Metals are used in a variety of ways, many of which lead to dissipative releases to the environment. Such releases are relevant from both a resource use and an environmental impact perspective. We present a historical analysis of copper dissipative releases in the United States from 1975 to 2000. We situate all dissipative releases in copper's life cycle and introduce a conceptual framework by ...

We use Monte Carlo simulations to study chains of Isingand XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, wh...

Article history: Received 16 May 2014 Received in revised form 3 September 2014 Accepted 15 September 2014 Available online 22 September 2014

Abstract. We propose a new notion of weak solutions (dissipative solutions) for nonisotropic, degenerate, second order, quasi-linear parabolic equations. This class of solutions is an extension of the notion of dissipative solutions for scalar conservation laws introduced by L. C. Evans. We analyze the relationship between the notions of dissipative and entropy weak solutions for non-isotropic,...

In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of...

We consider a class of differential equations, ẍ + γẋ + g(x) = f(ωt), with ω ∈ R, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We study existence and properties of trajectories with the same quasi-periodicity as the forcing. For g(x) = x, p ∈ N, we show that, when the dissipation coefficient is large enough, there is only one such...

By examining the Fourier transform of the initial datum near the origin, we define the decay character of the datum and provide a method to study the lower and upper algebraic rates of decay of solutions to a wide class of dissipative system of equations.

A loss of passivity in the face of certain frequency dynamics (eg: high frequency dynamics) given an otherwise passive system leads to the notion of a “mixed” system. A “mixed” system is one that has a concept of small gain associated with it over those frequency intervals where passivity is lost. In this paper, a test for determining “mixedness” for linear, time-invariant systems is provided a...

It is well known that a negative feedback interconnection of passive systems is passive. However, the extension of this fundamental property to the case of negative feedback interconnection of dissipative systems, which is a more general case, remains largely unaddressed. In this paper, we demonstrate that a negative feedback interconnection of dissipative systems, under appropriate assumptions...