Related papers: Exponential Entropy dissipation for weakly self-co…
In this work we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential fall offs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the…
We study qualitative behavior of the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant in order to understand isotop resonant separation. We show that the effective equation is a…
We discuss the dynamics and thermodynamics of systems with weak long-range interactions. Generically, these systems experience a violent collisionless relaxation in the Vlasov regime leading to a (usually) non-Boltzmannian quasi stationary…
Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By…
We consider an elliptic equation with the fractional Laplacian operator $(-\Delta)^{\frac{\alpha}{2}}$ in the dissipative term, a singular integral operator ${\bf A}(\cdot)$ in the nonlinear term, and an external source $f$. The key example…
We investigate the impact of weak collisions on Landau damping in the Vlasov-Poisson-Fokker-Planck system on a torus, specifically focusing on its proximity to a Maxwellian distribution. In the case where the Gevrey index satisfies…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial…
In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
The rate function for large deviations of the finite time Lyapunov exponent for the derived process in TM corresponding to a stochastic differential equation in M is related, via the Gartner-Ellis theorem, to the p-th moment Lyapunov…
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence…
Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
We show some interesting properties of tridiagonal and pentadiagonal matrices in the weak coupling limits. In the former case of this limit the ground state wave function amplitudes are identical to the Taylor expansion coefficients of the…
We deal with the problem of asymptotic distribution of first return times to shrinking balls under iteration generated by a large general class of dynamical systems called weakly Markov. Our ultimate main result is that these distributions…
We study the GENERIC (General Equation for Non-Equilibrium Reversible Irreversible Coupling) formulation of the nonlinear Vlasov-Fokker-Planck equation from the perspective of gradient flows along trajectories. After pulling back the…