We review two areas of recent research linking proportional fairness with product form networks. The areas concern, respectively, the heavy traffic and the large deviations limiting regimes for the stationary distribution of a flow model, where the flow model is a stochastic process representing the randomly varying number of document transfers present in a network sharing capacity according to...

We study energetics of a Josephson tunnel junction connecting a superconducting loop pierced by an external magnetic flux (an rf SQUID) and coupled to two independent thermal reservoirs of different temperature. In the framework of the theory of quantum dissipative systems, we analyze energy currents in stationary states. The stationary energy flow can be periodically modulated by the external ...

A system of traps is considered, each containing a large number of Bosecondensed atoms. This ensemble of traps is subject to the action of an external modulating field generating nonequilibrium nonground-state condensates. When the frequency of the modulating field is in resonance with the transition frequency between two different topological coherent modes, each trap becomes an analog of a fi...

Vibrators with deformable impact support under harmonic excitation are especially useful in the case when their stationary regimes of motion stable. This is practice by applying those vibrators to single direction manipulators and various robots space type.
 For practical application it necessary reveal dynamical qualities system from where would be possible determine optimal regimes. this...

The influence of a stationary mass flow on driven resonant MHD waves is studied for incoming slow and fast magnetosonic waves with frequencies in the slow and the Alfvén continua. In addition to the classic resonant absorption already present in a static plasma, driven resonant waves can also undergo overreflection. Depending on the strength of the equilibrium flow a variety of resonant MHD wav...

We study the high-dimensional asymptotic regimes of correlated Wishart matrices [Formula: see text], where text] is a Gaussian random matrix with and non-stationary entries. prove that under different normalizations, two distinct emerge as both grow to infinity. The first regime one central convergence, law properly renormalized becomes close in Wasserstein distance orthogonal ensemble matrix. ...