798 research outputs found
Vectorized multigrid Poisson solver for the CDC CYBER 205
The full multigrid (FMG) method is applied to the two dimensional Poisson equation with Dirichlet boundary conditions. This has been chosen as a relatively simple test case for examining the efficiency of fully vectorizing of the multigrid method. Data structure and programming considerations and techniques are discussed, accompanied by performance details
From the area under the Bessel excursion to anomalous diffusion of cold atoms
Levy flights are random walks in which the probability distribution of the
step sizes is fat-tailed. Levy spatial diffusion has been observed for a
collection of ultra-cold Rb atoms and single Mg+ ions in an optical lattice.
Using the semiclassical theory of Sisyphus cooling, we treat the problem as a
coupled Levy walk, with correlations between the length and duration of the
excursions. The problem is related to the area under Bessel excursions,
overdamped Langevin motions that start and end at the origin, constrained to
remain positive, in the presence of an external logarithmic potential. In the
limit of a weak potential, the Airy distribution describing the areal
distribution of the Brownian excursion is found. Three distinct phases of the
dynamics are studied: normal diffusion, Levy diffusion and, below a certain
critical depth of the optical potential, x~ t^{3/2} scaling. The focus of the
paper is the analytical calculation of the joint probability density function
from a newly developed theory of the area under the Bessel excursion. The
latter describes the spatiotemporal correlations in the problem and is the
microscopic input needed to characterize the spatial diffusion of the atomic
cloud. A modified Montroll-Weiss (MW) equation for the density is obtained,
which depends on the statistics of velocity excursions and meanders. The
meander, a random walk in velocity space which starts at the origin and does
not cross it, describes the last jump event in the sequence. In the anomalous
phases, the statistics of meanders and excursions are essential for the
calculation of the mean square displacement, showing that our correction to the
MW equation is crucial, and points to the sensitivity of the transport on a
single jump event. Our work provides relations between the statistics of
velocity excursions and meanders and that of the diffusivity.Comment: Supersedes arXiv: 1305.008
A highly optimized vectorized code for Monte Carlo simulations of SU(3) lattice gauge theories
New methods are introduced for improving the performance of the vectorized Monte Carlo SU(3) lattice gauge theory algorithm using the CDC CYBER 205. Structure, algorithm and programming considerations are discussed. The performance achieved for a 16(4) lattice on a 2-pipe system may be phrased in terms of the link update time or overall MFLOPS rates. For 32-bit arithmetic, it is 36.3 microsecond/link for 8 hits per iteration (40.9 microsecond for 10 hits) or 101.5 MFLOPS
Scaling Green-Kubo relation and application to three aging systems
The Green-Kubo formula relates the spatial diffusion coefficient to the
stationary velocity autocorrelation function. We derive a generalization of the
Green-Kubo formula valid for systems with long-range or nonstationary
correlations for which the standard approach is no longer valid. For the
systems under consideration, the velocity autocorrelation function asymptotically exhibits a certain scaling behavior and
the diffusion is anomalous . We
show how both the anomalous diffusion coefficient and exponent
can be extracted from this scaling form. Our scaling Green-Kubo relation thus
extends an important relation between transport properties and correlation
functions to generic systems with scale invariant dynamics. This includes
stationary systems with slowly decaying power law correlations as well as aging
systems, whose properties depend on the the age of the system. Even for systems
that are stationary in the long time limit, we find that the long time
diffusive behavior can strongly depend on the initial preparation of the
system. In these cases, the diffusivity is not unique and we
determine its values for a stationary respectively nonstationary initial state.
We discuss three applications of the scaling Green-Kubo relation: Free
diffusion with nonlinear friction corresponding to cold atoms diffusing in
optical lattices, the fractional Langevin equation with external noise recently
suggested to model active transport in cells and the L\'evy walk with numerous
applications, in particular blinking quantum dots. These examples underline the
wide applicability of our approach, which is able to treat very different
mechanisms of anomalous diffusion.Comment: 16 pages, 6 figures, 1 tabl
Random time averaged diffusivities for L\'evy walks
We investigate a L\'evy-Walk alternating between velocities with
opposite sign. The sojourn time probability distribution at large times is a
power law lacking its mean or second moment. The first case corresponds to a
ballistic regime where the ensemble averaged mean squared displacement (MSD) at
large times is , the latter to enhanced diffusion with , . The correlation function and the time averaged
MSD are calculated. In the ballistic case, the deviations of the time averaged
MSD from a purely ballistic behavior are shown to be distributed according to a
Mittag-Leffler density function. In the enhanced diffusion regime, the
fluctuations of the time averages MSD vanish at large times, yet very slowly.
In both cases we quantify the discrepancy between the time averaged and
ensemble averaged MSDs
Stochastic Ergodicity Breaking: a Random Walk Approach
The continuous time random walk (CTRW) model exhibits a non-ergodic phase
when the average waiting time diverges. Using an analytical approach for the
non-biased and the uniformly biased CTRWs, and numerical simulations for the
CTRW in a potential field, we obtain the non-ergodic properties of the random
walk which show strong deviations from Boltzmann--Gibbs theory. We derive the
distribution function of occupation times in a bounded region of space which,
in the ergodic phase recovers the Boltzmann--Gibbs theory, while in the
non-ergodic phase yields a generalized non-ergodic statistical law.Comment: 5 pages, 3 figure
A walnut-containing meal had similar effects on early satiety, CCK, and PYY, but attenuated the postprandial GLP-1 and insulin response compared to a nut-free control meal.
Regular nut consumption is associated with lower adiposity and reduced weight gain in adulthood. Walnut feeding studies have observed minimal effect on body weight despite potential additional energy intake. Several mechanisms may explain why consuming nuts promotes weight control, including increased early phase satiety, possibly reflected in postprandial response of gastrointestinal and pancreatic peptides hypothesized to affect appetite. The purpose of this study was to compare postprandial insulin, glucagon and gastrointestinal peptide response and satiety following a meal with ∼54% of energy from walnuts or cream cheese, using a within-subject crossover study design in overweight/obese adults (N = 28). Sixty minutes after the walnut-containing meal, glucagon-like peptide-1 was lower than after the reference meal (p=0.0433), and peptide YY, cholecystokinin and ghrelin did not differ after the two meals. Sixty and 120 min after the walnut-containing meal, pancreatic polypeptide (p = 0.0014 and p = 0.0002) and glucose-dependent insulinotropic peptide (p < 0.0001 and p = 0.0079) were lower than after the reference meal, and 120 min after the walnut-containing meal, glucagon was higher (p=0.0069). Insulin and C-peptide increased at 60 min in response to both meals but were lower at 120 min after the walnut-containing meal (p=0.0349 and 0.0237, respectively). Satiety measures were similar after both meals. These findings fail to support the hypothesis that acute postprandial gastrointestinal peptide response to a walnut-containing meal contributes to increased satiety. However, inclusion of walnuts attenuated the postprandial insulin response, which may contribute to the more favorable lipid profile observed in association with regular walnut consumption
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