Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential ill-posedness, the stability estimate obtained is optimal. AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90     

The inverse electromagnetic scattering problem by a penetrable cylinder at oblique incidence

In this work, we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We consider the indirect method and simple representations for the electric and the magnetic fields in order to derive a system of five integral equations, four on the boundary of the cylinder and one on the unit circle where we measure the far-field pattern of the scattered wave. We solve the system iteratively by linearizing only the far-field equation. Numerical results illustrate the feasibility of the proposed scheme.     

Inverse acoustical characterization of natural jute sound absorbing material by the particle swarm optimization method

For modeling of jute as acoustic material, knowledge of its non-acoustical parameters like porosity, tortuosity, air flow resistivity, thermal and viscous characteristic lengths is a prime requisite. Measurement of these non-acoustical parameters is not straightforward and involves a dedicated measurement setup. So in order to overcome this issue, the inverse acoustical characterization can be used. In this paper, the particle swarm optimization method (PSO) is used as an optimization method. This method estimates the non-acoustical parameters of jute material in felt form by minimizing the error between experimental and theoretical sound absorption data. In this work, the impedance prediction models for fibrous materials like Johnson–Champoux–Allard model with rigid and limp frame and Garai–Pompoli model is used for sound absorption coefficient calculation by the transfer matrix method along with the PSO. The inverse estimated non-acoustical parameters for jute material are then compared with estimated and experimentally measured parameters for jute felts. Using these inversely predicted parameters, sound absorption of multilayer sound absorbers is also studied.     

Stationary two-black-hole configurations: A non-existence proof

Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for equilibrium configurations consisting of two aligned rotating black holes. Our discussion is principally aimed at developing the ideas of the proof and summarizing the results of two preceding papers (Neugebauer and Hennig, 2009 [2], Hennig and Neugebauer, 2011 [3]). From a mathematical point of view, this paper is a further example (Meinel et al., (2008) [29]) for the application of the inverse (“scattering”) method to a non-linear elliptic differential equation.     

Direct numerical method for an inverse problem of a parabolic partial differential equation

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.     

Textile porosity determination based on a nonlinear heat and moisture transfer model

The inverse problems of textile materials design on heat and moisture transfer properties are important and indispensable in applications in the body-clothing-environment system. We present an inverse problem of textile porosity determination (IPTPD) based on a nonlinear heat and moisture transfer model. Adopting the idea of the least-squares, the mathematical formulation of IPTPD is deduced to a regularized optimization problem with collocation method applied. The continuity of the regularized minimization problem is proved. By means of genetic algorithm (GA), the approximate solution of the IPTPD is numerically obtained. To reduce the computational cost, an improved algorithm based on BP neural network with GA is proposed in the numerical simulation. Compared with the direct GA searching, the computational cost is greatly reduced, which presents a similar result.     

Study of modified silicas by inverse gas chromatography part II: Influence of chain length on surface properties of silicas grafted withα−ω diols

Summary The surface properties of silicas modified with – diols having between 4 and 16 carbon atoms were investigated by inverse gas chromatography. It is shown, that the value of the dispersive component of the surface energy does not change monotonously: a minimum value is recorded when the surface is covered by a monolayer of methylene groups. Further, when measuring the adsorption enthalpies of polar probes, an alternation of their H values is observed: grafts having an odd number of carbon atoms systematically show higher H values than the others. A trans-trans configuration of the grafted chains which allows optimum interactions is proposed, suggesting a preferential diesterification reaction of both terminal hydroxyl groups of odd diols.     

Magnetic Polymer Composite Particles Via In situ Inverse Miniemulsion Polymerization Process

We aimed at preparing magnetic iron oxide particles by the oxidation-precipitation method in order to encapsulate these particles in polymer matrices composed of poly(acrylamide-styrene sulfonic acid sodium salt). Nanocomposites were synthesized by the incorporation of surface treated magnetic nanoparticles in the synthesized polymers via in situ inverse mini-emulsion polymerization process. The study parameter was the ionic monomer content in the synthesized polymers. The structure and the morphology of the magnetic nanogels were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), dynamic light scattering (DLS), thermal gravimetric analysis (TGA) and scanning electron microscopy (SEM). FTIR and XRD showed that pure magnetite was formed and successfully encapsulated in the composite nanoparticles. The polymer encapsulation could reduce the susceptibility to leaching and could protect the magnetite particle surfaces from oxidation. The ionic monomer content had a great effect on the magnetization behavior. Magnetite prepared by the oxidation precipitation method, of 50 nm mean particle size, was embedded successfully into the polymer nanogels with a reasonable magnetic response, as proved by vibrating sample magnetometer measurement. Magnetic nanocomposites were proven to be super-ferromagnetic materials.