Physica D: Nonlinear Phenomena最新文献_第10页

Bifurcation analysis of a two-dimensional magnetic Rayleigh–Bénard problem 二维磁性 Rayleigh-Bénard 问题的分岔分析

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-24 DOI: 10.1016/j.physd.2024.134270

Fabian Laakmann , Nicolas Boullé

{"title":"Bifurcation analysis of a two-dimensional magnetic Rayleigh–Bénard problem","authors":"Fabian Laakmann , Nicolas Boullé","doi":"10.1016/j.physd.2024.134270","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134270","url":null,"abstract":"<div><p>We perform a bifurcation analysis of a two-dimensional magnetic Rayleigh–Bénard problem using a numerical technique called deflated continuation. Our aim is to study the influence of the magnetic field on the bifurcation diagram as the Chandrasekhar number <span><math><mi>Q</mi></math></span> increases and compare it to the standard (non-magnetic) Rayleigh–Bénard problem. We compute steady states at a high Chandrasekhar number of <span><math><mrow><mi>Q</mi><mo>=</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> over a range of the Rayleigh number <span><math><mrow><mn>0</mn><mo>≤</mo><mi>Ra</mi><mo>≤</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup></mrow></math></span>. These solutions are obtained by combining deflation with a continuation of steady states at low Chandrasekhar number, which allows us to explore the influence of the strength of the magnetic field as <span><math><mi>Q</mi></math></span> increases from low coupling, where the magnetic effect is almost negligible, to strong coupling at <span><math><mrow><mi>Q</mi><mo>=</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>. We discover a large profusion of states with rich dynamics and observe a complex bifurcation structure with several pitchfork, Hopf, and saddle–node bifurcations. Our numerical simulations show that the onset of bifurcations in the problem is delayed when <span><math><mi>Q</mi></math></span> increases, while solutions with fluid velocity patterns aligning with the background vertical magnetic field are privileged. Additionally, we report a branch of states that stabilizes at high magnetic coupling, suggesting that one may take advantage of the magnetic field to discriminate solutions.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167278924002215/pdfft?md5=2733084aff564156edd0196aa3c4945d&pid=1-s2.0-S0167278924002215-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486025","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}

引用次数: 0

A multi-domain model for microcirculation in optic nerve: Blood flow and oxygen transport 视神经微循环的多域模型血流和氧气运输

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-24 DOI: 10.1016/j.physd.2024.134272

Zilong Song , Shixin Xu , Robert Eisenberg , Huaxiong Huang

{"title":"A multi-domain model for microcirculation in optic nerve: Blood flow and oxygen transport","authors":"Zilong Song , Shixin Xu , Robert Eisenberg , Huaxiong Huang","doi":"10.1016/j.physd.2024.134272","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134272","url":null,"abstract":"<div><p>Microcirculation of blood and transport of oxygen play important roles in the biological function of the optic nerve and its diseases. This work develops a multi-domain model for the optic nerve, that includes important biological structures and various physical mechanisms in blood flow and oxygen delivery. The two vascular networks are treated as five domains in the same geometric region, with various exchanges among them (such as Darcy’s law for fluid flow) and with the tissue domain (such as water leak, diffusion). The numerical results of the coupled model for a uniform case of vasculature distribution show mechanisms and scales consistent with literature and intuition. The effects of various important model parameters (relevant to pathological conditions) are investigated to provide insights into the possible implications. The vasculature distribution (resting volume fractions here) has significant impacts on the blood circulation and could lead to insufficient blood supply in certain local regions and thereby affect the delivery of oxygen. The water leak across the capillary wall will have nontrivial effects after the leak coefficients pass a threshold. The pulsatile arterial pressure leads to expected pulsatile patterns and stable spatial profiles, and the uniform case is almost the averaged version of pulsatile case. The effects of viscosity, the stiffness of blood vessel wall, oxygen demand, etc. have also been analyzed. The framework can be extended to include ionic transport or to study the retina when more biological structural information is available.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486029","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}

引用次数: 0

Improved image denoising through fractional anisotropic diffusion and resolution-tailored differentiation in the Fourier domain 通过傅立叶域中的分数各向异性扩散和分辨率定制微分改进图像去噪

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-22 DOI: 10.1016/j.physd.2024.134248

Milorad P. Paskaš

{"title":"Improved image denoising through fractional anisotropic diffusion and resolution-tailored differentiation in the Fourier domain","authors":"Milorad P. Paskaš","doi":"10.1016/j.physd.2024.134248","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134248","url":null,"abstract":"<div><p>Fractional-order anisotropic diffusion-based denoising of images has been implemented in the literature through fractional differentiation in the Fourier domain. Furthermore, Fourier transform of the schemes on half-integer or integer mesh points has been used for the differentiation of images. In this paper, differentiation in the Fourier domain is proposed using schemes on fractional mesh points, aiming to enhance the performance of the algorithm. This can be regarded as employing fractional schemes at various resolutions, governed by a parameter of resolution within the range of (0.5, 1). Variations in resolution affect the pixel neighborhood by incorporating additional information from interpolated pixels. Experiments conducted on a reference image dataset, using three quantitative measures, demonstrate that the proposed method surpasses the method from the literature for higher values of the parameter of resolution. The improvement is particularly noticeable at higher noise levels, where the proposed method consistently outperforms the method from the literature across all values of the parameter of resolution. As a side effect, the proposed method is less time-consuming than the original method, as it requires higher time steps within the numerical scheme. Experiments and stability analysis show that the proposed method reduces the number of iterations by three to four times compared to the original method.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486023","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}

引用次数: 0

Baroclinic vortex pulsars in unstable westward flows 不稳定西流中的巴氏旋涡脉冲星

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-22 DOI: 10.1016/j.physd.2024.134263

Pavel Berloff , Georgi G. Sutyrin

{"title":"Baroclinic vortex pulsars in unstable westward flows","authors":"Pavel Berloff , Georgi G. Sutyrin","doi":"10.1016/j.physd.2024.134263","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134263","url":null,"abstract":"<div><p>We present a computational modeling study of geophysical coherent vortices embedded in horizontally homogeneous, baroclinically unstable, westward background flows with vertical shear. Within an idealized two-layer quasigeostrophic beta-plane model, we discovered two types of robust vortex-wave structures with distinct properties, which remain asymmetric and nonstationary in statistically-equilibrated turbulent flow regimes. The corresponding vortices, referred to as <em>baroclinic vortex pulsars</em>, are characterized by intense vorticity core coupled to the Rossby wave wake. The main conclusion — on the top of various analyses discussed in the paper — are that the vortex pulsars are fundamentally <em>non-isolated</em> coherent vortices, because they extract energy from the background circulation and expel excess potential vorticity, accumulating due to down-gradient material propagation, back into the environment. Both types may coexist as multiple statistically equilibrated states in some range of physical parameters, complicating any parameterization of eddy effects in climate-type models.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167278924002148/pdfft?md5=7f7981d30ce0e219d91829ea2c8b2962&pid=1-s2.0-S0167278924002148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486026","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}

引用次数: 0

Periodic orbits in a Hamiltonian system of stellar type 恒星型哈密顿系统中的周期轨道

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-20 DOI: 10.1016/j.physd.2024.134261

Jhon Vidarte , Yrina Vera-Damián , Walter Gonzales

引用次数: 0

Low dissipative configuration in flow networks subject to constraints 受约束的流动网络中的低耗散配置

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-19 DOI: 10.1016/j.physd.2024.134269

Antonio F. Miguel

{"title":"Low dissipative configuration in flow networks subject to constraints","authors":"Antonio F. Miguel","doi":"10.1016/j.physd.2024.134269","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134269","url":null,"abstract":"<div><p>The homothetic relationships for the design of dendritic networks are examined in terms of minimal size under constant flow resistance, and minimum flow resistance under constant size. Based on a comprehensive methodology, we offer a general approach for the homothety ratios of diameters and lengths that apply to different flow regimes and size constraints. In addition, scaling laws for diameters-lengths, sizes-diameters, and resistances-lengths are provided. Since the dendritic trees designed based on size homothety ratios have prefractal characteristics, a methodology for determining prefractal dimensions in terms of fluid flow and size constraint characteristics is also offered. Among the findings, we show that the homothety ratios are the same regardless of whether the functions we selected are used as the constraint or the cost function. The approaches presented and literature data were compared, and a significant degree of agreement was found.</p><p>The findings presented here not only serve as a tool for the design of microfluidic chip devices but also deepen our understanding of natural networks such as the ones that support the life of mammals.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141486028","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}

引用次数: 0

Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation 磁电分形、磁电参数共振和霍普夫分岔

IF 4 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-18 DOI: 10.1016/j.physd.2024.134257

M. Wanic , Z. Toklikishvili , S.K. Mishra , M. Trybus , L. Chotorlishvili

{"title":"Magnetoelectric fractals, Magnetoelectric parametric resonance and Hopf bifurcation","authors":"M. Wanic , Z. Toklikishvili , S.K. Mishra , M. Trybus , L. Chotorlishvili","doi":"10.1016/j.physd.2024.134257","DOIUrl":"https://doi.org/10.1016/j.physd.2024.134257","url":null,"abstract":"<div><p>In the present work, we study the dynamics of the magnetic nanodisc coupled through a magnetoelectric coupling to a ferroelectric crystal. The model of our interest is nonlinear, and we explore the problem under different limits of weak and strong non-linearity. By applying two electric fields with different frequencies, we control the form of the confinement potential of a ferroelectric subsystem and realize different types of dynamics. We proved that the system is more sensitive to magnetoelectric coupling in the case of double-well potential. In particular, in the case of strong non-linearity, arbitrary small values of magnetoelectric coupling lead to chaotic dynamics. In essence, magnetoelectric coupling plays a role akin to the small perturbations destroying invariant tori according to the KAM theorem. We showed that bifurcations in the system are of Hopf’s type. We observed the formation of magnetoelectric fractals in the system. In the limit of weak non-linearity, we studied a problem of parametric nonlinear resonance and enhancement of magnetic oscillations through magnetoelectric coupling.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":4.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141429514","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}

引用次数: 0

Transverse instability of traveling wave created by longwave Marangoni convection in the liquid layer covered by insoluble surfactant 不溶性表面活性剂覆盖的液层中由长波马兰戈尼对流产生的行波的横向不稳定性

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-15 DOI: 10.1016/j.physd.2024.134265

Alexander Mikishev , Alexander Nepomnyashchy

引用次数: 0

An energy-stable variable-step L1 scheme for time-fractional Navier–Stokes equations 用于时分数纳维-斯托克斯方程的能量稳定且无发散的变步长 L1 方案

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-15 DOI: 10.1016/j.physd.2024.134264

Ruimin Gao , Dongfang Li , Yaoda Li , Yajun Yin

引用次数: 0

Darboux transformation-based LPNN generating novel localized wave solutions 基于达尔布变换的 LPNN 生成新颖的局部波解决方案

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2024-06-15 DOI: 10.1016/j.physd.2024.134262

Juncai Pu , Yong Chen

{"title":"Darboux transformation-based LPNN generating novel localized wave solutions","authors":"Juncai Pu , Yong Chen","doi":"10.1016/j.physd.2024.134262","DOIUrl":"10.1016/j.physd.2024.134262","url":null,"abstract":"<div><p>Darboux transformation method is one of the most essential and important methods for solving localized wave solutions of integrable systems. In this work, we introduce the core idea of Darboux transformation of integrable systems into the Lax pairs informed neural networks (LPNNs), which we proposed earlier. By fully utilizing the data-driven solutions, spectral parameter and spectral function obtained from LPNNs, we present the novel Darboux transformation-based LPNN (DT-LPNN). The notable feature of DT-LPNN lies in its ability to solve data-driven localized wave solutions and spectral problems with high precision, and it also can employ Darboux transformation formulas of integrable systems and non-trivial seed solutions to discover novel localized wave solutions that were previously unobserved and unreported. The numerical results indicate that, by utilizing the single-soliton solutions as the non-trivial seed solutions, we obtain novel localized wave solutions for the Kraenkel–Manna–Merle (KMM) system by employing DT-LPNN, in which solution <span><math><mi>u</mi></math></span> changes from original bright single-soliton on zero background wave to new dark single-soliton dynamic behavior on a variable non-zero background wave. Moreover, by treating the two-soliton solutions as the non-trivial seed solutions, DT-LPNN generates novel localized wave solutions for the KMM system that exhibit completely different dynamic behaviors from prior two-soliton solutions. DT-LPNN combines the Darboux transformation theory of integrable systems with deep neural networks, offering a new approach for generating novel localized wave solutions using non-trivial seed solutions.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141399287","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}

引用次数: 0