It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation of the theory we present new results to the following topics: an elementary derivation of Bakry-Emery type...

In the framework of fundamentals of smart materials and structures, a proper mathematical modeling of electro-kinetic transport phenomena in micro-structures adhering to the law of conservation of mass is suggested. The reference multiphase medium is described by a nonlinear Poisson–Nernst–Planck model stated in a heterogeneous pore-particle space disjoint by the interface. For physical consist...

the mechanical aspect of entropy-exergy relationship, together with the thermal aspect usually consid-ered, leads to an extended formulation of physical exergy based on both maximum useful work and maximum useful heat that are the outcome of available energy of a thermodynamic system. this approach suggests that a mechanical entropy can be studied, in addition to the already used thermal entrop...

In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed point at the entrance, and prescribing the pressure at the exit of the nozzle. The Euler-Poisson system for subsonic flow is a hyperbolic-elliptic coupled non...

Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of ‘equipartition’ may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical struct...

‎Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models‎. ‎The model is composed of a univariate Poisson variable‎, ‎and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component‎. ‎Two characterizations of this model are shown‎, ‎...

Fundamental relations between information and estimation have been established in the literature for the discrete-time Gaussian and Poisson channels. In this work, we demonstrate that such relations hold for a much larger class of observation models. We introduce the natural family of discrete-time Lévy channels where the distribution of the output conditioned on the input is infinitely divisib...

The competition between strength and correlation of coupling terms in a Hamiltonian defines numerous phenomenological models exhibiting spectral properties interpolating those Poisson (integrable) Wigner-Dyson (chaotic) ensembles. It is important to understand how the off-diagonal evolve as one or more symmetries an integrable system are explicitly broken. We introduce deformed ensemble demonst...

RU4LEtWH&!4sl-A'ERG RU4LEtWH&!4sl Fig. 1. Fig. 1. Entropy per cell as function of average run length. Entropy per cell as function of average run length. distributed: for tl 2 0 for tl < 0 where t, is the (continuous) run length. The average run length is f, = 6. (20) Now, suppose the continuous run length tl is quantized to obtain the discrete run length t : t = [t1] + 1 (21) where [tl] = larg...