2,033 research outputs found
Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras
We compute the short distance expansion of fields or operators that live in
the coadjoint representation of an infinite dimensional Lie algebra by using
only properties of the adjoint representation and its dual. We explicitly
compute the short distance expansion for the duals of the Virasoro algebra,
affine Lie Algebras and the geometrically realized N-extended supersymmetric GR
Virasoro algebra.Comment: 19 pages, LaTeX twice, no figure, replacement has corrected Lie
algebr
Superspace Geometrical Realization of the N-Extended Super Virasoro Algebra and its Dual
We derive properties of N-extended GR super Virasoro algebras. These include
adding central extensions, identification of all primary fields and the action
of the adjoint representation on its dual. The final result suggest
identification with the spectrum of fields in supergravity theories and
superstring/M-theory constructed from NSR N-extended supersymmetric Virasoro algebras.Comment: 17 pages Latex Typos in TeX file has been correcte
Stretched exponentials and power laws in granular avalanching
We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the overdamped, sliding motion of particle clusters. The crossover in behaviour observed in experiments on piles of rice is attributed to a change in the dominant mode of transport. We predict that power law avalanching will be observed whenever surface flow is dominated by clustered motion.
Comment: 8 pages, more concise and some points clarified
A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion
We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins () above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form for the {\it whole} temperature range. The numerical values for
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request),
uses phyzzx.te
Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study
We have studied kinetics of random sequential adsorption of mixtures on a
square lattice using Monte Carlo method. Mixtures of linear short segments and
long segments were deposited with the probability and , respectively.
For fixed lengths of each segment in the mixture, the jamming limits decrease
when increases. The jamming limits of mixtures always are greater than
those of the pure short- or long-segment deposition.
For fixed and fixed length of the short segments, the jamming limits have
a maximum when the length of the long segment increases. We conjectured a
kinetic equation for the jamming coverage based on the data fitting.Comment: 7 pages, latex, 5 postscript figure
Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices
We study the statistical properties of eigenvalues of the Hessian matrix
(matrix of second derivatives of the potential energy) for a
classical atomic liquid, and compare these properties with predictions for
random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal
Mode or INM spectra) are evaluated numerically for configurations generated by
molecular dynamics simulations. We find that distribution of spacings between
nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction , with the agreement being better for higher densities at fixed
temperature. The deviations display a correlation with the number of localized
eigenstates (normal modes) in the liquid; there are fewer localized states at
higher densities which we quantify by calculating the participation ratios of
the normal modes. We confirm this observation by calculating the spacing
distribution for parts of the INM spectra with high participation ratios,
obtaining greater conformity with the Wigner form. We also calculate the
spectral rigidity and find a substantial dependence on the density of the
liquid.Comment: To appear in Phys. Rev. E; 10 pages, 6 figure
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