Physica D: Nonlinear Phenomena最新文献

{"title":"Efficiently and consistently energy-stable L2-phase-field method for the incompressible ternary fluid problems","authors":"Junxiang Yang ,&nbsp;Huan Han ,&nbsp;Shuhong Liu ,&nbsp;Zhigang Zuo","doi":"10.1016/j.physd.2024.134346","DOIUrl":"10.1016/j.physd.2024.134346","url":null,"abstract":"<div><p>Ternary incompressible fluid flows extensively exist in atmospheric science, chemical engineering, and energy and power engineering, etc. The phase-field method is popular in multi-phase fluid modeling thanks to its efficient ability of interface capturing. This work aims to develop an energy dissipation law-preserving and temporally second-order accurate algorithm for a ternary phase-field fluid system. To establish a simple energy estimation, an adapted auxiliary variable approach is used to transform the original model into its equivalent form. Later, a second-order backward difference strategy is used to design the fully decoupled and linear time-marching scheme. To improve the consistency between original and modified discrete energy functionals, a practical energy correction technique is presented. We analytically prove the discrete energy dissipation property and show that the energy estimation can be easily established without considering the complex treatments of nonlinear and coupling terms. To facilitate the interested readers, we briefly describe the numerical implementation in each time step. The numerical tests indicate that the proposed method not only has desired accuracy, but also satisfies the energy stability even if a larger time step is used. Moreover, the proposed method can well simulate various ternary fluid phenomena, such as the liquid lens, phase separation, droplet dynamics, Kelvin–Helmholtz instability, and billowing cloud.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157976","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":"Discretized boundary-oriented progressive learning method for predicting global basins of attraction with few data","authors":"Zigang Li ,&nbsp;Shumeng Ma ,&nbsp;Jun Jiang ,&nbsp;Wenjie Cheng ,&nbsp;Xuhui Cui","doi":"10.1016/j.physd.2024.134350","DOIUrl":"10.1016/j.physd.2024.134350","url":null,"abstract":"<div><p>Basins of attraction (BoAs) are crucial for evaluating quality of a response and unraveling reliability of complex systems and mechanism of nonlinear phenomena. As a global strategy, however, it will pose a significant challenge to quantify a high-dimensional BoAs due to the curse of dimensionality and the insufficiency of data. This paper proposes a boundary-oriented progressive learning method based on the state space discretization, which aims to perform the classification of dynamics using few samples needed for learning while still achieving high efficiency and accuracy. Using pattern recognition network, training samples are purposefully extracted from the discretized and limited region that covers cells of boundary, disregarding the region outside of it. The region is then refined and identified iteratively to enhance discriminability of data model. This method does not seek to approximate the structure of boundary by refine cells, but rather regards cells as a framework of training neural network. The three typical examples are illustrated to show the power of the proposed method. The results demonstrate that the higher the dimensions, the better cost-effectiveness when compared to state-of-the-art approaches. The performance is even improved by more than 4 orders of magnitude on the computing loads when coping with a formidable six-dimensional BoA with satisfactory accuracy. Also, we discuss how the boundary-oriented progressive learning can improve the overall accuracy and robustness of the data model. Furthermore, this idea has the potential to efficiently handle other tasks of classification of dynamics beyond BoA, from a perspective of engineering.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157974","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":"Chaotic discrete breathers in bcc lattice: Effect of the first- and second-neighbor interactions","authors":"D.V. Bachurin ,&nbsp;R.T. Murzaev ,&nbsp;D.U. Abdullina ,&nbsp;M.N. Semenova ,&nbsp;Yu.V. Bebikhov ,&nbsp;S.V. Dmitriev","doi":"10.1016/j.physd.2024.134344","DOIUrl":"10.1016/j.physd.2024.134344","url":null,"abstract":"<div><p>Numerical simulations are performed to investigate the formation of chaotic discrete breathers (DBs) in a bcc lattice using four zone-boundary modes with frequencies exceeding the crystal’s phonon spectrum. The study analyzes the impact of the stiffness of elastic bonds between first and second neighbors and identifies a specific range where the formation of chaotic DBs due to modulational instability of four vibrational modes is possible. The time evolution of the energy localization parameter and the maximum energy of all particles were monitored to control the formation of chaotic DBs. Their spontaneous nucleation was observed in a wide range of stiffness of elastic bonds and depends on the mode’s symmetry. Considering DBs in bcc metals, the paper focuses on the scenario where first-neighbor bonds are stiffer than second-neighbor bonds, as bond stiffness typically decreases with interatomic distance. In all four zone-boundary modes, formation of chaotic DB is observed under this condition.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157977","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":"Bigraded modified Toda hierarchy and its extensions","authors":"Yi Yang ,&nbsp;Wenjuan Rui ,&nbsp;Jipeng Cheng","doi":"10.1016/j.physd.2024.134343","DOIUrl":"10.1016/j.physd.2024.134343","url":null,"abstract":"<div><p>Modified Toda hierarchy is just the two-component first modified KP hierarchy, which is related to 2D Toda hierarchy through Miura transformation and also has been widely used in discussing the B-Toda and C-Toda hierarchies. In this paper, we firstly construct <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-bigraded modified Toda hierarchy (BMTH) as a reduction of modified Toda hierarchy, and give corresponding Lie algebra interpretation. After that, we propose two kinds of extensions of <span><math><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math></span>-BMTH. One is extended by using logarithmic flows, while the other is <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>D extension, which is corresponding to the toroidal Lie algebra <span><math><msubsup><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>tor</mi></mrow></msubsup></math></span>. At last, the relation of these two kinds of extensions also is discussed.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142095173","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":"Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions","authors":"Mingtao Xia ,&nbsp;Xiangting Li ,&nbsp;Tom Chou","doi":"10.1016/j.physd.2024.134339","DOIUrl":"10.1016/j.physd.2024.134339","url":null,"abstract":"<div><p>There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in predation or harvesting. Here, we apply a recently formulated kinetic population theory to formally construct an age-structured single-species population model that includes a cannibalistic interaction in which older individuals prey on younger ones. Depending on the age-dependent structure of this interaction, our model can exhibit transient or steady-state overcompensation of an increased death rate as well as oscillations of the total population, both phenomena that have been observed in ecological systems. Analytic and numerical analysis of our model reveals sufficient conditions for overcompensation and oscillations. We also show how our structured population partial integrodifferential equation (PIDE) model can be reduced to coupled ODE models representing piecewise constant parameter domains, providing additional mathematical insight into the emergence of overcompensation.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167278924002902/pdfft?md5=d6891be8287b28c6c6a1f4ad8d90f11f&pid=1-s2.0-S0167278924002902-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions","authors":"Ba Phi Nguyen ,&nbsp;Kihong Kim","doi":"10.1016/j.physd.2024.134342","DOIUrl":"10.1016/j.physd.2024.134342","url":null,"abstract":"<div><p>We conduct a numerical investigation into wave propagation and localization in one-dimensional lattices subject to nonlinear disorder, focusing on cases with fixed input conditions. Utilizing a discrete nonlinear Schrödinger equation with Kerr-type nonlinearity and a random coefficient, we compute the averages and variances of the transmittance, <span><math><mi>T</mi></math></span>, and its logarithm, as functions of the system size <span><math><mi>L</mi></math></span>, while maintaining constant intensity for the incident wave. In cases of purely nonlinear disorder, we observe power-law localization characterized by <span><math><mrow><mrow><mo>〈</mo><mi>T</mi><mo>〉</mo></mrow><mo>∝</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>a</mi></mrow></msub></mrow></msup></mrow></math></span> and <span><math><mrow><mrow><mo>〈</mo><mo>ln</mo><mi>T</mi><mo>〉</mo></mrow><mo>≈</mo><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>ln</mo><mi>L</mi></mrow></math></span> for sufficiently large <span><math><mi>L</mi></math></span>. At low input intensities, a transition from exponential to power-law decay in <span><math><mrow><mo>〈</mo><mi>T</mi><mo>〉</mo></mrow></math></span> occurs as <span><math><mi>L</mi></math></span> increases. The exponents <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> are nearly identical, converging to approximately 0.5 as the strength of the nonlinear disorder, <span><math><mi>β</mi></math></span>, increases. Additionally, the variance of <span><math><mi>T</mi></math></span> decays according to a power law with an exponent close to 1, and the variance of <span><math><mrow><mo>ln</mo><mi>T</mi></mrow></math></span> approaches a small constant as <span><math><mi>L</mi></math></span> increases. These findings are consistent with an underlying log-normal distribution of <span><math><mi>T</mi></math></span> and suggest that wave propagation behavior becomes nearly deterministic as the system size increases. When both linear and nonlinear disorders are present, we observe a transition from power-law to exponential decay in transmittance with increasing <span><math><mi>L</mi></math></span> when the strength of linear disorder, <span><math><mi>V</mi></math></span>, is less than <span><math><mi>β</mi></math></span>. As <span><math><mi>V</mi></math></span> increases, the region exhibiting power-law localization diminishes and eventually disappears when <span><math><mi>V</mi></math></span> exceeds <span><math><mi>β</mi></math></span>, leading to standard Anderson localization.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142095174","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":"The evolution of cooperative chasing on complex networks via a game-based chasing rule","authors":"Shaolin Tan ,&nbsp;Yicheng Lü","doi":"10.1016/j.physd.2024.134340","DOIUrl":"10.1016/j.physd.2024.134340","url":null,"abstract":"<div><p>Cooperative pursuit, which involves a set of multiple agents with combined effort to capture some target, is a typical kind of collective intelligent behavior in social populations. It is intriguing how autonomous agents communicate and interaction with each other to facilitate collaborative pursuit tactics. In this paper, we consider the scenario of a set of cops to capture a robber on complex networks. A game-based chasing rule is proposed to coordinate the action of cops. It is shown that cooperative pursuit behavior, such as encirclement, can be generated by the proposed game-based chasing rule. Through experiments on different kinds of networks, it is shown that the game-based chasing rule greatly reduces the required capture time, compared to that of independent chasing rule. This study provides new insight into the development of more sophisticated pursuit and evasion behaviors in complex environments.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142095175","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":"Rayleigh–Taylor instability in an arbitrary direction electrostatic field","authors":"J.J. Yao,&nbsp;Y.G. Cao","doi":"10.1016/j.physd.2024.134338","DOIUrl":"10.1016/j.physd.2024.134338","url":null,"abstract":"<div><p>Based on the potential flow theory, we carry out the nonlinear analysis for the inviscid incompressible Rayleigh–Taylor instability (RTI) in an arbitrary direction electrostatic field. The analytical expressions for the bubble amplitude and growth rate are presented. The effects of tangential and vertical electrostatic fields upon the bubble dynamics are opposite and depend on permittivity ratio. Agreements with recent simulations are found in the bubble amplitude. The direction of electrostatic field determines which (tangential or vertical) component plays the main role. The stability of the interface depends on whether the tangential and vertical components of the electrostatic field exceed the cut-off electrostatic field which is dependent of the permittivity ratio and the Atwood number. The results of this work demonstrate the importance of the direction of electrostatic field when considering the impact of electrostatic field on RTI.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157979","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":"Pairwise balancing of forces in traveling granular waves","authors":"Giorgos Kanellopoulos ,&nbsp;Dimitrios Razis ,&nbsp;Ko van der Weele","doi":"10.1016/j.physd.2024.134324","DOIUrl":"10.1016/j.physd.2024.134324","url":null,"abstract":"<div><p>A survey is given of the forces at work inside traveling roll waves and monoclinal flood waves in dry granular matter. By numerically solving the generalized Saint-Venant equations for shallow granular flow, we find a hierarchy of pairwise near-balancing forces, which together are responsible for sustaining the shape of the nonlinear waves in question. The leading force pair is gravity vs. friction, followed by inertia vs. pressure, while the minor imbalance left by the aforementioned pairs is settled by a (small though essential) diffusive force.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142083483","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":"Data-driven cold starting of good reservoirs","authors":"Lyudmila Grigoryeva ,&nbsp;Boumediene Hamzi ,&nbsp;Felix P. Kemeth ,&nbsp;Yannis Kevrekidis ,&nbsp;G. Manjunath ,&nbsp;Juan-Pablo Ortega ,&nbsp;Matthys J. Steynberg","doi":"10.1016/j.physd.2024.134325","DOIUrl":"10.1016/j.physd.2024.134325","url":null,"abstract":"<div><p>Using short histories of observations from a dynamical system, a workflow for the post-training initialization of reservoir computing systems is described. This strategy is called cold-starting, and it is based on a map called the starting map, which is determined by an appropriately short history of observations that maps to a unique initial condition in the reservoir space. The time series generated by the reservoir system using that initial state can be used to run the system in autonomous mode in order to produce accurate forecasts of the time series under consideration immediately. By utilizing this map, the lengthy “washouts” that are necessary to initialize reservoir systems can be eliminated, enabling the generation of forecasts using any selection of appropriately short histories of the observations.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167278924002768/pdfft?md5=38136431b1e879869e71cb14256a1466&pid=1-s2.0-S0167278924002768-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}