Abstract. This paper presents a theoretical approach for constructing a reduced model in the medium frequency range in the area of structural dynamics for a general three-dimensional anisotropic and inhomogeneous viscoelastic bounded medium. All the results presented can be used for beams, plates and shells. The boundary value problem in the frequency domain and its variational formulation are ...

The baker map is investigated by two different theories of irreversibility by Prigogine and his colleagues, namely, the Λ-transformation and complex spectral theories, and their structures are compared. In both theories, the evolution operatorU† of observables (the Koopman operator) is found to acquire dissipativity by restricting observables to an appropriate subspaceΦ of the Hilbert space L2 ...

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

We present calculations of the time-evolution driven-dissipative XYZ model using infinite Projected Entangled Pair Operator (iPEPO) method, introduced by [A. Kshetrimayum, H. Weimer and R. Orús, Nat. Commun. 8, 1291 (2017)]. explore conditions under which this approach reaches a steady state. In particular, we study where apparently converged may become unstable with increasing bond dimension t...

We construct a new class of efficient implicit–explicit (IMEX) BDFk schemes combined with scalar auxiliary variable (SAV) approach for general dissipative systems. show that these are unconditionally stable, and lead to uniform bound the numerical solution in norm based on principal linear operator free energy. Based this bound, we carry out rigorous error analysis kth-order (k=1,2,3,4,5) SAV u...

In this article we investigate the spectral properties of infinitesimal generator an infinite system master equations arising in analysis approach to equilibrium statistical mechanics. The under consideration thus consists infinitely many first-order differential governing time evolution probabilities susceptible describing jumps between eigenstates a operator with discrete point spectrum. tran...

Localized States in Driven Dissipative Systems

This article contains the outline of a 3-hour course that will be given by the authors at the ECC 2003. The course consists of 4 parts: 1. The basic concepts, 2. Linear differential systems, 3. Control in a behavioral setting, and 4. The synthesis of dissipative systems.