Related papers: Numerical approximation of the Frobenius-Perron op…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…
Weyl's formulation of quantum mechanics opened the possibility of studying the dynamics of quantum systems both in infinite-dimensional and finite-dimensional systems. Based on Weyl's approach, generalized by Schwinger, a self-consistent…
The spectral properties of the Frobenius-Perron operator of one-dimensional maps are studied when approaching a weakly intermittent situation. Numerical investigation of a particular family of maps shows that the spectrum becomes extremely…
The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a…
For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality…
A single queueing system with time-dependent exponentially distributed arrival processes and exponential machine processes (Kendall notation $M_t/M_t/1$) is analyzed. Modeling the time evolution for the discrete queue-length distribution by…
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…
We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…
A semiclassical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in…
In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently…
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…
In this article we present the Durrmeyer variant of generalized Bernstein operators that preserve the constant functions involving non-negative parameter ?. We derive the approximation behaviour of these operators including global…
In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, we obtain simple necessary and sufficient conditions for the existence and uniqueness…
The problem of phase space transport which is of interest both theoretically and from the point of view of applications has been investigated extensively using geometric and probabilistic methods. Two of the important tools for this that…
This paper concerns the analysis of random second order linear differential equations. Usually, solving these equations consists of computing the first statistics of the response process, and that task has been an essential goal in the…