3,260 research outputs found
Statistics and deterministic simulation models: Why not?
Statistical Methods;mathematische statistiek
Approximate Inference for Constructing Astronomical Catalogs from Images
We present a new, fully generative model for constructing astronomical
catalogs from optical telescope image sets. Each pixel intensity is treated as
a random variable with parameters that depend on the latent properties of stars
and galaxies. These latent properties are themselves modeled as random. We
compare two procedures for posterior inference. One procedure is based on
Markov chain Monte Carlo (MCMC) while the other is based on variational
inference (VI). The MCMC procedure excels at quantifying uncertainty, while the
VI procedure is 1000 times faster. On a supercomputer, the VI procedure
efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50
terabytes of images in 14.6 minutes, demonstrating the scaling characteristics
necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic
Systematic errors in diffusion coefficients from long-time molecular dynamics simulations at constant pressure
In molecular dynamics simulations under periodic boundary conditions,
particle positions are typically wrapped into a reference box. For diffusion
coefficient calculations using the Einstein relation, the particle positions
need to be unwrapped. Here, we show that a widely used heuristic unwrapping
scheme is not suitable for long simulations at constant pressure. Improper
accounting for box-volume fluctuations creates, at long times, unphysical
trajectories and, in turn, grossly exaggerated diffusion coefficients. We
propose an alternative unwrapping scheme that resolves this issue. At each time
step, we add the minimal displacement vector according to periodic boundary
conditions for the instantaneous box geometry. Here and in a companion paper
[J. Chem. Phys. XXX, YYYYY (2020)], we apply the new unwrapping scheme to
extensive molecular dynamics and Brownian dynamics simulation data. We provide
practitioners with a formula to assess if and by how much earlier results might
have been affected by the widely used heuristic unwrapping scheme.Comment: 6 pages, 5 figures. The following article has been accepted for
publication at The Journal of Chemical Physic
Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
We introduce an efficient and numerically stable method for calculating
linear response functions of quantum systems at finite
temperatures. The method is a combination of numerical solution of the
time-dependent Schroedinger equation, random vector representation of trace,
and Chebyshev polynomial expansion of Boltzmann operator. This method should be
very useful for a wide range of strongly correlated quantum systems at finite
temperatures. We present an application to the ESR spectrum of s=1/2
antiferromagnet Cu benzoate.Comment: 4 pages, 4 figure
Scalable explicit implementation of anisotropic diffusion with Runge-Kutta-Legendre super-time-stepping
An important ingredient in numerical modelling of high temperature magnetised
astrophysical plasmas is the anisotropic transport of heat along magnetic field
lines from higher to lower temperatures.Magnetohydrodynamics (MHD) typically
involves solving the hyperbolic set of conservation equations along with the
induction equation. Incorporating anisotropic thermal conduction requires to
also treat parabolic terms arising from the diffusion operator. An explicit
treatment of parabolic terms will considerably reduce the simulation time step
due to its dependence on the square of the grid resolution () for
stability. Although an implicit scheme relaxes the constraint on stability, it
is difficult to distribute efficiently on a parallel architecture. Treating
parabolic terms with accelerated super-time stepping (STS) methods has been
discussed in literature but these methods suffer from poor accuracy (first
order in time) and also have difficult-to-choose tuneable stability parameters.
In this work we highlight a second order (in time) Runge Kutta Legendre (RKL)
scheme (first described by Meyer et. al. 2012) that is robust, fast and
accurate in treating parabolic terms alongside the hyperbolic conversation
laws. We demonstrate its superiority over the first order super time stepping
schemes with standard tests and astrophysical applications. We also show that
explicit conduction is particularly robust in handling saturated thermal
conduction. Parallel scaling of explicit conduction using RKL scheme is
demonstrated up to more than processors.Comment: 15 pages, 9 figures, incorporated comments from the referee. This
version is now accepted for publication in MNRA
- …