Physica D: Nonlinear Phenomena最新文献

{"title":"Topological data analysis of three dimensional orbits in a convective flow","authors":"Ahtziri González ,&nbsp;Brayan Hernández ,&nbsp;Karla P. Acosta-Zamora ,&nbsp;Eduardo Ramos ,&nbsp;José Núñez","doi":"10.1016/j.physd.2025.134841","DOIUrl":"10.1016/j.physd.2025.134841","url":null,"abstract":"<div><div>We study the topological properties of the Lagrangian orbits of natural convection in a cube with Rayleigh numbers corresponding to steady-state motion. The Lagrangian orbits are considered clusters of points distributed in a three-dimensional space. This leads to the natural application of topological data analysis (TDA) tools that include alpha complexes, 0-, 1- and 2-persistent homologies, persistence diagrams, and the bottleneck metric. For low Rayleigh numbers, the analysis is applied to orbits that correspond to a region in a Poincaré map around an elliptic point. This leads to the conclusion that the points comprising individual Lagrangian orbits are embedded on the surfaces of nested tori. For larger Rayleigh numbers, the Poincaré map includes two elliptic points separated by a chaotic region. The points composing the orbits in the three dimensional space, form two nested tori structures separated by complex and difficult to classify orbits. The bottleneck metric applied to the 0-, 1- and 2-persistence diagrams, captures a smooth evolution of the structures’ geometrical properties, suggesting an order of the orbits present in the chaotic region. Interestingly, in the region between the two nested tori structures, an orbit with topological properties similar to a trivalent 2-stratifold was found.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134841"},"PeriodicalIF":2.7,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703393","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":"Finiteness of mirror-symmetric relative equilibria of point vortices","authors":"Kevin A. O’Neil","doi":"10.1016/j.physd.2025.134823","DOIUrl":"10.1016/j.physd.2025.134823","url":null,"abstract":"<div><div>Some relative equilibrium configurations of <span><math><mi>n</mi></math></span> point vortices in the plane have a mirror symmetry. In this paper it is proved that for arbitrary <span><math><mi>n</mi></math></span> and generic choice of vortex strengths, the mirror-symmetric configurations with no more than six vortices off the line of symmetry are finite in number. The same analysis is extended to include eight off-axis vortices when restricting to <span><math><mrow><mi>n</mi><mo>=</mo><mn>8</mn></mrow></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134823"},"PeriodicalIF":2.7,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702843","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":"Unveiling connections: Mobility and dengue case networks on an intraurban scale","authors":"Cátia S.N. Sepetauskas ,&nbsp;Vander L.S. Freitas ,&nbsp;Hugo S.P. Cardoso ,&nbsp;Leonardo B.L. Santos","doi":"10.1016/j.physd.2025.134812","DOIUrl":"10.1016/j.physd.2025.134812","url":null,"abstract":"<div><div>This study examines the intraurban connections between mobility and dengue case networks in São José dos Campos, São Paulo, Brazil. Our research aims to elucidate the correlation between human mobility patterns and the spread of dengue, a significant public health issue exacerbated by urban infrastructure deficits. We used daily dengue case data from 2014 to 2024 and mobility data derived from a 2011 urban mobility survey to build a complex network. Using mutual information, Spearman rank correlation, and linear regression, we quantified that regions that are geographically closer or have a greater flow of people between them have remarkable similarities between their time series of dengue cases. Our findings indicate that mobility significantly influences dengue spread, with higher mutual information values during periods of high dengue incidence, such as in 2015. As mobility increases, so does the correlation between dengue cases, underscoring the importance of considering intraurban mobility in public health strategies. In particular, our results demonstrate that mobility has a more significant influence than distance on the spread of cases. These insights could inform more effective epidemic control measures and urban planning policies to mitigate the impact of arboviruses in densely populated areas.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134812"},"PeriodicalIF":2.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679551","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":"Flow-induced variations in odour boundary formation","authors":"Bluest Lan,&nbsp;Sin-Tong Luo","doi":"10.1016/j.physd.2025.134827","DOIUrl":"10.1016/j.physd.2025.134827","url":null,"abstract":"<div><div>Odour tracking is vital for many biological organisms, underpinning behaviours such as foraging and navigation. However, due to the lack of systematic investigation, relevant applications remain underdeveloped. This study simulates the dispersion of odours from a single source, discussing the concept of an ‘odour boundary’. Utilising Schmidt numbers <span><math><mrow><mi>S</mi><mi>c</mi></mrow></math></span> ranging from 0.96 to 3.08 and Reynolds numbers <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> from 195 to 47,665, we explored the structure and variability of the odour boundary at different concentrations. Results demonstrate that the odour boundary width remains largely consistent within the <span><math><mrow><mi>S</mi><mi>c</mi></mrow></math></span> range, with minor variations at lower <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>. As <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> increases, the boundary narrows, although low <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> values limit odour spread due to incomplete lateral flow development. Additionally, the potential core length inversely affects the odour boundary width; a more extended core facilitates downstream airstream propagation while restricting lateral dispersion. When <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span> exceeds 10,000, the boundary width greatly decreases and stabilises. High-concentration regions within the lateral boundaries contract with higher wind speeds and at specific high <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>, the odour distribution adopts an M-shaped pattern rather than a bell-shaped curve, suggesting that the highest concentration may not align with the centreline. This supports the notion of an ‘odour barrier’ and could elucidate biological tracking mechanisms, such as those in silk moths. Insights from this study may inform robotic navigation systems, enabling more efficient odour source localisation in turbulent environments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134827"},"PeriodicalIF":2.7,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655898","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":"Stabilizing optical solitons by frequency-dependent linear gain–loss and the collisional Raman frequency shift","authors":"Avner Peleg ,&nbsp;Debananda Chakraborty","doi":"10.1016/j.physd.2025.134828","DOIUrl":"10.1016/j.physd.2025.134828","url":null,"abstract":"<div><div>We study transmission stabilization against radiation emission for solitons of the nonlinear Schrödinger (NLS) equation (optical solitons) by frequency-dependent linear gain–loss and the collisional Raman frequency shift. For this purpose, we consider soliton propagation in nonlinear optical waveguides in the presence of weak linear gain–loss, cubic loss, and the collisional Raman frequency shift perturbation. We first show how the collisional Raman perturbation arises in three different nonlinear physical setups. We then show by numerical simulations with a perturbed NLS equation that transmission in waveguides with weak frequency-independent linear gain is unstable. The radiative instability is stronger than the radiative instabilities that were observed in all earlier studies of soliton propagation in the presence of weak linear gain, cubic loss, and various frequency-shifting physical mechanisms. Moreover, we demonstrate by numerical simulations with another perturbed NLS equation that transmission in waveguides with weak frequency-dependent linear gain–loss, cubic loss, and the collisional Raman frequency shift is stable, despite the stronger radiative instability in the corresponding waveguide setup with weak linear gain. Additionally, we find that stabilization occurs via the following process: the collisional Raman frequency shift of the soliton leads to partial separation of the soliton’s and the radiation’s Fourier spectra, while the frequency-dependent linear gain–loss leads to efficient suppression of radiation emission. Thus, our study significantly extends the range of applicability of the soliton stabilization method, by showing that the method works even when the radiative instability is strong.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134828"},"PeriodicalIF":2.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144662088","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":"Communities for the Lagrangian dynamics of the turbulent velocity gradient tensor: A network participation approach","authors":"Christopher J. Keylock ,&nbsp;Maurizio Carbone","doi":"10.1016/j.physd.2025.134826","DOIUrl":"10.1016/j.physd.2025.134826","url":null,"abstract":"<div><div>In this paper, we present a network-based framework for analyzing the Lagrangian dynamics of the velocity gradient tensor (VGT). Each node represents a flow state, and link weights correspond to the transition probabilities between states, derived from Direct Numerical Simulation (DNS) of statistically steady, isotropic turbulence. The network provides a compact representation of the VGT’s continuum dynamics by discretizing it into a finite set of states. We investigate the optimal variables for this discretization, classifying VGT states into groups that best capture the flow’s physics. To this end, we test several classifications based on topology and various properties of the background flow coherent structures. We do this using the notion of “community” or “module”, namely clusters of nodes that are optimally distinct while also containing diverse nodal functions. The most effective classification, informed by VGT invariants frequently used in the literature, combines the signs of the principal invariants <span><math><mi>Q</mi></math></span>, <span><math><mi>R</mi></math></span>, and the discriminant <span><math><mi>Δ</mi></math></span>, distinguishing regions of real and complex eigenvalues. We refine this further by incorporating the relative magnitude of the non-normal contributions to enstrophy and straining, derived from the Schur decomposition of the VGT. Accounting for non-normality significantly enhances classification fidelity and underscores the critical role of the unclosed and complex contributions to VGT dynamics from the pressure Hessian and viscous terms. A comparison between the DNS data and an enhanced Gaussian closure model reveals the challenges for conventional modeling approaches in accurately capturing the non-normal contributions to the VGT dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134826"},"PeriodicalIF":2.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655901","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":"Modulational instability in the b-family equation","authors":"Lili Fan ,&nbsp;Xingchang Wang ,&nbsp;Runzhang Xu","doi":"10.1016/j.physd.2025.134817","DOIUrl":"10.1016/j.physd.2025.134817","url":null,"abstract":"<div><div>Consideration in this paper is the modulational instability of periodic traveling waves in the vicinity of the origin in the spectral plane of the <span><math><mi>b</mi></math></span>-family equation admitting quadratic nonlinearity with an arbitrary coefficient <span><math><mrow><mi>b</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. We derive modulational instability index as functions of both the nonlinear parameter <span><math><mi>b</mi></math></span> and the wave number of the underlying wave, and demonstrate that a sufficiently small periodic traveling wave of the <span><math><mi>b</mi></math></span>-family equation is spectrally unstable to long wavelength perturbations when the modulational instability index is negative. Based on this, the effects of the nonlinear terms on the instability mechanism are discussed and a phenomenon so-called the unstable “island” is observed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134817"},"PeriodicalIF":2.7,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655899","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 integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: Long-time asymptotics","authors":"Yan Rybalko ,&nbsp;Dmitry Shepelsky ,&nbsp;Shou-Fu Tian","doi":"10.1016/j.physd.2025.134820","DOIUrl":"10.1016/j.physd.2025.134820","url":null,"abstract":"<div><div>We consider the Cauchy problem for the integrable nonlocal nonlinear Schrödinger equation <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>q</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>̄</mo></mrow></mover><mrow><mo>(</mo><mo>−</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span>subject to the step-like initial data: <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>→</mo><mn>0</mn></mrow></math></span> as <span><math><mrow><mi>x</mi><mo>→</mo><mo>−</mo><mi>∞</mi></mrow></math></span> and <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>≃</mo><mi>A</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>i</mi><mi>B</mi><mi>x</mi></mrow></msup></mrow></math></span> as <span><math><mrow><mi>x</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, where <span><math><mrow><mi>A</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>B</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. The goal is to study the long-time asymptotic behavior of the solution of this problem assuming that <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> is close, in a certain spectral sense, to the “step-like” function <span><math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>R</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfenced><mrow><mtable><mtr><mtd><mn>0</mn><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>≤</mo><mi>R</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>A</mi><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>i</mi><mi>B</mi><mi>x</mi></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>&gt;</mo><mi>R</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></span> with <span><math><mrow><mi>R</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. A special attention is paid to how <span><math><mrow><mi>B</mi><mo>≠</mo><mn>0</mn></mrow></math></span> affects the asymptotics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134820"},"PeriodicalIF":2.7,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655952","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":"On the instability and stability of non-homogeneous fluid in a bounded domain under the influence of a general potential","authors":"Liang Li ,&nbsp;Tao Tan ,&nbsp;Quan Wang","doi":"10.1016/j.physd.2025.134816","DOIUrl":"10.1016/j.physd.2025.134816","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier–Stokes equations under the influence of a general potential &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. This potential is commonly used to model fluid motions in celestial bodies. First, we demonstrate that the system admits only steady-state solutions of the form &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;0&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; satisfy the hydrostatic balance condition &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Additionally, the relationship between &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and the potential function &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is constrained by the condition &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, which allows us to express &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Second, when there exists a point &lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, we establish the linear instability of these solutions. Furthermore, we demonstrate their nonlinear instability in both the Lipschitz and Hadamard senses through detailed nonlinear energy estimates. This instability aligns with the well-known Rayleigh–Taylor instability. Our study significantly extends and generalizes the existing ","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134816"},"PeriodicalIF":2.7,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623699","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":"Boundary and interior spikes in economic agglomeration of a spatial Solow model with capital-induced labor migration","authors":"Fanze Kong ,&nbsp;Qi Wang ,&nbsp;Shuangquan Xie","doi":"10.1016/j.physd.2025.134806","DOIUrl":"10.1016/j.physd.2025.134806","url":null,"abstract":"<div><div>Economic geography seeks to explore uneven spatial development commonly known as economic agglomeration, where economic activities concentrate in specific regions. While a variety of factors have been studied to explain the emergence of core–periphery economic patterns, labor mobility emerges as a fundamental and indispensable driver of such heterogeneity within the spatial economic framework. The spatial Solow model under consideration incorporates both wealth diffusion and labor migration to analyze the spatio-temporal economic growth. Labor migration is influenced by a combination of an unbiased random walk without economic incentives and a biased movement toward regions with better economic opportunities due to uneven capital distribution. In the regime of a large capital-induced labor migration rate, we first prove the existence of a steady state with a single boundary spike, and then prove its linearized stability using its asymptotic profile; moreover, this spike can be reflected and periodically extended to construct more stationary configurations with aggregates featuring interior spike and/or double-boundary spike. Further theoretical analysis shows that the single interior spike is inherently unstable and the double boundary spike is linearly stable. These results suggest that intense capital-induced labor migration can drive and stabilize economic agglomerations, concentrating wealth and labor in specific areas. Numerical simulations support these findings, revealing additional spatio-temporal dynamics such as phase transitions and spike insertion, and showcase the framework’s ability to capture complex economic behaviors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134806"},"PeriodicalIF":2.7,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655896","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}