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Within the framework of the Gross–Pitaevskii model, we deduce a system of equations that describes the motion of quantized vortices in Bose–Einstein condensates. We consider a strongly anisotropic magnetic trap whose trapping potential is much higher in the direction z than in the transverse direction. Under the action of this potential, the condensate takes the form of a plane disk. The transition to the two-dimensional case enables us to apply the method of matched asymptotic expansions and obtain the equations of vortex motion in the explicit form. We take into account the rotation of the condensate as a whole and the effect of dissipative processes as a result of which the system of vortices comes to the equilibrium state. Some examples of the vortex motion are presented for different values of the external parameters. [ABSTRACT FROM AUTHOR] more...

We deduce equations of motion of quantized vortices in rotating Bose-Einstein condensates in two cases, namely, for a homogeneous condensate in a rigid rotating cylinder and for an inhomogeneous condensate in a rotating magnetic trap in the Thomas-Fermi approximation. The Schrödinger equations for both media are reduced to a convenient dimensionless form. By the method of expansion in a small parameter, we obtain two asymptotic solutions in different space scales. The comparison of the principal terms of these solutions yields the required equations. The equations of motion of the vortices in the homogeneous condensate are reduced to the well-known equations of vortices in the ideal liquid. The inhomogeneity of the medium results in the appearance of additional terms. We deduce the equations of motion of the vortices in the most general case: for any number of vortices, for vessels of different shapes, and both in the presence and in the absence of rotation. It is shown that, in the partial case of motion of a single vortex, the corresponding equations are reduced to the well-known equations of precession of the vortex. We present the plots of motion of several vortices for various initial data. [ABSTRACT FROM AUTHOR] more...

The application of the resonant light pressure created by an axially symmetrical light field for collimating atomic beams has been considered. As an example, consideration is given to the possibility of collimating an atomic beam by the light field produced by the reflection of a plane wave from the internal surface of a metal cone. It has been shown that the radiation pressure can reduce the atomic-beam transverse velocities to the value of the order of 100 cm/s which corresponds to effective temperature of about 10 K. A method for producing collimated beams of cold atoms based on simultaneous deceleration and collimation of atomic beams by resonant laser radiation pressure is proposed. [ABSTRACT FROM AUTHOR] more...

The creation of electron-positron pairs in the collision of two heavy nuclei is considered. A systematic quantum-mechanical approach is developed for the complete electron-nuclear system. The finite size of the nuclei and the possible resonances of the superheavy compound nucleus formed from the initial nuclei are taken into account. The energetic approach known in the theory of the breakdown of quasisteady systems is generalized to the case of the collisional problem. This approach is combined with perturbation theory for the complete electron-nuclear system. The rearrangement of the negative-continuum spectrum is taken into account using the procedure of [14], which is generalized with the aim of introducing additional conditions, in particular, the condition associated with correct choice of the zero approximation. The method is the same for Z < Z and Z > Z, where Z is the minimum nuclear charge at which spontaneous pair creation is possible. The contribution of the 'spontaneous' channel to the amplitude of the process is automatically taken into account. [ABSTRACT FROM AUTHOR] more...

We have investigated the kinetics of the oxidation of cysteine and thiourea by an excess of potassium iodate under conditions corresponding to the production of auto-oscillations of concentration. First-order rate constants have been calculated for the disulfide oxidation of cystine by potassium iodate and of the disulfide of formamidine, the primary oxidation product of thiourea. It is shown that thorough oxidation of disulfides by iodate can occur and its stoichiometry is investigated. A new oscillating chemical system has been discovered, containing potassium iodate, hydrogen peroxide, thiourea, and a mixture of sulfuric and hydrochloric acids. [ABSTRACT FROM AUTHOR] more...

In order to determine the sufficient conditions for realization of oscillatory instability and the stages responsible for destabilization of the reaction regime in the potassium iodate-hydrogen peroxide-cysteine-sulfuric acid system, we have carried out bifurcation analysis of its mathematical model. We have determined the criteria for the appearance and size of the limit cycle in the phase space of the concentrations of the basic variables of the system; we have established the number and type of stability of the stationary states. [ABSTRACT FROM AUTHOR] more...

The accelerating effects of carbon monoxide in the hydropolymerization of ethylene and propylene in the presence of Co-clay catalyst depend both on its concentration and the reaction temperature. [ABSTRACT FROM AUTHOR] more...