23,419 research outputs found
Particle-based and Meshless Methods with Aboria
Aboria is a powerful and flexible C++ library for the implementation of
particle-based numerical methods. The particles in such methods can represent
actual particles (e.g. Molecular Dynamics) or abstract particles used to
discretise a continuous function over a domain (e.g. Radial Basis Functions).
Aboria provides a particle container, compatible with the Standard Template
Library, spatial search data structures, and a Domain Specific Language to
specify non-linear operators on the particle set. This paper gives an overview
of Aboria's design, an example of use, and a performance benchmark
On the Hardness of the Strongly Dependent Decision Problem
We present necessary and sufficient conditions for solving the strongly
dependent decision (SDD) problem in various distributed systems. Our main
contribution is a novel characterization of the SDD problem based on point-set
topology. For partially synchronous systems, we show that any algorithm that
solves the SDD problem induces a set of executions that is closed with respect
to the point-set topology. We also show that the SDD problem is not solvable in
the asynchronous system augmented with any arbitrarily strong failure
detectors.Comment: Appeared in ICDCN 201
Direct Numerical Simulation of decaying two-dimensional turbulence in a no-slip square box using Smoothed Particle Hydrodynamics
This paper explores the application of SPH to a Direct Numerical Simulation
(DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain.
In this bounded domain, the inverse energy cascade, and a net torque exerted by
the boundary, result in a spontaneous spin up of the fluid, leading to a
typical end state of a large monopole vortex that fills the domain. The SPH
simulations were compared against published results using a high accuracy
pseudo-spectral code. Ensemble averages of the kinetic energy, enstrophy and
average vortex wavenumber compared well against the pseudo-spectral results, as
did the evolution of the total angular momentum of the fluid. However, while
the pseudo-spectral results emphasised the importance of the no-slip boundaries
as generators of long lived coherent vortices in the flow, no such generation
was seen in the SPH results. Vorticity filaments produced at the boundary were
always dissipated by the flow shortly after separating from the boundary layer.
The kinetic energy spectrum of the SPH results was calculated using a SPH
Fourier transform that operates directly on the disordered particles. The
ensemble kinetic energy spectrum showed the expected k-3 scaling over most of
the inertial range. However, the spectrum flattened at smaller length scales
(initially less than 7.5 particle spacings and growing in size over time),
indicating an excess of small-scale kinetic energy
Solving k-Set Agreement with Stable Skeleton Graphs
In this paper we consider the k-set agreement problem in distributed
message-passing systems using a round-based approach: Both synchrony of
communication and failures are captured just by means of the messages that
arrive within a round, resulting in round-by-round communication graphs that
can be characterized by simple communication predicates. We introduce the weak
communication predicate PSources(k) and show that it is tight for k-set
agreement, in the following sense: We (i) prove that there is no algorithm for
solving (k-1)-set agreement in systems characterized by PSources(k), and (ii)
present a novel distributed algorithm that achieves k-set agreement in runs
where PSources(k) holds. Our algorithm uses local approximations of the stable
skeleton graph, which reflects the underlying perpetual synchrony of a run. We
prove that this approximation is correct in all runs, regardless of the
communication predicate, and show that graph-theoretic properties of the stable
skeleton graph can be used to solve k-set agreement if PSources(k) holds.Comment: to appear in 16th IEEE Workshop on Dependable Parallel, Distributed
and Network-Centric System
Diffusion of particles with short-range interactions
A system of interacting Brownian particles subject to short-range repulsive
potentials is considered. A continuum description in the form of a nonlinear
diffusion equation is derived systematically in the dilute limit using the
method of matched asymptotic expansions. Numerical simulations are performed to
compare the results of the model with those of the commonly used mean-field and
Kirkwood-superposition approximations, as well as with Monte Carlo simulation
of the stochastic particle system, for various interaction potentials. Our
approach works best for very repulsive short-range potentials, while the
mean-field approximation is suitable for long-range interactions. The Kirkwood
superposition approximation provides an accurate description for both short-
and long-range potentials, but is considerably more computationally intensive
Static solutions from the point of view of comparison geometry
We analyze (the harmonic map representation of) static solutions of the
Einstein Equations in dimension three from the point of view of comparison
geometry. We find simple monotonic quantities capturing sharply the influence
of the Lapse function on the focussing of geodesics. This allows, in
particular, a sharp estimation of the Laplacian of the distance function to a
given (hyper)-surface. We apply the technique to asymptotically flat solutions
with regular and connected horizons and, after a detailed analysis of the
distance function to the horizon, we recover the Penrose inequality and the
uniqueness of the Schwarzschild solution. The proof of this last result does
not require proving conformal flatness at any intermediate step.Comment: 41 page
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