We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier–Stokes equations. These ideas are motivated by the fact that dissipative dynamical systems possess finite numbers of determining parameters ...

We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expandin...

In the thermodynamic limit, steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between coherent and driven-dissipative dynamics. Here, we consider Markovian elucidate structures Liouville superoperator that generates time evolution. many cases interest, an operator-basis transformation bring Liouvillian into block-triangular form, m...

Coherent transport in mesoscopic devices is well described by the Schrödinger equation supplemented by open boundary conditions. When electronic devices are operated at room temperature, however, a realistic transport model needs to include carrier scattering. In this work the kinetic equation for the Wigner function is employed as a model for dissipative quantum transport. Carrier scattering i...

This article studies the telegrapher’s equations with boundary port variables. Firstly, a link is made between the telegrapher’s equations and a skewsymmetric linear operator on a spatial domain. Associated to this linear operator is a Dirac structure which includes the port variables on the boundary of this spatial domain. Secondly, we present all partitions of the port variables into inputs a...

Large time behavior of solutions to abstract differential equations is studied. The results give sufficient condition for the global existence of a solution to an abstract dynamical system (evolution problem), for this solution to be bounded, and for this solution to have a finite limit as t → ∞, in particular, sufficient conditions for this limit to be zero. The evolution problem is: u̇ = A(t)u...

Government information resource is the foundation of e-government, and government information resource organization pattern is the key factor that affects sustainable development of e-government. At present, a lack of the systematic plan in government information resource organization exists universally. The primary reason is that systematization and formalization of research on government info...

We study the time reversal phenomenon in a homogeneous and non-dissipative medium containing sound-hard obstacles. We propose two mathematical models of time reversal mirrors in the frequency domain. The first one takes into account the interactions between the mirror and the obstacles. The second one provides an approximation of these interactions. We prove, in both cases, that the time revers...

We study large-time asymptotic behavior of solutions to the Cauchy problem for a model of nonlinear dissipative evolution equation. The linear part is a pseudodifferential operator and the nonlinearity is a cubic pseudodifferential operator defined by means of the inverse Fourier transformation and represented by bilinear and trilinear forms with respect to the direct Fourier transform of the d...

A linear model for an age-structured population with random diiusion in a bounded domain R n is studied in the semigroup framework in L 2. Three diierent approaches to establishing well-posedness of the problem are presented. Two of them involve applying known results on the m-dissipativeness of the sum of two m-dissipative operators to the population operator and the diiusion operator. 1. Intr...