Analytical characterization of a quasi-lossless Raman-amplified fibre transmission scheme

In this paper, we explore theoretically a novel amplifier scheme, that combines second order bidirectional pumping and fiber Bragg grating reflectors to achieve quasi-lossless transmission over long spans. The scheme is shown to significantly reduce the signal power variation over the span as compared to commonly used schemes with the same number of pump sources. It is concluded that it can be practical to analyze a simplified system of three equations, obtained by neglecting noise terms, that would allow us to better understand the physical mechanisms and to find analytical estimates for the required pump power or the power variations along the fibre span

Call admission control algorithms in OFDM-based wireless multiservice networks

Orthogonal frequency division multiplexing (OFDM) is becoming a fundamental technology in future generation wireless communications. Call admission control is an effective mechanism to guarantee resilient, efficient, and quality-of-service (QoS) services in wireless mobile networks. In this paper, we present several call admission control algorithms for OFDM-based wireless multiservice networks. Call connection requests are differentiated into narrow-band calls and wide-band calls. For either class of calls, the traffic process is characterized as batch arrival since each call may request multiple subcarriers to satisfy its QoS requirement. The batch size is a random variable following a probability mass function (PMF) with realistically maximum value. In addition, the service times for wide-band and narrow-band calls are different. Following this, we perform a tele-traffic queueing analysis for OFDM-based wireless multiservice networks. The formulae for the significant performance metrics call blocking probability and bandwidth utilization are developed. Numerical investigations are presented to demonstrate the interaction between key parameters and performance metrics. The performance tradeoff among different call admission control algorithms is discussed. Moreover, the analytical model has been validated by simulation. The methodology as well as the result provides an efficient tool for planning next-generation OFDM-based broadband wireless access systems.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

Computation of rare transitions in the barotropic quasi-geostrophic equations

We investigate the theoretical and numerical computation of rare transitions in simple geophysical turbulent models. We consider the barotropic quasi-geostrophic and two-dimensional Navier–Stokes equations in regimes where bistability between two coexisting large-scale attractors exist. By means of large deviations and instanton theory with the use of an Onsager–Machlup path integral formalism for the transition probability, we show how one can directly compute the most probable transition path between two coexisting attractors analytically in an equilibrium (Langevin) framework and numerically otherWe adapt a class of numerical optimization algorithms known as minimum action methods to simple geophysical turbulent models. We show that by numerically minimizing an appropriate action functional in a large deviation limit, one can predict the most likely transition path for a rare transition between two states. By considering examples where theoretical predictions can be made, we show that the minimum action method successfully predicts the most likely transition path. Finally, we discuss the application and extension of such numerical optimization schemes to the computation of rare transitions observed in direct numerical simulations and experiments and to other, more complex, turbulent systems.