137,118 research outputs found
Billion-atom Synchronous Parallel Kinetic Monte Carlo Simulations of Critical 3D Ising Systems
An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm
developed by Martinez {\it et al} [{\it J.\ Comp.\ Phys.} {\bf 227} (2008)
3804] to discrete lattices is presented. The method solves the master equation
synchronously by recourse to null events that keep all processors time clocks
current in a global sense. Boundary conflicts are rigorously solved by adopting
a chessboard decomposition into non-interacting sublattices. We find that the
bias introduced by the spatial correlations attendant to the sublattice
decomposition is within the standard deviation of the serial method, which
confirms the statistical validity of the method. We have assessed the parallel
efficiency of the method and find that our algorithm scales consistently with
problem size and sublattice partition. We apply the method to the calculation
of scale-dependent critical exponents in billion-atom 3D Ising systems, with
very good agreement with state-of-the-art multispin simulations
Influence of long-range correlated surface and near the surface disorder on the process of adsorption of long-flexible polymer chains
The influence of long-range correlated surface and decaying near surface
disorder with quenched defects is studied. We consider a correlation function
for the defects of the form , where and
being the coordinate in the direction perpendicular to the surface and
denotes the distance parallel to the surface. We investigate the process of
adsorption of long-flexible polymer chains with excluded volume interactions on
a "marginal" and attractive wall in the framework of renormalization group
field theoretical approach up to first order of perturbation theory in a double
(,)- expansion (, ) for the
semi-infinite model with the above mentioned type of
surface and near the surface disorder in the limit . In particular we
study two limiting cases. First, we investigate the scenario where the chain's
extension it much larger then . Second, we consider the case where the
chain's extension is of the order of . For both cases we obtained series
for bulk and the whole set of surface critical exponents, characterizing the
process of adsorption of long-flexible polymer chains at the surface. The
polymer linear dimensions parallel and perpendicular to the surface and the
corresponding partition functions as well as the behavior of monomer density
profiles and the fraction of adsorbed monomers at the surface and in the volume
are studied.Comment: 31 pages, 5 figures, 2 table
Variations on Slavnov's scalar product
We consider the rational six-vertex model on an L-by-L lattice with domain
wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to
satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition
function is an (L-2N)-parameter extension of Slavnov's scalar product of a
Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX
spin-1/2 chain.
Decoupling the extra parameters, we obtain a third determinant expression for
the scalar product, where the first is due to Slavnov [1], and the second is
due to Kostov and Matsuo [2]. We show that the new determinant is a discrete KP
tau-function in the inhomogeneities, and consequently that tree-level N = 4 SYM
structure constants that are known to be determinants, remain determinants at
1-loop level.Comment: 17 page
A strategy for mapping unstructured mesh computational mechanics programs onto distributed memory parallel architectures
The motivation of this thesis was to develop strategies that would enable unstructured mesh based computational mechanics codes to exploit the computational advantages offered by distributed memory parallel processors. Strategies that successfully map structured mesh codes onto parallel machines have been developed over the previous decade and used to build a toolkit for automation of the parallelisation process. Extension of the capabilities of this toolkit to include unstructured mesh codes requires new strategies to be developed.
This thesis examines the method of parallelisation by geometric domain decomposition using the single program multi data programming paradigm with explicit message passing. This technique involves splitting (decomposing) the problem definition into P parts that may be distributed over P processors in a parallel machine. Each processor runs the same program and operates only on its part of the problem. Messages passed between the processors allow data exchange to maintain consistency with the original algorithm.
The strategies developed to parallelise unstructured mesh codes should meet a number of requirements:
The algorithms are faithfully reproduced in parallel.
The code is largely unaltered in the parallel version.
The parallel efficiency is maximised.
The techniques should scale to highly parallel systems.
The parallelisation process should become automated.
Techniques and strategies that meet these requirements are developed and tested in this dissertation using a state of the art integrated computational fluid dynamics and solid mechanics code. The results presented demonstrate the importance of the problem partition in the definition of inter-processor communication and hence parallel performance.
The classical measure of partition quality based on the number of cut edges in the mesh partition can be inadequate for real parallel machines. Consideration of the topology of the parallel machine in the mesh partition is demonstrated to be a more significant factor than the number of cut edges in the achieved parallel efficiency. It is shown to be advantageous to allow an increase in the volume of communication in order to achieve an efficient mapping dominated by localised communications. The limitation to parallel performance resulting from communication startup latency is clearly revealed together with strategies to minimise the effect.
The generic application of the techniques to other unstructured mesh codes is discussed in the context of automation of the parallelisation process. Automation of parallelisation based on the developed strategies is presented as possible through the use of run time inspector loops to accurately determine the dependencies that define the necessary inter-processor communication
The Statistical Mechanics for an Extended Nonlinear Epigenetic Dynamics. I
An extension of the control equations discussed by Goodwin is proposed which allows for arbitrary strong coupling and for arbitrary parallel coupling of metabolic pools and genetic loci. It is demonstrated that these generalized control equations can be put into canonical form and further that Liouville's theorem applies. In addition, it is demonstrated that after a suitable canonical transformation the resulting partition function can be solved in closed form, and this result, as well as that for the mean energy, is exhibited. Some remarks appropriate to additional extensions are presented
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