Given a dissipative system behavior with general supply rate, say a Σ-dissipative system, we propose a balanced truncation method to obtain a reduced-order system behavior which is again Σ-dissipative. This methods applies to driving variable representations of systems. A one-step error bound formula is discussed.

We realize an absolute position control of drifting dissipative optical solitons by injecting an incoherent amplitude parameter gradient onto the nonlinear optical system. This allows for two-dimensional, arbitrary control patterns. The control of the soliton drift velocity is studied applying a periodic, hexagonally shaped modulation. The guiding of dissipative solitons by one- and two-dimensi...

Conservative, Dissipative: Conservative dynamical systems (on a compact phase space) are those that preserve a finite measure equivalent to volume. Hamiltonian dynamical systems are important examples of conservative systems. Systems that are not conservative are called dissipative. Finding physically meaningful invariant measures for dissipative maps is a central object of study in smooth ergo...

A dissipative particle swarm optimization is developed according to the self-organization of dissipative structure. The negative entropy is introduced to construct an opening dissipative system that is far-from-equilibrium so as to driving the irreversible evolution process with better fitness. The testing of two multimodal functions indicates it improves the performance effectively.

We consider hermitian dissipative mappings δ which are densely defined in unital C∗-algebras A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij) → (δ(aij)), are dissipative on the n by n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completel...

Stability analysis of the numerical Method of characteristics applied to energy-preserving systems. Abstract We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Eu...

Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial st...

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the...

Excitation functions for the strongly dissipative collision 19F (Elab = 135 − 140 MeV)+89Y with an energy step of 250 keV in the lab. system have been measured. The data are consistent with previous measurements and exhibit oscillations, which are interpreted as an indication of quantum chaotic phenomena in dissipative heavy-ion collisions. The Fourier component of the energy autocorrelation of...

We propose a new perspective on the intermittency in weakly dissipative systems. It is focused on the elementary (burst-like) event separating states with different properties. This event is seen as a real-space-time manifestation of an instanton connecting in an extended space-time states with distinct topology of the idealized version of the system.