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Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators 基于能量的耦合阻尼驱动一般振荡器链中的自共振理论
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-05-07 DOI: arxiv-2405.04556
Ricardo Chacón, Faustino Palmero, Pedro J. Martínez, Somnath Roy
{"title":"Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators","authors":"Ricardo Chacón, Faustino Palmero, Pedro J. Martínez, Somnath Roy","doi":"arxiv-2405.04556","DOIUrl":"https://doi.org/arxiv-2405.04556","url":null,"abstract":"An energy-based theory of autoresonance in driven dissipative chains of\u0000coupled generic oscillators is discussed on the basis of a variational\u0000principle concerning the energy functional. The theory is applied to chains of\u0000delayed Duffing-Ueda oscillators and the equations that together govern the\u0000autoresonance forces and solutions are derived and solved analytically for\u0000generic values of parameters and initial conditions, including the case of\u0000quenched time-delay disorder. Remarkably, the presence of retarded potentials\u0000with time-delayed feedback drastically modify the autoresonance scenario\u0000preventing the growth of the energy oscillation over specific regions of the\u0000parameter space. Additionally, effective harmonic forces with a slowly varying\u0000frequency are derived from the exact autoresonant excitations and the\u0000effectiveness of the theory is demonstrated at suppressing the chaos induced by\u0000homogeneous periodic excitations in such oscillator chains. Numerical\u0000experiments confirmed all the theoretical predictions.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938347","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
Modulational instability in a quasi-one-dimensional Bose-Einstein condensates 准一维玻色-爱因斯坦凝聚体中的调制不稳定性
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-05-03 DOI: arxiv-2405.02282
Sherzod R. Otajonov, Bakhram A. Umarov, Fatkhulla Kh. Abdullaev
{"title":"Modulational instability in a quasi-one-dimensional Bose-Einstein condensates","authors":"Sherzod R. Otajonov, Bakhram A. Umarov, Fatkhulla Kh. Abdullaev","doi":"arxiv-2405.02282","DOIUrl":"https://doi.org/arxiv-2405.02282","url":null,"abstract":"In this work, we investigate the modulational instability of plane wave\u0000solutions within a modified Gross-Pitaevskii equation framework. The equation\u0000features cubic and quartic nonlinearity. It models the behaviour of\u0000quasi-one-dimensional Bose-Einstein condensates in symmetric Bose-Bose mixtures\u0000of ultra-dilute cold atoms. Our study demonstrates the pivotal role of the\u0000competition between mean-field attractions and quantum fluctuation-induced\u0000repulsions. This competition significantly affects the emergence and evolution\u0000of modulational instability. By employing linear stability analysis, we\u0000identify the essential conditions that lead to modulational instability. We\u0000find that the stability of plane wave solutions significantly depends on the\u0000interaction among system parameters. Further development of the instability\u0000leads to the fragmentation of the BEC into a chain of quantum droplets. We\u0000calculated the quantity of quantum droplets generated during the nonlinear\u0000phase of the instability. Our analytical results are corroborated by numerical\u0000simulations of the modified quasi-1D Gross-Pitaevskii equation. These\u0000simulations vividly depict the formation, interaction, and coalescence of\u0000droplets during the nonlinear phase of modulational instability. The\u0000investigation shows that linear stability analysis of the modified\u0000Gross-Pitaevskii equation, considering quantum fluctuations, precisely\u0000forecasts modulational instability phenomena across different domains of\u0000parameter spaces.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885289","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
Remote Nucleation and Stationary Domain Walls via Transition Waves in Tristable Magnetoelastic Lattices 通过三稳态磁弹性晶格中的转换波实现远程成核和固定域壁
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-05-02 DOI: arxiv-2405.01168
Anusree Ray, Samanvay Anand, Vivekanand Dabade, Rajesh Chaunsali
{"title":"Remote Nucleation and Stationary Domain Walls via Transition Waves in Tristable Magnetoelastic Lattices","authors":"Anusree Ray, Samanvay Anand, Vivekanand Dabade, Rajesh Chaunsali","doi":"arxiv-2405.01168","DOIUrl":"https://doi.org/arxiv-2405.01168","url":null,"abstract":"We present a tunable magnetoelastic lattice with a multistable onsite\u0000potential, focusing on a tristable potential. Through experimental and\u0000numerical analysis, we verify the existence of three types of transition waves\u0000with distinct amplitudes and velocities. Additionally, we establish the\u0000presence of a scaling law that elucidates various characteristics of these\u0000transition waves. By manipulating the onsite potential, we investigate the\u0000collision dynamics of two transition waves within the system. In chains\u0000featuring an asymmetric potential well, the collision of similar transition\u0000waves leads to the remote nucleation of a new phase. In chains with a symmetric\u0000potential well, the collision of dissimilar transition waves results in the\u0000formation of a stationary domain wall","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828973","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
Delamination Detection in Layered Waveguides using Ostrovsky Wave Packets 利用奥斯特洛夫斯基波包探测层状波导中的分层
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-05-01 DOI: arxiv-2405.00388
J. S. Tamber, D. J. Chappell, M. R. Tranter
{"title":"Delamination Detection in Layered Waveguides using Ostrovsky Wave Packets","authors":"J. S. Tamber, D. J. Chappell, M. R. Tranter","doi":"arxiv-2405.00388","DOIUrl":"https://doi.org/arxiv-2405.00388","url":null,"abstract":"We examine the scattering of Ostrovsky wave packets, generated from an\u0000incident solitary wave, in a two layered waveguide with a delamination in the\u0000centre and soft (imperfect) bonding either side of the centre. The layers of\u0000the waveguide are assumed to consist of different materials, and the strains\u0000are described by a system of coupled Boussinesq equations. A semi-analytical\u0000approach consisting of matched asymptotic multiple-scale expansions is applied,\u0000leading to Ostrovsky equations in soft bonded regions and Korteweg-de Vries\u0000equations in the delaminated region. This semi-analytical method has good\u0000agreement with direct numerical simulations, validating the approach. In the delaminated regions, Ostrovsky wave packets evolve into a train of\u0000solitary waves, which subsequently evolve into Ostrovsky wave packets in the\u0000second bonded region. Analysis of the phase shift in the wave packet,\u0000introduced from the delaminated region, allows us to predict both the position\u0000and the length of the delamination; the first time this has been achieved using\u0000nonlinear waves. These results motivate experiments to validate the theoretical\u0000results, with the aim of creating a tool to monitor the integrity of layered\u0000structures.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140829234","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
Ring-Shaped Linear Waves and Solitons in a Square Lattice of Acoustic Waveguides 声波导方格中的环形线性波和孤子
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-29 DOI: arxiv-2404.18966
I. Ioannou Sougleridis, O. Richoux, V. Achilleos G. Theocharis, D. J. Frantzeskakis
{"title":"Ring-Shaped Linear Waves and Solitons in a Square Lattice of Acoustic Waveguides","authors":"I. Ioannou Sougleridis, O. Richoux, V. Achilleos G. Theocharis, D. J. Frantzeskakis","doi":"arxiv-2404.18966","DOIUrl":"https://doi.org/arxiv-2404.18966","url":null,"abstract":"We study the propagation of both low- and high-amplitude ring-shaped sound\u0000waves in a 2D square lattice of acoustic waveguides with Helmholtz resonators.\u0000We show that the inclusion of the Helmholtz resonators suppresses the inherent\u0000anisotropy of the system in the low frequency regime allowing for radially\u0000symmetric solutions. By employing the electroacoustic analogue approach and\u0000asymptotic methods we derive an effective cylindrical Korteweg de Vries (cKdV)\u0000equation. Low-amplitude waveforms are self-similar structures of the Airy\u0000function profile, while high-amplitude ones are of the form of cylindrical\u0000solitons. Our analytical predictions are corroborated by results of direct\u0000numerical simulations, with a very good agreement between the two.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140829148","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
Generation of kink-antikink pairs through the excitation of an oscillon in the $φ^4$ model 在φ^4$模型中通过激发振子产生 "磕碰"-"反磕碰 "对
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-27 DOI: arxiv-2404.17848
Fabiano C. Simas, E. da Hora
{"title":"Generation of kink-antikink pairs through the excitation of an oscillon in the $φ^4$ model","authors":"Fabiano C. Simas, E. da Hora","doi":"arxiv-2404.17848","DOIUrl":"https://doi.org/arxiv-2404.17848","url":null,"abstract":"We examine the oscillon decay in a model with a single scalar field and two\u0000asymmetric fundamental states. Specifically, we verify how the evolution of an\u0000initially excited oscillon leads to the formation of antikink-kink pairs in the\u0000presence of a centered long-lived pulse. In such a context, the magnitude of\u0000the original perturbation stands for the most important factor influencing the\u0000process. For intermediary values of this magnitude, we find a transitory\u0000behavior which suggests that the energy exchange between translational and\u0000vibrational modes begins to play an important role in the overall evolution. As\u0000the magnitude increases, the centered pulse intermediates an interaction\u0000between the inner structures which compose the pairs whose behavior mimics that\u0000of a standard antikink-kink collision and therefore reinforces the role played\u0000by the energy transfer mechanism. For different values of width, an almost pure\u0000antikink-kink pair escapes to the infinity after multiple bounces.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140829100","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
Hydrodynamics of a Discrete Conservation Law 离散守恒定律的流体力学
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-25 DOI: arxiv-2404.16750
Patrick Sprenger, Christopher Chong, Emmanuel Okyere, Michael Herrmann, P. G. Kevrekidis, Mark A. Hoefer
{"title":"Hydrodynamics of a Discrete Conservation Law","authors":"Patrick Sprenger, Christopher Chong, Emmanuel Okyere, Michael Herrmann, P. G. Kevrekidis, Mark A. Hoefer","doi":"arxiv-2404.16750","DOIUrl":"https://doi.org/arxiv-2404.16750","url":null,"abstract":"The Riemann problem for the discrete conservation law $2 dot{u}_n +\u0000u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a\u0000quasi-continuum approximation, and numerical simulations. A surprisingly\u0000elaborate set of solutions to this simple discrete regularization of the\u0000inviscid Burgers' equation is obtained. In addition to discrete analogues of\u0000well-known dispersive hydrodynamic solutions -- rarefaction waves (RWs) and\u0000dispersive shock waves (DSWs) -- additional unsteady solution families and\u0000finite time blow-up are observed. Two solution types exhibit no known\u0000conservative continuum correlates: (i) a counterpropagating DSW and RW solution\u0000separated by a symmetric, stationary shock and (ii) an unsteady shock emitting\u0000two counter-propagating periodic wavetrains with the same frequency connected\u0000to a partial DSW or a RW. Another class of solutions called traveling DSWs,\u0000(iii), consists of a partial DSW connected to a traveling wave comprised of a\u0000periodic wavetrain with a rapid transition to a constant. Portions of solutions\u0000(ii) and (iii) are interpreted as shock solutions of the Whitham modulation\u0000equations.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804163","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
Third order interactions shift the critical coupling in multidimensional Kuramoto models 三阶相互作用使多维库拉莫托模型中的临界耦合发生变化
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-25 DOI: arxiv-2404.16715
Ricardo Fariello, Marcus A. M. de Aguiar
{"title":"Third order interactions shift the critical coupling in multidimensional Kuramoto models","authors":"Ricardo Fariello, Marcus A. M. de Aguiar","doi":"arxiv-2404.16715","DOIUrl":"https://doi.org/arxiv-2404.16715","url":null,"abstract":"The study of higher order interactions in the dynamics of Kuramoto\u0000oscillators has been a topic of intense recent research. Arguments based on\u0000dimensional reduction using the Ott-Antonsen ansatz show that such interactions\u0000usually facilitate synchronization, giving rise to bi-stability and hysteresis.\u0000Here we show that three body interactions shift the critical coupling for\u0000synchronization towards higher values in all dimensions, except D=2, where a\u0000cancellation occurs. After the transition, three and four body interactions\u0000combine to facilitate synchronization. We show simulations in D=3 and 4 to\u0000illustrate the dynamics.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804155","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
Collective lattice excitations in the dynamic route for melting hydrodynamic 2D-crystals 流体动力二维晶体熔化动态路线中的集体晶格激发
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-24 DOI: arxiv-2404.15912
Mikheil Kharbedia, Niccolò Caselli, Macarena Calero, Lara H. Moleiro, Jesús F. Castillo, José A. Santiago, Diego Herráez-Aguilar, Francisco Monroy
{"title":"Collective lattice excitations in the dynamic route for melting hydrodynamic 2D-crystals","authors":"Mikheil Kharbedia, Niccolò Caselli, Macarena Calero, Lara H. Moleiro, Jesús F. Castillo, José A. Santiago, Diego Herráez-Aguilar, Francisco Monroy","doi":"arxiv-2404.15912","DOIUrl":"https://doi.org/arxiv-2404.15912","url":null,"abstract":"Surface stiffnesses engender steady patterns of Faraday waves (FWs), so\u0000called hydrodynamic crystals as correspond to ordered wave lattices made of\u0000discrete subharmonics under monochromatic driving. Mastering rules are both\u0000inertia-imposed parametric resonance for frequency-halving together with\u0000rigidity-driven nonlinearity for wavefield self-focusing. They harness the\u0000discretization needed for coherent FW-packets to localize in space and time.\u0000Collective lattice excitations are observed as dispersionless propagating\u0000dislocations that lead periodic modulations arising from explicit symmetry\u0000breaking. In a field theory perspective, a halving genesis for the collective\u0000distorting modes is revealed as the natural pathway for hydrodynamic crystal\u0000melting.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"92 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804098","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
A new derivation of the amplitude of asymptotic oscillatory tails of weakly delocalized solitons 弱脱域孤子渐近振荡尾振幅的新推导
arXiv - PHYS - Pattern Formation and Solitons Pub Date : 2024-04-23 DOI: arxiv-2404.15020
Gyula Fodor, Péter Forgács, Muneeb Mushtaq
{"title":"A new derivation of the amplitude of asymptotic oscillatory tails of weakly delocalized solitons","authors":"Gyula Fodor, Péter Forgács, Muneeb Mushtaq","doi":"arxiv-2404.15020","DOIUrl":"https://doi.org/arxiv-2404.15020","url":null,"abstract":"The computation of the amplitude, $alpha$, of asymptotic standing wave tails\u0000of weakly delocalized, stationary solutions in a fifth-order Korteweg-de Vries\u0000equation is revisited. Assuming the coefficient of the fifth order derivative\u0000term, $epsilon^2ll1$, a new derivation of the ``beyond all orders in\u0000$epsilon$'' amplitude, $alpha$, is presented. It is shown by asymptotic\u0000matching techniques, extended to higher orders in $epsilon$, that the value of\u0000$alpha$ can be obtained from the asymmetry at the center of the unique\u0000solution exponentially decaying in one direction. This observation,\u0000complemented by some fundamental results of Hammersley and Mazzarino [Proc. R.\u0000Soc. Lond. A 424, 19 (1989)], not only sheds new light on the computation of\u0000$alpha$, but also greatly facilitates its numerical determination to a\u0000remarkable precision for so small values of $epsilon$, which are beyond the\u0000capabilities of standard numerical methods.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806618","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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