Integrability of generalized (matrix) Ernst equations in string theory

The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\times 2d$-linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop ``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004, Gallipoli (Lecce), Italy. Minor typos, language and references corrections. To be published in the proceedings in Theor. Math. Phy

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.Comment: 75 pages (plus optional table of contents). Sign errors in elliptic case equations (1A.13), (1A.15) and (1A.25) are corrected. Not relevant to proof contained in pape

Accuracy of one-dimensional collision integral in the rigid spheres approximation

The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate values of collision frequency. For moderate masses of buffer molecules the error of one-dimensional approximation is found not to exceed 5%.Comment: LaTeX, 24 pages, 8 figure

The second fossil species of <i>Cathartosilvanus</i> (Coleoptera: Cucujoidea: Silvanidae) from Eocene Baltic amber

A new fossil species of the silvanid flat bark beetle genus Cathartosilvanus Grouvelle is described and illustrated from Baltic amber. Cathartosilvanus siteiterralevis sp. nov. differs from recent and fossil congeners in the distinct, sharp denticle found along its posterior pronotal angle. The phenomenon of specific body parts becoming disconnected, and the compression of specimens is briefly discussed and interpreted in the context of amber taphonomy. The specimen under study appears to be an uncommon case of a weakly sclerotized beetle imago becoming entrapped in resin shortly after moulting.</p

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2\pi) under the influence of a time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither symmetric function of t nor antisymmetric under time shifts $E(t \pm T/2) \neq -E(t)$, an ensemble of trajectories with zero current at t=0 yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.Comment: 2 figure

External voltage sources and Tunneling in quantum wires

We (re) consider in this paper the problem of tunneling through an impurity in a quantum wire with arbitrary Luttinger interaction parameter. By combining the integrable approach developed in the case of Quantum Hall edge states with the introduction of radiative boundary conditions to describe the adiabatic coupling to reservoirs, we are able to obtain the exact equilibrium and non equilibrium current. One of the most striking features observed is the appearance of negative differential conductances out of equilibrium in the strongly interacting regime g <=.2. In spite of the various charging effects, a remarkable form of duality is still observed. New results on the computation of transport properties in integrable impurity problems are gathered in appendices. In particular, we prove that the TBA results satisfy a remarkable relation, originally derived using the Keldysh formalism, between the order T^2 correction to the current out of equilibrium and the second derivative of this current at T=0 with respect to the voltage.Comment: 16 pages, 7 figure

Some possible techniques for improving the strength characteristics of folded cores from sheet composite materials

We consider some general problems of improving the strength characteristics of folded cores as well as the corresponding techniques for modifying the core material polymer surfaces with the use of nanotechnologies and the "mass-strength" criteria. © Allerton Press, Inc., 2009

Determination of load-carrying capacity in panels with chevron-type cores

In this paper, the problem on creation of a mathematical model describing the behavior of a sandwich panel with chevron-type cores is considered. The model is meant for calculating the ultimate shearing compressive loads and its parameters are determined by the identification methods on the basis of experimental data. © Allerton Press, Inc. 2007