Thibault Bonnemain, Benjamin Doyon, Gino Biondini, Giacomo Roberti, Gennady A. El
We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This (2+0)D reduction enables the construction of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalised hydrodynamics of the Boussinesq equation. We then use the kinetic theory to analytically describe two basic types of 2D soliton gas interactions: (i) refraction of a line soliton by a stationary soliton gas, and (ii) oblique interference of two soliton gases. We verify the analytical predictions by numerically implementing the corresponding KPII soliton gases via exact N-soliton solutions with N-large and appropriately chosen random distributions for the soliton parameters. We also explicitly evaluate the long-distance correlations for the two-component interference configurations. The results can be applied to a variety of physical systems, from shallow water waves to Bose-Einstein condensates.
我们在Kadomtsev-Petviashvili（KPII）方程与时间无关的还原框架下研究二维静止孤子气，KPII方程与xy平面上可积分的双向 "好 "布辛斯方程相吻合。这种 (2+0)D 的还原使得我们能够通过引用最近关于 (1+1)D 双向孤子气体和布西尼斯克方程广义流体力学的结果，构建 KP 孤子静止气体的动力学方程。然后，我们利用动力学理论分析描述了二维孤子气体相互作用的两种基本类型：(i) 线孤子对静止孤子气体的折射，以及 (ii) 双孤子气体的斜干涉。我们通过精确的 N 个孤子解，并适当选择 N 个大孤子参数的随机分布，在数值上实现了相应的 KPII 孤子气体，从而验证了分析预测。我们还明确评估了双分量干涉配置的长距离相关性。这些结果可应用于从浅水波到玻色-爱因斯坦凝聚态等各种物理系统。
{"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}
We generalize the Kuramoto model by interpreting the $N$ variables on the unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$, in three versions: general unitary, symmetric unitary and special orthogonal. The time evolution is generated by $N^2$ coupled differential equations for the matrix elements of $U$, and synchronization happens when $U$ evolves into a multiple of the identity. The Ott-Antonsen ansatz is related to the Poisson kernels that are so useful in quantum transport, and we prove it in the case of identical natural frequencies. When the coupling constant is a matrix, we find some surprising new dynamical behaviors.
{"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}
We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous state determining the conditions for the emergence of a Hopf-type bifurcation. We then examine the effects of a specific autocatalytic chemical reaction, and computationally determine the full solutions to the partial differential equations. We find that when both species phase separate, sustained pulsed dynamics arise in one dimension. When considered in two dimensions, the system generates persistent, complex dynamic droplets, which do not generally appear if only one of the species can phase separate. We finally discuss the emergence of dynamics with complex features, which can be understood using the framework of a cellular automata.
{"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}
In the framework of the model of a spatially non-uniform Bose-Einstein condensate with helicoidal spin-orbit (SO) coupling, we find abnormal Peregrine solitons (PSs) on top of flat and periodic backgrounds, with ultra-high amplitudes. We explore the roles of the SO coupling strength and helicity pitch in the creation of these anomalously tall PSs and find that their amplitude, normalized to the background height, attains indefinitely large values. The investigation of the modulation instability (MI) in the same system demonstrates that these PSs exist in a range of relatively weak MI, maintaining the feasibility of their experimental observation.
{"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}
Carlos E. S. Santos, João G. F. Campos, Azadeh Mohammadi
This study deals with a piecewise $phi^2$ scalar field theory in $(1+1)$ dimensions. The scalar field potential is designed with a triple-well shape, engendering kink solutions with asymmetric square-well linearized potentials. Thus, the localized and delocalized modes in this model can be obtained analytically in terms of transcendental equations. This allows us to explore kink-antikink and antikink-kink collisions with any desired number of localized and delocalized modes. We obtain new scenarios of resonance windows suppression, shedding light on the role of higher excited modes in kink scattering.
{"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}
Rohit Radhakrishnan, Induja Pavithran, Valerie Livina, Jürgen Kurths, R. I. Sujith
Early warning signals (EWSs) forewarn a sudden transition (or tipping) from a desirable state to an undesirable state. However, we observe that EWSs detect an impending tipping past bifurcation points when control parameters are varied fast; this questions the applicability of EWSs in real-world systems. When a control parameter is changed at a finite rate, the tipping is also delayed, providing a borrowed stability (in the parameter space) before the system tips. In this study, we use the Hurst exponent as EWS in a thermoacoustic system - a horizontal Rijke tube. We find that upon receiving an EWS alert, a quick reversal of the control parameter within the region of borrowed stability cannot always prevent tipping in real-world systems. We show this failure is due to the (i) delay in receiving the EWS alert and (ii) dispersion observed in the warning points received. For fast variation of parameters, where preventive measures fall short, we demonstrate EWS-based control actions to rescue the system after tipping. Our results in a real-world system for a fast variation of parameter highlight the limits of applicability of EWSs in preventing tipping.
{"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}
Like Life, Lenia CA support a range of patterns that move, interact with their environment, and/or are modified by said interactions. These patterns maintain a cohesive, self-organizing morphology, i.e. they exemplify autopoiesis, the self-organization principle of a network of components and processes maintaining themselves. Recent work implementing Asymptotic Lenia as a reaction-diffusion system reported that non-Platonic behavior in standard Lenia may depend on the clipping function, and that ALenia gliders are likely not subject to non-Platonic instability. In this work I show an example of a glider in ALenia that depends on a certain simulation coarseness for autopoietic competence: when simulated with too fine spatial or temporal resolution the glider no longer maintains its morphology or dynamics. I also show that instability maps of the asymptotic Lenia glider, and others in different CA framworks, show fractal retention of fine boundary detail down to the limit of floating point precision.
与生命一样，"蕾妮娅 CA "也支持一系列模式，这些模式会移动、与环境互动和/或因互动而改变。这些模式保持着一种内聚的、自组织的形态学，即它们是自组织的典范，自组织原则是一个由维持自身的组件和过程组成的网络。最近的研究报告指出，标准莱尼亚中的非柏拉图行为可能取决于剪切函数，而莱尼亚滑翔机很可能不会出现非柏拉图不稳定性。在这项工作中，我展示了一个 ALenia 滑翔机的例子，它的自造血能力依赖于一定的模拟粗糙度：当模拟的空间或时间分辨率太细时，滑翔机不再保持其形态或动力学。我还展示了渐近 Lenia 滑翔机的不稳定性图，以及其他与 CA 框架无关的不稳定性图，这些图显示了细小边界细节的分形保留，直至浮点精度的极限。
{"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}
Juan Balzer, Rico Berner, Kathy Lüdge, Sebastian Wieczorek, Jürgen Kurths, Serhiy Yanchuk
Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a fast-slow phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasi-stationary states. In this letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. Firstly, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Secondly, we uncover multiple saddle slow manifolds (unstable quasi-stationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organises different unstable quasi-stationary states into an intricate fast-slow limit cycle. Although individual quasi-stationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes.
在具有全局自适应耦合的动力学网络中可以观察到卡纳德级联（CC）现象。在这封信中，我们以全局自适应耦合半导体激光器为例，揭示了 CC 背后的动力学机制。首先，我们证明了 CC 是一种稳健的、真正的自适应网络效应，它可以随着网络规模的扩大而扩展，并且在没有自适应的情况下不会发生。其次，我们在系统的相空间中发现了多个鞍慢流形（不稳定的准稳态），这些鞍慢流形由外折线轨道（快速转换）连接。这使我们能够识别出 CC 具有一种新的异折线卡纳轨道，它将不同的不稳定准稳态组织成一个错综复杂的快慢极限循环。虽然单个准稳态是不稳定的（鞍状），但 CC 循环作为一个整体对参数变化具有吸引力和稳健性。
{"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}
Xi-Yu Chen, Lijia Jiang, Wen-Kai Bai, Tao Yang, Jun-Hui Zheng
We propose a scheme to create monopoles with half-integer magnetic charges in a spinful cold atom system. With a minimal monopole in the center, we derive the ground-state single-vortex wave function on the sphere and develop the vortex's kinematic equation in the presence of an external electromagnetic field. The vortex's trajectory is generally depicted by the precession of the system. We further formulate the inter-vortex interaction and build up a theory of multi-vortex dynamics in high-charge monopole systems. We predict the vortices'trajectory in the bi-vortex system and figure out stable vortex (line) patterns in multi-vortex systems. Our study provides deep insights into properties of magnetic monopoles and vortices and paves the way for experimental verification.
{"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}
We consider interaction between the small amplitude travelling waves ("sound") and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors. We calculate for the "sound" wave the coefficient of reflection from (the coefficient of transmission through) the shock wave. These coefficients are expressed in terms of the wave speeds and the wave impedances. When only the capacitors or only the inductors are nonlinear, the coefficients are expressed in terms of the wave speeds only. We explicitly include into consideration of the shocks the dissipation, introducing ohmic resistors shunting the inductors and also in series with the capacitors. This allows us to describe the shocks as physical objects of finite width and study their profiles. In some particular cases the profiles were obtained in terms of elementary functions.
{"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}
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