Quantum fluids and classical determinants

Cvitanović, Predrag; Vattay, Gábor; Wirzba, A.

doi:10.1007/bfb0105968

Cited by 168 publications

(377 citation statements)

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“…When the analytic structure of the zeta function is known, from (9) we may single out the leading singularity in the logarithmic derivative, and then estimate the asymptotic behavior of (8), for instance by employing Tauberian theorems for Laplace transforms [21].…”

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confidence: 99%

Anomalous Transport: A Deterministic Approach

Artuso

Cristadoro

2003

Phys. Rev. Lett.

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confidence: 99%

Anomalous Transport: A Deterministic Approach

Artuso

Cristadoro

2003

Phys. Rev. Lett.

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“…17), and to T. Prellberg for critical comments. G. T. and R. A. thank the Center for Nonlinear Science for hospitality at Georgia Tech, where part of the work was done with support by Glen P. Robinson Chair.…”

Section: Acknowledgementsmentioning

confidence: 99%

Cycle Expansions for Intermittent Maps

Artuso

Cvitanović

Tanner

2003

Prog. Theor. Phys. Suppl.

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In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself through intermittency, dynamics where long periods of nearly regular motions are interrupted by irregular chaotic bursts. We discuss the Perron-Frobenius operator formalism for such systems, and show by means of a 1-dimensional intermittent map that intermittency induces branch cuts in dynamical zeta functions. Marginality leads to long-time dynamical correlations, in contrast to the exponentially fast decorrelations of purely chaotic dynamics. We apply the periodic orbit theory to quantitative characterization of the associated power-law decays. §1. IntroductionIn fluid dynamics one often observes long periods of regular dynamics (laminar phases) interrupted by irregular chaotic bursts, with the distribution of laminar phase intervals well described by a power law. This phenomenon is called intermittency, 1), 2) and it is a very general aspect of dynamics, a shadow cast by nonhyperbolic and marginally stable phase space regions. Complete hyperbolicity is indeed the exception rather than the rule: almost any dynamical system of interest exhibits a mixed phase space where islands of stability or regular regions coexist with hyperbolic regions with dynamics mixing exponentially fast. The trajectories on the border between chaos and regular dynamics are marginally stable, and trajectories from chaotic regions which come close to marginally stable regions can stay 'glued' there for arbitrarily long times. These intervals of regular motion are interrupted by irregular bursts as the trajectory is re-injected into the chaotic part of the phase space. How the trajectories are precisely 'glued' to the marginally stable region is often hard to describe. What coarsely looks like a border of an island in a Hamiltonian system with a mixed phase space, will under magnification dissolve into infinities of island chains of decreasing sizes and cantori.3)The existence of marginal or nearly marginal orbits is due to incomplete intersections of stable and unstable manifolds in a Smale horseshoe type dynamics. Following * )

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“…The unstable periodic orbits (UPOs) of a dynamical system provide us with a fertile representation of the chaotic dynamics on the attractor of that system and allow for the computation of time averages in terms of an exact expansion, based on the dynamical zeta function (Artuso et al 1990;Cvitanović et al 2004). A small number of these UPOs should furnish accurate predictions of turbulent flow.…”

Section: Identification Of Unstable Periodic Orbits In the Navier-stomentioning

confidence: 99%

Real science at the petascale

Saksena

Boghosian

Fazendeiro

et al. 2009

Phil. Trans. R. Soc. A.

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We describe computational science research that uses petascale resources to achieve scientific results at unprecedented scales and resolution. The applications span a wide range of domains, from investigation of fundamental problems in turbulence through computational materials science research to biomedical applications at the forefront of HIV/AIDS research and cerebrovascular haemodynamics. This work was mainly performed on the US TeraGrid 'petascale' resource, Ranger, at Texas Advanced Computing Center, in the first half of 2008 when it was the largest computing system in the world available for open scientific research. We have sought to use this petascale supercomputer optimally across application domains and scales, exploiting the excellent parallel scaling performance found on up to at least 32 768 cores for certain of our codes in the so-called 'capability computing' category as well as highthroughput intermediate-scale jobs for ensemble simulations in the 32-512 core range. Furthermore, this activity provides evidence that conventional parallel programming with MPI should be successful at the petascale in the short to medium term. We also report on the parallel performance of some of our codes on up to 65 636 cores on the IBM Blue Gene/P system at the Argonne Leadership Computing Facility, which has recently been named the fastest supercomputer in the world for open science.

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Quantum fluids and classical determinants

Cited by 168 publications

References 45 publications

Anomalous Transport: A Deterministic Approach

Anomalous Transport: A Deterministic Approach

Cycle Expansions for Intermittent Maps

Real science at the petascale

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