Related papers: Energy decay for evolution equations with glassy t…
We consider the wave equation with a boundary condition of memory type. Under natural conditions on the acoustic impedance $\hat{k}$ of the boundary one can define a corresponding semigroup of contractions (Desch, Fasangova, Milota, Probst…
It has been established empirically that the rate of addition of molecules to the crystal during crystal growth from the melt is proportional to exp(-|{\Delta}S_fus|/R) where {\Delta}S_fus is the entropy of fusion. Here we show that this…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
We study by means of numerical simulations the model of dissipative particle dynamics with energy conservation for the simple case of thermal conduction. It is shown that the model displays correct equilibrium fluctuations and reproduces…
Accelerating mirrors provide a simple conceptual laboratory for studying particle production and the relation between trajectory and particle, energy, and entropy fluxes. We focus on the relation between energy and entropy, studying some…
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…
Individuals often develop reluctance to change their social relations, called "secondary homebody", even though their interactions with their environment evolve with time. Some memory effect is loosely present deforcing changes. In other…
Many recent experiments probed the off equilibrium dynamics of spin glasses and other glassy systems through temperature cycling protocols and observed memory and rejuvenation phenomena. Here we show through numerical simulations, using…
We explore the effects of including the energy dependence determined from evolution equations within the color glass condensate framework on observables in ultra-relativistic heavy-ion collisions. This amounts to integrating the JIMWLK…
The nature of the glass transition is one of the most important unsolved problems in condensed matter physics. The difference between glasses and liquids is believed to be caused by very large free energy barriers for particle…
We establish the comparison principle and the existence of solutions of the integro-differential equations with L{\'e}vy operators. The L{\'e}vy operators of our interest are infinitesmal generator of the jump processes which could be…
The transition into a glassy state of the ensemble of static, mechanically stable configurations of a tapped granular pile is explored using extensive molecular dynamics simulations. We show that different horizontal sub-regions ("layers")…
In a glassy system different degrees of freedom have well-separated characteristic times, and are described by different temperatures. The stationary state is essentially non-equilibrium. A generalized statistical thermodynamics is…
In this paper, we study two Energy Balance Models with Memory arising in climatology, which consist in a 1D degenerate nonlinear parabolic equation involving a memory term, and possibly a set-valued reaction term (of Sellers type and of…
We develop a general energy method for proving the optimal time decay rates of the solutions to the dissipative equations in the whole space. Our method is applied to classical examples such as the heat equation, the compressible…
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce…
We try to improve the Thomas-Fermi model for the total energy and electron density of atoms and molecules by directly modifying the Euler equation for the electron density, which we argue is less affected by nonlocal corrections. Here we…
We analyze fluctuation-dissipation relations in the Backgammon model: a system that displays glassy behavior at zero temperature due to the existence of entropy barriers. We study local and global fluctuation relations for the different…