Effective Radius and Underpressure of an Air Extraction Well in a Heterogeneous Porous Medium

We consider the compressible steady state air flow in a porous medium caused by an extraction well and governed by Darcy's law. For a homogeneous soil matrix we have derived formulas (in 2-D and 3-D) to determine the effective radius of a single well depending on the well position and the depth of the domain. For inhomogeneous case (in 2-D) the influence of the heterogeneity, well position and the depth of the water table on the effective radius and on the pressure at the well is studied.     

Mathematical Treatment of Point Sources in a Flow Through Porous Media Governed by Darcy's Law

We consider stationary air flow in a porous medium caused by extraction wells and governed by Darcy's law. Point sinks are described by Dirac functions. We distinguish two different situations: locally continuous and discontinuous conductivity near the wells. In both cases, well-posedness is proved. We propose a finite-element scheme in the general case and show the convergence of the approximated solution to the exact one.     

On the use of realistic wave functions in the coherent pion photoproduction on 3He nuclei

We analyze the influence of the nuclear wave functions generated from a set of different realistic soft-core two-body potentials on the coherent charged pion photoproduction on ³He nuclei at threshold and for small momentum transfers. This process is calculated in the framework of the impulse approximation including the Fermi motion. At threshold and below the resonance, our results reproduce fairly well the experimental data. At the first γN resonance region, the agreement with experiments varies with the momentum transfer.     

Joint probabilities of noncommuting operators and incompleteness of quantum mechanics

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.⁽¹⁾ The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond it, by a more general theory of single events, using hidden variables, for example.     

Diagonalization of the spin part of the exchange hamiltonian in the second-quantization method for composite particles

Using the atomic second-quantization procedure an explicit expression is derived for the operator of exchange interaction between two atoms a and b in a state of any value of their atomic orbital and spin momenta, in the approximation of one and two pairs of exchanging electrons and without assuming the orthogonality between the orbitals of a and b. The obtained exchange interaction operator diagonalized in spin space is a second-order polynomial in the scalar product ?_a · ?_b. The coefficients of the polynomial are given operators operating in orbital space only. The possible physical implications are discussed.     

Control of Diabetes with Artificial Systems for Insulin Delivery Algorithm Independent Limitations Revealed by a Modeling Study

The causes of the inability of insulin infusion systems to restore normal metabolic conditions in diabetic subjects have been investigated with the aid of modeling and computer simulation. It has been possible to compute, by the model, the so-called minimal insulin profile with peripheral insulin infusion, i. e., the time course of plasma insulin which should be observed in a diabetic subject after an oral glucose test, when insulin is infused in a peripheral vein, in order to have a normal blood glucose profile. This profile allows assessment of the performance of insulin infusion systems by evidencing the relative role of the route of infusion and of the control algorithm on the normalization of metabolic control. It is concluded that the route of infusion is of major importance, while the control algorithm plays a minor role. The importance of modeling and simulation in circumstances, which make in vivo experiments; unfeasible or unethical, is emphasized along with the clinical and physiological relevance of the results.