Construction of a model of the Venus surface and its use in processing radar observations

An algorithm is described for constructing the model of the Venus surface as an expansion in spherical functions. The relief expansion coefficients were obtained up to the coefficient S sub 99. The surface picture representation is given according to this expansion. The surface model constructed was used for processing radar observations. The use of the surface model allows improved agreement between the design and measured values of radar ranges

Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

We study weakly nonlinear wave perturbations propagating in a cold nonrelativistic and magnetized ideal quark-gluon plasma. We show that such perturbations can be described by the Ostrovsky equation. The derivation of this equation is presented for the baryon density perturbations. Then we show that the generalized nonlinear Schr{\"o}dinger (NLS) equation can be derived from the Ostrovsky equation for the description of quasi-harmonic wave trains. This equation is modulationally stable for the wave number $k < k_m$ and unstable for $k > k_m$, where $k_m$ is the wave number where the group velocity has a maximum. We study numerically the dynamics of initial wave packets with the different carrier wave numbers and demonstrate that depending on the initial parameters they can evolve either into the NLS envelope solitons or into dispersive wave trains

The inverse problem for the Gross - Pitaevskii equation

Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE, with the potential function proportional to the corresponding solutions. The second method is based on the "inverse problem" for the GPE, i.e. construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for 1D and 2D cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE

Motion Parameters Determination of the SC and Phobos in the Project Phobos-Grunt

The SC "Phobos-Grunt" flight is planned to 2009 in Russia with the purpose to deliver to the Earth the soil samples of the Mars satellite Phobos. The mission will pass under the following scheme [1-4]: the SC flight from the Earth to the Mars, the SC transit on the Mars satellite orbit, the motion round the Mars on the observation orbit and on the quasi-synchronous one [5], landing on Phobos, taking of a ground and start in the direction to the Earth. The implementation of complicated dynamical operations in the Phobos vicinity is foreseen by the project. The SC will be in a disturbance sphere of gravitational fields from the Sun, the Mars and the Phobos. The SC orbit determination is carried out on a totality of trajectory measurements executed from ground tracking stations and measurements of autonomous systems onboard space vehicle relatively the Phobos. As ground measurements the radio engineering measurements of range and range rate are used. There are possible as onboard optical observations of the Phobos by a television system and ranges from the SC up to the Phobos surface by laser locator. As soon as the Phobos orbit accuracy is insufficient for a solution of a problem of landing its orbit determination will be carried out together with determination of the SC orbit. Therefore the algorithms for joint improving of initial conditions of the SC and the Phobos are necessary to determine parameters of the SC relative the Phobos motion within a single dynamical motion model. After putting on the martial satellite orbit, on the Phobos observation orbit, on the quasi-synchronous orbit in the Phobos vicinity the equipment guidance and the following process of the SC orbit determination relatively Phobos requires a priori knowledge of the Phobos orbit parameters with sufficiently high precision. These parameters should be obtained beforehand using both all modern observations and historical ones

Frequency downshifting in decaying wavetrains on the ocean surface covered by ice floes

We study analytically and numerically a frequency downshifting due to power-type frequency-dependent decay of surface waves in the ocean covered by ice floes. The downshifting is obtained both within the linear model and within the nonlinear Schrodinger (NLS) equation augmented by viscous terms for the initial condition in the form of an NLS envelope soliton. It is shown that the frequency-dependent dissipation produces a more substantial downshifting when the spectrum is relatively wide. As a result, the nonlinear adiabatic scenario of wavetrain evolution provides a downshifting remarkably smaller in magnitude than in the linear regime. Meanwhile, interactions between nonlinear wavegroups lead to spectral broadening and, thus, result in fast substantial frequency downshifts. Analytic estimates are obtained for an arbitrary power n of the dependence of a dissipation rate on frequency to the power n. The developed theory is validated by the numerical modeling of the generalized NLS equation with dissipative terms. Estimates of frequency downshift are given for oceanic waves of realistic parameters

A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions

Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections to mostly short-distance connections. Furthermore, not all potentially possible synapses are formed, and only a fraction of axons (called filling fraction) establish synapses with spatially neighboring neurons. We explored what aspects of these connectivity patterns can be explained simply by random axonal outgrowth. We found that random axonal growth away from the soma can already reproduce the known distance distribution of connections. We also observed that experimentally observed filling fractions can be generated by competition for available space at the target neurons--a model markedly different from previous explanations. These findings may serve as a baseline model for the development of connectivity that can be further refined by more specific mechanisms.Comment: 31 pages (incl. supplementary information); Cerebral Cortex Advance Access published online on May 12, 200

Helical solitons in vector modified Korteweg-de Vries equations

We study existence of helical solitons in the vector modified Korteweg-de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations.Comment: 20 pages, 10 figure

2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011)

In cooling systems of open-pool nuclear reactors contaminant particles and radionuclides move and interact with each other in the cooling fluid (e.g., water). Because of ionising radiation produced by the reactor, the particles may acquire electric charges. We study the interaction of two charged solid particles in viscous fluid. It is assumed that the particles move side by side under the influence of the buoyancy/gravity force, Coulomb electric force, and viscous drag force. The drag force consists of two components: the quasi-stationary Stokes drag force and Boussinesq–Basset drag force resulting from the unsteady motion. Governing equations are analysed analytically and numerically for an ideal-fluid approximation and then for the viscous fluid case