Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.     

Hyperbolic stefan problem in a curvilinear sector

The problem with unknown boundaries for a first-order semilinear hyperbolic system is studied in the case where the curve of definition of the initial conditions degenerates to a point. An existence and uniqueness theorem for a classical solution of the problem is proved for small t.     

A covariant quasipotential operator for a composite system of two scaler particles

A quasipotential operator for a system of two scalar particles, and also an integral equation and a normalization condition for the wave function of the connected state, are obtained by the method of two-time Green's functions in an explicitly covariant form. The cases are considered of scalar and electromagnetic interactions of particles of the system.Frantsiska Skoriny Gomel' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 112–118, June, 1993.     

Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinder's end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 10⁴ times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies.     

Thermoluminescence of KMgF3(RE) crystals

Optical properties of pure and RE doped KMgF₃ crystals were studied. Thermoluminescence curves are independent of the introduced impurity for all dopant besides europium. Emission, radiation damage and TL are found to be significantly dependent on the types of Eu-dopant added to the melt: europium fluoride or oxide. An intensive high temperature TL peak at 390°C in KMgF₃(Eu₂O₃) may be used as a dosimetric one not only for ionizing but also for UV radiation.     

Size of the interpolated cation and hole carrier density: two key parameters for the optimisation of colossal magnetoresistive properties of Pr-based manganites

The exploration of the magnetic and transport properties of four series of manganese perovskites, Pr_0.7Ca_0.34−xA_xMnO_3−δ (A=Sr, Ba), Pr_0.7−xLa_xCa_0.3 MnO_3−δ and Pr_0.66Ca_0.34−x Sr_xMnO_3−δ has allowed four phases with colossal magnetoresistive (CMR) properties to be isolated: Pr_0.7Ca_0.25Sr_0.025MnO_3−δ and Pr_0.66Ca_0.26Sr_0.08MnO_3−δ that exhibit a variation of resistance of 2.5. 10⁷% and 10⁹% at μ₀ H=5 T for T=88 K and 50 K respectively, Pr_0.58La_0.12Ca_0.3 MnO_3−δ that exhibits a variation of 6.10⁶% for μ₀ H=5 T at T=80 K and Pr_0.7Ba_0.025Ca_0.275MnO_3−δ for which a resistance variation of 5.10⁹%, at T=50 K, for μ₀ H=5 T is evidenced. for each compound of this series except the barium phase, one observes that the temperature T_max, which corresponds to the resistance maximum on the R(T) curves in zero magnetic field, increases dramatically as the mean size of the interpolated cations increases, and that the CMR effect correlatively decreases dramatically. The comparison of the two series Pr_0.7Ca_0.3−xSr_xMnO_3−δ and Pr_0.66Ca_0.34−xSr_xMnO_3−δ shows also the crucial role of the hole carrier density: for a same mean ionic radius of the interpolated cation T_max is decreased of about 50 K by introducing 0.034 hole per Mn mole.     

To the problem of energy recuperation in gyrotrons

A relatively high level of the minimal electron energy at the gyrotron output even at very large spread in pitch factor is explained. An estimation of the recuperation efficiency, which can be obtained due to this effect, is given.