66 research outputs found
Eigenvalue Spacing Distribution for the Ensemble of Real Symmetric Toeplitz Matrices
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv
from a fixed probability distribution p of mean 0, variance 1, and finite
higher moments. The limiting spectral measure (the density of normalized
eigenvalues) converges weakly to a new universal distribution with unbounded
support, independent of p. This distribution's moments are almost those of the
Gaussian's; the deficit may be interpreted in terms of Diophantine
obstructions. With a little more work, we obtain almost sure convergence. An
investigation of spacings between adjacent normalized eigenvalues looks
Poissonian, and not GOE.Comment: 24 pages, 3 figure
On micro-structural effects in dielectric mixtures
The paper presents numerical simulations performed on dielectric properties
of two-dimensional binary composites on eleven regular space filling
tessellations. First, significant contributions of different parameters, which
play an important role in the electrical properties of the composite, are
introduced both for designing and analyzing material mixtures. Later, influence
of structural differences and intrinsic electrical properties of constituents
on the composite's over all electrical properties are investigated. The
structural differences are resolved by the spectral density representation
approach. The numerical technique, without any {\em a-priori} assumptions, for
extracting the spectral density function is also presented.Comment: 24 pages, 8 figure and 7 tables. It is submitted to IEEE Transactions
on Dielectrics and Electrical Insulatio
A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations
Incorporating covariate information in the covariance structure of misaligned spatial data
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