Inverse resistivity problem: Geoelectric uncertainty principle and numerical reconstruction method

Mathematical model of vertical electrical sounding by using resistivity method is studied. The model leads to an inverse problem of determination of the unknown leading coefficient (conductivity) of the elliptic equation in R²$R^2$ in a slab. The direct problem is obtained in the form of mixed BVP in axisymmetric cylindrical coordinates. The additional (available measured) data is given on the upper boundary of the slab, in the form of tangential derivative. Due to ill-conditionedness of the considered inverse problem the logarithmic transformation is applied to the unknown coefficient and the inverse problem is studied as a minimization problem for the cost functional, with respect to the reflection coefficient. The Conjugate Gradient method (CGM) is applied for the numerical solution of this problem. Computational experiments were performed with noise free and random noisy data.     

Temperature dependence of the rate constant of hydrogen isotope interactions with a lithium capillary-porous system under reactor irradiation

Experiments with a sample of a lithium capillary-porous system (CPS) were performed at the reactor IVG-1.M of the Institute of Atomic Energy NNC RK to study the effects of neutron irradiation on the parameters of hydrogen isotope interactions with a lithium CPS. The absorption technique was used during the experiments, and this technique allowed the temperature dependences of the hydrogen isotope interaction rate constants with the lithium CPS to be obtained under various reactor powers. The obtained dependencies were used to determine the main interaction parameters: the activation energies and the pre-exponents of the Arrhenius dependence of the hydrogen interaction rate constants with lithium and the lithium CPS. An increase of the hydrogen isotope interaction rate with the lithium CPS was observed under reactor irradiation.