elusive due to the difficulties in collecting fine-grained data. Here, we use the maintenance energy usage in buildings at the Massachusetts Institute of Technology (MIT) from 2009 to 2024 to analyze energetic trends at the scale of individual buildings and their sensitivity to strong external perturbations. We find that, similar to the baseline metabolism of biological organisms, large buildings are on average $24\%$ more energetically efficient per unit size than smaller buildings. Because it has become debatable how to better measure the efficiency of buildings, this scaling pattern naturally establishes a baseline efficiency for buildings, where deviations from the mean would imply a more or less efficient building than the baseline according to volume. This relative efficiency progressively increased to $34\%$ until 2020. However, the strong activity disruption caused by the COVID-19 pandemic acted as a major shock, removing this trend and leading to a reversal to the expected $24\%$ baseline level. This suggests that energetic adaptations are contingent on relatively stable conditions.

[18] arXiv:2506.12867 (替换) [中文pdf, pdf, html, 其他]

标题： 矩阵模型作为可积方程UC层次的tau函数。 II 显示英文标题

标题： Matrix models as tau functions of the UC hierarchy of integrable equations. II

Chuanzhong Li, Andrei Mironov, Alexander Yu. Orlov

评论： 20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)

我们提出了一类矩阵模型，其划分函数是通用字符（UC）层次的tau函数。 这发展了我们之前论文arXiv:2410.14823中的一个主题。 我们通过粘合矩阵发现了与嵌入图的两个球面乘积相关的新矩阵模型。 我们还将这些研究推广到多矩阵模型的情况，这对应于多分量UC层次。 显示英文摘要

We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to multi-matrix models case, which corresponds to the multi-component UC hierarchy.