Physica D: Nonlinear Phenomena最新文献

{"title":"Variational principles for fully coupled stochastic fluid dynamics across scales","authors":"Arnaud Debussche,&nbsp;Etienne Mémin","doi":"10.1016/j.physd.2025.134777","DOIUrl":"10.1016/j.physd.2025.134777","url":null,"abstract":"<div><div>This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of equations that captures both scales, using a variational principle formulated with Lagrangians defined on the full flow, and incorporating stochastic transport constraints. The approach smooths the noise term along time, leading to stochastic dynamics as a regularization parameter approaches zero. Initially, fixed noise terms are considered, resulting in a generalized stochastic Euler equation, which becomes problematic as the regularization parameter diminishes. The study then examines connections with existing stochastic frameworks and proposes a new variational principle that couples noise dynamics with large-scale fluid motion. This comprehensive framework provides a stochastic representation of large-scale dynamics while accounting for fine-scale components. Our main result is that the evolution of the small-scale velocity component is governed by a linearized Euler equation with random coefficients, influenced by large-scale transport, stretching, and pressure forcing.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134777"},"PeriodicalIF":2.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Order and chaos in systems of two and three coaxial vortex pairs","authors":"Christiana Mavroyiakoumou ,&nbsp;Wenzheng Shi","doi":"10.1016/j.physd.2025.134767","DOIUrl":"10.1016/j.physd.2025.134767","url":null,"abstract":"<div><div>Systems of coaxial vortex pairs in an inviscid flow give rise to complex dynamics, with motions ranging from ordered to chaotic. This complexity arises due to the problem’s high nonlinearity and numerous degrees of freedom. We analyze the periodic interactions of two vortex pairs with the same absolute strength moving along the same axis and in the same direction. We derive an explicit formula for the leapfrogging period, considering different initial sizes and horizontal separations, and find excellent quantitative agreement with the numerically computed leapfrogging period. We then extend our study to three coaxial vortex pairs with differing strengths, exploring a broad range of initial geometric configurations, and identify conditions that lead to escape to infinity, periodic or quasi-periodic leapfrogging, and chaotic interactions. We also quantify the occurrence of periodic leapfrogging, revealing that the system transitions to two subsystems when vortex pairs have dissimilar strengths and sizes. By performing a sensitivity analysis using neural networks, we find that the initial horizontal separation between the vortex pairs has the most significant effect on the leapfrogging period.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134767"},"PeriodicalIF":2.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterization of mixing in turbulent jet with off-source heating","authors":"Chandra Shekhar Pant ,&nbsp;Amitabh Bhattacharya ,&nbsp;Amit Agrawal","doi":"10.1016/j.physd.2025.134759","DOIUrl":"10.1016/j.physd.2025.134759","url":null,"abstract":"<div><div>Jets with volumetric off-source heating are studied due to their resemblance to Cumulus clouds, where droplet condensation leads to diabatic heating of updrafts. This study investigates the effects of volumetric heating on jet dynamics through large eddy simulations, focusing on acceleration, velocity, concentration widths, and mass flux behavior under varying Richardson (Ri) numbers. The results reveal that heating accelerates the jet, with the lowest Ri number exhibiting the smallest acceleration and the farthest location of acceleration. Whereas the velocity and concentration widths decrease with heating, the mass flux increases with Ri, influenced by the choice of length scale for calculations. The radial velocity and the entrainment coefficient (<span><math><mi>α</mi></math></span>) increase with the heating rate, and the axial and radial turbulent intensities rise, confirming no re-laminarization within the studied parameters. The temperature field shows a flattened Gaussian profile for the lowest Ri, reverting to the Gaussian post-heated interaction zone (HIZ). In contrast, the maximum axial temperature is achieved for the lowest Ri case due to reduced mixing at higher Ri values. No evidence of detrainment is observed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134759"},"PeriodicalIF":2.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144306768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient-enhanced PINN with residual unit for studying forward-inverse problems of variable coefficient equations","authors":"Hui-Juan Zhou ,&nbsp;Yong Chen","doi":"10.1016/j.physd.2025.134764","DOIUrl":"10.1016/j.physd.2025.134764","url":null,"abstract":"<div><div>Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena, are of considerable physical significance and research value. This study proposes a gradient-enhanced PINN with residual unit (R-gPINN) method to solve the data-driven solution and function discovery for variable coefficient PDEs. On the one hand, the proposed method incorporates residual units into the neural networks to mitigate gradient vanishing and network degradation, unify linear and nonlinear coefficient problem. We present two types of residual unit structures in this work to offer more flexible solutions in problem-solving. On the other hand, by including gradient terms of variable coefficients, the method penalizes collocation points that fail to satisfy physical properties. This enhancement improves the network’s adherence to physical constraints and aligns the prediction function more closely with the objective function. Numerical experiments including solve the forward-inverse problems of variable coefficient Burgers equation, variable coefficient KdV equation, variable coefficient Sine–Gordon equation, and high-dimensional variable coefficient Kadomtsev–Petviashvili equation. The results show that using R-gPINN method can greatly improve the accuracy of predict solution and predict variable coefficient in solving variable coefficient equations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134764"},"PeriodicalIF":2.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Characterizing temporal correlations in the output of a semiconductor laser with optical feedback","authors":"María Duque-Gijón ,&nbsp;Jordi Tiana-Alsina ,&nbsp;Cristina Masoller ,&nbsp;Andrés Aragoneses","doi":"10.1016/j.physd.2025.134760","DOIUrl":"10.1016/j.physd.2025.134760","url":null,"abstract":"<div><div>We perform an experimental study of the dynamics of a semiconductor laser with optical feedback. We use two event-based methods to characterize the time series of the emitted intensity, one based on events that are defined by threshold-crossings (we refer to this method as spikes analysis), and the other one on events that are defined by intensity minima that are below a threshold (we refer to this method as peak analysis). By applying ordinal analysis to sequences of time intervals between consecutive events, we identify temporal correlations in the timing of the events that vary with the method used to define the events, as well as with the experimental control parameters, the laser pump current and feedback strength. The events defined by spike analysis are usually slower than those defined by peak analysis (their frequencies depend on the experimental conditions and are typically <span><math><mrow><mo>≈</mo><mn>10</mn></mrow></math></span> MHz and <span><math><mrow><mo>≈</mo><mn>1</mn></mrow></math></span> GHz respectively). We show that the two methods used to define events in the intensity time series provide a complementary characterization of the dynamics. We also find, with the two methods and in broad parameter regions, that the ordinal probabilities are organized in clusters formed by pairs of probabilities with similar values. We propose three diagnostic tools to analyze the clustering of the ordinal probabilities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134760"},"PeriodicalIF":2.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of convergence angle of Ranque-Hilsch vortex tube on the optimization of thermal separation in compressible swirl flow","authors":"Kannan Shaji ,&nbsp;Vinod Narayanan ,&nbsp;Abhilash Suryan ,&nbsp;Heuy Dong Kim","doi":"10.1016/j.physd.2025.134761","DOIUrl":"10.1016/j.physd.2025.134761","url":null,"abstract":"<div><div>Ranque-Hilsch vortex tube is a highly efficient fluidic expansion device with thermal separation features. Geometric optimization of the device is necessary for getting the best performance. Current study aims to conduct a validated and comparative analysis of the significance of angle of convergence in a convergent vortex tube compared to a straight tube design. Numerical simulations of the swirl flow field are performed to maximize thermal separation. The result shows a strong correlation between swirl flow intensity distribution and vortex tube convergence angle, suggesting that adjusting the angle can remodel vortex core to improve temperature separation. The occurrence and analysis of the bifurcation point confirm the critical angle of convergence, where optimal temperature separation occurs most effectively and efficiently. Exergy and enthalpy-entropy analyses validate the design features, indicating a reduction in cold exit flow irreversibility when the design features critical convergence angle. Further studies are warranted for a comprehensive optimization of the design.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134761"},"PeriodicalIF":2.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144280361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Wave turbulence, thermalization and multimode locking in optical fibers","authors":"M. Ferraro ,&nbsp;K. Baudin ,&nbsp;M. Gervaziev ,&nbsp;A. Fusaro ,&nbsp;A. Picozzi ,&nbsp;J. Garnier ,&nbsp;G. Millot ,&nbsp;D. Kharenko ,&nbsp;E. Podivilov ,&nbsp;S. Babin ,&nbsp;F. Mangini ,&nbsp;S. Wabnitz","doi":"10.1016/j.physd.2025.134758","DOIUrl":"10.1016/j.physd.2025.134758","url":null,"abstract":"<div><div>We present a comprehensive overview of recent advances in theory and experiments on complex light propagation phenomena in nonlinear multimode fibers. On the basis of the wave turbulence theory, we derive kinetic equations describing the out-of-equilibrium process of optical thermalization toward the Rayleigh–Jeans (RJ) equilibrium distribution. Our theory is applied to explain the effect of beam self-cleaning (BSC) in graded-index (GRIN) fibers, whereby a speckled beam transforms into a bell-shaped beam at the fiber output as the input peak power grows larger. Although the output beam is typically dominated by the fundamental mode of the fiber, higher-order modes (HOMs) cannot be fully depleted, as described by the turbulence cascades associated to the conserved quantities. We theoretically explore the role of random refractive index fluctuations along the fiber core, and show how these imperfections may turn out to assist the observation of BSC in a practical experimental setting. This conclusion is supported by the derivation of wave turbulence kinetic equations that account for the presence of a time-dependent disorder (random mode coupling). The kinetic theory reveals that a weak disorder accelerates the rate of RJ thermalization and beam cleaning condensation. On the other hand, although strong disorder is expected to suppress wave condensation, the kinetic equation reveals that an out-of-equilibrium process of condensation and RJ thermalization can occur in a regime where disorder predominates over nonlinearity. In general, the kinetic equations are validated by numerical simulations of the generalized nonlinear Schrodinger equation. We outline a series of recent experiments, which permit to confirm the statistical mechanics approach for describing beam propagation and thermalization. For example, we highlight the demonstration of entropy growth, and point out that there are inherent limits to peak-power scaling in multimode fiber lasers. We conclude by pointing out the experimental observation that BSC is accompanied by an effect of modal phase-locking. From the one hand this explains the observed preservation of the spatial coherence of the beam, but also it points to the need of extending current descriptions in future research.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134758"},"PeriodicalIF":2.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144313502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Plane-symmetric capillary turbulence: Five-wave interactions","authors":"E.A. Kochurin ,&nbsp;P.A. Russkikh","doi":"10.1016/j.physd.2025.134763","DOIUrl":"10.1016/j.physd.2025.134763","url":null,"abstract":"<div><div>The theory of isotropic capillary turbulence was developed in the late 1960s by Zakharov and Filonenko. To date, the analytical solution of the kinetic equation describing the stationary transfer of energy to small scales due to three-wave resonant interactions, called the Zakharov–Filonenko spectrum, has been confirmed with high accuracy. However, in the case of strong anisotropy in wave propagation, where all waves are collinear, the situation changes significantly. In such a degenerate geometry, the conditions of resonant interaction cease to be fulfilled not only for three waves, but also for four interacting waves. In this work, we perform fully nonlinear simulations of plane-symmetric capillary turbulence. We demonstrate that the system of interacting waves evolves into a quasi-stationary state with a direct energy cascade, despite the absence of low-order resonances. The calculated spectra of surface elevations are accurately described by analytical estimates derived dimensionally under the assumption of the dominant influence of five-wave resonant interactions. A detailed study of the statistical characteristics of the weakly turbulent state does not reveal the influence of any coherent or strongly nonlinear structures. The performed high-order correlation analysis indicates a variety of non-trivial five-wave resonances. We show that the process of wave decay into two pairs of counter-propagating waves is responsible for the local energy transfer to small scales. Overall, the calculation results are in good agreement with both the weak turbulence theory and recent experiments made by Ricard and Falcon.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134763"},"PeriodicalIF":2.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear structures in laboratory and space dusty plasmas","authors":"L.M. Zelenyi ,&nbsp;S.I. Popel","doi":"10.1016/j.physd.2025.134721","DOIUrl":"10.1016/j.physd.2025.134721","url":null,"abstract":"<div><div>A brief review of studies on nonlinear wave structures in dusty plasmas is presented, for which effects that appear specifically in dusty plasmas, for example, anomalous dissipation associated with the processes of dust particle charging, are presented. Examples of such structures in laboratory and space plasmas are given. In particular, a description is presented of the experiments at the Institute of Space and Astronautical Sciences (Japan) and at the University of Iowa (USA). A significant accent is made to space research, namely, the formation of bow shock arising from the interaction of the comet’s dust coma and the solar wind, and the formation of a nonlinear structure in the region of the lunar terminator.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134721"},"PeriodicalIF":2.7,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rigorous convergence bounds for stochastic differential equations with application to uncertainty quantification","authors":"Liam A.A. Blake,&nbsp;John Maclean,&nbsp;Sanjeeva Balasuriya","doi":"10.1016/j.physd.2025.134742","DOIUrl":"10.1016/j.physd.2025.134742","url":null,"abstract":"<div><div>Prediction via continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we consider a general class of stochastic differential equations and provide rigorous convergence bounds to an analytically solvable approximation. We provide the explicit convergence rate for all moments of a fully non-autonomous model with both multiplicative noise and uncertain initial conditions. Our second main contribution is to extend stochastic sensitivity, a recently introduced uncertainty quantification tool, to arbitrary dimensions and provide a new calculation method that empowers rapid computation. We demonstrate the power and adaptability of our contributions on a diverse set of numerical examples in 1-, 2-, 3-, and 4-dimensions, including providing stochastic sensitivity calculations for an idealised eddy parameterisation of the Gulf Stream.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134742"},"PeriodicalIF":2.7,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144222000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}