On gauge fields - strings duality as an integrable system

It was suggested in hep-th/0002106, that semiclassically, a partition function of a string theory in the 5 dimensional constant negative curvature space with a boundary condition at the absolute satisfy the loop equation with respect to varying the boundary condition, and thus the partition function of the string gives the expectation value of a Wilson loop in the 4 dimensional QCD. In the paper, we present the geometrical framework, which reveals that the equations of motion of such string theory are integrable, in the sense that they can be written via a Lax pair with a spectral parameter. We also show, that the issue of the loop equation rests solely on the properly posing the boundary condition

A note on the glueball mass spectrum

A conjectured duality between supergravity and $N=\infty$ gauge theories gives predictions for the glueball masses as eigenvalues for a supergravity wave equations in a black hole geometry, and describes a physics, most relevant to a high-temeperature expansion of a lattice QCD. We present an analytical solution for eigenvalues and eigenfunctions, with eigenvalues given by zeroes of a certain well-computable function $r(p)$, which signify that the two solutions with desired behaviour at two singular points become linearly dependent. Our computation shows corrections to the WKB formula $m^2= 6n(n+1)$ for eigenvalues corresponding to glueball masses QCD-3, and gives the first states with masses $m^2=$ 11.58766; 34.52698; 68.974962; 114.91044; 172.33171; 241.236607; 321.626549, ... . In $QCD_4$, our computation gives squares of masses 37.169908; 81.354363; 138.473573; 208.859215; 292.583628; 389.671368; 500.132850; 623.97315 ... for $O++$. In both cases, we have a powerful method which allows to compute eigenvalues with an arbitrary precision, if needed so, which may provide quantative tests for the duality conjecture. Our results matches with the numerical computation of [5] well withing precision reported there in both $QCD_3$ and $QCD_4$ cases. As an additional curiosity, we report that for eigenvalues of about 7000, the power series, although convergent, has coefficients of orders ${10}^{34}$; tricks we used to get reliably the function $r(p)$, as also the final answer gets small, of order ${10}^{-6}$ in $QCD_4$. In principle we can go to infinitely high eigenavalues, but such computations maybe impractical due to corrections.Comment: References, acknowledgments added; some presentation improvement

Simulation of the Elastic Properties of Reinforced Kevlar-Graphene Composites

The compressive strength of unidirectional fiber composites in the form of Kevlar yarn with a thin outer layer of graphene was investigated and modeled. Such fiber structure may be fabricated by using a strong chemical bond between Kevlar yarn and graphene sheets. Chemical functionalization of graphene and Kevlar may achieved by modification of appropriate surface-bound functional (e.g., carboxylic acid) groups on their surfaces. In this report we studied elastic response to unidirectional in-plane applied load with load peaks along the diameter. The 2D linear elasticity model predicts that significant strengthening occurs when graphene outer layer radius is about 4 % of kevlar yarn radius. The polymer chains of Kevlar are linked into locally planar structure by hydrogen bonds across the chains, with transversal strength considerably weaker than longitudinal one. This suggests that introducing outer enveloping layer of graphene, linked to polymer chains by strong chemical bonds may significantly strengthen Kevlar fiber with respect to transversal deformations

Reactive self-heating model of aluminum spherical nanoparticles

Aluminum-oxygen reaction is important in many highly energetic, high pressure generating systems. Recent experiments with nanostructured thermites suggest that oxidation of aluminum nanoparticles occurs in a few microseconds. Such rapid reaction cannot be explained by a conventional diffusion-based mechanism. We present a rapid oxidation model of a spherical aluminum nanoparticle, using Cabrera-Mott moving boundary mechanism, and taking self-heating into account. In our model, electric potential solves the nonlinear Poisson equation. In contrast with the Coulomb potential, a "double-layer" type solution for the potential and self-heating leads to enhanced oxidation rates. At maximal reaction temperature of 2000 C, our model predicts overall oxidation time scale in microseconds range, in agreement with experimental evidence.Comment: submitte