Rolling in the Higgs Model and Elliptic Functions

Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (climbing), more precisely the rolling from a top (climbing to a top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated.Comment: Latex, 36 Pages, 8 figures, typos correcte

The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions

The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.Comment: 83 pages, 31 figures. Topical review. Corrected typo

The Dynamics of Charges Induced by a Charged Particle Traversing a Dielectric Slab

We studied the dynamics of surfacea and wake charges induced by a charged particle traversing a dielectric slab. It is shown that after the crossing of the slab first boundary, the induced on the slab surface charge (image charge) is transformed into the wake charge, which overflows to the second boundary when the particle crosses it. It is also shown, that the polarization of the slab is of an oscillatory nature, and the net induced charge in a slab remains zero at all stages of the motion.Comment: 12 pages, 1 figur

Non-minimal Split Supersymmetry

We present an extension of the minimal split supersymmetry model, which is capable of explaining the baryon asymmetry of the Universe. Instead of MSSM we start from NMSSM and split its spectrum in such a way that the low energy theory contains neutral particles, in addition to the content of minimal split supersymmetry. They trigger the strongly first order electroweak phase transition (EWPT) and provide an additional source of CP-violation. In this model, we estimate the amount of the baryon asymmetry produced during EWPT, using WKB approximation for CP-violating sources in diffusion equations. We also examine the contribution of CP-violating interactions to the electron and neutron electric dipole moments and estimate the production of the neutralino dark matter. We find that both phenomenological and cosmological requirements can be fulfilled in this model.Comment: 31 pages, 9 figures, typos correcte

Investigation of Input Signal Curve Effect on Formed Pulse of Hydraulic-Powered Pulse Machine

Well drilling machines should have as high efficiency factor as it is possible. This work proposes factors that are affected by change of input signal pulse curve. A series of runs are conducted on mathematical model of hydraulic-powered pulse machine. From this experiment, interrelations between input pulse curve and construction parameters are found. Results of conducted experiment are obtained with the help of the mathematical model, which is created in Simulink Matlab