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The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher…

Soft Condensed Matter · Physics 2012-05-11 Iwan Schenker , Frank T. Filser , Markus Hütter , Ludwig J. Gauckler

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…

This paper is about nonequilibrium steady states (NESS) of a class of stochastic models in which particles exchange energy with their "local environments" rather than directly with one another. The physical domain of the system can be a…

Mathematical Physics · Physics 2016-03-25 Yao Li , Peter Nandori , Lai-Sang Young

We propose a nonlocal theory of single-particle excitations. It is based on an off-diagonal effective medium and the projection operator method for treating the retarded Green function. The theory determines the nonlocal effective medium…

Strongly Correlated Electrons · Physics 2015-05-14 Y. Kakehashi , T. Nakamura , P. Fulde

A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…

Applied Physics · Physics 2018-11-26 Rosaria Del Toro , Andrea Bacigalupo , Marco Paggi

Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely…

Strongly Correlated Electrons · Physics 2021-04-07 P. Karpov , R. Verdel , Y. -P. Huang , M. Schmitt , M. Heyl

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of…

Soft Condensed Matter · Physics 2015-05-13 M. Wyart , H. Liang , A. Kabla , L. Mahadevan

This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…

Analysis of PDEs · Mathematics 2025-10-24 Amartya Chakrabortty , Georges Griso , Julia Orlik

Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fuelling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions,…

Statistical Mechanics · Physics 2025-09-16 Robert Mattes , Igor Lesanovsky , Federico Carollo

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal…

Computational Engineering, Finance, and Science · Computer Science 2022-01-05 Wei Ding , Sansit Patnaik , Fabio Semperlotti

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…

Statistical Mechanics · Physics 2014-09-09 Michele Castellana , Aurelien Decelle , Silvio Franz , Marc Mezard , Giorgio Parisi

The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…

Analysis of PDEs · Mathematics 2017-03-21 Judith Berendsen , Martin Burger , Jan-Frederik Pietschmann

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…

Analysis of PDEs · Mathematics 2019-10-02 Annika Bach , Andrea Braides , Marco Cicalese

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we…

Numerical Analysis · Mathematics 2014-08-12 Marta Lewicka , Pablo Ochoa

The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network…

Disordered Systems and Neural Networks · Physics 2015-09-02 Le Yan , Matthieu Wyart

We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent \nu. This class…

Statistical Mechanics · Physics 2014-11-19 Rahul Nandkishore , Andrew C. Potter

In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven…

Applied Physics · Physics 2020-09-01 Raffaele Barretta , Marko Čanađija , Francesco Marotti de Sciarra

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…

Analysis of PDEs · Mathematics 2019-08-07 Tomas Roubicek , Giuseppe Tomassetti

We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…

Analysis of PDEs · Mathematics 2024-05-20 Juan Casado-Díaz

A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…

Pattern Formation and Solitons · Physics 2020-06-30 Giulia Cencetti , Federico Battiston , Timoteo Carletti , Duccio Fanelli