The pseudo-potential PAW method of the density functional theory is employed to study the localization of superstoichiometric oxygen in ferrite CaBaFe
4
O
7
with the orthorhombic swedenborgite ...structure. The geometric characteristics of oxygen defects are determined by the crystal lattice relaxation procedure. It is shown that the formation of defects in calcium and barium coordination are energetically unfavorable. Oxygen intercalation into structural trigonal iron-oxygen and Kagomé layers is more favorable. In these layers, two edge-sharing Fe
2
O
5
bipyramides are formed instead of FeO
4
tetrahedra connected via one oxygen atom. The structural instability of ferrite CaBaFe
4
O
7
is shown to be caused by the population of anti-bonding 2
p
O states during oxygen intercalation. The asymmetric location of the intercalated oxygen ion relative to the neighboring iron ions promotes the appearance of local electric polarization, which can induce ferroelectric effects in the presence of ferromagnetic order.
The problem of calculating the moisture content of pore space of sediment after its mechanical drying in a centrifuge with a peripheral filtering surface is studied. An analytical equation was ...derived along the radius of moisture filling of the sediment by filtrate of the capillary fringe, taking account of lognormal distribution of pore sizes. The proportion of moisture imported into the pores by the bound filtrate is determined. The presence of a basal layer of the capillary fringe is illustrated. The possibility of limiting determination of the smallest pore diameter toward larger size for constructing histograms and calculating the moisture content of the sediment is confirmed. The agreement of the results with the known experimental data received for suspensions of chemical and oil refining industries in filtering centrifuges is confirmed by an example of calculation. The main variable design and technological parameters for calculations based on effective mechanical drying of sediment in the filtering centrifuge rotor are the radius of the circumference of its filtering surface, the angular velocity, and the maximum size of pores in the sediment.
The electronic energy-band structure of the PrBaCo
2
O
5 + δ
cobaltite at the oxygen content close to 5.5 are calculated by the first-principle PAW methods. The semiconductor–metal phase transition ...at 5 + δ = 5.5 is shown to be a result of the transition of cobalt atoms in the octahedral environment from the high-spin to low-spin state. The cause of the appearance of the metallic conduction is an increase in the energy of antibonding
e
g
states of pyramidal cobalt atoms, and, as a result, they are at the Fermi level, thereby determining the metallic character of the system. The effect of a deviation of the oxygen content from 5.5 on the energy-band structure and the conductivity is studied. The semiconductor–metal transition is shown can be observed only in a narrow range of the values of 5 + δ lower 5.5.
Sharply focused pulses are required to modify transparent materials by femtosecond laser pulses. To model the modification process, it is necessary to compute the distribution of the electric field ...of the laser pulse at distances of the order of hundreds of microns from the focus. The frequently used paraxial approximation in the case of a sharp focus is not applicable. It is necessary to calculate a specific optical system. In the case when a parabolic mirror is used as a focusing element, the desired field distribution can be obtained using the Stratton–Chu integral (SCI). In this paper the generalization of the SCI to the case of a finite-time (femtosecond) pulse and a simplification of the SCI for the case of a large mirror located far from the focus are presented. This is typical for a wide range of practical problems. In addition, specific formulas of the SCI for frequently used polarizations of laser pulses are given. The main achievement of this paper is the development of extremely effective numerical methods of computing the SCI, which is the integral of a rapidly oscillating function. As an example, the calculation of the field of a focused laser pulse with a cylindrical intensity distribution along the radius (top-hat pulse) is given.
In this paper, we present results of the development of certain parallel numerical methods for solving three-dimensional evolutionary and stationary problems of diffusion and heat transfer. We ...present a detailed description of a special, explicit iteration scheme for parabolic equations and discuss a multigrid technology used for solving elliptic equations and implicit schemes for parabolic equations.
Changes in apparent electrical resistivity are calculated using one of the electrical survey methods—the median gradient—over the earthquake nucleation area in the shape of a sphere. Changes in the ...specific electrical resistivity of rocks in the source region of the earthquake nucleation are estimated taking into account the published estimates of changes in strain and strain-sensitivity coefficients. We consider the models where the sphere-shaped inclusion has a constant size in time and its electrical conductivity and depth of occurrence increase. Also considered is a model where the depth of the sphere is constant and the resistivity of the rocks in it decreases. A model is presented in which the size of the inhomogeneity increases with a simultaneous decrease in the electrical resistivity of rocks in it and the further localization of the decrease in a smaller volume, which corresponds to the ideas of tightening the nucleation zone of the main rupture into a narrow zone. According to this model, the graphs of changes in apparent resistivity return to background values shortly before the earthquake, i.e., changes in apparent resistivity over time will have the shape of a bay. A comparison of changes in electrical resistivity according to this model with variations in the resistivity of rocks at the Ashgabat Geodynamic Survey site, as well as limestone samples under laboratory conditions during their deformation and destruction, show their qualitative similarity and the possibility of using the results of laboratory tests of samples for modeling and analyzing the process of earthquake nucleation.
Wind-related weather hazards remain difficult to recognize targets for weather radars. Methods that use estimates of the width of the reflected-signal spectrum are able to improve the current ...situation. The main obstacle on this way is that the same width of the spectrum can be ensured by various phenomena, including non-dangerous ones. This leads to the ambiguity of the results obtained. Therefore, it is proposed to use a new parameter—the received-signal base equal to the product of the spectrum width and the correlation interval of the input signal. Theoretical calculations of the dependence of the signal base value on the degree of non-uniformity of the wind field, as well as the numerical simulation results, are given. The conclusion is made about the possibility of practical use of the developed method.
Finite-order invariants (Vassiliev invariants) of knots are expressed in terms of weight systems, that is, functions on chord diagrams (embedded graphs with a single vertex) satisfying the four-term ...relations. Weight systems have graph analogues, the so-called 4-invariants of graphs, i.e., functions on graphs that satisfy the four-term relations for graphs. Each 4-invariant determines a weight system.
The notion of a weight system is naturally generalized to the case of embedded graphs with an arbitrary number of vertices. Such embedded graphs correspond to links; to each component of a link there corresponds a vertex of an embedded graph. Recently, two approaches have been suggested to extend the notion of 4-invariants of graphs to the case of combinatorial structures corresponding to embedded graphs with an arbitrary number of vertices. The first approach is due to V. Kleptsyn and E. Smirnov, who considered functions on Lagrangian subspaces in a 2
n
-dimensional space over F2 endowed with a standard symplectic form and introduced four-term relations for them. The second approach, due to V. Zhukov and S. Lando, gives four-term relations for functions on binary delta-matroids.
In this paper, these two approaches are proved to be equivalent.
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear ...initial-value problem has to be solved. We compare this method to the backward Euler method combined with nonlinear iterations. For both methods we show monotonicity and boundedness of the solutions and give sufficient conditions for convergence of the nonlinear iterations. Numerical tests are presented to examine performance of the two schemes. The presented exponential Euler scheme is implemented based on restarted Krylov subspace methods and, hence, is essentially explicit (involves only matrix-vector products).
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