81 research outputs found
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 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 , which signify that the two
solutions with desired behaviour at two singular points become linearly
dependent. Our computation shows corrections to the WKB formula
for eigenvalues corresponding to glueball masses QCD-3, and gives the first
states with masses 11.58766; 34.52698; 68.974962; 114.91044; 172.33171;
241.236607; 321.626549, ... . In , our computation gives squares of
masses 37.169908; 81.354363; 138.473573; 208.859215; 292.583628; 389.671368;
500.132850; 623.97315 ... for . 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 and cases. As an additional curiosity, we report
that for eigenvalues of about 7000, the power series, although convergent, has
coefficients of orders ; tricks we used to get reliably the function
, as also the final answer gets small, of order in .
In principle we can go to infinitely high eigenavalues, but such computations
maybe impractical due to corrections.Comment: References, acknowledgments added; some presentation improvement
Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy
Let O be a closed geodesic polygon in S 2 . Maps from O into S 2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S 2 , we compute the infimum Dirichlet energy, E(H), for continuous maps satisfying tangent boundary conditions of arbitrary homotopy type H. The expression for E(H) involves a topological invariant – the spelling length – associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S 2 − {s1 , . . . , sn }, ∗). The lower bound for E(H) is obtained from combinatorial group theory arguments, while the upper bound is obtained by constructing explicit representatives which, on all but an arbitrarily small subset of O, are alternatively locally conformal or anticonformal. For conformal and anticonformal classes (classes containing wholly conformal and anticonformal representatives respectively), the expression for E(H) reduces to a previous result involving the degrees of a set of regular values s1 , . . . , sn in the target S 2 space. These degrees may be viewed as invariants associated with the abelianization of π1 (S 2 − {s1 , . . . , sn }, ∗). For nonconformal classes, however, E(H) may be strictly greater than the abelian bound. This stems from the fact that, for nonconformal maps, the number of preimages of certain regular values may necessarily be strictly greater than the absolute value of their degrees.\ud
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This work is motivated by the theoretical modelling of nematic liquid crystals in confined polyhedral geometries. The results imply new lower and upper bounds for the Dirichlet energy (one-constant Oseen-Frank energy) of reflection-symmetric tangent unit-vector fields in a rectangular prism
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
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