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Two-dimensional stationary soliton gas 二维静止孤子气体
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-08-10 DOI: arxiv-2408.05548
Thibault Bonnemain, Benjamin Doyon, Gino Biondini, Giacomo Roberti, Gennady A. El
{"title":"Two-dimensional stationary soliton gas","authors":"Thibault Bonnemain, Benjamin Doyon, Gino Biondini, Giacomo Roberti, Gennady A. El","doi":"arxiv-2408.05548","DOIUrl":"https://doi.org/arxiv-2408.05548","url":null,"abstract":"We study two-dimensional stationary soliton gas in the framework of the\u0000time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which\u0000coincides with the integrable two-way ``good'' Boussinesq equation in the\u0000xy-plane. This (2+0)D reduction enables the construction of the kinetic\u0000equation for the stationary gas of KP solitons by invoking recent results on\u0000(1+1)D bidirectional soliton gases and generalised hydrodynamics of the\u0000Boussinesq equation. We then use the kinetic theory to analytically describe\u0000two basic types of 2D soliton gas interactions: (i) refraction of a line\u0000soliton by a stationary soliton gas, and (ii) oblique interference of two\u0000soliton gases. We verify the analytical predictions by numerically implementing\u0000the corresponding KPII soliton gases via exact N-soliton solutions with N-large\u0000and appropriately chosen random distributions for the soliton parameters. We\u0000also explicitly evaluate the long-distance correlations for the two-component\u0000interference configurations. The results can be applied to a variety of\u0000physical systems, from shallow water waves to Bose-Einstein condensates.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kuramoto variables as eigenvalues of unitary matrices 作为单元矩阵特征值的仓本变量
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-08-07 DOI: arxiv-2408.04035
Marcel Novaes, Marcus A. M. de Aguiar
{"title":"Kuramoto variables as eigenvalues of unitary matrices","authors":"Marcel Novaes, Marcus A. M. de Aguiar","doi":"arxiv-2408.04035","DOIUrl":"https://doi.org/arxiv-2408.04035","url":null,"abstract":"We generalize the Kuramoto model by interpreting the $N$ variables on the\u0000unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$, in three\u0000versions: general unitary, symmetric unitary and special orthogonal. The time\u0000evolution is generated by $N^2$ coupled differential equations for the matrix\u0000elements of $U$, and synchronization happens when $U$ evolves into a multiple\u0000of the identity. The Ott-Antonsen ansatz is related to the Poisson kernels that\u0000are so useful in quantum transport, and we prove it in the case of identical\u0000natural frequencies. When the coupling constant is a matrix, we find some\u0000surprising new dynamical behaviors.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complex Dynamics in Reaction-Phase Separation Systems 反应相分离系统中的复杂动力学
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-08-06 DOI: arxiv-2408.03458
Dino Osmanovic, Elisa Franco
{"title":"Complex Dynamics in Reaction-Phase Separation Systems","authors":"Dino Osmanovic, Elisa Franco","doi":"arxiv-2408.03458","DOIUrl":"https://doi.org/arxiv-2408.03458","url":null,"abstract":"We investigate the emergence of sustained spatio-temporal behaviors in\u0000reaction-phase separation systems. We focus on binary systems, in which either\u0000one or both species can phase separate, and we discuss the stability of the\u0000homogeneous state determining the conditions for the emergence of a Hopf-type\u0000bifurcation. We then examine the effects of a specific autocatalytic chemical\u0000reaction, and computationally determine the full solutions to the partial\u0000differential equations. We find that when both species phase separate,\u0000sustained pulsed dynamics arise in one dimension. When considered in two\u0000dimensions, the system generates persistent, complex dynamic droplets, which do\u0000not generally appear if only one of the species can phase separate. We finally\u0000discuss the emergence of dynamics with complex features, which can be\u0000understood using the framework of a cellular automata.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ultra-high-amplitude Peregrine solitons induced by helicoidal spin-orbit coupling 螺旋自旋轨道耦合诱导的超高振幅百灵鸟孤子
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-08-01 DOI: arxiv-2408.00322
Cui-Cui Ding, Qin Zhou, B. A. Malomed
{"title":"Ultra-high-amplitude Peregrine solitons induced by helicoidal spin-orbit coupling","authors":"Cui-Cui Ding, Qin Zhou, B. A. Malomed","doi":"arxiv-2408.00322","DOIUrl":"https://doi.org/arxiv-2408.00322","url":null,"abstract":"In the framework of the model of a spatially non-uniform Bose-Einstein\u0000condensate with helicoidal spin-orbit (SO) coupling, we find abnormal Peregrine\u0000solitons (PSs) on top of flat and periodic backgrounds, with ultra-high\u0000amplitudes. We explore the roles of the SO coupling strength and helicity pitch\u0000in the creation of these anomalously tall PSs and find that their amplitude,\u0000normalized to the background height, attains indefinitely large values. The\u0000investigation of the modulation instability (MI) in the same system\u0000demonstrates that these PSs exist in a range of relatively weak MI, maintaining\u0000the feasibility of their experimental observation.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the localized and delocalized modes in kink-antikink interactions: a toy model 关于扭结-反扭结相互作用中的局部和脱局部模式：一个玩具模型
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-08-01 DOI: arxiv-2408.00945
Carlos E. S. Santos, João G. F. Campos, Azadeh Mohammadi
{"title":"On the localized and delocalized modes in kink-antikink interactions: a toy model","authors":"Carlos E. S. Santos, João G. F. Campos, Azadeh Mohammadi","doi":"arxiv-2408.00945","DOIUrl":"https://doi.org/arxiv-2408.00945","url":null,"abstract":"This study deals with a piecewise $phi^2$ scalar field theory in $(1+1)$\u0000dimensions. The scalar field potential is designed with a triple-well shape,\u0000engendering kink solutions with asymmetric square-well linearized potentials.\u0000Thus, the localized and delocalized modes in this model can be obtained\u0000analytically in terms of transcendental equations. This allows us to explore\u0000kink-antikink and antikink-kink collisions with any desired number of localized\u0000and delocalized modes. We obtain new scenarios of resonance windows\u0000suppression, shedding light on the role of higher excited modes in kink\u0000scattering.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Early warnings are too late when parameters change rapidly 当参数快速变化时，预警为时已晚
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-07-30 DOI: arxiv-2408.07296
Rohit Radhakrishnan, Induja Pavithran, Valerie Livina, Jürgen Kurths, R. I. Sujith
{"title":"Early warnings are too late when parameters change rapidly","authors":"Rohit Radhakrishnan, Induja Pavithran, Valerie Livina, Jürgen Kurths, R. I. Sujith","doi":"arxiv-2408.07296","DOIUrl":"https://doi.org/arxiv-2408.07296","url":null,"abstract":"Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a\u0000desirable state to an undesirable state. However, we observe that EWSs detect\u0000an impending tipping past bifurcation points when control parameters are varied\u0000fast; this questions the applicability of EWSs in real-world systems. When a\u0000control parameter is changed at a finite rate, the tipping is also delayed,\u0000providing a borrowed stability (in the parameter space) before the system tips.\u0000In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a\u0000horizontal Rijke tube. We find that upon receiving an EWS alert, a quick\u0000reversal of the control parameter within the region of borrowed stability\u0000cannot always prevent tipping in real-world systems. We show this failure is\u0000due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in\u0000the warning points received. For fast variation of parameters, where preventive\u0000measures fall short, we demonstrate EWS-based control actions to rescue the\u0000system after tipping. Our results in a real-world system for a fast variation\u0000of parameter highlight the limits of applicability of EWSs in preventing\u0000tipping.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"292 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-Platonic Autopoiesis of a Cellular Automaton Glider in Asymptotic Lenia 渐近列尼亚中的细胞自动机滑翔机的非平态自致性
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-07-30 DOI: arxiv-2407.21086
Q. Tyrell Davis
{"title":"Non-Platonic Autopoiesis of a Cellular Automaton Glider in Asymptotic Lenia","authors":"Q. Tyrell Davis","doi":"arxiv-2407.21086","DOIUrl":"https://doi.org/arxiv-2407.21086","url":null,"abstract":"Like Life, Lenia CA support a range of patterns that move, interact with\u0000their environment, and/or are modified by said interactions. These patterns\u0000maintain a cohesive, self-organizing morphology, i.e. they exemplify\u0000autopoiesis, the self-organization principle of a network of components and\u0000processes maintaining themselves. Recent work implementing Asymptotic Lenia as\u0000a reaction-diffusion system reported that non-Platonic behavior in standard\u0000Lenia may depend on the clipping function, and that ALenia gliders are likely\u0000not subject to non-Platonic instability. In this work I show an example of a\u0000glider in ALenia that depends on a certain simulation coarseness for\u0000autopoietic competence: when simulated with too fine spatial or temporal\u0000resolution the glider no longer maintains its morphology or dynamics. I also\u0000show that instability maps of the asymptotic Lenia glider, and others in\u0000different CA framworks, show fractal retention of fine boundary detail down to\u0000the limit of floating point precision.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Canard cascading in networks with adaptive mean-field coupling 具有自适应平均场耦合的网络中的卡农级联
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-07-30 DOI: arxiv-2407.20758
Juan Balzer, Rico Berner, Kathy Lüdge, Sebastian Wieczorek, Jürgen Kurths, Serhiy Yanchuk
{"title":"Canard cascading in networks with adaptive mean-field coupling","authors":"Juan Balzer, Rico Berner, Kathy Lüdge, Sebastian Wieczorek, Jürgen Kurths, Serhiy Yanchuk","doi":"arxiv-2407.20758","DOIUrl":"https://doi.org/arxiv-2407.20758","url":null,"abstract":"Canard cascading (CC) is observed in dynamical networks with global adaptive\u0000coupling. It is a fast-slow phenomenon characterized by a recurrent sequence of\u0000fast transitions between distinct and slowly evolving quasi-stationary states.\u0000In this letter, we uncover the dynamical mechanisms behind CC, using an\u0000illustrative example of globally and adaptively coupled semiconductor lasers,\u0000where CC represents sequential switching on and off the lasers. Firstly, we\u0000show that CC is a robust and truly adaptive network effect that is scalable\u0000with network size and does not occur without adaptation. Secondly, we uncover\u0000multiple saddle slow manifolds (unstable quasi-stationary states) linked by\u0000heteroclinic orbits (fast transitions) in the phase space of the system. This\u0000allows us to identify CC with a novel heteroclinic canard orbit that organises\u0000different unstable quasi-stationary states into an intricate fast-slow limit\u0000cycle. Although individual quasi-stationary states are unstable (saddles), the\u0000CC cycle as a whole is attractive and robust to parameter changes.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Synthetic monopole with half-integer magnetic charge in Bose-Einstein condensates 玻色-爱因斯坦凝聚体中具有半整数磁荷的合成单极子
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-07-29 DOI: arxiv-2407.19690
Xi-Yu Chen, Lijia Jiang, Wen-Kai Bai, Tao Yang, Jun-Hui Zheng
{"title":"Synthetic monopole with half-integer magnetic charge in Bose-Einstein condensates","authors":"Xi-Yu Chen, Lijia Jiang, Wen-Kai Bai, Tao Yang, Jun-Hui Zheng","doi":"arxiv-2407.19690","DOIUrl":"https://doi.org/arxiv-2407.19690","url":null,"abstract":"We propose a scheme to create monopoles with half-integer magnetic charges in\u0000a spinful cold atom system. With a minimal monopole in the center, we derive\u0000the ground-state single-vortex wave function on the sphere and develop the\u0000vortex's kinematic equation in the presence of an external electromagnetic\u0000field. The vortex's trajectory is generally depicted by the precession of the\u0000system. We further formulate the inter-vortex interaction and build up a theory\u0000of multi-vortex dynamics in high-charge monopole systems. We predict the\u0000vortices'trajectory in the bi-vortex system and figure out stable vortex (line)\u0000patterns in multi-vortex systems. Our study provides deep insights into\u0000properties of magnetic monopoles and vortices and paves the way for\u0000experimental verification.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shock waves in nonlinear transmission lines 非线性传输线中的冲击波
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-07-29 DOI: arxiv-2408.01463
Eugene Kogan
{"title":"Shock waves in nonlinear transmission lines","authors":"Eugene Kogan","doi":"arxiv-2408.01463","DOIUrl":"https://doi.org/arxiv-2408.01463","url":null,"abstract":"We consider interaction between the small amplitude travelling waves\u0000(\"sound\") and the shock waves in the transmission line containing both\u0000nonlinear capacitors and nonlinear inductors. We calculate for the \"sound\" wave\u0000the coefficient of reflection from (the coefficient of transmission through)\u0000the shock wave. These coefficients are expressed in terms of the wave speeds\u0000and the wave impedances. When only the capacitors or only the inductors are\u0000nonlinear, the coefficients are expressed in terms of the wave speeds only. We\u0000explicitly include into consideration of the shocks the dissipation,\u0000introducing ohmic resistors shunting the inductors and also in series with the\u0000capacitors. This allows us to describe the shocks as physical objects of finite\u0000width and study their profiles. In some particular cases the profiles were\u0000obtained in terms of elementary functions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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