Stable Determination of the Discontinuous Conductivity Coefficient of a Parabolic Equation

We deal with the problem of determining a time varying inclusion within a thermal conductor. In particular we study the continuous dependance of the inclusion from the Dirichlet-to-Neumann map. Under a priori regularity assumptions on the unknown defect we establish logarithmic stability estimates.Comment: 36 page

Fundamental material properties of the 2LiBH4-MgH2 reactive hydride composite for hydrogen storage: (I) Thermodynamic and heat transfer properties

Thermodynamic and heat transfer properties of the 2LiBH4-MgH2 composite (Li-RHC) system are experimentally determined and studied as a basis for the design and development of hydrogen storage tanks. Besides the determination and discussion of the properties, different measurement methods are applied and compared to each other. Regarding thermodynamics, reaction enthalpy and entropy are determined by pressure-concentration-isotherms and coupled manometric-calorimetric measurements. For thermal diffusivity calculation, the specific heat capacity is measured by high-pressure differential scanning calorimetry and the effective thermal conductivity is determined by the transient plane source technique and in situ thermocell. Based on the results obtained from the thermodynamics and the assessment of the heat transfer properties, the reaction mechanism of the Li-RHC and the issues related to the scale-up for larger hydrogen storage systems are discussed in detail.Fil: Jepsen, Julian. Helmholtz-Zentrum Geesthacht; AlemaniaFil: Milanese, Chiara. University of Pavia; ItaliaFil: Puszkiel, Julián Atilio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Helmholtz-Zentrum Geesthacht; AlemaniaFil: Girella, Alessandro. University of Pavia; ItaliaFil: Schiavo, Benedetto. Universidad de Palermo; Argentina. Istituto per le Tecnologie Avanzate; ItaliaFil: Lozano, Gustavo A.. Helmholtz-Zentrum Geesthacht; Alemania. BASF; AlemaniaFil: Capurso, Giovanni. Helmholtz-Zentrum Geesthacht; AlemaniaFil: Von Colbe, José M. Bellosta. Helmholtz-Zentrum Geesthacht; AlemaniaFil: Marini, Amedeo. University of Pavia; ItaliaFil: Kabelac, Stephan. Leibniz Universität Hannover; AlemaniaFil: Dornheim, Martin. Helmholtz-Zentrum Geesthacht; AlemaniaFil: Klassen, Thomas. Helmholtz-Zentrum Geesthacht; Alemani

Inverse Problems for the Heat Equation Using Conjugate Gradient Methods

In many engineering systems, e.g., in heat exchanges, reflux condensers, combustion chambers, nuclear vessels, etc. concerned with high temperatures/pressures/loads and/or hostile environments, certain properties of the physical medium, geometry, boundary and initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible. In such a situation, one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available. The purpose of this thesis is to determine the unknown space-dependent coefficients and/or initial temperature in inverse problems of heat transfer, especially to simultaneously reconstruct several unknown quantities. These inverse problems are investigated from additional pieces of information, such as internal temperature observations, final measured temperature and time-integral temperature measurement. The main difficulty involved in the solution of these inverse problems is that they are typically ill-posed. Thus, their solutions are unstable under small perturbations of the input data and classical numerical techniques fail to provide accurate and stable numerical results. Throughout this thesis, the inverse problems are transformed into optimization problems, and their minimizers are shown to exist. A variational method is employed to obtain their Fréchet gradients with respect to the unknown quantities. Based on this gradient, the conjugate gradient method (CGM) is established together with the adjoint and sensitivity problems. The stability of the numerical solution is investigated by introducing Gaussian random noise into the input measured data. Accurate and stable numerical solutions are obtained when using the CGM regularized by the discrepancy principle

Recovering time-dependent inclusion in heat conductive bodies by a dynamical probe method

We consider an inverse boundary value problem for the heat equation $\partial_t v = {\rm div}_x\,(\gamma\nabla_x v)$ in $(0,T)\times\Omega$, where $\Omega$ is a bounded domain of $R^3$, the heat conductivity $\gamma(t,x)$ admits a surface of discontinuity which depends on time and without any spatial smoothness. The reconstruction and, implicitly, uniqueness of the moving inclusion, from the knowledge of the Dirichlet-to-Neumann operator, is realised by a dynamical probe method based on the construction of fundamental solutions of the elliptic operator $-\Delta + \tau^2\cdot$, where $\tau$ is a large real parameter, and a couple of inequalities relating data and integrals on the inclusion, which are similar to the elliptic case. That these solutions depend not only on the pole of the fundamental solution, but on the large parameter $\tau$ also, allows the method to work in the very general situation

Stable determination of an inclusion in an elastic body by boundary measurements (unabridged)

We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion are constant and different from those of the surrounding material. Under mild a-priori regularity assumptions on the unknown defect, we establish a logarithmic stability estimate. For the proof, we extend the approach used for electrical and thermal conductors in a novel way. Main tools are propagation of smallness arguments based on three-spheres inequality for solutions to the Lam\'e system and refined local approximation of the fundamental solution of the Lam\'e system in presence of an inclusion.Comment: 58 pages, 4 figures. This is the extended, and revised, version of a paper submitted for publication in abridged for

Numerical Simulations of Gravity-Driven Fingering in Unsaturated Porous Media Using a Non-Equilibrium Model

This is a computational study of gravity-driven fingering instabilities in unsaturated porous media. The governing equations and corresponding numerical scheme are based on the work of Nieber et al. [Ch. 23 in Soil Water Repellency, eds. C. J. Ritsema and L. W. Dekker, Elsevier, 2003] in which non-monotonic saturation profiles are obtained by supplementing the Richards equation with a non-equilibrium capillary pressure-saturation relationship, as well as including hysteretic effects. The first part of the study takes an extensive look at the sensitivity of the finger solutions to certain key parameters in the model such as capillary shape parameter, initial saturation, and capillary relaxation coefficient. The second part is a comparison to published experimental results that demonstrates the ability of the model to capture realistic fingering behaviour