We present a solid state system which spontaneously generates remarkable engraving patterns on the surface of Ge. The layered construction, with a metal film on the Ge surface, results in coupling of the metal catalyzed etching reaction with the long range stress field at the Ge - metal interface. The etching patterns generated have similarities with Turing patterns, hydrodynamic patterns, crack propagation, and biological form. We describe spirals, radial patterns, and more disordered structures. Euler buckling of the metal layer generates a characteristic wavelength for some patterns.
我们介绍了一种固态系统，它能在 Ge 表面自发生成显著的雕刻图案。这种分层结构在 Ge 表面形成了一层金属膜，从而使金属催化的蚀刻反应与 Ge - 金属界面的长程应力场耦合在一起。所产生的蚀刻模式与图灵模式、流体力学模式、裂纹传播和生物形态有相似之处。我们描述了螺旋、径向图案和更无序的结构。金属层的欧拉屈曲产生了某些图案的特征波长。
{"title":"Metal Assisted Chemical Etching patterns at a Ge/Cr/Au interface modulated by the Euler instability","authors":"Yilin Wong, Giovanni Zocchi","doi":"arxiv-2405.20544","DOIUrl":"https://doi.org/arxiv-2405.20544","url":null,"abstract":"We present a solid state system which spontaneously generates remarkable\u0000engraving patterns on the surface of Ge. The layered construction, with a metal\u0000film on the Ge surface, results in coupling of the metal catalyzed etching\u0000reaction with the long range stress field at the Ge - metal interface. The\u0000etching patterns generated have similarities with Turing patterns, hydrodynamic\u0000patterns, crack propagation, and biological form. We describe spirals, radial\u0000patterns, and more disordered structures. Euler buckling of the metal layer\u0000generates a characteristic wavelength for some patterns.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141253866","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}
C. Gaafele, Edmond B. Madimabe, K. Ndebele, P. Otlaadisa, B. Mozola, T. Matabana, K. Seamolo, P. Pilane
We study the Coupled Nonlinear volatility and option price model via both Modulational instability analysis and direct simulations. Since the coupling term for both the volatility and the option price equation is the same, the MI results are dependent on it, and the stability of the volatility exists for the same condition as that of the price. The numerical simulations are done to comfirm the conditions of MI
我们通过模拟不稳定性分析和直接模拟来研究耦合非线性波动率和期权价格模型。由于波动率方程和期权价格方程的耦合项是相同的，因此 MI 结果取决于耦合项，波动率的稳定性与期权价格的稳定性存在相同的条件。数值模拟的目的是确认 MI
{"title":"Modulational Instability of the Coupled Nonlinear volatility and option price model","authors":"C. Gaafele, Edmond B. Madimabe, K. Ndebele, P. Otlaadisa, B. Mozola, T. Matabana, K. Seamolo, P. Pilane","doi":"arxiv-2405.19887","DOIUrl":"https://doi.org/arxiv-2405.19887","url":null,"abstract":"We study the Coupled Nonlinear volatility and option price model via both\u0000Modulational instability analysis and direct simulations. Since the coupling\u0000term for both the volatility and the option price equation is the same, the MI\u0000results are dependent on it, and the stability of the volatility exists for the\u0000same condition as that of the price. The numerical simulations are done to\u0000comfirm the conditions of MI","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190945","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}
G. Bougas, G. C. Katsimiga, P. G. Kevrekidis, S. I. Mistakidis
We unravel stationary states in the form of dark soliton stripes, bubbles, and kinks embedded in a two-dimensional droplet-bearing setting emulated by an extended Gross-Pitaevskii approach. The existence of these configurations is corroborated through an effectively reduced potential picture demonstrating their concrete parametric regions of existence. The excitation spectra of such configurations are analyzed within the Bogoliubov-de-Gennes framework exposing the destabilization of dark soliton stripes and bubbles, while confirming the stability of droplets, and importantly unveiling spectral stability of the kink against transverse excitations. Additionally, a variational approach is constructed providing access to the transverse stability analysis of the dark soliton stripe for arbitrary chemical potentials and widths of the structure. This is subsequently compared with the stability analysis outcome demonstrating very good agreement at small wavenumbers. Dynamical destabilization of dark soliton stripes via the snake instability is showcased, while bubbles are found to feature both a splitting into a gray soliton pair and a transverse instability thereof. These results shed light on unexplored stability and instability properties of nonlinear excitations in environments featuring a competition of mean-field repulsion and beyond-mean-field attraction that can be probed by state-of-the-art experiments.
{"title":"Stability and dynamics of nonlinear excitations in a two-dimensional droplet-bearing environment","authors":"G. Bougas, G. C. Katsimiga, P. G. Kevrekidis, S. I. Mistakidis","doi":"arxiv-2405.20106","DOIUrl":"https://doi.org/arxiv-2405.20106","url":null,"abstract":"We unravel stationary states in the form of dark soliton stripes, bubbles,\u0000and kinks embedded in a two-dimensional droplet-bearing setting emulated by an\u0000extended Gross-Pitaevskii approach. The existence of these configurations is\u0000corroborated through an effectively reduced potential picture demonstrating\u0000their concrete parametric regions of existence. The excitation spectra of such\u0000configurations are analyzed within the Bogoliubov-de-Gennes framework exposing\u0000the destabilization of dark soliton stripes and bubbles, while confirming the\u0000stability of droplets, and importantly unveiling spectral stability of the kink\u0000against transverse excitations. Additionally, a variational approach is\u0000constructed providing access to the transverse stability analysis of the dark\u0000soliton stripe for arbitrary chemical potentials and widths of the structure.\u0000This is subsequently compared with the stability analysis outcome demonstrating\u0000very good agreement at small wavenumbers. Dynamical destabilization of dark\u0000soliton stripes via the snake instability is showcased, while bubbles are found\u0000to feature both a splitting into a gray soliton pair and a transverse\u0000instability thereof. These results shed light on unexplored stability and\u0000instability properties of nonlinear excitations in environments featuring a\u0000competition of mean-field repulsion and beyond-mean-field attraction that can\u0000be probed by state-of-the-art experiments.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190940","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}
O. Pavón-Torres, M. A. Agüero-Granados, M. E. Maguiña-Palma
Unlike expected from the Hodgkin-Huxley model predictions, in which there is annihilation once orthodromic and antidromic impulses collide, the Heimburg-Jackson model demonstrates that both impulses penetrate each other as it has been shown experimentally. These impulses can be depicted as low amplitude nonlinear excitations in a weakly dissipative soliton model described by the damped NLSE. In view of the above, the Karpman-Solov'ev-Maslov perturbation theory turns out to be ideal to study the interaction and adiabatic evolution of orthodromic and antidromic impulses once axoplasmic fluid is present.
{"title":"Interaction and adiabatic evolution of orthodromic and antidromic impulses in the axoplasmic fluid","authors":"O. Pavón-Torres, M. A. Agüero-Granados, M. E. Maguiña-Palma","doi":"arxiv-2405.19370","DOIUrl":"https://doi.org/arxiv-2405.19370","url":null,"abstract":"Unlike expected from the Hodgkin-Huxley model predictions, in which there is\u0000annihilation once orthodromic and antidromic impulses collide, the\u0000Heimburg-Jackson model demonstrates that both impulses penetrate each other as\u0000it has been shown experimentally. These impulses can be depicted as low\u0000amplitude nonlinear excitations in a weakly dissipative soliton model described\u0000by the damped NLSE. In view of the above, the Karpman-Solov'ev-Maslov\u0000perturbation theory turns out to be ideal to study the interaction and\u0000adiabatic evolution of orthodromic and antidromic impulses once axoplasmic\u0000fluid is present.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198114","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}
The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. Following the linear stability analysis of weakly nonlinear waves, the classical MI dynamics, can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system is usually required to initiate the wave focusing process. Breather solutions of the nonlinear Schr"odinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with minor distinctions.
调制不稳定性（MI）是导致周期性非线性波列解体的原因，并可能导致来自逆波的强局部性。这一机制已在流体力学、光学、等离子体、机械系统、电力传输线和玻色-爱因斯坦凝聚体等多种非线性色散介质中得到研究，其对应用科学的影响也在稳步增长。根据弱非线性波的线性稳定性分析，当一对小振幅边带在主峰频率周围的特定频率范围内被激发时，经典的 MI 动力学就会被触发。也就是说，启动波聚焦过程通常需要一个三波系统。当时的非线性薛定谔方程（NLSE）的呼吸解揭示了 MI 可以产生更复杂的局部结构，超越三波系统初始化方法或通过连续谱的方式。在这项工作中，我们报告了一项针对深水表面重力波的实验研究，断言 MI 过程可以仅由单个不稳定边带触发，因此，当包括峰值频率的贡献时，可以由双波过程触发。实验数据与全非线性流体力学数值波槽模拟进行了验证，结果显示两者非常吻合。这种不稳定波列的长期演化表明，反复出现的费米-帕斯塔-乌兰-钦古聚焦周期发生了明显的变化，NLSE 和完全非线性流体力学模拟捕捉到了这种变化，但两者之间存在细微差别。
{"title":"Hydrodynamic modulation instability triggered by a two-wave system","authors":"Yuchen He, Jinghua Wang, Bertrand Kibler, Amin Chabchoub","doi":"arxiv-2405.19365","DOIUrl":"https://doi.org/arxiv-2405.19365","url":null,"abstract":"The modulation instability (MI) is responsible for the disintegration of a\u0000regular nonlinear wave train and can lead to strong localizations in a from of\u0000rogue waves. This mechanism has been studied in a variety of nonlinear\u0000dispersive media, such as hydrodynamics, optics, plasma, mechanical systems,\u0000electric transmission lines, and Bose-Einstein condensates, while its impact on\u0000applied sciences is steadily growing. Following the linear stability analysis\u0000of weakly nonlinear waves, the classical MI dynamics, can be triggered when a\u0000pair of small-amplitude sidebands are excited within a particular frequency\u0000range around the main peak frequency. That is, a three-wave system is usually\u0000required to initiate the wave focusing process. Breather solutions of the\u0000nonlinear Schr\"odinger equation (NLSE) revealed that MI can generate much more\u0000complex localized structures, beyond the three-wave system initialization\u0000approach or by means of a continuous spectrum. In this work, we report an\u0000experimental study for deep-water surface gravity waves asserting that a MI\u0000process can be triggered by a single unstable sideband only, and thus, from a\u0000two-wave process when including the contribution of the peak frequency. The\u0000experimental data are validated against fully nonlinear hydrodynamic numerical\u0000wave tank simulations and show very good agreement. The long-term evolution of\u0000such unstable wave trains shows a distinct shift in the recurrent\u0000Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and\u0000fully nonlinear hydrodynamic simulations with minor distinctions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190936","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}
Christopher Chong, Dmitry E. Pelinovsky, Guido Schneider
We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coefficients. These q-gap breathers are the counterparts to the classical space-localized and time-periodic breathers found in space-periodic systems. Using normal form transformations, we establish rigorously the existence of such solutions with oscillating tails (in the time domain) that can be made arbitrarily small, but finite. Due to the presence of the oscillating tails, these solutions are coined generalized q-gap breathers. Using a multiple-scale analysis, we also derive a tractable amplitude equation that describes the dynamics of breathers in the limit of small amplitude. In the presence of damping, we demonstrate the existence of transition fronts that connect the trivial state to the time-periodic ones. The analytical results are corroborated by systematic numerical simulations.
{"title":"On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices","authors":"Christopher Chong, Dmitry E. Pelinovsky, Guido Schneider","doi":"arxiv-2405.15621","DOIUrl":"https://doi.org/arxiv-2405.15621","url":null,"abstract":"We prove the existence of a class of time-localized and space-periodic\u0000breathers (called q-gap breathers) in nonlinear lattices with time-periodic\u0000coefficients. These q-gap breathers are the counterparts to the classical\u0000space-localized and time-periodic breathers found in space-periodic systems.\u0000Using normal form transformations, we establish rigorously the existence of\u0000such solutions with oscillating tails (in the time domain) that can be made\u0000arbitrarily small, but finite. Due to the presence of the oscillating tails,\u0000these solutions are coined generalized q-gap breathers. Using a multiple-scale\u0000analysis, we also derive a tractable amplitude equation that describes the\u0000dynamics of breathers in the limit of small amplitude. In the presence of\u0000damping, we demonstrate the existence of transition fronts that connect the\u0000trivial state to the time-periodic ones. The analytical results are\u0000corroborated by systematic numerical simulations.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"97 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169536","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}
Pedro Fittipaldi de Castro, Wladimir Alejandro Benalcazar
The nonlinear Schrodinger equation can support solitons, self-interacting states that remain sharply localized and behave as nearly independent objects. Here, we demonstrate the existence of solitons with self-induced nonreciprocal dynamics in a discrete version of the nonlinear Schrodinger equation. This nonreciprocal behavior depends on the soliton's power, indicating an interplay between linear and nonlinear terms in the Hamiltonian. Starting from static stable solitons at high power, the nonreciprocal behavior manifests as the power is lowered first by the appearance of nonreciprocal linear instabilities on static solitons and then by a full self-induced nonreciprocal regime, in which the solitons propagate with unidirectional acceleration and amplification. We show this behavior to be topologically protected by winding numbers on the solitons' mean-field Hamiltonian and their linear stability matrix, revealing an intimate connection between nonlinear, nonreciprocal dynamics and point gap topology in non-Hermitian linear Hamiltonians.
{"title":"Solitons with Self-induced Topological Nonreciprocity","authors":"Pedro Fittipaldi de Castro, Wladimir Alejandro Benalcazar","doi":"arxiv-2405.14919","DOIUrl":"https://doi.org/arxiv-2405.14919","url":null,"abstract":"The nonlinear Schrodinger equation can support solitons, self-interacting\u0000states that remain sharply localized and behave as nearly independent objects.\u0000Here, we demonstrate the existence of solitons with self-induced nonreciprocal\u0000dynamics in a discrete version of the nonlinear Schrodinger equation. This\u0000nonreciprocal behavior depends on the soliton's power, indicating an interplay\u0000between linear and nonlinear terms in the Hamiltonian. Starting from static\u0000stable solitons at high power, the nonreciprocal behavior manifests as the\u0000power is lowered first by the appearance of nonreciprocal linear instabilities\u0000on static solitons and then by a full self-induced nonreciprocal regime, in\u0000which the solitons propagate with unidirectional acceleration and\u0000amplification. We show this behavior to be topologically protected by winding\u0000numbers on the solitons' mean-field Hamiltonian and their linear stability\u0000matrix, revealing an intimate connection between nonlinear, nonreciprocal\u0000dynamics and point gap topology in non-Hermitian linear Hamiltonians.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169609","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}
Soil is a critical component of terrestrial ecosystems, directly influencing global biogeochemical cycles. Despite its importance, the complex architecture of soil pores and their impact on greenhouse gas emissions remain poorly understood. This perspective aims to address this gap by applying symmetry and symmetry-breaking concepts through fractal geometry to elucidate the structural and functional complexities of soil pores. We highlight how fractal parameters can quantify the self-similar nature of soil pore structures, revealing their size, shape, and connectivity. These geometric attributes influence soil properties such as permeability and diffusivity, which are essential for understanding gas exchange and microbial activity within the soil matrix. Furthermore, we emphasize the effects of various land management practices, including tillage and wetting-drying cycles, on soil pore complexity using three-dimensional multi-fractal analysis. Literature indicates that different agricultural practices significantly alter pore heterogeneity and connectivity, affecting greenhouse gas emissions. Conventional tillage decreases pore connectivity and increases randomness, whereas no-tillage preserves larger, more complex pore structures. We propose that integrating combinatorial, geometric, and functional symmetry concepts offers a comprehensive framework for examining the structure-property-function relationships in soil. This novel approach could enhance our understanding of soil's role in the global cycle of greenhouse gases and provide insights into sustainable land management practices aimed at mitigating climate change.
{"title":"Symmetry and symmetry-breaking in soil pores and climate change mitigation: What fractal geometry can tell us?","authors":"Abhijeet Das","doi":"arxiv-2405.14217","DOIUrl":"https://doi.org/arxiv-2405.14217","url":null,"abstract":"Soil is a critical component of terrestrial ecosystems, directly influencing\u0000global biogeochemical cycles. Despite its importance, the complex architecture\u0000of soil pores and their impact on greenhouse gas emissions remain poorly\u0000understood. This perspective aims to address this gap by applying symmetry and\u0000symmetry-breaking concepts through fractal geometry to elucidate the structural\u0000and functional complexities of soil pores. We highlight how fractal parameters\u0000can quantify the self-similar nature of soil pore structures, revealing their\u0000size, shape, and connectivity. These geometric attributes influence soil\u0000properties such as permeability and diffusivity, which are essential for\u0000understanding gas exchange and microbial activity within the soil matrix.\u0000Furthermore, we emphasize the effects of various land management practices,\u0000including tillage and wetting-drying cycles, on soil pore complexity using\u0000three-dimensional multi-fractal analysis. Literature indicates that different\u0000agricultural practices significantly alter pore heterogeneity and connectivity,\u0000affecting greenhouse gas emissions. Conventional tillage decreases pore\u0000connectivity and increases randomness, whereas no-tillage preserves larger,\u0000more complex pore structures. We propose that integrating combinatorial,\u0000geometric, and functional symmetry concepts offers a comprehensive framework\u0000for examining the structure-property-function relationships in soil. This novel\u0000approach could enhance our understanding of soil's role in the global cycle of\u0000greenhouse gases and provide insights into sustainable land management\u0000practices aimed at mitigating climate change.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150925","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}
Dennis Hardt, Reza Doostani, Sebastian Diehl, Nina del Ser, Achim Rosch
Active matter encompasses many-particle systems with self-propelling units, such as flocks of birds or schools of fish. Here, we show how self-propelling domain walls can be realised in a solid-state system when a ferrimagnet is weakly driven out of thermal equilibrium by an oscillating field. This activates the Goldstone mode, inducing a rotation of the antiferromagnetic xy-order in a clockwise or anticlockwise direction, determined by the sign of the ferromagnetic component. Two opposite directions of rotation meet at a ferromagnetic domain wall, resulting in 'dynamical frustration', with three main consequences. (i) Domain walls move actively in a direction chosen by spontaneous symmetry breaking. Their speed is proportional to the square root of the driving power across large parameter regimes. (ii) In one dimension (1D), after a quench into the ferrimagnetic phase, this motion and strong hydrodynamic interactions lead to a linear growth of the magnetic correlation length over time, much faster than in equilibrium. (iii) The dynamical frustration makes the system highly resilient to noise. The correlation length of the weakly driven 1D system can be orders of magnitude larger than in the corresponding equilibrium system with the same noise level.
{"title":"Active Magnetic Matter: Propelling Ferrimagnetic Domain Walls by Dynamical Frustration","authors":"Dennis Hardt, Reza Doostani, Sebastian Diehl, Nina del Ser, Achim Rosch","doi":"arxiv-2405.14320","DOIUrl":"https://doi.org/arxiv-2405.14320","url":null,"abstract":"Active matter encompasses many-particle systems with self-propelling units,\u0000such as flocks of birds or schools of fish. Here, we show how self-propelling\u0000domain walls can be realised in a solid-state system when a ferrimagnet is\u0000weakly driven out of thermal equilibrium by an oscillating field. This\u0000activates the Goldstone mode, inducing a rotation of the antiferromagnetic\u0000xy-order in a clockwise or anticlockwise direction, determined by the sign of\u0000the ferromagnetic component. Two opposite directions of rotation meet at a\u0000ferromagnetic domain wall, resulting in 'dynamical frustration', with three\u0000main consequences. (i) Domain walls move actively in a direction chosen by\u0000spontaneous symmetry breaking. Their speed is proportional to the square root\u0000of the driving power across large parameter regimes. (ii) In one dimension\u0000(1D), after a quench into the ferrimagnetic phase, this motion and strong\u0000hydrodynamic interactions lead to a linear growth of the magnetic correlation\u0000length over time, much faster than in equilibrium. (iii) The dynamical\u0000frustration makes the system highly resilient to noise. The correlation length\u0000of the weakly driven 1D system can be orders of magnitude larger than in the\u0000corresponding equilibrium system with the same noise level.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151381","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 this letters, we propose a novel self-mapping transformation of the (2+1) dimensional KdV equation, and construct rather general classes of solutions with decaying property with three arbitrary functions of time. The highlight of this method is that it allows us to generate various of basic rogue waves excited on zero-background, including the exponentially decaying line-soliton and dromion as well as the algebraically decaying lump in the -plane turn out to be special cases of these solutions. Our findings unravels new interesting relations between rogue wave and line-soliton, dromion and lump.
{"title":"Rogue waves excitation on zero-background in the (2+1)-dimensional KdV equation","authors":"Jie-Fang Zhang, Mei-zhen Jin, Meng-yang Zhang","doi":"arxiv-2405.11228","DOIUrl":"https://doi.org/arxiv-2405.11228","url":null,"abstract":"In this letters, we propose a novel self-mapping transformation of the (2+1)\u0000dimensional KdV equation, and construct rather general classes of solutions\u0000with decaying property with three arbitrary functions of time. The highlight of\u0000this method is that it allows us to generate various of basic rogue waves\u0000excited on zero-background, including the exponentially decaying line-soliton\u0000and dromion as well as the algebraically decaying lump in the -plane turn out\u0000to be special cases of these solutions. Our findings unravels new interesting\u0000relations between rogue wave and line-soliton, dromion and lump.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141151347","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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