Asif Hamid, Danish Rafiq, Shahkar Ahmad Nahvi, Mohammad Abid Bazaz
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several computational challenges during simulation as the underlying dynamics vary and span wide spatiotemporal scales of interest. To capture the fast-evolving features, finer time steps are required while ensuring that the simulation time is long enough to capture the slow-scale behavior, making the analyses computationally unmanageable. This paper showcases how deep learning techniques can be used to develop a precise time-stepping approach for multiscale systems using the joint discovery of coordinates and flow maps. While the former allows us to represent the multiscale dynamics on a representative basis, the latter enables the iterative time-stepping estimation of the reduced variables. The resulting framework achieves state-of-the-art predictive accuracy while incurring lesser computational costs. We demonstrate this ability of the proposed scheme on the large-scale Fitzhugh Nagumo neuron model and the 1D Kuramoto-Sivashinsky equation in the chaotic regime.
{"title":"Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps","authors":"Asif Hamid, Danish Rafiq, Shahkar Ahmad Nahvi, Mohammad Abid Bazaz","doi":"arxiv-2407.00011","DOIUrl":"https://doi.org/arxiv-2407.00011","url":null,"abstract":"Complex systems often show macroscopic coherent behavior due to the\u0000interactions of microscopic agents like molecules, cells, or individuals in a\u0000population with their environment. However, simulating such systems poses\u0000several computational challenges during simulation as the underlying dynamics\u0000vary and span wide spatiotemporal scales of interest. To capture the\u0000fast-evolving features, finer time steps are required while ensuring that the\u0000simulation time is long enough to capture the slow-scale behavior, making the\u0000analyses computationally unmanageable. This paper showcases how deep learning\u0000techniques can be used to develop a precise time-stepping approach for\u0000multiscale systems using the joint discovery of coordinates and flow maps.\u0000While the former allows us to represent the multiscale dynamics on a\u0000representative basis, the latter enables the iterative time-stepping estimation\u0000of the reduced variables. The resulting framework achieves state-of-the-art\u0000predictive accuracy while incurring lesser computational costs. We demonstrate\u0000this ability of the proposed scheme on the large-scale Fitzhugh Nagumo neuron\u0000model and the 1D Kuramoto-Sivashinsky equation in the chaotic regime.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"216 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515172","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}
Data-driven discovery of governing equations has kindled significant interests in many science and engineering areas. Existing studies primarily focus on uncovering equations that govern nonlinear dynamics based on direct measurement of the system states (e.g., trajectories). Limited efforts have been placed on distilling governing laws of dynamics directly from videos for moving targets in a 3D space. To this end, we propose a vision-based approach to automatically uncover governing equations of nonlinear dynamics for 3D moving targets via raw videos recorded by a set of cameras. The approach is composed of three key blocks: (1) a target tracking module that extracts plane pixel motions of the moving target in each video, (2) a Rodrigues' rotation formula-based coordinate transformation learning module that reconstructs the 3D coordinates with respect to a predefined reference point, and (3) a spline-enhanced library-based sparse regressor that uncovers the underlying governing law of dynamics. This framework is capable of effectively handling the challenges associated with measurement data, e.g., noise in the video, imprecise tracking of the target that causes data missing, etc. The efficacy of our method has been demonstrated through multiple sets of synthetic videos considering different nonlinear dynamics.
{"title":"Vision-based Discovery of Nonlinear Dynamics for 3D Moving Target","authors":"Zitong Zhang, Yang Liu, Hao Sun","doi":"arxiv-2404.17865","DOIUrl":"https://doi.org/arxiv-2404.17865","url":null,"abstract":"Data-driven discovery of governing equations has kindled significant\u0000interests in many science and engineering areas. Existing studies primarily\u0000focus on uncovering equations that govern nonlinear dynamics based on direct\u0000measurement of the system states (e.g., trajectories). Limited efforts have\u0000been placed on distilling governing laws of dynamics directly from videos for\u0000moving targets in a 3D space. To this end, we propose a vision-based approach\u0000to automatically uncover governing equations of nonlinear dynamics for 3D\u0000moving targets via raw videos recorded by a set of cameras. The approach is\u0000composed of three key blocks: (1) a target tracking module that extracts plane\u0000pixel motions of the moving target in each video, (2) a Rodrigues' rotation\u0000formula-based coordinate transformation learning module that reconstructs the\u00003D coordinates with respect to a predefined reference point, and (3) a\u0000spline-enhanced library-based sparse regressor that uncovers the underlying\u0000governing law of dynamics. This framework is capable of effectively handling\u0000the challenges associated with measurement data, e.g., noise in the video,\u0000imprecise tracking of the target that causes data missing, etc. The efficacy of\u0000our method has been demonstrated through multiple sets of synthetic videos\u0000considering different nonlinear dynamics.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140831647","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}
Mattia Coccolo, Jesús M. Seoane, Stefano Lenci, Miguel A. F. Sanjuán
We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of {phi_{OPT}} simeq {pi}, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference {phi} and the fractional parameter {alpha} as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal {phi} value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.
{"title":"Phase control of escapes in the fractional damped Helmholtz oscillator","authors":"Mattia Coccolo, Jesús M. Seoane, Stefano Lenci, Miguel A. F. Sanjuán","doi":"arxiv-2404.16869","DOIUrl":"https://doi.org/arxiv-2404.16869","url":null,"abstract":"We analyze the nonlinear Helmholtz oscillator in the presence of fractional\u0000damping, a characteristic feature in several physical situations. In our\u0000specific scenario, as well as in the non-fractional case, for large enough\u0000excitation amplitudes, all initial conditions are escaping from the potential\u0000well. To address this, we incorporate the phase control technique into a\u0000parametric term, a feature commonly encountered in real-world situations. In\u0000the non-fractional case it has been shown that, a phase difference of\u0000{phi_{OPT}} simeq {pi}, is the optimal value to avoid the escapes of the\u0000particles from the potential well. Here, our investigation focuses on\u0000understanding when particles escape, considering both the phase difference\u0000{phi} and the fractional parameter {alpha} as control parameters. Our\u0000findings unveil the robustness of phase control, as evidenced by the consistent\u0000oscillation of the optimal {phi} value around its non-fractional counterpart\u0000when varying the fractional parameter. Additionally, our results underscore the\u0000pivotal role of the fractional parameter in governing the proportion of bounded\u0000particles, even when utilizing the optimal phase.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812097","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}
Alexandre R. Nieto, Rubén Capeáns, Miguel A. F. Sanjuán
In the seminal paper (Phys. Rep. 52, 263, 1979), Boris Chirikov showed that the standard map does not exhibit a boundary to chaos, but rather that there are small islands (islets) of stability for arbitrarily large values of the nonlinear perturbation. In this context, he established that the area of the islets in the phase space and the range of parameter values where they exist should decay following power laws with exponents -2 and -1, respectively. In this paper, we carry out a systematic numerical search for islets of stability and we show that the power laws predicted by Chirikov hold. Furthermore, we use high-resolution 3D islets to reveal that the islets volume decays following a similar power law with exponent -3.
{"title":"Systematic search for islets of stability in the standard map for large parameter values","authors":"Alexandre R. Nieto, Rubén Capeáns, Miguel A. F. Sanjuán","doi":"arxiv-2404.12027","DOIUrl":"https://doi.org/arxiv-2404.12027","url":null,"abstract":"In the seminal paper (Phys. Rep. 52, 263, 1979), Boris Chirikov showed that\u0000the standard map does not exhibit a boundary to chaos, but rather that there\u0000are small islands (islets) of stability for arbitrarily large values of the\u0000nonlinear perturbation. In this context, he established that the area of the\u0000islets in the phase space and the range of parameter values where they exist\u0000should decay following power laws with exponents -2 and -1, respectively. In\u0000this paper, we carry out a systematic numerical search for islets of stability\u0000and we show that the power laws predicted by Chirikov hold. Furthermore, we use\u0000high-resolution 3D islets to reveal that the islets volume decays following a\u0000similar power law with exponent -3.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628705","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 one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which can be a cumbersome task and is code-specific. To propose an adjoint solver that is not code-specific, we develop a data-driven strategy. We demonstrate its application on the computation of gradients of long-time averages of chaotic flows. First, we deploy a parameter-aware echo state network (ESN) to accurately forecast and simulate the dynamics of a dynamical system for a range of system's parameters. Second, we derive the adjoint of the parameter-aware ESN. Finally, we combine the parameter-aware ESN with its adjoint version to compute the sensitivities to the system parameters. We showcase the method on a prototypical chaotic system. Because adjoint sensitivities in chaotic regimes diverge for long integration times, we analyse the application of ensemble adjoint method to the ESN. We find that the adjoint sensitivities obtained from the ESN match closely with the original system. This work opens possibilities for sensitivity analysis without code-specific adjoint solvers.
{"title":"Adjoint Sensitivities of Chaotic Flows without Adjoint Solvers: A Data-Driven Approach","authors":"Defne E. Ozan, Luca Magri","doi":"arxiv-2404.12315","DOIUrl":"https://doi.org/arxiv-2404.12315","url":null,"abstract":"In one calculation, adjoint sensitivity analysis provides the gradient of a\u0000quantity of interest with respect to all system's parameters. Conventionally,\u0000adjoint solvers need to be implemented by differentiating computational models,\u0000which can be a cumbersome task and is code-specific. To propose an adjoint\u0000solver that is not code-specific, we develop a data-driven strategy. We\u0000demonstrate its application on the computation of gradients of long-time\u0000averages of chaotic flows. First, we deploy a parameter-aware echo state\u0000network (ESN) to accurately forecast and simulate the dynamics of a dynamical\u0000system for a range of system's parameters. Second, we derive the adjoint of the\u0000parameter-aware ESN. Finally, we combine the parameter-aware ESN with its\u0000adjoint version to compute the sensitivities to the system parameters. We\u0000showcase the method on a prototypical chaotic system. Because adjoint\u0000sensitivities in chaotic regimes diverge for long integration times, we analyse\u0000the application of ensemble adjoint method to the ESN. We find that the adjoint\u0000sensitivities obtained from the ESN match closely with the original system.\u0000This work opens possibilities for sensitivity analysis without code-specific\u0000adjoint solvers.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140628707","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}
Dust particles in protoplanetary disks, lacking support from pressure, rotate at velocities exceeding those of the surrounding gas. Consequently, they experience a head-wind from the gas that drives them toward the central star. Radial drift occurs on timescales much shorter than those inferred from disk observations or those required for dust to aggregate and form planets. Additionally, turbulence is often assumed to amplify the radial drift of dust in planet-forming disks when modeled through an effective viscous transport. However, the local interactions between turbulent eddies and particles are known to be significantly more intricate than in a viscous fluid. Our objective is to elucidate and characterize the dynamic effects of Keplerian turbulence on the mean radial and azimuthal velocities of dust particles. We employ 2D shearing-box incompressible simulations of the gas, which is maintained in a developed turbulent state while rotating at a sub-Keplerian speed. Dust is modeled as Lagrangian particles set at a Keplerian velocity, therefore experiencing a radial force toward the star through drag. Turbulent eddies are found to reduce the radial drift, while simultaneously enhancing the azimuthal velocities of small particles. This dynamic behavior arises from the modification of dust trajectories due to turbulent eddies.
{"title":"Reduction of dust radial drift by turbulence in protoplanetary disks","authors":"Fabiola Antonietta Gerosa, Jérémie Bec, Héloïse Méheut, Anand Utsav Kapoor","doi":"arxiv-2404.11544","DOIUrl":"https://doi.org/arxiv-2404.11544","url":null,"abstract":"Dust particles in protoplanetary disks, lacking support from pressure, rotate\u0000at velocities exceeding those of the surrounding gas. Consequently, they\u0000experience a head-wind from the gas that drives them toward the central star.\u0000Radial drift occurs on timescales much shorter than those inferred from disk\u0000observations or those required for dust to aggregate and form planets.\u0000Additionally, turbulence is often assumed to amplify the radial drift of dust\u0000in planet-forming disks when modeled through an effective viscous transport.\u0000However, the local interactions between turbulent eddies and particles are\u0000known to be significantly more intricate than in a viscous fluid. Our objective\u0000is to elucidate and characterize the dynamic effects of Keplerian turbulence on\u0000the mean radial and azimuthal velocities of dust particles. We employ 2D\u0000shearing-box incompressible simulations of the gas, which is maintained in a\u0000developed turbulent state while rotating at a sub-Keplerian speed. Dust is\u0000modeled as Lagrangian particles set at a Keplerian velocity, therefore\u0000experiencing a radial force toward the star through drag. Turbulent eddies are\u0000found to reduce the radial drift, while simultaneously enhancing the azimuthal\u0000velocities of small particles. This dynamic behavior arises from the\u0000modification of dust trajectories due to turbulent eddies.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140615798","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}
Amirhossein Nazerian, Joseph D Hart, Matteo Lodi, Francesco Sorrentino
Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the efficiency of the synchronization dynamics has received far less attention. Here we address this question in terms of both coupling efficiency and energy efficiency. We use our understanding of the transient dynamics towards synchronization to design a coupling-efficient and energy-efficient synchronization strategy, which varies the coupling strength dynamically, instead of using the same coupling strength at all times. Our proposed synchronization strategy is able in both simulation and in experiments to synchronize networks by using an average coupling strength that is significantly lower (and, when there is an upper bound on the coupling strength, significantly higher) than what is needed for the case of constant coupling. In either case, the improvement can be of orders of magnitude. In order to characterize the effects of the network topology on the transient dynamics towards synchronization, we propose the concept of network syncreactivity. This is distinct from the previously introduced network synchronizability, which describes the ability of a network to synchronize asymptotically. We classify real-world examples of complex networks in terms of both their synchronizability and syncreactivity.
{"title":"The Efficiency of Synchronization Dynamics and the Role of Network Syncreactivity","authors":"Amirhossein Nazerian, Joseph D Hart, Matteo Lodi, Francesco Sorrentino","doi":"arxiv-2404.16864","DOIUrl":"https://doi.org/arxiv-2404.16864","url":null,"abstract":"Synchronization of coupled oscillators is a fundamental process in both\u0000natural and artificial networks. While much work has investigated the\u0000asymptotic stability of the synchronous solution, the fundamental question of\u0000the efficiency of the synchronization dynamics has received far less attention.\u0000Here we address this question in terms of both coupling efficiency and energy\u0000efficiency. We use our understanding of the transient dynamics towards\u0000synchronization to design a coupling-efficient and energy-efficient\u0000synchronization strategy, which varies the coupling strength dynamically,\u0000instead of using the same coupling strength at all times. Our proposed\u0000synchronization strategy is able in both simulation and in experiments to\u0000synchronize networks by using an average coupling strength that is\u0000significantly lower (and, when there is an upper bound on the coupling\u0000strength, significantly higher) than what is needed for the case of constant\u0000coupling. In either case, the improvement can be of orders of magnitude. In\u0000order to characterize the effects of the network topology on the transient\u0000dynamics towards synchronization, we propose the concept of network\u0000syncreactivity. This is distinct from the previously introduced network\u0000synchronizability, which describes the ability of a network to synchronize\u0000asymptotically. We classify real-world examples of complex networks in terms of\u0000both their synchronizability and syncreactivity.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140812385","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 established thermodynamic formalism of chaotic dynamics,valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the phase-space average of an integrated observable (e.g. Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most notably, the thermodynamic treatment may predict the finite-time distributions of any integrated observable from the leading and subleading eigenfunctions of the Perron-Frobenius/Koopman transfer operator. Examples of that equivalence are shown, and the theory is tested numerically in three paradigms of chaos.
{"title":"Thermodynamics of chaotic relaxation processes","authors":"Domenico Lippolis","doi":"arxiv-2404.09130","DOIUrl":"https://doi.org/arxiv-2404.09130","url":null,"abstract":"The established thermodynamic formalism of chaotic dynamics,valid at\u0000statistical equilibrium, is here generalized to systems out of equilibrium,\u0000that have yet to relax to a steady state. A relation between information,\u0000escape rate, and the phase-space average of an integrated observable (e.g.\u0000Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most\u0000notably, the thermodynamic treatment may predict the finite-time distributions\u0000of any integrated observable from the leading and subleading eigenfunctions of\u0000the Perron-Frobenius/Koopman transfer operator. Examples of that equivalence\u0000are shown, and the theory is tested numerically in three paradigms of chaos.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"239 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572059","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}
With derivatives for physical insights and with mathematical analyses, technical variations and many applications though, the dynamical nature of Galerkin truncation in nonlinear systems is still not clear. Here, I show with such Galerkin-regularized Burgers-Hopf (GrBH) equation that the truncation corresponds to a nonlinear dispersion, supporting solitons and soliton-like structures (called "longons") and rhyming with recent expositions of dispersive objects. The formulation and scenarios resemble those of soliton turbulence, thus suggesting "longon turbulence" with large degree of freedoms (finite though). I also argue and numerically demonstrate that appropriate linearly dispersion models with an asymptotic large jump converge to the GrBH dynamics.
{"title":"Nonlinearly dispersive nature of Galerkin-regularization and longon turbulence","authors":"Jian-Zhou Zhu","doi":"arxiv-2404.08583","DOIUrl":"https://doi.org/arxiv-2404.08583","url":null,"abstract":"With derivatives for physical insights and with mathematical analyses,\u0000technical variations and many applications though, the dynamical nature of\u0000Galerkin truncation in nonlinear systems is still not clear. Here, I show with\u0000such Galerkin-regularized Burgers-Hopf (GrBH) equation that the truncation\u0000corresponds to a nonlinear dispersion, supporting solitons and soliton-like\u0000structures (called \"longons\") and rhyming with recent expositions of dispersive\u0000objects. The formulation and scenarios resemble those of soliton turbulence,\u0000thus suggesting \"longon turbulence\" with large degree of freedoms (finite\u0000though). I also argue and numerically demonstrate that appropriate linearly\u0000dispersion models with an asymptotic large jump converge to the GrBH dynamics.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"237 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571809","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}
Francesco Vercesi, Susie Poirier, Anna Minguzzi, Léonie Canet
We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation.
{"title":"Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation","authors":"Francesco Vercesi, Susie Poirier, Anna Minguzzi, Léonie Canet","doi":"arxiv-2404.08530","DOIUrl":"https://doi.org/arxiv-2404.08530","url":null,"abstract":"We study the phase turbulence of the one-dimensional complex Ginzburg-Landau\u0000equation, in which the defect-free chaotic dynamics of the order parameter maps\u0000to a phase equation well approximated by the Kuramoto-Sivashinsky model. In\u0000this regime, the behaviour of the large wavelength modes is captured by the\u0000Kardar-Parisi-Zhang equation, determining universal scaling and statistical\u0000properties. We present numerical evidence of the existence of an additional\u0000scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at\u0000scales which are intermediate between the microscopic, intrinsic to the\u0000modulational instability, and the macroscopic ones. We argue that this new\u0000regime is a signature of the universality class corresponding to the inviscid\u0000limit of the Kardar-Parisi-Zhang equation.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571812","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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