We introduce a family of heavy-traffic regimes for large-scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to economies-of-scales, so that the system utilization approaches 100% while congestion remains limited. We obt...

This paper gives a survey of recent results on generalized Jackson networks , where classical exponential or i.i.d. assumptions on services and routings are replaced by stationary and ergodic assumptions. We rst show that the most basic features of the network may exhibit unexpected behavior. Several probabilistic properties are then discussed, including a strong law of large numbers for the nu...

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively diierent regimes are observed, corresponding to intermittent and regular behaviour. In the boundary between them, the mean value of the relevant variable is...

We consider the propagation of extremely short pulses through a di-electric thin film containing resonant atoms (two level atoms) with permanent dipole. Assuming that the film width is less than the field wave length, we can solve the wave equation and reduce the problem to a system of generalized Bloch equations describing the resonant atoms. We compute the stationary solutions for a constant ...

A numerical scheme for the one dimensional stationary Schrödinger-Poisson model is described. The scheme is used to simulate a Resonant Tunneling Diode and provides an important reduction of the simulation time. The improvement is twofold. First the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the WKB asymptotics. Then the discr...

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is...

Nonlinear Schrödinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schrödinger equation describes coherent states. Such modes are also named topological because the solutions corresponding to different spectral levels have principally different spatial dependences. The theory of resonant e...

Figure rotation substantially increases the fraction of stochastic orbits in triaxial systems. This increase is most dramatic in systems with shallow cusps showing that it is not a direct consequence of scattering by a central density cusp or black hole. In a recent study of stationary triaxial potentials (Valluri & Merritt 1998) it was found that the most important elements that define the str...

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and zigzag ins...

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process X ≡ {X(t) : t ∈ R} with stationary increments and variance function σ X(·), equipped with a deterministic drift c > 0, reflected at 0: Q (c) X (t) = sup −∞<s≤t (X(t)−X(s)− c(t− s)). We study the resulting stationary workload processQ (c...