Vol 8, No 6 (2016)

The Fermi–Dirac functions of the integer index are widely used in electron transport problems in dense substances. Polynomial approximations are constructed for their quick calculation. A simple algorithm yielding the coefficients of such approximations based on the interpolation with a special linear-trigonometric grid is developed. It is demonstrated that this grid gives almost optimal results. For the functions of indices 1, 2, and 3, the coefficients of such interpolations ensuring the relative error of 2 × 10⁻¹⁶ under 9 free parameters are obtained.

This paper presents a cell-centered conservative scheme based on a quasi-one-dimensional (1D) reconstruction of variables for the solution of a system of hyperbolic equations on 3D unstructured meshes. Only the case of smooth solutions is considered. Test examples are used to demonstrate that the accuracy and computational costs of the studied scheme are about the same as of the vertexcentered EBR scheme and the preferability of the vertex-centered or cell-centered scheme is determined by the prevalent types of elements in the computational mesh.

An economic iterative method is proposed for simulating stationary conditions in complex gas transport systems of any topology. The method exploits a fast algebraic pipe model with periodic identification, which is used to adjust the model to the stationary conditions under consideration and to provide the required accuracy of calculation. The identification procedure is based on the solution of stationary hydrodynamic equations. The gas transport system is represented as a list of pipes and a list of nodes. As an initial approximation, we define gas pressures and temperatures in the nodes and thus setting boundary conditions for the stationary flow. In the global iterations of the method, the pressures and temperatures are updated to make the flow disbalance tend to zero. The method allows parallel computing on multiprocessor computers. It is implemented as a separate module in the VOLNA software. Its efficiency is demonstrated through a sample calculation for the gas transport system. A number of related issues are considered, including simulation accuracy, peculiarities in the solution of stationary equations, and the correctness of the calculation setup. The method can be used in combination with any other model of piped compressible gas.

For the model of the waveguide which is a multilayered medium with a cylindrical seamount, the asymptotic behavior of the unknowns in the corresponding infinite system is studied. The obtained asymptotic behavior of the unknowns allows us to use the method of improved reduction for finding the coefficients of the normal modes. The convergence of the algorithm is illustrated by the example of some geophysical waveguides.

Two-dimensional (2D) inverse scattering problems for the acoustic wave equation consisting of obtaining the density and acoustic impedance of the medium are considered. A necessary and sufficient condition for the unique solvability of these problems in the form of the law of energy conservation has been established. It is proved that this condition is that for each pulse oscillation source located on the boundary of a half-plane, the energy flow of the scattered waves is less than the energy flux of waves propagating from the boundary of this half-plane. This shows that for inverse dynamic scattering problems in acoustics and geophysics when the law of energy conservation holds it is possible to determine the elastic density parameters of the medium. The obtained results significantly increase the class of mathematical models currently used in solving multidimensional inverse scattering problems. Some specific aspects of interpreting inverse problems solutions are considered.

The paper presents a modified model of the interaction between corrupt power hierarchies and civil society. The suggested improvements and generalizations consist of more comprehensively defining the damage from corruption and the value of suppressing corruption that are more coherent with the considered phenomenon, and the different types of bureaucratic reactions to anticorruption policies, as well as setting the boundary conditions for the model’s equations, are considered. The modified model serves as a base for computing the relative efficiency of different anticorruption strategies for hierarchies of different topologies and behaviors, taking into account the intensity of the influence of civil society on government bodies and agencies. It is found that, based on the assumptions of this model, suppressing corruption among the low-ranked bureaucrats in weakly branched hierarchies and among high-ranked bureaucrats among strongly branched hierarchies are the most efficient strategies. At the same time, strongly centralized hierarchies are the most sensitive to the choice of anticorruption strategies. In addition, it is shown that the suppression of senior bureaucrats is more efficient for more irresponsible hierarchies, whereas the suppression of low-ranked bureaucrats is most efficient for hierarchies with a relatively strong influence of civil society on power distribution. A brief comparison of the traditional approach to the mathematical investigation of corruption, using the game-theoretic model, with the systemic-social approach presented in the current and earlier papers, is also given.

High performance computing hardware is developed faster than the algorithms for fundamental mathematical models such as classical molecular dynamics are adapted. A wide variety of choice makes it necessary to determine clear criteria based on the computational efficiency of a specific algorithm on a particular hardware. The LINPACK benchmark can no longer serve this purpose. In this paper, we analyze the solution time–peak performance metric based on practical considerations. In this metric, we compare different hardware (both current and obsolete) based on the example of the LAMMPS benchmark, which is widely used for atomistic simulations. It is shown that the considered metric can be used for unambiguous comparison of different combinations of CPUs, accelerators, and interconnection.