Model-hierarchical column generation and heuristic for the routing and wavelength assignment problem

The routing and wavelength assignment (RWA) problem typically occurs in wavelength division multiplexing optical networks. Given a number of available wavelengths, we consider here the problem of maximising the number of accepted connections with respect to the clash and continuity constraints. We first propose a new strategy which combines two existing models. This leads to an improved column generation scheme. We also present two heuristics to compute feasible solutions: a hybrid heuristic and the integer solution at the root node of the column generation. Our approaches are compared with the best existing results on a set of classic RWA instances.     

On a Class of Elliptic Problems and Its Application to Heat Transfer in Nonconvex Bodies

This work presents a procedure for constructing the solution to a class of problems with application to heat transfer processes in which the energy reemission is not negligible. Such problems are characterized by a Poisson equation subjected to certain nonlinear boundary conditions. The solution is constructed from a sequence whose elements may be obtained from a minimum principle. Some practical situations are presented.     

Technical note: A fourth‐order finite difference scheme for a system of a 2D nonlinear elliptic partial differential equations

In this article we present a fourth‐order finite difference scheme, for a system of two‐dimensional, second‐order, nonlinear elliptic partial differential equations with mixed spatial derivative terms, using 13‐point stencils with a uniform mesh size h on a square region R subject to Dirichlet boundary conditions. The scheme of order h⁴ is derived using the local solution of the system on a single stencil. The resulting system of algebraic equations can be solved by iterative methods. The difference scheme can be easily modified to obtain formulae for grid points near the boundary. Computational results are given to demonstrate the performance of the scheme on some problems including Navier‐Stokes equations. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 43–53, 2001     

Kinetic and mechanistic study of oxidation of diethylamine by N‐sodio‐N‐bromobenzene sulphonamide (Bromamine‐B) in acid solution: Catalyzed by Ru(III)

Kinetics of oxidation of diethylamine (DEA) by Bromamine‐B (BAB) has been investigated at 303 K in acid solution with Ru(III) as catalyst. The oxidation behavior obeys the rate law, rate = k [BAB] [DEA] [Ru(III)] [H⁺]^−x where ‘x’ is less than unity indicating retardation of rate by [H⁺]. Added halide ions, the reaction product benzenesulphonamide, variation of ionic strength and dielectric constant of the medium do not have any significant effect on the rate. The protonation constant of monobromamine‐B evaluated for the reaction is 32.3 at 303 K. Activation parameters have been evaluated from Arrhenius plot. A mechanism consistent with experimental results has been proposed. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 744–752, 1999     

The single-mode rate equations for semiconductor lasers with thermal effects

A mathematical model describing the coupling of electrical,optical and thermal effects in semiconductor lasers is introduced.Numerical and asymptotic solutions are derived, including expressionsfor key physical quantities such as the initial time delay,the frequency of spike oscillation and the temperature rise,together with its influence on the photon density, the electronconcentration and the threshold current. The consequences ofthermal effects in reducing efficiency are thus quantified.