Related papers: A Dissipation Theory for Three-Dimensional FDTD wi…
The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the thermal noise of physical systems in equilibrium. In general however, thermal equilibrium is an approximation, or cannot be assumed at all. A more general…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for…
The traditional finite-difference time-domain (FDTD) method is constrained by the Courant-Friedrich-Levy (CFL) condition and suffers from the notorious staircase error in electromagnetic simulations. This paper proposes a three-dimensional…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
This is one of our series works on discrete energy analysis of the variable-step BDF schemes. In this part, we present stability and convergence analysis of the third-order BDF (BDF3) schemes with variable steps for linear diffusion…
The goal of the paper is to derive a revised condition of global equilibrium in complex chemical systems as variational principle in formalism of recently developed discrete thermodynamics (DTD) of chemical equilibria. In classical approach…
The existence of a generalized fluctuation-dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
For systems in equilibrium at a temperature $T$, thermal noise and energy damping are related to $T$ through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out of equilibrium steady state: a…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which…
Fluctuations associated with relaxations in far-from-equilibrium regime is of fundamental interest for a large variety of systems within broad scales. Recent advances in techniques such as spectroscopy have generated the possibility for…
The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter.By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the…
A semi-discretization in time, according to a full implicit Euler scheme, for a 2D dissipative quasi geostrophic equation, is studied. We prove existence, uniqueness and regularity results of the solution to the predicted discretization, in…
This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…