1,713 research outputs found
Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem
Numerical simulations of the incompressible Euler equations are performed
using the Taylor-Green vortex initial conditions and resolutions up to
. The results are analyzed in terms of the classical analyticity strip
method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of
the time-decay of the width of the analyticity strip is observed at
the highest resolution for while preliminary 3D visualizations
show the collision of vortex sheets. The BKM criterium on the power-law growth
of supremum of the vorticity, applied on the same time-interval, is not
inconsistent with the occurrence of a singularity around .
These new findings lead us to investigate how fast the analyticity strip
width needs to decrease to zero in order to sustain a finite-time singularity
consistent with the BKM theorem. A new simple bound of the supremum norm of
vorticity in terms of the energy spectrum is introduced and used to combine the
BKM theorem with the analyticity-strip method. It is shown that a finite-time
blowup can exist only if vanishes sufficiently fast at the
singularity time. In particular, if a power law is assumed for then
its exponent must be greater than some critical value, thus providing a new
test that is applied to our Taylor-Green numerical simulation.
Our main conclusion is that the numerical results are not inconsistent with a
singularity but that higher-resolution studies are needed to extend the
time-interval on which a well-resolved power-law behavior of takes
place, and check whether the new regime is genuine and not simply a crossover
to a faster exponential decay
Exceptional type-I superconductivity of the layered silver oxide AgPbO
We report zero-resistivity transition and the details of magnetic transition
of a layered silver oxide AgPbO single crystal, which make
definitive evidence of superconductivity in this compound. In the AC
susceptibility of a mono-crystal, we observed large supercooling, as well as
positive peaks in the real part of the susceptibility indicating the
reversibility of magnetic process. These observations reveal that
AgPbO is probably the first oxide that shows type-I
superconductivity. Evaluation of the superconducting parameters not only gives
confirming evidence of type-I superconductivity, but also indicates that it is
a dirty-limit superconductor. We also analyze supercooling to determine the
upper limit of the Ginzburg-Landau parameter.Comment: v2: PACS numbers are adde
Form factors for semi-leptonic B decays
We report on form factors for the B->K l^+ l^- semi-leptonic decay process.
We use several lattice spacings from a=0.12 fm down to 0.06 fm and a variety of
dynamical quark masses with 2+1 flavors of asqtad quarks provided by the MILC
Collaboration. These ensembles allow good control of the chiral and continuum
extrapolations. The b-quark is treated as a clover quark with the Fermilab
interpretation. We update our results for f_\parallel and f_\perp, or,
equivalently, f_+ and f_0. In addition, we present new results for the tensor
form factor f_T. Model independent results are obtained based upon the
z-expansion.Comment: 7 pages, 4 figures, presented at The XXXth International Symposium on
Lattice Field Theory - Lattice 2012, June 24-29, 2012 Cairns, Australia, to
appear as PoS(Lattice 2012)12
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
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
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