Abstract:
Mathematical statement of elastodynamic contact problem for cracked body with considering unilateral restrictions and friction of the crack faces is done in classical and weak forms. Different variational formulations of unilateral contact problems with friction based on boundary variational principle are considered. Nonsmooth optimization algorithms of Udzawa’s type for solution of unilateral contact problem with friction have been developed. Convergence of the proposed algorithms has been studied numerically.

Precessing ball solitons (PBS) in a ferromagnet during the first order phase transition is induced by a magnetic field directed along the axis of anisotropy, while the action of the periodic field perpendicular to the main magnetic field has been analyzed. Under these conditions, the characteristics of arising equilibrium PBS are uniquely determined by the frequency of the periodic field, but the solitons with other frequencies are impossible. For such structure, the entropy increase connected with dissipation is compensated by the decrease of the entropy due to the external periodic field. It is shown that the equilibrium PBS are essentially the “self-organizing systems” that can arise spotaneously in a metastable state of ferromagnet.

Abstract:
Precessing ball solitons (PBS) in a ferromagnet during the first order phase transition induced by a magnetic field directed along the axis of anisotropy, while the additional action of high-frequency field perpendicular to the main magnetic field, are analyzed. It is shown that the spatial motion of solitons, associated with thermal fluctuations in the crystal, does not destroy the equilibrium of self-organized PBS.

Abstract:
An attempt to predict the new atomic dark matter lines is done on the example of a dark lepton atom-positronium. Its Layman-alpha line with the energy near 3 GeV may be observable if the appropriate conditions are realized. For this we have studied a γ-ray excess in the center of our galaxy. In principle, this excess may be produced by the L_{α} line of a dark positronium in the medium with Compton scattering. The possibility of observations of an annihilation line (E~300 TeV) of dark positronium is also predicted. Other proposals to observe the atomic dark matter are shortly described. Besides, H_{α} line (1.3μ) of usual positronum must be observable in the direction on the center of our galaxy.

Abstract:
Particle-particle collisions in materials give rise to a particle distribution in energy and momentum in such a way that a most probable distribution is realized. I will show that an evaporating liquid generates a molecular imbalance in the equilibrium energy distribution. The molecular collisions by their inherent nature are able to repair the imbalance and in so doing it is shown that the liquids cool down. Similarly an external electric field creates substantial imbalance in the momentum distribution for the electrons in ionic semiconductors. Electron-electron collisions are able to restore the imbalance and as a consequence, similar to the evaporating liquid, the electron gas loses thermal energy and cools down.

Abstract:
Research into the read structure of space at ways leads to the conclusion on the existence of a privileged (absolute) system of reference, with all the equations remaining invariant about Lorentz’s transformations. The expansion of these transformations makes it possible to obtain easily the Schwarzshild matrix and, also, all the results of Einstein’s theory of gravity. The untangling of the physical meaning of velocity as a measure of relative deformation of elementary space cells eliminates, at last, all the paradoxes of Lorentz’s transformations and allows visual observation of the mechanism of gravity and Coulomb interaction in imaginary experiments.

In this study, the characterization of the depth of the Mohorovicic discontinuity under the crust of Funafuti island was determined by analyzing the 3 component seismograms from 54 different earthquake events recorded by the station between 2008 and 2012. These seismograms were from teleseismic earthquakes whose epicenter lay at distances greater than 3000 km from the station. The seismograms were iteratively deconvolved in the time domain to remove the unwanted noise and then stacked to obtain better receiver functions. For analysis of the receiver functions, it was assumed that the range in which the Vp/Vs ratio would lie for the given region would be between 1.60-1.85 and the depth of the discontinuity was assumed to lie between 5-20 km. Analysis of the receiver functions showed that the Mohorovicic discontinuity was at a depth of 11 km and the Vp/Vs ratio was 1.75 for the region.

Abstract:
In India, with ever increasing population and stress on natural resources, especially water, rejuvenation of rainwater harvesting (RWH) technique which was forgotten over the days is becoming very essential. Large number of RWH methods that are available in the literature are demand specific and site specific, since RWH system depends on the topography, land use, land cover, rainfall and demand pattern. Thus for each and every case, a detailed evaluation of RWH structures is required for implementation, including the analy-sis of hydrology, topography and other aspects like site availability and economics, however a common methodology could be evolved. The present study was aimed at evaluation of various RWH techniques in order to identify the most appropriate technique suitable for a large scale industrial area to meet its daily wa-ter demand. An attempt is made to determine the volume of water to be stored using mass balance method, Ripple diagram method, analytical method, and sequent peak algorithm method. Based on various satisfying criteria, analytical hierarchy process (AHP) is employed to determine the most appropriate type of RWH method and required number of RWH structures in the study area. If economy alone is considered along with hydrological and site specific parameters, recharging the aquifer has resulted as a better choice. However other criteria namely risk, satisfaction in obtaining required volume of water for immediate utilization etc. has resulted in opting for concrete storage structures method. From the results it is found that AHP, if used with all possible criteria can result in a better tool for evaluation of RWH methods and structures. This RWH structures not only meets the demand but saves transportation cost of water and reduces the dependability of the industry on irrigation reservoir. Besides monetary benefits it is hoped that the micro environment inside the industry will improve due to the cooling effect of the stored water.

Cooperative communication is going to play a vital role in the next generation wireless networks. In this paper we derive the expression for symbol error probability (SEP) of a two-user cooperative diversity system, where two users cooperate through the decode-and-forward (DF) relaying with binary phase-shift keying (BPSK) modulation in a flat Rayleigh fading environment. We compare the computational results obtained by the SEP expression with the simulation results using maximal-ratio combining (MRC), equal-gain combining (EGC) and selection combining (SC) techniques. Numerical results show the performance of a cooperative diversity system with maximal-ratio combining is giving better results compared to SC and EGC techniques.

In this paper, we propose an algorithm for solving multi-objective assignment problem (MOAP) through Hungarian Algorithm, and this approach emphasizes on optimal solution of each objective function by minimizing the resource. To illustrate the algorithm a numerical example (Sec. 4; Table 1) is presented.