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Marchuk A.G.,Institute of Computational Mathematics and Mathematical Geophysics
Science of Tsunami Hazards | Year: 2016

In this paper, the kinematics of tsunami wave rays and fronts over an uneven bottom are studied. A formula for the wave height along a ray tube is obtained. An exact analytical solution for wave rays and fronts over a sloping bottom is derived. This solution makes possible to determine a tsunami wave height in an area with a sloping bottom from the initial source in the ray approximation. The distribution of wave-height maxima calculated in an area with a sloping bottom is compared to that obtained with a shallow-water model. © 2016 - TSUNAMI SOCIETY INTERNATIONAL.


Plotnikov M.Y.,RAS Institute of Thermophysics | Shkarupa E.V.,Institute of Computational Mathematics and Mathematical Geophysics
Computers and Fluids | Year: 2012

In this work the problem of selection of a number of numerical parameters of the direct simulation Monte Carlo (DSMC) method (such as time step, cell size, and number of time steps) is addressed. We study the errors of the DSMC method relating to the quality and amount of information sampled during simulation for three main macroparameters of a gas flow (density, velocity, and temperature). The expressions for optimal selection of the sampling time step, the number of sampling cells, and the sample size which guarantee attaining a specified level of the error are proposed on the basis of the theory of functional Monte Carlo algorithms. Practical recommendations are given for evaluating the quantities involved in the expressions simultaneously with the calculation of the flow macroparameters. The proposed approaches are examined on the examples of the Fourier problem, the gas recondensation problem between two infinite parallel plates, and the supersonic plane-parallel rarefied gas flow around a flat plate. © 2012 Elsevier Ltd.


Afanasyev I.,Institute of Computational Mathematics and Mathematical Geophysics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

A cellular automata model of population dynamics of eight organisms in Lake Baikal is proposed and investigated. The model allows to take into account spatial organisms distribution, seasonal dependency of birth rates, possible habitat pollution and water streams. Computational experiment is presented. It demonstrates that population dynamics tends to stable oscillating process with period equal to 1 year. The model was verified within production-to-biomass and frequency of occurrence ratios. © 2013 Springer-Verlag Berlin Heidelberg.


Shakhov V.,Institute of Computational Mathematics and Mathematical Geophysics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2016

Wireless Sensor Networks is considered as one of the most important elements in the upcoming Internet of Things. As sensors based applications are widely deployed, limited battery power of the sensor nodes becomes a serious problem. Intrusions or malfunction of legitimate sensor protocols can lead to the quick depletion of sensors batteries and a network failure. Energy harvesting facilities provide an attractive solution to this problem. The potential of the energy harvesting wireless sensor networks can be properly applied if the corresponding efficient network operations protocols will be implemented. Development of this protocols requires the corresponding mathematical tools for system performance evaluation. Most papers in this area focus on some concrete technical problem, but there is lack of papers analyzing common principles of energy harvesting wireless sensor networks operating. In this paper we partially fill this gap. © Springer International Publishing Switzerland 2016.


Getling A.V.,Moscow State University | Buchnev A.A.,Institute of Computational Mathematics and Mathematical Geophysics
Astronomy Reports | Year: 2010

An algorithm for measuring horizontal photospheric velocities previously employed to process aerospace images is adapted for problems in solar physics and realized in a computational code. It differs from the standard procedure of local correlation tracking in a special choice of trial areas ("targets"), whose displacements are determined bymaximizing the correlation between the original and various shifted positions of the target. Specifically, an area is chosen as a target in a certain neighborhood of each node of a predefined grid if either the contrast or the entropy of the brightness distribution reaches its maximum in this area. The horizontal velocities obtained are then interpolated to the positions of imaginary "corks" using the Delaunay triangulation and affine transformations specified by the deformation of the obtained triangles at the time step considered. The motion of the corks is represented by their trajectories. A superposition of flows on different scales, from mesogranular to supergranular, can clearly be seen. "Large mesogranules" with sizes of order 15 Mm are revealed. In many cases, these are stellate in shape. Areas of strong convergence of the horizontal flows are detected; this convergence is sometimes accompanied by swirling. Evidence is found for the possible coexistence of convection cells with different circulation directions, so-called l-type and g-type cells. © 2010 Pleiades Publishing, Ltd.

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