Search results for "equation"
showing 10 items of 4219 documents
On a topology optimization problem governed by two-dimensional Helmholtz equation
2015
The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given. peerReviewed
Numerical Determination of Intrinsic Diffusion in Fe-Cr-Al Systems
2010
The intrinsic diffusion coefficients in diffusion aluminide coatings based on Fe-30Cr were determined at 1000oC. The diffusion fluxes were given by the Nernst Planck formulae and the Darken method for multicomponent systems was applied. This paper summarizes some numerical results to determine the composition dependent diffusivities in Fe-Cr-Al systems. The method presented in this study to obtain average intrinsic diffusion coefficients is as an alternative to the Dayananda method. Our method based on empirical parameters allowed us to predict the concentration profile during the interdiffusion process.
CAD of complex passive devices composed of arbitrarily shaped waveguides using Nyström and BI-RME methods
2004
In this paper, a novel computer-aided design (CAD) tool of complex passive microwave devices in waveguide technology is proposed. Such a tool is based on a very efficient integral-equation analysis technique that provides a full-wave characterization of discontinuities between arbitrarily shaped waveguides defined by linear, circular, and/or elliptical arcs. For solving the modal analysis of such arbitrary waveguides, a modified version of the well-known boundary integral-resonant-mode expansion (BI-RME) method using the Nyström approach, instead of the traditional Galerkin version of the method of moments, is proposed, thus providing significant savings on computational costs and implement…
Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method
2000
A general theoretical formulation to analyze inhomogeneously filled waveguides with lossy dielectrics is presented in this paper. The wave equations for the tranverse-field components are written in terms of a nonself-adjoint linear operator and its adjoint. The eigenvectors of this pair of linear operators define a biorthonormal-basis, allowing for a matrix representation of the wave equations in the basis of an auxiliary waveguide. Thus, the problem of solving a system of differential equations is transformed into a linear matrix eigenvalue problem. This formulation is applied to rectangular waveguides loaded with an arbitrary number of dielectric slabs centered at arbitrary points. The c…
Some notes on a second-order random boundary value problem
2017
We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution.
Thickness Dependence of Random Field Distribution in Thin Films Made of Disordered Ferroelectrics
2005
Abstract We present the calculation of first moment E 0 and variance ΔE of distribution function of random fields in a ferroelectric of finite size. Specific calculations have been performed for the case of slab-shaped ferroelectric thin film. We have shown that E 0 and ΔE can be expressed through the integrals from first and second degree of Green's function of ferroelectric in k-space. To obtain the Green's function, we solve the differential equation minimizing Landau free energy of a ferroelectric with respect to the boundary conditions on its surfaces. We show that both E 0 and ΔE depend on film thickness L.
Crystal growth and refined Sellmeier equations over the complete transparency range of RbTiOPO4
2003
Abstract The phase-matching directions sum- and difference-frequency generations are measured in the principal planes of RbTiOPO 4 crystals grown from a halide flux. The use of crystals with a cylindrical shape and of a tunable laser source allows us to perform accurate measurements over the complete transparency range of that material, and to determine a refined set of Sellmeier equations valid for any phase-matched interaction in that crystal.
Dynamic self-assembly of photo-switchable nanoparticles
2012
Nanoparticles functionalized with photo-switchable ligands can be assembled into a broad range of structures by controlled light exposure. In particular, alternating light exposures provide the means to control formation of assemblies of various sizes and symmetries. Here, we use scaling arguments and Kinetic Monte Carlo simulations to study the evolution of reversible aggregates in a solution of periodically irradiated photo-switchable nanoparticles. Scaling estimates of the characteristic size and the mean separation of aggregates agree with the simulations. The transition probabilities in the Kinetic Monte Carlo scheme are derived from a renormalized master equation of the diffusion proc…
Analysis of small-angle scattering patterns from a commercial Al-Li alloy by means of a model incorporating a repulsive step potential
1992
Abstract Small-angle X-ray scattering measurements are reported for a commercial Al-8·49%Li-51% Cu (atomic composition) alloy solution treated at 520°C and thermally aged for several times at several temperatures. Data have been analysed by means of a model of ellipsoidal precipitate particles previously proposed by some of us and by a modification of this model where, in the interparticle interference term, allowance is made for interactions between the precipitate particles at longer range than previously. This was achieved by the introduction, in addition to the hard-sphere interaction potential, of a potential step. Our fits indicate that the precipitate particles interact through a rep…
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
2018
We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …