Random walks in disordered systems and their investigations by means of magnetic resonance and relaxation of polarized beta-active nuclei

The experimental investigations of the polarization transport in the disordered spin system⁸Li −⁶Li in LiF crystal are considered. This process is initiated by one originally polarized beta-active⁸Li nucleus produced in a nuclear reaction. The autocorrelation function Foo(t) for the ran dom-walks-in-disordered-system problem has been measured over the range Foo(t)≥0.1 Foo(0) by analysing the β-emission anisotropy. The influence of the resonance process at double larmor frequency and of the thermal translational motion of⁸Li and⁶Li spins is studied. Results are in a good agre ement with the theory.     

Dynamic problem of thermoelasticity for a two-layer space

The method of influence functions is applied to construct a closed-form solution of the dynamic problem of thermoelasticity for a two-layer space (in one-dimensional framework) with nonideal thermal contact and ideal mechanical contact at the layer interface. The influence functions are constructed by the operational method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 95–102, 1985.     

Crystallization of X-type zeolite from concentrated sodium silicate and aluminate solutions

Crystallization of an X-type zeolite from concentrated solutions of sodium aluminate (Al₂O₃ 90–330 g l^?1) and silicate (SiO₂ 110–180 g l^?1) was studied.     

Multiparameter models for random walks in disordered lattice systems

Multidimensional asymptotically exactly solvable models are suggested for random walks in a stationary random lattice environment. These models differ from the well-known ones in that they involve arbitrarily many independent local random parameters per lattice site and allow for slowly decreasing intensities with increasing intersite distance. In particular, the suggested models describe the first nontrivial exactly solvable multidimensional systems with symmetrical interaction. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 2 pp. 332–344, May 1999.     

Solution of the matrix equation AX− XB = C

Under the assumption of existence and uniqueness of the solution of the matrix equation AX–XB=C we obtain a finite expression for X.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 449–451, March, 1976.The author thanks M. S. Marinov for posing the problem.     

Diffusion in a system of impurity centers with dipole-dipole hopping rates

Random walks in disordered media with dipole-dipole transition rates are considered. The long-time asymptotics of the process are investigated on the basis of a new numerical simulation method, which includes periodic continuation of the system without periodic continuation of the initial condition. It is shown that the long-time asymptotics have a diffusive character. The concentration dependence of the diffusion coefficient for simple cubic and face-centered cubic lattices is studied. Zh. éksp. Teor. Fiz. 114, 2166–2181 (December 1998)     

Magnetic resonance of beta-active nuclei at double Larmor frequency in LiF polycrystals with dislocations

β-NMR-spectroscopy investigations of the resonance at double Larmor frequency of β-active nuclei⁸Li in LiF polycrystals are presented. The quantitative analysis of the dislocation influence on this resonance is developed. An important role of correlations in dislocation distributions as well as high responsivity of this resonance to quadrupole interactions are found.