We show that the coupled balance equations for a large class of dissipative materials can be cast in the form of GENERIC (General Equations for Non-Equilibrium Reversible Irreversible Coupling). In dissipative solids, also called generalized standard materials, the state of a material point is decribed by dissipative internal variables in addition to the elastic deformation and the temperature....

In this paper we explore connections between the underlying physics of dissipative systems and nonlinear robust control. In particular, we concentrate on the problem of stabilizing stationary solutions of nonlinear dissipative systems with states distributed in space. Dissipative systems are equipped with an entropy function which we employ to relate dissipation with the Hamilton-Jacobi-Bellman...

The 2D quasi-geostrophic (QG) equation is a two dimensional model of the 3D incompressible Euler equations. When dissipation is included in the model then solutions always exist if the dissipation’s wave number dependence is super-linear. Below this critical power the dissipation appears to be insufficient. For instance, it is not known if the critical dissipative QG equation has global smooth ...

This paper deals with the dissipative problem for uncertain time-delay networked control systems with both multiple measurement and control packet dropouts. The uncertainty is assumed to satisfy a dissipative inequality, and the multiple measurement and control packet dropouts are described by two independent Bernoulli distributed sequences. By utilizing the Lyapunov functional method, a robust...

The method of product integration is used to obtain solutions to the time dependent Banach space differential equation u'(t) = A(t)(u(t)), iäO, where A is a function from [0, oo) to the set of nonlinear operators from the Banach space X to itself and « is a function from [0, oo) to X. The main requirements placed on A are that A is m-dissipative and product stable on its domain. Applications ar...

In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...

Our contribution in this paper is twofold. In the first part, we study Lyapunov functions when a plant is interconnected with a dissipative stabilizing controller. In the second, we present results on data-driven approach to dissipative systems. In particular, we provide conditions under which an observed trajectory can be used to determine whether a system is dissipative with respect to a give...

We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) avalanche distributions, in general, do not follow simple power laws, but rather have the form P(s) approximately s(-tau(s))(ln s)(gamma)f(s/s(c)), with f a cutoff function; (2) the exponents for sizes of dissipative av...

We derive a phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets. The theory captures the reactive and dissipative current-induced torques and the conventional effects of magnetic fields and damping. A Walker ansatz describes the dc current-induced domain-wall motion when there is no dissipation. If magnetic damping and dissipative torques are included...

The method of product integration is used to obtain solutions to the time dependent Banach space differential equation u'(t) = A(t)(u(t)), iäO, where A is a function from [0, oo) to the set of nonlinear operators from the Banach space X to itself and « is a function from [0, oo) to X. The main requirements placed on A are that A is m-dissipative and product stable on its domain. Applications ar...