Identification of a heterogeneous orthotropic conductivity in a rectangular domain

This paper investigates the problem of identifying a heterogeneous transient orthotropic thermal conductivity in a two-dimensional rectangular domain using initial and Dirichlet boundary conditions and fluxes as overdetermination conditions. The measurement data represented by the heat fluxes are shown to ensure the unique solvability of the inverse problem solution. The finite-difference method is employed as the direct solver which is fed iteratively in a nonlinear minimization routine. Exact and noisy input data are inverted numerically. Numerical results indicate that accurate and stable solutions are obtained

Simultaneous determination of time and space-dependent coefficients in a parabolic equation

This paper investigates a couple of inverse problems of simultaneously determining time and space dependent coefficients in the parabolic heat equation using initial and boundary conditions of the direct problem and overdetermination conditions. The measurement data represented by these overdetermination conditions ensure that these inverse problems have unique solutions. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization method. The finite-difference method (FDM) is employed as a direct solver which is fed iteratively in a nonlinear minimization routine. Both exact and noisy data are inverted. Numerical results for a few benchmark test examples are presented, discussed and assessed with respect to the FDM mesh size discretisation, the level of noise with which the input data is contaminated, and the chosen regularization parameters

WAYS OF IMPROVING THE RESULTS OF SURGICAL TREATMENT OF GASTRIC MALIGNANT TUMORS, COMPLICATED BY GASTROINTESTINAL BLEEDING IN THE CONDITIONS OF EMERGENCY CARE

The aim is to improve the results of surgical treatment of patients with gastric malignant tumors, complicated by gastrointestinal bleeding, by developing and implementing in clinical practice a new treatment tactic. Materials and methods. The study was conducted on the basis of the Kyiv City Center for Emergency Care of Patients with Gastrointestinal Bleedings and at the Kyiv City Clinical Ambulance Hospital (Ukraine) for the period from 2010 to 2020. A comprehensive examination and analysis of reatment’s results of 140 patients with malignant gastric tumors complicated by acute gastrointestinal bleeding, which amounted to 2.2 % of all reated patients with gastrointestinal bleeding during this period. Results. Radical operations were performed in 97 (69.3 %) patients, palliative and symptomatic – in 43 (30.7 %). Comparing the frequency of complications in the two periods of treatment of patients, a decrease in the second period, compared with the first period, the frequency of complications from 27.2 % to 11.4 % due to a decrease of 1.8 times (from 68.8 % to 37,5 %) complications after emergencies and related fatalities from 36.4 % to 0 and 2.2 times (from 20.8 % to 9.6 %) the incidence of complications after early delayed operations with a decrease in frequency fatalities from 20.9 % to 18.2 %. Conclusions. Operations at the height of acute bleeding in patients with gastric cancer are too dangerous due to the high postoperative mortality. The optimal standard is the use of a set of minimally invasive methods of endosurgical hemostasis to stop active bleeding and prevent its recurrence and operate on patients in the early delayed period. Adherence to such tactics is expedient from the point of view of reduction of risk for a life of the patient and possibility of carrying out radical operations

Competitive Adsorption and Diffusion of Gases in a Microporous Solid

The experimental and theoretical study of the co-adsorption and co-diffusion of several gases through a microporous solid and the instantaneous (out of equilibrium) distribution of the adsorbed phases is particularly important in many fields, such as gas separation, heterogeneous catalysis, purification of confined atmospheres, reduction of exhaust emissions contributing to global warming, etc. The original NMR imaging technique used gives a signal characteristic of each adsorbed gas at each instant and at each level of the solid and therefore the distribution of several gases in competitive diffusion and adsorption. But it does not allow to determine separately the inter- and intra-crystallite quantities. A new fast and accurate analytical method for the calculation of the coefficients of co-diffusing gases in the intra- and inter-crystallite spaces of microporous solid (here ZSM 5 zeolite) is developed, using high-performance methods (iterative gradient methods of residual functional minimization and analytical methods of influence functions) and mathematical co-adsorption models, as well as the NMR spectra of each adsorbed gas in the bed. These diffusion coefficients and the gas concentrations in the inter- and intra-crystallite spaces are obtained for each position in the bed and for different adsorption times

Retrieving the time-dependent thermal conductivity of an orthotropic rectangular conductor

The aim of this paper is to determine the thermal properties of an orthotropic planar structure characterised by the thermal conductivity tensor in the coordinate system of the main directions (Oxy) being diagonal. In particular, we consider retrieving the timedependent thermal conductivity components of the an orthotropic rectangular conductor from nonlocal overspecified heat flux conditions. Since only boundary measurements are considered, this inverse formulation belongs to the desirable approach of non-destructive testing of materials. The unique solvability of this inverse coefficient problem is proved based on the Schauder fixed point theorem and the theory of Volterra integral equations of the second kind. Furthermore, the numerical reconstruction based on a nonlinear least-squares minimization is performed using the MATLAB optimization toolbox routine lsqnonlin. Numerical results are presented and discussed in order to illustrate the performance of the inversion for orthotropic parameter identification

An inverse problem of finding the time-dependent diffusion coefficient from an integral condition

We consider the inverse problem of determining the time-dependent diffusivity in one-dimensional heat equation with periodic boundary conditions and nonlocal over-specified data. The problem is highly nonlinear and it serves as a mathematical model for the technological process of external guttering applied in cleaning admixtures from silicon chips. First, the well-posedness conditions for the existence, uniqueness, and continuous dependence upon the data of the classical solution of the problem are established. Then, the problem is discretized using the finite-difference method and recasts as a nonlinear least-squares minimization problem with a simple positivity lower bound on the unknown diffusivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. In order to investigate the accuracy, stability, and robustness of the numerical method, results for a few test examples are presented and discussed

Reconstruction of time-dependent coefficients from heat moments

This paper investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as well as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank–Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed