Related papers: Energy decay for evolution equations with glassy t…
We look at estimates for the Green's function of time-fractional evolution equations of the form $D^{\nu}_{0+*} u = Lu$, where $D^{\nu}_{0+*}$ is a Caputo-type time-fractional derivative, depending on a L\'evy kernel $\nu$ with variable…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows…
Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental…
In this paper, we review the general features of the out-of-equilibrium dynamics of spin glasses. We use this example as a guideline for a brief description of glassy dynamics in other disordered systems like structural and polymer glasses,…
Let P be a long range metric perturbation of the Euclidean Laplacian on R^d, d>1. We prove local energy decay for the solutions of the wave, Klein-Gordon and Schroedinger equations associated to P. The problem is decomposed in a low and…
We identify the fluctuations of the partition function for a class of random energy models, where the energies are given by the positions of the particles of the complex-valued branching Brownian motion (BBM). Specifically, we provide the…
The mechanism of decoherence for a quantum system with rotational degrees of freedom is studied. From a simple model of elastic scattering, we show that the non-diagonal density matrix elements of the system exponentially decay. The decay…
The nature of glassy dynamics and the glass transition are long-standing problems under active debate. In the presence of a structural disorder widely believed to be an essential characteristic of structural glass, identifying and…
We study the small vibrations of an axially travelling string with a dashpoint damping at one end. The string is modelled by a wave equation in a time-dependent interval with two endpoints moving at a constant speed $v$. For the undamped…
Glasses feature a broad distribution of relaxation times and activation energies without an obvious characteristic scale. At the same time, macroscopic quantities such as Newtonian viscosity and nonlinear plastic deformation, are…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
After GGH model was proposed by M. Ghisi, M. Gobbino and A. Haraux (2016), R. Ikehata and S. Iyota (2018) showed decay estimates for the total energy of solutions to GGH equations uniformly in the initial data. However, their results imply…
We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…
Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that in-cludes a "memory term", i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn…
We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…
We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we discuss the transition from the low-density…
In this article, we consider the energy decay of a viscoelastic wave in an heterogeneous medium. To be more specific, the medium is composed of two different homogeneous medium with a memory term located in one of the medium. We prove…
We report the results of our study of fractional entropy enhancement in the intra-cluster medium (ICM) of the clusters from the representative XMM-Newton cluster structure survey (REXCESS). We compare the observed entropy profile of these…
A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error estimates are proved for the related…