7,638 research outputs found
Rigorous stability results for a Laplacian moving boundary problem with kinetic undercooling
We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and non-trivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time t ! 1. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behaviour of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solution
Regularization of moving boundaries in a Laplacian field by a mixed Dirichlet-Neumann boundary condition : exact results
The dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically which shows that the uniformly propagating solution is linearly convectively stabl
The equation of state with nonzero chemical potential for 2+1 flavors
We present results for the QCD equation of state with nonzero chemical
potential using the Taylor expansion method with terms up to sixth order in the
expansion. Our calculations are performed on asqtad 2+1 quark flavor lattices
at .Comment: Talk given at the XXV International Symposium on Lattice Field
Theory, July 30-4 August 2007, Regensburg, German
Scaling studies of QCD with the dynamical HISQ action
We study the lattice spacing dependence, or scaling, of physical quantities
using the highly improved staggered quark (HISQ) action introduced by the
HPQCD/UKQCD collaboration, comparing our results to similar simulations with
the asqtad fermion action. Results are based on calculations with lattice
spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical
HISQ quarks. The strange and charm quark masses are near their physical values,
and the light-quark mass is set to 0.2 times the strange-quark mass. We look at
the lattice spacing dependence of hadron masses, pseudoscalar meson decay
constants, and the topological susceptibility. In addition to the commonly used
determination of the lattice spacing through the static quark potential, we
examine a determination proposed by the HPQCD collaboration that uses the decay
constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the
lattice artifacts in the HISQ simulations are much smaller than those in the
asqtad simulations at the same lattice spacings and quark masses.Comment: 36 pages, 11 figures, revised version to be published. Revisions
include discussion of autocorrelations and several clarification
The locality of the fourth root of staggered fermion determinant in the interacting case
The fourth root approximation in LQCD simulations with dynamical staggered
fermions requires justification. We test its validity numerically in the
interacting theory in a renormalization group framework.Comment: 6 pages, Talk presented at Lattice 2005 (Machines and Algorithms
Semileptonic Decays of Heavy Mesons with the Fat Clover Action
We are studying a variety of semileptonic decays of heavy-light mesons in an
effort to improve the determination of the heavy-quark Standard-Model CKM
matrix elements. Our fermion action is a novel, improved ``fat'' clover action
that promises to reduce problems with exceptional configurations. Dynamical sea
quarks are included in a mixed approach, i.e. we use staggered sea quarks and
fat-clover valence quarks. Here we report preliminary results.Comment: LATTICE99(heavyqk) - 3p, 4 Postscript fig
Rigorous stability results for a Laplacian moving boundary problem with kinetic undercooling
We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and non-trivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time t ! 1. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behaviour of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solution
A Lattice Study of the Gluon Propagator in Momentum Space
We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the
gluon propagator both in time at zero 3-momentum and in momentum space. From
the former quantity we obtain evidence for a dynamically generated effective
mass, which at beta=6.0 and beta=6.3 increases with the time separation of the
sources, in agreement with earlier results. The momentum space propagator G(k)
provides further evidence for mass generation. In particular, at beta=6.0, for
k less than 1 GeV, the propagator G(k) can be fit to a continuum formula
proposed by Gribov and others, which contains a mass scale b, presumably
related to the hadronization mass scale. For higher momenta Gribov's model no
longer provides a good fit, as G(k) tends rather to follow an inverse power
law. The results at beta=6.3 are consistent with those at beta=6.0, but only
the high momentum region is accessible on this lattice. We find b in the range
of three to four hundred MeV and the exponent of the inverse power law about
2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1
GeV) G(k) is best fit to a simple massive boson propagator with mass m. We
argue that such a discrepancy may be related to a lack of scaling for low
momenta at beta=5.7. {}From our results, the study of correlation functions in
momentum space looks promising, especially because the data points in Fourier
space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture
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