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A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the...
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term ( which does not share the...
Low order edge elements are widely used for electromagnetic field problems. Higher order edge approximations are receiving increasing interest but their definition become rather complex.
In this paper we propose a simple definition for Whitney edge elements of polynomial degree higher than one.
We give a geometrical localization of all degrees of freedom over particular edges and provide
a basis for these elements on simplicial meshes.
As for Whitney edge elements of degree one, the basis is...
We propose transmission conditions of order 1, 2 and 3
approximating the shielding behaviour of thin conducting curved
sheets for the magneto-quasistatic eddy current model in 2D. This
model reduction applies to sheets whose thicknesses ε are at
the order of the skin depth or essentially smaller. The sheet has
itself not to be resolved, only its midline is represented by an
interface. The computation is directly in one step with almost no
additional cost. We prove the well-posedness w.r.t. to...
We propose transmission conditions of order 1, 2 and 3
approximating the shielding behaviour of thin conducting curved
sheets for the magneto-quasistatic eddy current model in 2D. This
model reduction applies to sheets whose thicknesses ε are at
the order of the skin depth or essentially smaller. The sheet has
itself not to be resolved, only its midline is represented by an
interface. The computation is directly in one step with almost no
additional cost. We prove the well-posedness w.r.t. to...
Cell motility is an integral part of a diverse set of biological processes. The quest for
mathematical models of cell motility has prompted the development of automated approaches
for gathering quantitative data on cell morphology, and the distribution of molecular
players involved in cell motility. Here we review recent approaches for quantifying cell
motility, including automated cell segmentation and tracking. Secondly, we present our own
novel...
We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies O(1 / ε) and amplitude O(1), over long time intervals O(1 / ε), in the limit ε → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].
The Maxwell equations in a heterogeneous medium are studied. Nguetseng’s method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.
The Maxwell equations with uniformly monotone nonlinear electric conductivity in a heterogeneous medium, which may be non-periodic, are homogenized by two-scale convergence. We introduce a new set of function spaces appropriate for the nonlinear Maxwell system. New compactness results, of two-scale type, are proved for these function spaces. We prove existence of a unique solution for the heterogeneous system as well as for the homogenized system. We also prove that the solutions of the heterogeneous...
In this paper, an artificial neural network (ANN) based on hybrid algorithm combining
particle swarm optimization (PSO) with back-propagation (BP) is proposed to forecast the
daily streamflows in a catchment located in a semi-arid region in Morocco. The PSO
algorithm has a rapid convergence during the initial stages of a global search, while the
BP algorithm can achieve faster convergent speed around the global optimum. By combining
the PSO with...
We give an algebraic description of (wave) fronts that appear in strictly hyperbolic Cauchy problems. A concrete form of a defining function of the wave front issued from the initial algebraic variety is obtained with the aid of Gauss-Manin systems satisfied by Leray's residues.
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