3,759 research outputs found
Strong Stability Preserving Two-Step Runge-Kutta Methods
We investigate the strong stability preserving (SSP) property of two-step Rungeâ Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple\ud
subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP RungeâKutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order WENO discretizations
The Chiral Extension of Lattice QCD
The chiral extension of Quantum Chromodynamics (XQCD) adds to the standard
lattice action explicit pseudoscalar meson fields for the chiral condensates.
With this action, it is feasible to do simulations at the chiral limit with
zero mass Goldstone modes. We review the arguments for why this is expected to
be in the same universality class as the traditional action. We present
preliminary results on convergence of XQCD for naive fermions and on the
methodology for introducing counter terms to restore chiral symmetry for Wilson
fermions.Comment: 7 pages, LATTICE 94 talk by R. Brower: Latex file with 2 postscript
figures for encapsulatio
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
Effects of Chemical Potential on Hadron Masses in the Phase Transition Region
We study the response of hadron masses with respect to chemical potential at
. Our preliminary results of the pion channel show that in the confinement phase is significantly larger than that in
the deconfinement phase, which is consistent with the chiral restoration.Comment: LATTICE99 (finite temperature and density), 3 pages, 3 figure
The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme
The Traveling Salesman Problem (TSP) is among the most famous NP-hard
optimization problems. We design for this problem a randomized polynomial-time
algorithm that computes a (1+eps)-approximation to the optimal tour, for any
fixed eps>0, in TSP instances that form an arbitrary metric space with bounded
intrinsic dimension.
The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the
above result holds in the special case of TSP in a fixed-dimensional Euclidean
space. Thus, our algorithm demonstrates that the algorithmic tractability of
metric TSP depends on the dimensionality of the space and not on its specific
geometry. This result resolves a problem that has been open since the
quasi-polynomial time algorithm of Talwar (T-04)
NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist
Tables of ^1H and ^(13)C NMR chemical shifts have been compiled for common organic compounds often used as reagents or found as products or contaminants in deuterated organic solvents. Building upon the work of Gottlieb, Kotlyar, and Nudelman in the Journal of Organic Chemistry, signals for common impurities are now reported in additional NMR solvents (tetrahydrofuran-d_8, toluene-d_8, dichloromethane-d_2, chlorobenzene-d_5, and 2,2,2-trifluoroethanol-d_3) which are frequently used in organometallic laboratories. Chemical shifts for other organics which are often used as reagents or internal standards or are found as products in organometallic chemistry are also reported for all the listed solvents
SUSY on the lattice
The motivation and perspectives of numerical simulations of supersymmetric
Yang-Mills theories are reviewed.Comment: latex, 6 pages, 4 figures; Talk presented at LATTICE9
Responses of hadrons to chemical potential at finite temperature
We present a framework to compute the responses of hadron masses to the
chemical potential in lattice QCD simulations. As a first trial, the screening
mass of the pseudoscalar meson and its first and second responses are
evaluated. We present results on a lattice with two
flavors of staggered quarks below and above . The responses to both the
isoscalar and isovector chemical potentials are obtained. They show different
behavior in the low and the high temperature phases, which may be explained as
a consequence of chiral symmetry breaking and restoration, respectively.Comment: 10 pages, 11 figure
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