6,863 research outputs found
An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition
A non-intrusive proper generalized decomposition (PGD) strategy, coupled with
an overlapping domain decomposition (DD) method, is proposed to efficiently
construct surrogate models of parametric linear elliptic problems. A parametric
multi-domain formulation is presented, with local subproblems featuring
arbitrary Dirichlet interface conditions represented through the traces of the
finite element functions used for spatial discretization at the subdomain
level, with no need for additional auxiliary basis functions. The linearity of
the operator is exploited to devise low-dimensional problems with only few
active boundary parameters. An overlapping Schwarz method is used to glue the
local surrogate models, solving a linear system for the nodal values of the
parametric solution at the interfaces, without introducing Lagrange multipliers
to enforce the continuity in the overlapping region. The proposed DD-PGD
methodology relies on a fully algebraic formulation allowing for real-time
computation based on the efficient interpolation of the local surrogate models
in the parametric space, with no additional problems to be solved during the
execution of the Schwarz algorithm. Numerical results for parametric diffusion
and convection-diffusion problems are presented to showcase the accuracy of the
DD-PGD approach, its robustness in different regimes and its superior
performance with respect to standard high-fidelity DD methods
Annihilation of Immobile Reactants on the Bethe Lattice
Two-particle annihilation reaction, A+A -> inert, for immobile reactants on
the Bethe lattice is solved exactly for the initially random distribution. The
process reaches an absorbing state in which no nearest-neighbor reactants are
left. The approach of the concentration to the limiting value is exponential.
The solution reproduces the known one-dimensional result which is further
extended to the reaction A+B -> inert.Comment: 12 pp, TeX (plain
Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process
We consider the dynamics of the disordered, one-dimensional, symmetric zero
range process in which a particle from an occupied site hops to its nearest
neighbour with a quenched rate . These rates are chosen randomly from the
probability distribution , where is the lower cutoff.
For , this model is known to exhibit a phase transition in the steady
state from a low density phase with a finite number of particles at each site
to a high density aggregate phase in which the site with the lowest hopping
rate supports an infinite number of particles. In the latter case, it is
interesting to ask how the system locates the site with globally minimum rate.
We use an argument based on local equilibrium, supported by Monte Carlo
simulations, to describe the approach to the steady state. We find that at
large enough time, the mass transport in the regions with a smooth density
profile is described by a diffusion equation with site-dependent rates, while
the isolated points where the mass distribution is singular act as the
boundaries of these regions. Our argument implies that the relaxation time
scales with the system size as with for and
suggests a different behaviour for .Comment: Revtex, 7 pages including 3 figures. Submitted to Pramana -- special
issue on mesoscopic and disordered system
Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
We present a driven diffusive model which we call the Bus Route Model. The
model is defined on a one-dimensional lattice, with each lattice site having
two binary variables, one of which is conserved (``buses'') and one of which is
non-conserved (``passengers''). The buses are driven in a preferred direction
and are slowed down by the presence of passengers who arrive with rate lambda.
We study the model by simulation, heuristic argument and a mean-field theory.
All these approaches provide strong evidence of a transition between an
inhomogeneous ``jammed'' phase (where the buses bunch together) and a
homogeneous phase as the bus density is increased. However, we argue that a
strict phase transition is present only in the limit lambda -> 0. For small
lambda, we argue that the transition is replaced by an abrupt crossover which
is exponentially sharp in 1/lambda. We also study the coarsening of gaps
between buses in the jammed regime. An alternative interpretation of the model
is given in which the spaces between ``buses'' and the buses themselves are
interchanged. This describes a system of particles whose mobility decreases the
longer they have been stationary and could provide a model for, say, the flow
of a gelling or sticky material along a pipe.Comment: 17 pages Revtex, 20 figures, submitted to Phys. Rev.
A Novel Approach for the Particle-in-Cell Modelling of Gridded Ion Engine Plume Neutralisation
The Particle-in-Cell modelling of gridded ion engine plume neutralisation has been simplified when compared to traditional methods. This results in significantly less computational resources being required. The NSTAR engine was modelled as a reference, where simulated specific impulse values were found to be 5% higher than the real engine. This method will be most suited to rapid prototyping and optimisation studies, where speed of simulations is an important factor
Statistics of leaders and lead changes in growing networks
We investigate various aspects of the statistics of leaders in growing
network models defined by stochastic attachment rules. The leader is the node
with highest degree at a given time (or the node which reached that degree
first if there are co-leaders). This comprehensive study includes the full
distribution of the degree of the leader, its identity, the number of
co-leaders, as well as several observables characterizing the whole history of
lead changes: number of lead changes, number of distinct leaders, lead
persistence probability. We successively consider the following network models:
uniform attachment, linear attachment (the Barabasi-Albert model), and
generalized preferential attachment with initial attractiveness.Comment: 28 pages, 14 figures, 1 tabl
Kinetics of catalysis with surface disorder
We study the effects of generalised surface disorder on the monomer-monomer
model of heterogeneous catalysis, where disorder is implemented by allowing
different adsorption rates for each lattice site. By mapping the system in the
reaction-controlled limit onto a kinetic Ising model, we derive the rate
equations for the one and two-spin correlation functions. There is good
agreement between these equations and numerical simulations. We then study the
inclusion of desorption of monomers from the substrate, first by both species
and then by just one, and find exact time-dependent solutions for the one-spin
correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st
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