21,589 research outputs found
Self-organized critical behavior: the evolution of frozen spin networks model in quantum gravity
In quantum gravity, we study the evolution of a two-dimensional planar open
frozen spin network, in which the color (i.e. the twice spin of an edge)
labeling edge changes but the underlying graph remains fixed. The mainly
considered evolution rule, the random edge model, is depending on choosing an
edge randomly and changing the color of it by an even integer. Since the change
of color generally violate the gauge invariance conditions imposed on the
system, detailed propagation rule is needed and it can be defined in many ways.
Here, we provided one new propagation rule, in which the involved even integer
is not a constant one as in previous works, but changeable with certain
probability. In random edge model, we do find the evolution of the system under
the propagation rule exhibits power-law behavior, which is suggestive of the
self-organized criticality (SOC), and it is the first time to verify the SOC
behavior in such evolution model for the frozen spin network. Furthermore, the
increase of the average color of the spin network in time can show the nature
of inflation for the universe.Comment: 5 pages, 5 figure
Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques
We present a multigrid algorithm for self consistent solution of the
Kohn-Sham equations in real space. The entire problem is discretized on a real
space mesh with a high order finite difference representation. The resulting
self consistent equations are solved on a heirarchy of grids of increasing
resolution with a nonlinear Full Approximation Scheme, Full Multigrid
algorithm. The self consistency is effected by updates of the Poisson equation
and the exchange correlation potential at the end of each eigenfunction
correction cycle. The algorithm leads to highly efficient solution of the
equations, whereby the ground state electron distribution is obtained in only
two or three self consistency iterations on the finest scale.Comment: 13 pages, 2 figure
Functional Inequalities and Subordination: Stability of Nash and Poincar\'e inequalities
We show that certain functional inequalities, e.g.\ Nash-type and
Poincar\'e-type inequalities, for infinitesimal generators of semigroups
are preserved under subordination in the sense of Bochner. Our result improves
\cite[Theorem 1.3]{BM} by A.\ Bendikov and P.\ Maheux for fractional powers,
and it also holds for non-symmetric settings. As an application, we will derive
hypercontractivity, supercontractivity and ultracontractivity of subordinate
semigroups.Comment: 15 page
Strong Feller Continuity of Feller Processes and Semigroups
We study two equivalent characterizations of the strong Feller property for a
Markov process and of the associated sub-Markovian semigroup. One is described
in terms of locally uniform absolute continuity, whereas the other uses local
Orlicz-ultracontractivity. These criteria generalize many existing results on
strong Feller continuity and seem to be more natural for Feller processes. By
establishing the estimates of the first exit time from balls, we also
investigate the continuity of harmonic functions for Feller processes which
enjoy the strong Feller property.Comment: 24 page
On the Coupling Property of L\'{e}vy Processes
We give necessary and sufficient conditions guaranteeing that the coupling
for L\'evy processes (with non-degenerate jump part) is successful. Our method
relies on explicit formulae for the transition semigroup of a compound Poisson
process and earlier results by Mineka and Lindvall-Rogers on couplings of
random walks. In particular, we obtain that a L\'{e}vy process admits a
successful coupling, if it is a strong Feller process or if the L\'evy (jump)
measure has an absolutely continuous component.Comment: 14 page
The vortex dynamics of a Ginzburg-Landau system under pinning effect
It is proved that the vortices are attracted by impurities or inhomogeities
in the superconducting materials. The strong H^1-convergence for the
corresponding Ginzburg-Landau system is also proved.Comment: 23page
Spin Sum Rules at Low
Recent precision spin-structure data from Jefferson Lab have significantly
advanced our knowledge of nucleon structure at low . Results on the
neutron spin sum rules and polarizabilities in the low to intermediate
region are presented. The Burkhardt-Cuttingham Sum Rule was verified within
experimental uncertainties. When comparing with theoretical calculations,
results on spin polarizability show surprising disagreements with Chiral
Perturbation Theory predictions. Preliminary results on first moments at very
low are also presented.Comment: 4 pages, to be published in the Proceedings of the 10th Conference on
Intersections of Nuclear and Particle Physics (CIPANP
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