4,151 research outputs found
Combinatorial Identities and Quantum State Densities of Supersymmetric Sigma Models on N-Folds
There is a remarkable connection between the number of quantum states of
conformal theories and the sequence of dimensions of Lie algebras. In this
paper, we explore this connection by computing the asymptotic expansion of the
elliptic genus and the microscopic entropy of black holes associated with
(supersymmetric) sigma models. The new features of these results are the
appearance of correct prefactors in the state density expansion and in the
coefficient of the logarithmic correction to the entropy.Comment: 8 pages, no figures. To appear in the European Physical Journal
Torus knots and mirror symmetry
We propose a spectral curve describing torus knots and links in the B-model.
In particular, the application of the topological recursion to this curve
generates all their colored HOMFLY invariants. The curve is obtained by
exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved
conifold, and should be regarded as the mirror of the topological D-brane
associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we
derive the curve as the large N limit of the matrix model computing torus knot
invariants.Comment: 30 pages + appendix, 3 figure
Quantum States, Thermodynamic Limits and Entropy in M-Theory
We discuss the matching of the BPS part of the spectrum for (super)membrane,
which gives the possibility of getting membrane's results via string
calculations. In the small coupling limit of M--theory the entropy of the
system coincides with the standard entropy of type IIB string theory (including
the logarithmic correction term). The thermodynamic behavior at large coupling
constant is computed by considering M--theory on a manifold with topology
. We argue that the finite temperature
partition functions (brane Laurent series for ) associated with BPS
brane spectrum can be analytically continued to well--defined functionals.
It means that a finite temperature can be introduced in brane theory, which
behaves like finite temperature field theory. In the limit (point
particle limit) it gives rise to the standard behavior of thermodynamic
quantities.Comment: 7 pages, no figures, Revtex style. To be published in the Physical
Review
Exchange bias effect in alloys and compounds
The phenomenology of exchange bias effects observed in structurally
single-phase alloys and compounds but composed of a variety of coexisting
magnetic phases such as ferromagnetic, antiferromagnetic, ferrimagnetic,
spin-glass, cluster-glass and disordered magnetic states are reviewed. The
investigations on exchange bias effects are discussed in diverse types of
alloys and compounds where qualitative and quantitative aspects of magnetism
are focused based on macroscopic experimental tools such as magnetization and
magnetoresistance measurements. Here, we focus on improvement of fundamental
issues of the exchange bias effects rather than on their technological
importance
Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial
An elementary introduction to Khovanov construction of superpolynomials.
Despite its technical complexity, this method remains the only source of a
definition of superpolynomials from the first principles and therefore is
important for development and testing of alternative approaches. In this first
part of the review series we concentrate on the most transparent and
unambiguous part of the story: the unreduced Jones superpolynomials in the
fundamental representation and consider the 2-strand braids as the main
example. Already for the 5_1 knot the unreduced superpolynomial contains more
items than the ordinary Jones.Comment: 33 page
The phase portrait of a matter bounce in Horava-Lifshitz cosmology
The occurrence of a bounce in FRW cosmology requires modifications of general
relativity. An example of such a modification is the recently proposed
Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term
with a negative coefficient in the analog of the Friedmann equation. This paper
describes a phase space analysis of models of this sort with the aim of
determining to what extent bouncing solutions can occur. A simplification,
valid in the relevant region, allows a reduction of the dimension of phase
space so that visualization in three dimensions is possible. It is found that a
bounce is possible, but not generic in models under consideration. Apart from
previously known bouncing solutions some new ones are also described. Other
interesting solutions found include ones which describe a novel sort of
oscillating universes.Comment: 14 pages, 8 figure
Tachyon Field Quantization and Hawking Radiation
We quantize the tachyon field in a static two dimensional dilaton gravity
black hole background,and we calculate the Hawking radiation rate. We find that
the thermal radiation flux, due to the tachyon field, is larger than the
conformal matter one. We also find that massive scalar fields which do not
couple to the dilaton, do not give any contribution to the thermal radiation,
up to terms quadratic in the scalar curvature.Comment: 13 pages, Latex file, 1 figure available upon reques
Black Hole Entropy Associated with Supersymmetric Sigma Model
By means of an identity that equates elliptic genus partition function of a
supersymmetric sigma model on the -fold symmetric product of
(, is the symmetric group of elements) to the
partition function of a second quantized string theory, we derive the
asymptotic expansion of the partition function as well as the asymptotic for
the degeneracy of spectrum in string theory. The asymptotic expansion for the
state counting reproduces the logarithmic correction to the black hole entropy.Comment: 11 pages, no figures, version to appear in the Phys. Rev. D (2003
CO2 dissolution and design aspects of a multiorifice oscillatory baffled column
Dissolution of CO2 in water was studied for a batch vertical multiorifice baffled column (MOBC) with varying orifice diameters (d0) of 6.4-30 mm and baffle open area (α) of 15-42%. Bubble size distributions (BSDs) and the overall volumetric CO2 mass transfer coefficient (KLa) were experimentally evaluated for very low superficial gas velocities, UG of 0.12-0.81 mm s-1, using 5% v/v CO2 in the inlet gas stream at a range of fluid oscillations (f = 0-10 Hz and x0 = 0-10 mm). Remarkably, baffles presenting large do = 30 mm and α = 36%, therefore in the range typically found for single-orifice oscillatory baffled columns, were outperformed with respect to BSD control and CO2 dissolution by the other baffle designs or the same aerated column operating without baffles or fluid oscillations. Flow visualization and bubble tracking experiments also presented in this study established that a small do of 10.5 mm combined with a small value of α = 15% generates sufficient, strong eddy mixing capable of generating and trapping an extremely large fraction of microbubbles in the MOBC. This resulted in increased interfacial area yielding KLa values up to 65 ± 12 h-1 in the range of the UG tested, representing up to 3-fold increase in the rate of CO2 dissolution when compared to the unbaffled, steady column. In addition, a modi fied oscillatory Reynolds number, Re′o and Strouhal number, St' were presented to assist on the design and scale-up of gas-liquid systems based on multiorifice oscillatory ba ffled columns. This work is relevant to gas-liquid or multiphase chemical and biological systems relying on efficient dissolution of gaseous compounds into a liquid medium.BBSRC -European Commissio
HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
Explicit answer is given for the HOMFLY polynomial of the figure eight knot
in arbitrary symmetric representation R=[p]. It generalizes the old
answers for p=1 and 2 and the recently derived results for p=3,4, which are
fully consistent with the Ooguri-Vafa conjecture. The answer can be considered
as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the
"special" polynomials (they define the leading asymptotics of HOMFLY at q=1),
and arises in a form, convenient for comparison with the representation of the
Jones polynomials as sums of dilogarithm ratios. In particular, we construct a
difference equation ("non-commutative A-polynomial") in the representation
variable p. Simple symmetry transformation provides also a formula for
arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes
some obvious checks. Also straightforward is a deformation from HOMFLY to
superpolynomials. Further generalizations seem possible to arbitrary Young
diagrams R, but these expressions are harder to test because of the lack of
alternative results, even partial.Comment: 14 page
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