Approximate method of converting the law of one-dimensional shock propagation

A method is proposed for the approximate calculation of the correction to the universal law of one-dimensional shock propagation in a polytropic gas at rest in the case when the wave proceeds over an inhomogeneous medium.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 55–57, January–February, 1972.     

Modified Fues potential for many-electron atoms

A modification of the model Fues potential based on taking into account the effects of Coulomb screening and polarization of the core in the ground and lower excited states of many-electron atoms in the parameters of this potential is proposed. Numerical values of parameters of the modified model potential are obtained for the ground states of alkali metal, alkaline earth, and inert gas atoms and for the metastable triplet state of helium. The numerical values of polarizabilities and hyperpolarizabilities calculated with the use of the modified potential are in significantly better agreement (as compared to the results obtained by using the traditional approach) with the most accurate literature data.     

Modeling of magnetic field perturbations in electrophysical devices due to the steel reinforcement of buildings

We have proposed an effective method for modeling the steel reinforcement in the buildings for electrophysical devices to take into account the magnetic field perturbation caused by the magnetization of bars. The reinforcement lattice has been represented by one or several layers of a homogeneous isotropic material with preliminarily calculated equivalent (averaged) magnetic properties. Examples of calculating these magnetic properties have been considered using a simplified analytic approach, as well as by the numerical simulation of the magnetic field in a 3D cell of a periodic reinforcement lattice. The efficiency of the method has been demonstrated based on an important practical example of simulating the perturbation of a uniform magnetic field caused by the reinforced slab. The results have been compared with the simulation data based on different approaches.     

Change in the frequency and intensity of the spectral lines of a hydrogen-like atom in the field of a point charge

The changes in the wave functions and the energies of a hydrogen-like atom in the static field of a structureless charged particle are calculated in the asymptotic approximation. The corrections to the energy of states, as well as to the dipole matrix elements of radiative transitions caused by the interaction of the atom with the point charge at long range are calculated using the perturbation theory and the Sturm series for a reduced Coulomb Green’s function in parabolic coordinates. The analytical expressions are derived and tables of numerical values of the coefficients of asymptotic series that determine the corrections to the matrix elements and the intensities of transitions of the Lyman and Balmer series are presented.     

On bifurcations of multidimensional diffeomorphisms having a homoclinic tangency to a saddle-node

We study the main bifurcations of multidimensional diffeomorphisms having a nontransversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a small neighborhood of the homoclinic orbit. Also, a relation of our results to the well-known codimension one bifurcations of a saddle fixed point with a quadratic homoclinic tangency and a saddle-node fixed point with a transversal homoclinic orbit is discussed.     

Electron transport in manganite bicrystal junctions

The transport and magnetic properties of junctions created in La_0.67Sr_0.33MnO₃ thin films epitaxially grown on substrates with a bicrystal boundary have been investigated. In tilted neodymium gallate bicrystal substrates, the NdGaO₃(110) planes are inclined at angles of 12° and 38°. The temperature dependences of the electrical resistance, magnetoresistance, and differential conductance of the junctions at different voltages have been measured and analyzed. It has been found that the magnetoresistance and electrical resistance of the junction significantly increase with an increase in the misorientation angle, even though the misorientation of the easy magnetization axes remains nearly unchanged. The ratio of the spin-dependent and spin-independent contributions to the conductance of the bicrystal junction increases by almost an order of magnitude with an increase in the misorientation angle from 12° to 38°. The magnetoresistance of the junction increases with decreasing temperature, which is most likely associated with an increase of the magnetic polarization of the electrons. It has been shown that, at low (liquid-helium) temperatures, the conductance depends on the voltage V according to the law V ^1/2, which indicates the dominant contribution from the electron-electron interaction to the electrical resistance of the junction. An increase in the temperature leads to a decrease in this contribution and an increase in the contribution proportional to V ^3/2, which is characteristic of the mechanism involving inelastic spin scattering by surface antiferromagnetic magnons.