We study a Helmholtz-type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a twodimensional periodic medium; the defect is infinitely extended and aligned with one of the coordinate axes. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, un...

The EM algorithm is a commonly cited solution in the literature for the problem of maximum likelihood estimation of covariance matrices under a Toeplitz constraint. In this paper, the solution is extended to the case of twodimensional signals, where spatial stationarity enforces a Toeplitz-block-Toeplitz structure on the covariance matrix. A further generalisation which is presented involves th...

A multi-layered environment is a representation of the walkable space in a 3D virtual environment that comprises a set of twodimensional layers together with the locations where the different layers touch, which are called connections. This representation can be used for crowd simulations, e.g. to determine evacuation times in complex buildings. Since the execution times of many algorithms depe...

An efficient numerical method is developed for modal analysis of twodimensional photonic crystal waveguides. Using the Dirichlet-to-Neumann (DtN) map of the supercell, the waveguide modes are solved from an eigenvalue problem formulated on two boundaries of the supercell, leading to significantly smaller matrices when it is discretized. The eigenvalue problem is linear even when the medium is d...

The problem considered here is to determine the shape of a symmetric twodimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process...

We consider the singular limit of a perturbed Allen–Cahn model on a bounded twodimensional domain: { ut = ε2Δu− 2(u− εa)(u2 − 1), x ∈ Ω ⊂ R2 ∂nu = 0, x ∈ ∂Ω where ε is a small parameter and a is an O(1) quantity. We study equilibrium solutions that have the form of a curved interface. Using singular perturbation techniques, we fully characterize the stability of such an equilibrium in terms of ...

We propose a three-field formulation for efficiently solving a twodimensional Stokes problem in the case of nonstandard boundary conditions. More specifically, we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary. The proposed computational methodology consists in reformulating the considered bounda...

Array operations are useful in a large number of important scientific codes, such as molecular dynamics, finite-element methods, climate modeling, etc. It is a challenging problem to provide an efficient data distribution for irregular problems. Multi-dimensional (MD) sparse array operations can be used in atmosphere and ocean sciences, image processing, etc., and have been an extensively inves...

AbstructThis paper addresses the application of genetic algorithm (GA)-based optimization techniques to problems in image and video coding, demonstrating the success of GA’s when used to solve real design problems with both performance and implementation constraints. Issues considered include problem representation, problem complexity, and fitness evaluation methods. For off-line problems, such...