相关论文: Non-local energetics of random heterogeneous latti…

This work examines a discrete elastic energy system with local interactions described by a discrete second-order functional in the symmetric gradient and additional non-local random long-range interactions. We analyze the asymptotic…

Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…

The localization of energy in the discrete nonlinear Schroedinger equation is explained with statistical methods. The partition function and the entropy of the system are computed for low-amplitude initial conditions. Detailed predictions…

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and…

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in…

We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of…

In this paper we study Maxwell lattices with non-rectilinear constraints, where the elastic energy is determined by the collective motion of three or more particles, in contrast to a rectilinear spring whose elastic energy only relies on…

This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…

This study investigates the use of the $J$-integral to compute the statistics of the energy release rate of a random elastic medium. The spatial variability of the elastic modulus is modeled as a homogeneous lognormal random field. Within…

We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity,…

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent non-dissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming the…

We study the real-time dynamics of the local energy density in the spin-1/2 XXZ chain starting from initial states with an inhomogeneous profile of bond energies. Numerical simulations of the dynamics of the initial states are carried out…

We study the statistical mechanics of the one-dimensional discrete nonlinear Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the…

We investigate the local and global dynamics of two 1-Dimensional (1D) Hamiltonian lattices whose inter-particle forces are derived from non-analytic potentials. In particular, we study the dynamics of a model governed by a "graphene-type"…

We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…

We investigate the local structural fluctuations of a model equilibrium fluid with an aim of better understanding the structural basis of locally heterogeneous dynamics identified in recent simulations and experimental studies of…

We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which…

We extend the duality of Kipnis Marchioro and Presutti to inhomogeneous lattice gas systems where either the components have different degrees of freedom or the rate of interaction depends on the spatial location. Then the dual process is…

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. Here we give necessary conditions for this…