Representation of Solutions to the Equations of Statics for Transversely Isotropic Mildly Sloping Shells

A representation of solutions to the system of differential equations for the statics of elastic, transversely isotropic, mildly sloping shells is found in the form of a series in terms of a parameter that characterizes the difference of the median surface from spherical. Recurrence relations are obtained that can be used for solving boundary value problems by expansion in terms of a small parameter to arbitrary approximations.     

AdS3/CFT2 on a Torus in the Sum over Geometries

We investigate the AdS₃/CFT₂ correspondence for the Euclidean AdS₃ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at a finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In the sum over geometries in both the regular and the ℤ _N orbifold cases, the two-point correlation function for massless modes transforms into a finite sum of products of the conformal-anticonformal CFT Green's functions up to divergent terms proportional to the volume of the SL(2, ℤ)/ℤ group. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 17–30, January, 2006.     

The Three-Dimensional Theory of Stability of Fibrous and Laminated Materials

An analysis is made of the results of investigations into the internal and surface instability of fibrous and laminated composites within the framework of the piecewise-homogeneous model and the equations of the three-dimensional linearized theory of stability. The possible buckling modes of the reinforcing elements in composites with either an elastic (polymeric) or elastoplastic (metallic) matrix are studied. The reliability domains of applied approximate design models are determined and some applications of results on fracture (due to structural instability) of unidirectional composites are presented     

Extension of Geodesic Algebras to Continuous Genus

Using the Penner–Fock parameterization for Teichmüller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit.     

Infrared absorption in dense sodium vapor

The absorption spectra of a dense resonance medium were experimentally studied for the example of thermally heated dense sodium vapor. Several mechanisms that might cause substantial absorption and enhanced intensity of emission in the IR spectral region, λ τ; 0.9 μm, were considered. For the first time, a detailed study of the structure of the absorption spectra of sodium vapor in the specified wavelength range was performed to determine the influence of the kind and pressure of the buffer gas. It was found that buffer gas characteristics had a substantial effect on the absorption coefficient of vapor. The presence of the molecular component (dimers and trimers) in sodium vapor could not explain the experimental dependences of absorption in the infrared region. Possible influence of microparticles formed in condensation of convective sodium vapor flows in heated cells on the optical properties of vapor was considered. Microparticles could contribute to the observed absorption, but were incapable of explaining the substantial intensity of vapor radiation reported earlier. Possible many-particle effects on the absorption in the far spectral line wing were discussed. For the first time, the method of molecular dynamics was used to show for the example of the distribution function of ionic microfields in a dense plasma that such effects were in principle capable of substantially raising the profile of the line and increasing absorption in the region of large detunings from the resonance compared with the simple quasi-static model in the nearest-neighbor approximation.     

Topological recursion for chord diagrams,RNA complexes,and cells in moduli spaces

We introduce and study the Hermitian matrix model with potential _Vs,t(x)=x²/2−stx/(1−tx)$V_{s,t}(x)=x^2/2-stx/(1-tx)$, which enumerates the number of linear chord diagrams with no isolated vertices of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s   as a perturbation of the Gaussian potential, which arises for st=0$st=0$. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann?s moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly in genus less than four.     

Riemann surfaces with orbifold points

We interpret the previously developed Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces) as the Teichmüller theory of Riemann surfaces with orbifold points of order 2. In the Poincaré uniformization pattern, we describe necessary and sufficient conditions for the group generated by the Fuchsian group of the surface with added inversions to be of the almost hyperbolic Fuchsian type. All the techniques elaborated for the bordered surfaces (quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebra of geodesic functions) are equally applicable to the surfaces with orbifold points.     

Influence of surface load on stability of laminar bodies

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 24, No. 9, pp. 10–17, September, 1988.     

The Stability of Tribotechnical Laminated Polymeric Coatings

The stability of a laminated elastic coating with a polymeric bonding layer is considered within the framework of a piecewise-homogeneous model. The principle of critical strains is used in combination with the Volterra principle to account for the viscoelastic properties of polymers. Explicit expressions for determination of critical loads and time are derived. The range of variation in these parameters within which the coating does not buckle is found numerically