Multidimensional Classical and Quantum Cosmology with Intersecting p-branes

Multidimensional cosmological model describing the evolution of n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane Ansatz is adopted the field equations are reduced to the equations for Toda-like system. The Wheeler-De Witt equation is obtained. In the case when n "internal" spaces are Ricci-flat, one space M_0 has a non-zero curvature, and all p-branes do not "live" in M_0, the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically-symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D > 11 models (that may be related to hypothetical higher dimensional supergravities and F-theories) is suggested.Comment: 26 pages, Latex. Submit. to J. Math. Phy

Curved branes from string dualities

We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with 2-d CFT's representing different parts of space-time. We illustrate our method with many examples, some of which are associated with conformally invariant sigma models. Using U-duality, we also obtain supergravity solutions with RR charges which can be interpreted as D-branes with non-trivial worldvolume geometry. In particular, we discuss the case of a D5-brane wrapped on AdS_3 x S^3, a solution interpolating between AdS_3 x S^3 x R^5 and AdS_3 x S^3 x S^3 x R, and a D3-brane wrapped over S^3 x R or AdS_2 x S^2. Another class of solutions we discuss involves NS5-branes intersecting over a 3-space and NS5-branes intersecting over a line. These solutions are similar to D7-brane or cosmic string backgrounds.Comment: 21 pages, harvmac; misprint correcte

Billiard Representation for Multidimensional Cosmology with Intersecting p-branes near the Singularity

Multidimensional model describing the cosmological evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N-1)-dimensional Lobachevsky space, N = n+l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of (N-2)-dimensional sphere by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in ``truncated'' D = 11 supergravity model (without the Chern-Simons term) are considered. It is shown that the inclusion of the Chern-Simons term destroys the confining of a billiard.Comment: 27 pages Latex, 3 figs., submit. to Class. Quantum Gra

Toda p-brane black holes and polynomials related to Lie algebras

Black hole generalized p-brane solutions for a wide class of intersection rules are obtained. The solutions are defined on a manifold that contains a product of n - 1 Ricci-flat internal spaces. They are defined up to a set of functions H_s obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. A conjecture on polynomial structure of governing functions H_s for intersections related to semisimple Lie algebras is suggested. This conjecture is proved for Lie algebras: A_m, C_{m+1}, m > 0. For simple Lie algebras the powers of polynomials coincide with the components of twice the dual Weyl vector in the basis of simple coroots. The coefficients of polynomials depend upon the extremality parameter \mu >0. In the extremal case \mu = 0 such polynomials were considered previously by H. L\"u, J. Maharana, S. Mukherji and C.N. Pope. Explicit formulas for A_2-solution are obtained. Two examples of A_2-dyon solutions, i.e. dyon in D = 11 supergravity with M2 and M5 branes intersecting at a point and Kaluza-Klein dyon, are considered.Comment: 24 pages, Latex, typos are eliminated, a correct relation on parameters of special block-orthogonal solution is added in third line after eq. (4.10

МАШИННО-ТРАНСФОРМАТОРНИЙ АГРЕГАТ ДЛЯ ВІТРОЕНЕРГЕТИЧНИХ УСТАНОВОК

Background. Electric generators of wind turbines must meet the following requirements: they must be multi-pole; to have a minimum size and weight; to be non-contact, but controlled; to ensure the maximum possible output voltage when working on the power supply system. Multipole and contactless are relatively simply realized in the synchronous generator with permanent magnet excitation and synchronous inductor generator with electromagnetic excitation; moreover the first one has a disadvantage that there is no possibility to control the output voltage, and the second one has a low magnetic leakage coefficient with the appropriate consequences. Purpose. To compare machine dimensions and weight of the transformer unit with induction generators and is an opportunity to prove their application for systems with low RMS-growth rotation. Methodology. A new design of the electric inductor machine called in technical literature as machine-transformer unit (MTU) is presented. A ratio for estimated capacity determination of such units is obtained. Results. In a specific example it is shown that estimated power of MTU may exceed the same one for traditional synchronous machines at the same dimensions. The MTU design allows placement of stator coil at some distance from the rotating parts of the machine, namely, in a closed container filled with insulating liquid. This will increase capacity by means of more efficient cooling of coil, as well as to increase the output voltage of the MTU as a generator to a level of 35 kV or more. The recommendations on the certain parameters selection of the MTU stator winding are presented. The formulas for copper cost calculating on the MTU field winding and synchronous salient-pole generator are developed. In a specific example it is shown that such costs in synchronous generator exceed 2.5 times the similar ones in the MTU.В работе предложена новая конструкция индукторной электрической машины, которая в технической литературе называется – машинно-трансформаторный агрегат (МТА). Для такого агрегата получено соотношение для определения расчетной мощности. На конкретном примере показано, что при одинаковых габаритах расчетная мощность МТА может превышать таковую для обычных синхронных машин. Конструкция МТА позволяет разместить катушки обмотки статора на некотором расстоянии от подвижных элементов машины, а именно, в закрытой емкости, заполненной электроизоляционной жидкостью. Это позволит увеличить мощность за счет более эффективного охлаждения обмотки, а также повысить выходное напряжение МТА как генератора до уровня 35 кВ и более.В роботі запропонована нова конструкція індукторної електричної машини, яка в технічній літературі називається – машинно-трансформаторним агрегатом (МТА). Для такого агрегату отримано співвідношення для визначення розрахункової потужності. На конкретному прикладі показано, що при однакових габаритах розрахункова потужність МТА може перевищувати таку для звичайних синхронних машин. Конструкція МТА дозволяє розмістити котушки обмотки статора на деякій відстані від рухомих елементів машини, а саме, у закритій ємності, заповненій електроізоляційною рідиною. Це дасть змогу збільшити потужність за рахунок більш ефективного охолодження обмотки, а також підвищити вихідну напругу МТА як генератора до рівня 35 кВ і більше

Black-brane solution for C_2 algebra

Black p-brane solutions for a wide class of intersection rules and Ricci-flat ``internal'' spaces are considered. They are defined up to moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra C_2 is obtained. The functions H_1 and H_2 for this solution are polynomials of degree 3 and 4.Comment: 12 pages, Latex, submitted to J. Math. Phy