Archive for Rational Mechanics and Analysis最新文献_第10页

Beyond the Classical Cauchy–Born Rule 超越经典柯西-伯恩法则

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-11-07 DOI: 10.1007/s00205-023-01942-0

Andrea Braides, Andrea Causin, Margherita Solci, Lev Truskinovsky

{"title":"Beyond the Classical Cauchy–Born Rule","authors":"Andrea Braides, Andrea Causin, Margherita Solci, Lev Truskinovsky","doi":"10.1007/s00205-023-01942-0","DOIUrl":"10.1007/s00205-023-01942-0","url":null,"abstract":"<div><p>Physically motivated variational problems involving non-convex energies are often formulated in a discrete setting and contain boundary conditions. The long-range interactions in such problems, combined with constraints imposed by lattice discreteness, can give rise to the phenomenon of geometric frustration even in a one-dimensional setting. While non-convexity entails the formation of microstructures, incompatibility between interactions operating at different scales can produce nontrivial mixing effects which are exacerbated in the case of incommensurability between the optimal microstructures and the scale of the underlying lattice. Unraveling the intricacies of the underlying interplay between non-convexity, non-locality and discreteness represents the main goal of this study. While in general one cannot expect that ground states in such problems possess global properties, such as periodicity, in some cases the appropriately defined ‘global’ solutions exist, and are sufficient to describe the corresponding continuum (homogenized) limits. We interpret those cases as complying with a Generalized Cauchy–Born (GCB) rule, and present a new class of problems with geometrical frustration which comply with GCB rule in one range of (loading) parameters while being strictly outside this class in a complimentary range. A general approach to problems with such ‘mixed’ behavior is developed.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

A Remark on the Uniqueness of Solutions to Hyperbolic Conservation Laws 关于双曲型守恒律解的唯一性的评述

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-10-30 DOI: 10.1007/s00205-023-01936-y

Alberto Bressan, Camillo De Lellis

引用次数: 1

Epsilon-Regularity for Griffith Almost-Minimizers in Any Dimension Under a Separating Condition 分离条件下任意维格里菲斯几乎极小解的epsilon -正则性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-10-13 DOI: 10.1007/s00205-023-01935-z

Camille Labourie, Antoine Lemenant

引用次数: 0

The Yang–Mills–Higgs Functional on Complex Line Bundles: (Gamma )-Convergence and the London Equation 复线束上的Yang-Mills-Higgs泛函:(Gamma ) -收敛性和伦敦方程

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-10-09 DOI: 10.1007/s00205-023-01933-1

Giacomo Canevari, Federico Luigi Dipasquale, Giandomenico Orlandi

引用次数: 1

Long-time asymptotics for coagulation equations with injection that do not have stationary solutions 不具有平稳解的注射混凝方程的长时间渐近性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-10-06 DOI: 10.1007/s00205-023-01934-0

Iulia Cristian, Marina A. Ferreira, Eugenia Franco, Juan J. L. Velázquez

{"title":"Long-time asymptotics for coagulation equations with injection that do not have stationary solutions","authors":"Iulia Cristian, Marina A. Ferreira, Eugenia Franco, Juan J. L. Velázquez","doi":"10.1007/s00205-023-01934-0","DOIUrl":"10.1007/s00205-023-01934-0","url":null,"abstract":"<div><p>In this paper we study a class of coagulation equations including a source term that injects in the system clusters of size of order one. The coagulation kernel is homogeneous, of homogeneity <span>(gamma < 1)</span>, such that <i>K</i>(<i>x</i>, <i>y</i>) is approximately <span>(x^{gamma + lambda } y^{-lambda })</span>, when <i>x</i> is larger than <i>y</i>. We restrict the analysis to the case <span>(gamma + 2 lambda ge 1 )</span>. In this range of exponents, the transport of mass toward infinity is driven by collisions between particles of different sizes. This is in contrast with the case considered in Ferreira et al. (Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 2023), where <span>(gamma + 2 lambda <1)</span>. In that case, the transport of mass toward infinity is due to the collision between particles of comparable sizes. In the case <span>(gamma +2lambda ge 1)</span>, the interaction between particles of different sizes leads to an additional transport term in the coagulation equation that approximates the solution of the original coagulation equation with injection for large times. We prove the existence of a class of self-similar solutions for suitable choices of <span>(gamma )</span> and <span>(lambda )</span> for this class of coagulation equations with transport. We prove that for the complementary case such self-similar solutions do not exist.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-023-01934-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50012287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 2

Stability of the Nonlinear Milne Problem for Radiative Heat Transfer System 辐射传热系统非线性Milne问题的稳定性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-09-27 DOI: 10.1007/s00205-023-01930-4

Mohamed Ghattassi, Xiaokai Huo, Nader Masmoudi

{"title":"Stability of the Nonlinear Milne Problem for Radiative Heat Transfer System","authors":"Mohamed Ghattassi, Xiaokai Huo, Nader Masmoudi","doi":"10.1007/s00205-023-01930-4","DOIUrl":"10.1007/s00205-023-01930-4","url":null,"abstract":"<div><p>This paper focuses on the nonlinear Milne problem of the radiative heat transfer system on the half-space. The nonlinear model is described by a second order ODE for temperature coupled to transport equation for radiative intensity. The nonlinearity of the fourth power Stefan–Boltzmann law of black body radiation, brings additional difficulty in mathematical analysis, compared to the well-developed theory for the Milne problem of the linear transport equation. To overcome this difficulty, the monotonicity properties of the second order ODE are used, together with the uniform estimate and compactness method, to prove the existence of the nonlinear Milne problem and to show the exponential decay of solutions. Moreover, the linear stability of the problem is established under a spectral assumption on its solutions, and the uniqueness of the nonlinear Milne problem is established in a neighborhood of solutions satisfying a spectral assumption or when the boundary conditions are close to the well-prepared case. The current work extends the study of Milne problem for linear transport equations and provides a comprehensive study on the nonlinear Milne problem of radiative heat transfer systems.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50103429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1

Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels 奇异核相互作用粒子系统的高斯涨落

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-09-27 DOI: 10.1007/s00205-023-01932-2

Zhenfu Wang, Xianliang Zhao, Rongchan Zhu

引用次数: 13

Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria 液体中气泡的自由边界问题及球对称平衡流形的指数稳定性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-09-25 DOI: 10.1007/s00205-023-01927-z

Chen-Chih Lai, Michael I. Weinstein

{"title":"Free Boundary Problem for a Gas Bubble in a Liquid, and Exponential Stability of the Manifold of Spherically Symmetric Equilibria","authors":"Chen-Chih Lai, Michael I. Weinstein","doi":"10.1007/s00205-023-01927-z","DOIUrl":"10.1007/s00205-023-01927-z","url":null,"abstract":"<div><p>We consider the dynamics of a gas bubble immersed in an incompressible fluid of fixed temperature, and focus on the relaxation of an expanding and contracting spherically symmetric bubble due to thermal effects. We study two models, both systems of PDEs with an evolving free boundary: the full mathematical model and an approximate model, arising, for example, in the study of sonoluminescence. For fixed physical parameters (surface tension of the gas–liquid interface, liquid viscosity, thermal conductivity of the gas, etc.), both models share a family of spherically symmetric equilibria, smoothly parametrized by the mass of the gas bubble. Our main result concerns the approximate model. We prove the nonlinear asymptotic stability of the manifold of equilibria with respect to small spherically symmetric perturbations. The rate of convergence is exponential in time. To prove this result we first prove a weak form of nonlinear asymptotic stability –with no explicit rate of time-decay– using the energy dissipation law, and then, via a center manifold analysis, bootstrap the weak time-decay to exponential time-decay. We also study the uniqueness of the family of spherically symmetric equilibria within each model. The family of spherically symmetric equilibria captures all spherically symmetric equilibria of the approximate system. However within the full model, this family is embedded in a larger family of spherically symmetric solutions. For the approximate system, we prove that all equilibrium bubbles are spherically symmetric, by an application of Alexandrov’s theorem on closed surfaces of constant mean curvature.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50048395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 1

Exterior Stability of Minkowski Space in Generalized Harmonic Gauge 广义谐波规范中Minkowski空间的外部稳定性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-09-24 DOI: 10.1007/s00205-023-01931-3

Peter Hintz

引用次数: 0

Global Bifurcation and Highest Waves on Water of Finite Depth 有限深度水上的全局分岔和最高波

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2023-09-20 DOI: 10.1007/s00205-023-01929-x

Vladimir Kozlov, Evgeniy Lokharu

{"title":"Global Bifurcation and Highest Waves on Water of Finite Depth","authors":"Vladimir Kozlov, Evgeniy Lokharu","doi":"10.1007/s00205-023-01929-x","DOIUrl":"10.1007/s00205-023-01929-x","url":null,"abstract":"<div><p>We consider the two-dimensional problem for steady water waves with vorticity on water of finite depth. While neglecting the effects of surface tension we construct connected families of large amplitude periodic waves approaching a limiting wave, which is either a solitary wave, the highest solitary wave, the highest Stokes wave or a Stokes wave with a breaking profile. In particular, when the vorticity is nonnegative we prove the existence of highest Stokes waves with an included angle of 120<span>(^circ )</span>. In contrast to previous studies, we fix the Bernoulli constant and consider the wavelength as a bifurcation parameter, which guarantees that the limiting wave has a finite depth. In fact, this is the first rigorous proof of the existence of extreme Stokes waves with vorticity on water of finite depth. Aside from the existence of highest waves, we provide a new result about the regularity of Stokes waves of arbitrary amplitude (including extreme waves). Furthermore, we prove several new facts about steady waves, such as a lower bound for the wavelength of Stokes waves, while also eliminating a possibility of the wave breaking for waves with non-negative vorticity.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-023-01929-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50094765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 9