Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.

Shock waves in superconducting cosmic strings: growth of current

Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term \chi. The hypersurface of discontinuity propagates at finite velocity determined by finite increment \Delta \chi =\chi_+ -\chi_-. The current increases \chi_+>\chi_- in stable shocks but transition between spacelike (\chi >0) and timelike (\chi<0) currents is impossible.Comment: 13 pages, 3 figure

FROM EXPERIENCE OF DEVELOPMENT AND DEPLOYMENT OF THE ELECTRONIC EDUCATIONAL RESOURCE «GAME THEORY»

В рамках статьи представлены возможности использования электронного образовательного ресурса по учебной дисциплине «Теория игр» с целью обеспечения прикладной направленности процесса обучения. Отмечается, что в процессе разработки и внедрения электронного образовательного ресурса следует учитывать, что он является дополнительным инструментальным средством и ресурсом, поддерживающим управление самостоятельной работой студентовWithin article possibilities of use of an electronic educational resource on a subject matter "Games theory" for the purpose of ensuring applied orientation of training activity are presented. It is noted that in development process and implementations of an electronic educational resource it is necessary to consider that it is the additional instrumental tool and a resource supporting management of independent work of student

Interaction between superconducting vortices and Bloch wall in ferrite garnet film

Interaction between a Bloch wall in a ferrite-garnet film and a vortex in a superconductor is analyzed in the London approximation. Equilibrium distribution of vortices formed around the Bloch wall is calculated. The results agree quantitatively with magneto-optical experiment where an in-plane magnetized ferrite-garnet film placed on top of NbSe2 superconductor allows observation of individual vortices. In particular, our model can reproduce a counter-intuitive attraction observed between vortices and a Bloch wall having the opposite polarity. It is explained by magnetic charges appearing due to discontinuity of the in-plane magnetization across the wall.Comment: 4 pages, 5 figure

Clifford algebras and universal sets of quantum gates

In this paper is shown an application of Clifford algebras to the construction of computationally universal sets of quantum gates for $n$-qubit systems. It is based on the well-known application of Lie algebras together with the especially simple commutation law for Clifford algebras, which states that all basic elements either commute or anticommute.Comment: 4 pages, REVTeX (2 col.), low-level language corrections, PR

New and Old Results in Resultant Theory

Resultants are getting increasingly important in modern theoretical physics: they appear whenever one deals with non-linear (polynomial) equations, with non-quadratic forms or with non-Gaussian integrals. Being a subject of more than three-hundred-year research, resultants are of course rather well studied: a lot of explicit formulas, beautiful properties and intriguing relationships are known in this field. We present a brief overview of these results, including both recent and already classical. Emphasis is made on explicit formulas for resultants, which could be practically useful in a future physics research.Comment: 50 pages, 15 figure