Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

ВЛИЯНИЕ ПАРАМЕТРОВ ПЛАСТИЧЕСКОГО ФОРМОВАНИЯ НА СТРУКТУРНЫЕ ХАРАКТЕРИСТИКИ ТЕРМОЭЛЕКТРИЧЕСКОГО МАТЕРИАЛА В ПРОЦЕССЕ ГОРЯЧЕЙ ЭКСТРУЗИИ

We used mathematical modeling to compare the stress and deformation in a Bi0.4Sb1.6Te3 solid solution base thermoelectric material for extrusion through different diameter dies. The results show that extrusion through a 20 mm diameter die produces a more inhomogeneous deformation compared with extrusion through a 30 mm diameter die. Extrusion through a die of a larger diameter produces a structure that is coarser but has a more homogeneous grain size distribution. The degree of preferential grain orientation is higher for extrusion through a larger diameter die. We found a change in the lattice parameter of the solid solution along the extruded rod, correlating with detect formation during extrusion. The concentration of vacancies is higher for extrusion through a smaller diameter die. This difference between the structures results from a more intense dynamic recrystallization for a smaller diameter die. Increasing the die diameter and lowering the extrusion temperature allow retaining the thermoelectric properties of the material due to a better texture.С помощью математического моделирования проведено сравнение напряжений и деформаций в термоэлектрическом материале на основе твердого раствора Bi0,4Sb1,6Te3 при экструзии через фильеры с разным диаметром. Показано, что при экструзии через фильеру диаметром 20 мм возникает более неоднородная деформация, чем при экструзии через фильеру 30 мм. Установлено, что при увеличении диаметра фильеры структура материала получается менее дисперсная, но более однородная по размерам. Степень преимущественной ориентации зерен при экструзии через фильеру большего диаметра более высокая. Обнаружено изменение параметра решетки твердого раствора по длине экструдированного стержня, связанного с дефектообразованием в процессе экструзии. Выявлено, что концентрация вакансий больше при экструзии через фильеру меньшего диаметра. Это является следствием более интенсивного протекания процессов динамической рекристаллизации. При переходе к большему диаметру фильеры и более низкой температуре экструзии термоэлектрические свойства материала сохраняются за счет лучшей текстуры

Decay properties of neutron-deficient nuclei in the region Z = 86-92

Neutron deficient isotopes of elements Z = 86–92 have been produced by heavy-ion fusion reactions 12C + 208Pb, 209Bi, 22Ne + 208Pb, 51V + 170Er, and 50Ti + 170Er. The evaporation residues were investigated by means of α- and α-γ-spectroscopy after in-flight separation from the projectile beam by the velocity filter SHIP and implantation into a 16-strip position-sensitive Si-detector. New or improved decay data for 225,226U, 216,217m,218Pa, 215,216,217Th, 214,215,216,216mAc, 214Ra and 213Rn have been obtained