We study convergence to equilibrium for certain spatially inhomogenous kinetic equations, such as discrete velocity models or a linearization of a kinetic model for cometary flow. For such equations, the convergence to a unique equilibrium state is the result of, firstly, the dissipative effects of the collision operator, which morphs the solution towards an entropy minimizing local equilibrium...

Abstract The main objective of the paper is to obtain sharp Lipschitz type estimates for norm operator differences pairs and commuting maximal dissipative operators. To such estimates, we use double integrals with respect semi‐spectral measures associated . Note that situation considerably more complicated than in case functions two contractions overcome difficulties had elaborate new technique...

We study the transport and mixing properties of flows in a variety of settings, connecting the classical geometrical approach via invariant manifolds with a probabilistic approach via transfer operators. For non-divergent fluid-like flows, we demonstrate that eigenvectors of numerical transfer operators efficiently decompose the domain into invariant regions. For dissipative chaotic flows such ...

The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is discussed, and after that a derivation based upon a virtual work principle. The latter approach o...

This paper proposes the use of optical flow from a moving robot to provide force feedback to an operator’s joystick to facilitate collision free teleoperation. Optic flow is measured by a pair of wide angle cameras on board the vehicle and used to generate a virtual environmental force that is reflected to the user through the joystick, as well as feeding back into the control of the vehicle. W...

Reversibility is a concept widely studied in several research fields. Several contributions have been provided in physics and computer science. Reversible computation is characterized by means of invertible properties [1]. Reversibility is studied in computer science also in order to design less dissipative computers. The evolution of quantum systems is described by the time evolution operator ...

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is fundamental importance in many areas science: from information biology. An efficient numerical simulation large open systems two spatial dimensions a challenge. In this work, we develop tensor network method, based on an infinite Projected Entangled Pair Operato...

In this article, we present new inequalities for the numerical radius of sum two Hilbert space operators. These will enable us to obtain many generalizations and refinements some well known inequalities, including multiplicative behavior norm bounds. Among other applications, it is shown that if T accretive-dissipative, then 1/?2 ||T|| ? ?(T), where ?(?) ||?||denote usual operator norm, respect...

This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation ut + (−△) u = F (u) for initial data in the Lebesgue space L(R) with r ≥ rd , nb/(2α− d) or the homogeneous Besov space Ḃ p,∞(R ) with σ = (2α − d)/b − n/p and 1 ≤ p ≤ ∞, where α > 0, F (u) = f(u) or Q(D)f(u) with Q(D) being a homogeneous pseudo-differential operator of order d ∈ [0, 2α) and f(u) is a ...