32,866 research outputs found
Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
A maximal minor of the Laplacian of an -vertex Eulerian digraph
gives rise to a finite group
known as the sandpile (or critical) group of . We determine
of the generalized de Bruijn graphs with
vertices and arcs for and , and closely related generalized Kautz graphs, extending and
completing earlier results for the classical de Bruijn and Kautz graphs.
Moreover, for a prime and an -cycle permutation matrix
we show that is isomorphic to the
quotient by of the centralizer of in
. This offers an explanation for the coincidence of
numerical data in sequences A027362 and A003473 of the OEIS, and allows one to
speculate upon a possibility to construct normal bases in the finite field
from spanning trees in .Comment: I+24 page
An Efficient Block Circulant Preconditioner For Simulating Fracture Using Large Fuse Networks
{\it Critical slowing down} associated with the iterative solvers close to
the critical point often hinders large-scale numerical simulation of fracture
using discrete lattice networks. This paper presents a block circlant
preconditioner for iterative solvers for the simulation of progressive fracture
in disordered, quasi-brittle materials using large discrete lattice networks.
The average computational cost of the present alorithm per iteration is , where the stiffness matrix is partioned into
-by- blocks such that each block is an -by- matrix, and
represents the operational count associated with solving a block-diagonal
matrix with -by- dense matrix blocks. This algorithm using the block
circulant preconditioner is faster than the Fourier accelerated preconditioned
conjugate gradient (PCG) algorithm, and alleviates the {\it critical slowing
down} that is especially severe close to the critical point. Numerical results
using random resistor networks substantiate the efficiency of the present
algorithm.Comment: 16 pages including 2 figure
Comparison of computed tomography pulmonary angiography and point-of-care tests for pulmonary thromboembolism diagnosis in dogs
The Dynamics of Charges Induced by a Charged Particle Traversing a Dielectric Slab
We studied the dynamics of surfacea and wake charges induced by a charged
particle traversing a dielectric slab. It is shown that after the crossing of
the slab first boundary, the induced on the slab surface charge (image charge)
is transformed into the wake charge, which overflows to the second boundary
when the particle crosses it. It is also shown, that the polarization of the
slab is of an oscillatory nature, and the net induced charge in a slab remains
zero at all stages of the motion.Comment: 12 pages, 1 figur
Phase transition in the Higgs model of scalar dyons
In the present paper we investigate the phase transition
"Coulomb--confinement" in the Higgs model of abelian scalar dyons -- particles
having both, electric and magnetic , charges. It is shown that by dual
symmetry this theory is equivalent to scalar fields with the effective squared
electric charge e^{*2}=e^2+g^2. But the Dirac relation distinguishes the
electric and magnetic charges of dyons. The following phase transition
couplings are obtained in the one--loop approximation:
\alpha_{crit}=e^2_{crit}/4\pi\approx 0.19,
\tilde\alpha_{crit}=g^2_{crit}/4\pi\approx 1.29 and \alpha^*_{crit}\approx
1.48.Comment: 16 pages, 2 figure
Excitation of surface plasmon-polaritons in metal films with double periodic modulation: anomalous optical effects
We perform a thorough theoretical analysis of resonance effects when an
arbitrarily polarized plane monochromatic wave is incident onto a double
periodically modulated metal film sandwiched by two different transparent
media. The proposed theory offers a generalization of the theory that had been
build in our recent papers for the simplest case of one-dimensional structures
to two-dimensional ones. A special emphasis is placed on the films with the
modulation caused by cylindrical inclusions, hence, the results obtained are
applicable to the films used in the experiments. We discuss a spectral
composition of modulated films and highlight the principal role of
``resonance'' and ``coupling'' modulation harmonics. All the originating
multiple resonances are examined in detail. The transformation coefficients
corresponding to different diffraction orders are investigated in the vicinity
of each resonance. We make a comparison between our theory and recent
experiments concerning enhanced light transmittance and show the ways of
increasing the efficiency of these phenomena. In the appendix we demonstrate a
close analogy between ELT effect and peculiarities of a forced motion of two
coupled classical oscillators.Comment: 24 pages, 17 figure
Radiating Shear-Free Gravitational Collapse with Charge
We present a new shear free model for the gravitational collapse of a
spherically symmetric charged body. We propose a dissipative contraction with
radiation emitted outwards. The Einstein field equations, using the junction
conditions and an ansatz, are integrated numerically. A check of the energy
conditions is also performed. We obtain that the charge delays the black hole
formation and it can even halt the collapse.Comment: 22 pages, 9 figures. It has been corrected several typos and included
several references. Accepted for publication in GR
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