16,754 research outputs found
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
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
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
On generating functions of Hausdorff moment sequences
The class of generating functions for completely monotone sequences (moments
of finite positive measures on ) has an elegant characterization as the
class of Pick functions analytic and positive on . We establish
this and another such characterization and develop a variety of consequences.
In particular, we characterize generating functions for moments of convex and
concave probability distribution functions on . Also we provide a simple
analytic proof that for any real and with , the Fuss-Catalan or
Raney numbers , are the moments
of a probability distribution on some interval {if and only if}
and . The same statement holds for the binomial
coefficients , .Comment: 23 pages, LaTeX; Minor corrections and explanations added, literature
update. To appear in Transactions Amer. Math. So
Scattering and radiation analysis of three-dimensional cavity arrays via a hybrid finite element method
A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite element and boundary integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate gradient method in conjunction with the Fast Fourier Transform (FFT) thus achieving an O(N) storage requirement. By virtue of the finite element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique
Non-degenerate colorings in the Brook's Theorem
Let and be two integers. We will call a proper coloring
of the graph a \textit{-nondegenerate}, if for any vertex of
with degree at least there are at least vertices of different colors
adjacent to it. In our work we prove the following result, which generalizes
Brook's Theorem. Let and be a graph without cliques on
vertices and the degree of any vertex in this graph is not greater than .
Then for every integer there is a proper -nondegenerate vertex
-coloring of , where During the primary proof,
some interesting corollaries are derived.Comment: 18 pages, 10 figure
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