We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the mathematical theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of tot...

Sufficient conditions under which a class of nonlinear discrete-time systems which are non-affine in the control input and the states can be rendered locally dissipative are derived. Two methodologies in order to render nonlinear single-input single-output discrete-time systems locally dissipative are given. Dissipativity is seen as a “perturbation” of the storage energy invariance or the feedb...

We study both dissipative and nondissipative quantum transport in discrete Brownian rectifiers being driven by nonthermal noise that is unbiased on average. In the absence of dissipation the current is always zero and the ballistic diffusion changes into normal diffusion. The dissipative quantum dynamics exhibits current (with distinctive reversals) as a result of the cooperative interplay betw...

We present a novel generic framework to approximate the nonequilibrium steady states of dissipative quantum many-body systems. It is based on the variational minimization of a suitable norm of the quantum master equation describing the dynamics. We show how to apply this approach to different classes of variational quantum states and demonstrate its successful application to a dissipative exten...

The angular cross correlation function is investigated for fluctuating cross sections in dissipative heavy ion colhslons. We consider the dissipative colhslon in the framework of formation and decay of the intermediate dlnuclear system while the elastic scattering phase shifts are given in terms of the deflection functmn q~ and its first derlvat~ve ~, both taken at the grazing angular momentum....

Until recent years it was widely held that damage to part of the nerve supply of a voluntary muscle had a permanent effect and that the surviving nerve fibres were unable to reinnervate muscle fibres deprived of their nerve supply. It was assumed that the only possibility of recovery of power in the muscle was by hypertrophy of muscle fibres whose nerve supply had escaped damage. The problen ha...

We present a novel class of theories where supersymmetry is only preserved in a partial (non-isolated) sector. The supersymmetric sector consists of CFT bound-states that can coexist with fundamental states which do not respect supersymmetry. These theories arise from the 4D holographic interpretation of 5D theories in a slice of AdS where supersymmetry is broken on the UV boundary. In particul...