30 research outputs found
Parallel Computers and Complex Systems
We present an overview of the state of the art and future trends in high performance parallel and distributed computing, and discuss techniques for using such computers in the simulation of complex problems in computational science. The use of high performance parallel computers can help improve our understanding of complex systems, and the converse is also true --- we can apply techniques used for the study of complex systems to improve our understanding of parallel computing. We consider parallel computing as the mapping of one complex system --- typically a model of the world --- into another complex system --- the parallel computer. We study static, dynamic, spatial and temporal properties of both the complex systems and the map between them. The result is a better understanding of which computer architectures are good for which problems, and of software structure, automatic partitioning of data, and the performance of parallel machines
Baryon resonances from a novel fat-link fermion action
We present first results for masses of positive and negative parity excited
baryons in lattice QCD using an O(a^2) improved gluon action and a Fat Link
Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators
are constructed with fat links. The results are in agreement with earlier
calculations of N^* resonances using improved actions and exhibit a clear mass
splitting between the nucleon and its chiral partner, even for the Wilson
fermion action. The results also indicate a splitting between the lowest J^P =
1/2^- states for the two standard nucleon interpolating fields.Comment: 5 pages, 3 figures, talk given by W.Melnitchouk at LHP 2001 workshop,
Cairns, Australi
Novel fat-link fermion actions
The hadron mass spectrum is calculated in lattice QCD using a novel fat-link
clover fermion action in which only the irrelevant operators of the fermion
action are constructed using smeared links. The simulations are performed on a
16^3 X 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with
n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat Link
Irrelevant Clover (FLIC) action provides scaling which is superior to
mean-field improvement, and offers advantages over nonperturbative O(a)
improvement.Comment: 5 pages, 2 figures, talk given by J.Zanotti at LHP 2001 workshop,
Cairns, Australi
A lattice study of 3D compact QED at finite temperature
We study the deconfinement phase transition and monopole properties in the
finite temperature 3D compact Abelian gauge model on the lattice. We predict
the critical coupling as function of the lattice size in a simplified model to
describe monopole binding. We demonstrate numerically that the monopoles are
sensitive to the transition. In the deconfinement phase the monopoles appear in
the form of a dilute gas of magnetic dipoles. In the confinement phase both
monopole density and string tension differ from semiclassical estimates if
monopole binding is neglected. However, the analysis of the monopole clusters
shows that the relation between the string tension and the density of monopoles
in charged clusters is in reasonable agreement with those predictions. We study
the cluster structure of the vacuum in both phases of the model.Comment: 18 pages, 14 EPS figures, LaTeX uses epsfig.st
Orbital stability: analysis meets geometry
We present an introduction to the orbital stability of relative equilibria of
Hamiltonian dynamical systems on (finite and infinite dimensional) Banach
spaces. A convenient formulation of the theory of Hamiltonian dynamics with
symmetry and the corresponding momentum maps is proposed that allows us to
highlight the interplay between (symplectic) geometry and (functional) analysis
in the proofs of orbital stability of relative equilibria via the so-called
energy-momentum method. The theory is illustrated with examples from finite
dimensional systems, as well as from Hamiltonian PDE's, such as solitons,
standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the
wave equation, and for the Manakov system
Monopoles, confinement and deconfinement of (2+1)D compact lattice QED in external fields
The compact Abelian model in three space--time dimensions is studied in the
presence of external electromagnetic fields at finite temperatures. We show
that the deconfinement phase transition is independent on the strength of the
external fields. This result is in agreement with our observation that the
external fields create small--size magnetic dipoles from the vacuum which do
not influence the confining properties of the model. Contrary to the
deconfinement phase, the internal field in the direction of the applied
external field is attenuated in the confinement phase, this screening becomes
stronger with decreasing temperature.Comment: 22 pages, 24 EPS figures, LaTeX uses epsfig.st
Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions
We study, via Monte Carlo simulation, the dynamic critical behavior of the
Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which
generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to
non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in
steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic
critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95
the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also
present plausible fits compatible with this conjecture. We show that the
Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire
range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of
our work, we also obtain evidence concerning the corrections to scaling in
static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure
Path Integral Monte Carlo Approach to the U(1) Lattice Gauge Theory in (2+1) Dimensions
Path Integral Monte Carlo simulations have been performed for U(1) lattice
gauge theory in (2+1) dimensions on anisotropic lattices. We extractthe static
quark potential, the string tension and the low-lying "glueball" spectrum.The
Euclidean string tension and mass gap decrease exponentially at weakcoupling in
excellent agreement with the predictions of Polyakov and G{\" o}pfert and Mack,
but their magnitudes are five times bigger than predicted. Extrapolations are
made to the extreme anisotropic or Hamiltonian limit, and comparisons are made
with previous estimates obtained in the Hamiltonian formulation.Comment: 12 pages, 16 figure
Asymptotic stability of solitary waves
We show that the family of solitary waves (1-solitons) of the Korteweg-de Vries equation is asymptotically stable. Our methods also apply for the solitary waves of a class of generalized Korteweg-de Vries equations, In particular, we study the case where f(u)=u p+1 / (p+1) , p =1, 2, 3 (and 30, with f â C 4 ). The same asymptotic stability result for KdV is also proved for the case p =2 (the modified Korteweg-de Vries equation). We also prove asymptotic stability for the family of solitary waves for all but a finite number of values of p between 3 and 4. (The solitary waves are known to undergo a transition from stability to instability as the parameter p increases beyond the critical value p =4.) The solution is decomposed into a modulating solitary wave, with time-varying speed c(t) and phase Îł( t ) ( bound state part ), and an infinite dimensional perturbation ( radiating part ). The perturbation is shown to decay exponentially in time, in a local sense relative to a frame moving with the solitary wave. As p â4 â , the local decay or radiation rate decreases due to the presence of a resonance pole associated with the linearized evolution equation for solitary wave perturbations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46489/1/220_2005_Article_BF02101705.pd
Deconfinement transitions in lattice gauge theories]
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