Related papers: Generic stability in dissipative generalized mecha…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…
The first mathematical problems of the global analysis of dynamical models can be traced back to the engineering problem of the Watt governor design. Engineering requirements and corresponding mathematical problems led to the fundamental…
The explanation of the apparent universality of thermodynamics points toward the extension of the usual conceptual background of the second law. Arguments are collected that a basic guiding idea of stability of thermodynamic equilibrium…
Drawing inspiration from transportation theory, in this work we introduce the notions of "well-structured" and "stable" Gibbs states and we investigate their implications for quantum thermodynamics and its resource theory approach via…
We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
The generalised hydrodynamic theory of an electron gas, which does not rely on an assumption of a local equilibrium, is derived as the long-wave limit of a kinetic equation. Apart from the common hydrodynamics variables the theory includes…
The fluctuation theorem characterizes the distribution of the dissipation in nonequilibrium systems and proves that the average dissipation will be positive. For a large system with no external source of fluctuation, fluctuations in…
Motivated by the problem of robustness to deformations of the input for deep convolutional neural networks, we identify signal classes which are inherently stable to irregular deformations induced by distortion fields $\tau\in…
We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…
We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an…
An efficient time-stepping algorithm is proposed based on operator-splitting and the space-time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
We consider the numerical approximation of linear damped wave systems by Galerkin approximations in space and appropriate time-stepping schemes. Based on a dissipation estimate for a modified energy, we prove exponential decay of the…
We present a general abstract framework for the systematic numerical approximation of dissipative evolution problems. The approach is based on rewriting the evolution problem in a particular form that complies with an underlying energy or…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.
Thermodynamic equations for a solid and a solid continuum under stress are derived on the basis of a multicomponent mean field Markov process for thermofluctuation kinetics of microcracks. The resulting continuum is viscous elastoplastic…