Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy

The Abelian Chern-Simons Gauge Field Theory in 2+1 dimensions and its relation with holomorphic Burgers' Hierarchy is considered. It is shown that the relation between complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics, has meaning of the analytic Cole-Hopf transformation, linearizing the Burgers Hierarchy in terms of the holomorphic Schr\"odinger Hierarchy. Then the motion of planar vortices in Chern-Simons theory, appearing as pole singularities of the gauge field, corresponds to motion of zeroes of the hierarchy. Using boost transformations of the complex Galilean group of the hierarchy, a rich set of exact solutions, describing integrable dynamics of planar vortices and vortex lattices in terms of the generalized Kampe de Feriet and Hermite polynomials is constructed. The results are applied to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing dynamics of magnetic vortices and corresponding lattices in terms of complexified Calogero-Moser models. Corrections on two vortex dynamics from the Moyal space-time non-commutativity in terms of Airy functions are found.Comment: 15 pages, talk presented in Workshop `Nonlinear Physics IV: Theory and Experiment`, 22-30 June 2006, Gallipoli, Ital

A priori estimates for the Hill and Dirac operators

Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps \g_n,n\ge 1 with length |\g_n|\ge 0. We obtain a priori estimates of the gap lengths, effective masses, action variables for the KDV. For example, if \m_n^\pm are the effective masses associated with the gap \g_n=(\l_n^-,\l_n^+), then |\m_n^-+\m_n^+|\le C|\g_n|^2n^{-4} for some constant $C=C(q)$ and any $n\ge 1$. In order prove these results we use the analysis of a conformal mapping corresponding to quasimomentum of the Hill operator. That makes possible to reformulate the problems for the differential operator as the problems of the conformal mapping theory. Then the proof is based on the analysis of the conformal mapping and the identities. Moreover, we obtain the similar estimates for the Dirac operator

A Dipole Vortex Model of Obscuring Tori in Active Galaxy Nuclei

The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when the torus "twisting" by the radiation or wind transforms it into a dipole toroidal vortex which in turn can be a source of matter replenishing the accretion disk. Thus emerging instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. The "Matreshka" scheme for an obscuring vortex torus structure capable of explaining the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations.Comment: 17 pages, 11 figures, version of this paper is published in Astronomy Report

Can inertial electrostatic confinement work beyond the ion–ion collisional time scale?

Inertial electrostatic confinement systems are predicated on a non-equilibrium ion distribution function. Coulomb collisions between ions cause this distribution to relax to a Maxwellian on the ion-ion collisional time-scale. The power required to prevent this relaxation and maintain the IEC configuration for times beyond the ion-ion collisional time scale is shown to be at least an order of magnitude greater than the fusion power produced. It is concluded that IEC systems show little promise as a basis for the development of commercial electric power plants

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССА ЭКСТРУЗИИ ТЕРМОЭЛЕКТРИЧЕСКОГО МАТЕРИАЛА

We derive a mathematical model for the composite material extrusion process which describes the main features of the resulting material stress−strain state. The extrusion process includes extrusion of a cylindrical billet of pressed powder through a die of desired geometry. Die geometrical parameters and process speed can be preset. The computational model is based on combined elastic−plastic body approximation. The numericaltechnique uses a finite element approximation on Lagrangian grid, which changes over time with changes in sample shape. To perform it we use adaptive grid units generation in areas of sample high stress and strain. The calculations were performed in Crystmo/Marc software package. We study the basic featuresof stress−strain state of the material obtained at different stages of extrusion process.Для процесса экструзии композиционного материала предложена математическаямодель и на ее основе рассмотрены основные особенности напряженно−деформированногосостояния получаемого стержня. Заданы геометрические параметры фильеры и скорость перемещения Пуансона. Расчетная модель основана на совместном использовании приближенийупругопластического тела. Численная методика использует конечно−элементную аппроксимацию на лагранжевой сетке, которая меняется во времени с изменением формы образца. Для этого применена адаптивная генерация сеточных узлов в зонах больших напряжений и деформаций образца. Расчеты проведены с использованием комплекса программ Crystmo/Marc. На примере термоэлектрического композита на основе Bi2Te3 изучены основные особенности напряженно−деформированного состояния материала, полученного на разных стадиях процесса экструзии

CТРУКТУРА ОБЪЕМНОГО ТЕРМОЭЛЕКТРИЧЕСКОГО МАТЕРИАЛА НА ОСНОВЕ (Bi,Sb)2Te3, ПОЛУЧЕННОГО МЕТОДОМ ИСКРОВОГО ПЛАЗМЕННОГО СПЕКАНИЯ

Bulk nanostructured BixSb1−xTe3 based material was fabricated with spark plasma sintering (SPS) method. The starting powders with a particle size of 10—12 nm were prepared by ball milling. The regularity of fine structure changes as a function of sintering temperature in the 250—550 °C range was investigated by X−raydiffractometry, scanning and transmission electron microscopy (TEM, HRTEM). For the first time coherent dispersion areas (CDA) size was found not to increase monotonously with sintering temperature, and at temperatures of above 400 °C the CDA size decreased as a result of repeated recrystallization. Apparently,the structural changes are associated with a redistribution of intrinsic vacancy type structural defects during sintering.Исследованы образцы объемного наноструктурированного материала на основе твердого раствора BixSb1−xTe3, полученного методом искрового плазменного спекания. Исходные порошки с размером частиц 10—12 нм изготовлены помолом в шаровой мельнице. С помощью методов рентгеновской дифрактометрии, растровой и просвечивающей (в том числе высокого разрешения) электронной микроскопии изучены закономерности изменения тонкой структуры в зависимости от температуры спекания в интервале 250—550 °С. Впервые установлено, что размеры областей когерентного рассеяния не возрастают монотонно с ростом температуры спекания, а при температуре выше 400 °С происходит их измельчение в результате процесса повторной рекристаллизации. Наиболее вероятно, что изменения структуры связаны с перераспределением собственных структурных дефектов вакансионного типа в процессе спекания образцов