Search results for "perturbed domain"

showing 3 items of 3 documents

Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface

2019

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ?. We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For ? small, we prove that the effective conductivity can be represented as a convergent power series in ? and we determine the coefficients in terms of the solutions of explicit systems of integral equations.

Materials scienceasymptotic expansionGeneral MathematicsThermal resistanceInterface (computing)Composite numberperiodic dilute compositeConductivityEffective conductivitySettore MAT/05 - Analisi MatematicaPhase (matter)Mathematics (all)non-ideal contact conditionComposite materialSeries expansionsingularly perturbed domainasymptotic expansion; Effective conductivity; non-ideal contact condition; periodic dilute composite; singularly perturbed domain; Mathematics (all)
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Multi-parameter analysis of the obstacle scattering problem

2022

Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.

integral equationsshape sensitivity analysisassociated exterior Dirichlet problemDirichlet-to-Neumann operatorApplied MathematicsHelmholtz equation; acoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; shape sensitivity analysis; perturbed domain; integral equationsacoustic scatteringComputer Science ApplicationsTheoretical Computer Scienceperturbed domainMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaSignal ProcessingFOS: Mathematicsacoustic scattering; associated exterior Dirichlet problem; Dirichlet-to-Neumann operator; Helmholtz equation; integral equations; perturbed domain; shape sensitivity analysisHelmholtz equation35J25 35J05 35P25 31B10 45A05Mathematical PhysicsAnalysis of PDEs (math.AP)
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Dependence of effective properties upon regular perturbations

2022

In this survey, we present some results on the behavior of effective properties in presence of perturbations of the geometric and physical parameters. We first consider the case of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders. We show the results of [43], where it is proven that the average longitudinal flow depends real analytically upon perturbations of the periodicity structure and the cross section of the cylinders. Next, we turn to the effective conductivity of a periodic two-phase composite with ideal contact at the interface. The composite is obtained by introducing a periodic set of inclusions into an infinite homogeneous matrix made of a di…

perturbed domainintegral equationsSettore MAT/05 - Analisi Matematicatransmission problemEffective conductivity; Integral equations; Longitudinal flow; Periodic composite; Perturbed domain; Transmission problemperiodic compositeeffective conductivityLongitudinal flow
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