Application of renormalization group techniques to transport in the presence of nonlinear sources and sinks

The paper considers the problem of spreading of a localized distribution due to diffusion in the presence of nonlinear sources and sinks modeling annihilation and creation of material in chemical reactions. The evolution of the parameters characterizing the problem, namely, the amplitude and radius of the distribution, has been investigated under the assumption that the distribution is self-similar. These parameters have been calculated using the renormalization-group method with renormalization of the diffusion coefficient and the total amount of material. As a result, it is possible to classify various regimes of the asymptotic behavior of the system at long times according to the sign of nonlinear interaction constant and the spatial dimensionality. In particular, the conditions under which the regime of asymptotic freedom and the peaking regime are realized have been found. The renormalization group method not only allows us to calculate the exponents of functions with power-law behavior, but also to track the transition to the asymptotic regime and calculate numerical coefficients. Zh. éksp. Teor. Fiz. 115, 1497–1510 (April 1999)     

Study of the Influence of the Excitation Laser Power Density on the Intermediate-Field Electric Modulation Component of the GaAs Photoreflection E 0-Signal

The influence of the excitation laser power density L on the amplitude A and characteristic time constant of the intermediate-field electric modulation component of photoreflection spectra measured in the region of the E ₀ fundamental transition of GaAs is studied. Crystalline samples with the charge carrier concentration n 10¹⁶ cm^–3 are investigated for L = 100 W/cm²–1 W/cm². A logarithmic dependence of the electric modulation signal on the excitation laser power density has been established for all examined samples. It is demonstrated that the observed change in the characteristic time constant does not have any noticeable effect on the dependence A(L).     

Calculation of binding energy in negative ions of the alkaline-earth atoms Ca and Sr

The electron binding energy in negative ions of the alkaline-earth atoms Ca and Sr is calculated on the basis of the polarization-potential formalism and relativistic perturbation theory with a zeroth-order model potential. The results improve the data available in the literature for these negative ions. Odessa Hydrometeorological Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 27–31, September, 1996.     

Calculation of the structure of the 4s band for Ni3Mn and Ni3Fe ordered alloys

Perturbation theory has been applied to the structure of the 4s band of Ni₃Mn and Ni₃Fe ordered alloys; the Fermi surfaces have been constructed for these alloys in the one-wave approximation, and the electron state densities and electron energy change on ordering have been calculated. It is found that the contribution of the 4s electrons to the ordering energy is much less than that of the 3d electrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 102–106, July, 1972.     

On the exactness of certain inequalities in approximation theory

We prove the following: for every sequence {F_v}, F_v ? 0, F_v > 0 there exists a functionf such that

1. E_n(f)?F_n (n=0, 1, 2, ...) and
2. A_kn^?k? _v=1 ⁿ v^k?1 F_v?1?Ω_k (f, n^?1) (n=1, 2, ...).