1,943 research outputs found
Projective and Coarse Projective Integration for Problems with Continuous Symmetries
Temporal integration of equations possessing continuous symmetries (e.g.
systems with translational invariance associated with traveling solutions and
scale invariance associated with self-similar solutions) in a ``co-evolving''
frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with
the evolving solution) leads to improved accuracy because of the smaller time
derivative in the new spatial frame. The slower time behavior permits the use
of {\it projective} and {\it coarse projective} integration with longer
projective steps in the computation of the time evolution of partial
differential equations and multiscale systems, respectively. These methods are
also demonstrated to be effective for systems which only approximately or
asymptotically possess continuous symmetries. The ideas of projective
integration in a co-evolving frame are illustrated on the one-dimensional,
translationally invariant Nagumo partial differential equation (PDE). A
corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is
used to illustrate the coarse-grained method. A simple, one-dimensional
diffusion problem is used to illustrate the scale invariant case. The
efficiency of projective integration in the co-evolving frame for both the
macroscopic diffusion PDE and for a random-walker particle based model is again
demonstrated
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems
In "equation-free" multiscale computation a dynamic model is given at a fine,
microscopic level; yet we believe that its coarse-grained, macroscopic dynamics
can be described by closed equations involving only coarse variables. These
variables are typically various low-order moments of the distributions evolved
through the microscopic model. We consider the problem of integrating these
unavailable equations by acting directly on kinetic Monte Carlo microscopic
simulators, thus circumventing their derivation in closed form. In particular,
we use projective multi-step integration to solve the coarse initial value
problem forward in time as well as backward in time (under certain conditions).
Macroscopic trajectories are thus traced back to unstable, source-type, and
even sometimes saddle-like stationary points, even though the microscopic
simulator only evolves forward in time. We also demonstrate the use of such
projective integrators in a shooting boundary value problem formulation for the
computation of "coarse limit cycles" of the macroscopic behavior, and the
approximation of their stability through estimates of the leading "coarse
Floquet multipliers".Comment: Submitted to Journal of Computational Physic
Group inquiry to aid organisational learning in enterprises
This paper describes a method for surfacing and exploring ‘situated knowledge’ in medium-sized organisations, with employee groups utilising a ‘low impact’ form of group support system (GSS), based on wireless handsets. Some results of piloting this method are summarised and one intervention is presented in detail. The method encouraged organisational members to give voice to the emotions and politics of leadership and learning in organisations, and helped to articulate how situated knowledge was ignored, as well as utilised. The method is practical, and may be used by organisations for themselves to aid the development of group as well as individual reflection, to stimulate the consideration of change
Active Brownian particles with velocity-alignment and active fluctuations
We consider a model of active Brownian particles with velocity-alignment in
two spatial dimensions with passive and active fluctuations. Hereby, active
fluctuations refers to purely non-equilibrium stochastic forces correlated with
the heading of an individual active particle. In the simplest case studied
here, they are assumed as independent stochastic forces parallel (speed noise)
and perpendicular (angular noise) to the velocity of the particle. On the other
hand, passive fluctuations are defined by a noise vector independent of the
direction of motion of a particle, and may account for example for thermal
fluctuations.
We derive a macroscopic description of the active Brownian particle gas with
velocity-alignment interaction. Hereby, we start from the individual based
description in terms of stochastic differential equations (Langevin equations)
and derive equations of motion for the coarse grained kinetic variables
(density, velocity and temperature) via a moment expansion of the corresponding
probability density function.
We focus here in particular on the different impact of active and passive
fluctuations on the onset of collective motion and show how active fluctuations
in the active Brownian dynamics can change the phase-transition behaviour of
the system. In particular, we show that active angular fluctuation lead to an
earlier breakdown of collective motion and to emergence of a new bistable
regime in the mean-field case.Comment: 5 figures, 22 pages, submitted to New Journal of Physic
iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes
We describe and implement iMapD, a computer-assisted approach for
accelerating the exploration of uncharted effective Free Energy Surfaces (FES),
and more generally for the extraction of coarse-grained, macroscopic
information from atomistic or stochastic (here Molecular Dynamics, MD)
simulations. The approach functionally links the MD simulator with nonlinear
manifold learning techniques. The added value comes from biasing the simulator
towards new, unexplored phase space regions by exploiting the smoothness of the
(gradually, as the exploration progresses) revealed intrinsic low-dimensional
geometry of the FES
SCUBA - A submillimetre camera operating on the James Clerk Maxwell Telescope
The Submillimetre Common-User Bolometer Array (SCUBA) is one of a new
generation of cameras designed to operate in the submillimetre waveband. The
instrument has a wide wavelength range covering all the atmospheric
transmission windows between 300 and 2000 microns. In the heart of the
instrument are two arrays of bolometers optimised for the short (350/450
microns) and long (750/850 microns) wavelength ends of the submillimetre
spectrum. The two arrays can be used simultaneously, giving a unique
dual-wavelength capability, and have a 2.3 arc-minute field of view on the sky.
Background-limited performance is achieved by cooling the arrays to below 100
mK. SCUBA has now been in active service for over a year, and has already made
substantial breakthroughs in many areas of astronomy. In this paper we present
an overview of the performance of SCUBA during the commissioning phase on the
James Clerk Maxwell Telescope (JCMT).Comment: 14 pages, 13 figures (1 JPEG), Proc SPIE vol 335
Optimized Forest-Ruth- and Suzuki-like algorithms for integration of motion in many-body systems
An approach is proposed to improve the efficiency of fourth-order algorithms
for numerical integration of the equations of motion in molecular dynamics
simulations. The approach is based on an extension of the decomposition scheme
by introducing extra evolution subpropagators. The extended set of parameters
of the integration is then determined by reducing the norm of truncation terms
to a minimum. In such a way, we derive new explicit symplectic Forest-Ruth- and
Suzuki-like integrators and present them in time-reversible velocity and
position forms. It is proven that these optimized integrators lead to the best
accuracy in the calculations at the same computational cost among all possible
algorithms of the fourth order from a given decomposition class. It is shown
also that the Forest-Ruth-like algorithms, which are based on direct
decomposition of exponential propagators, provide better optimization than
their Suzuki-like counterparts which represent compositions of second-order
schemes. In particular, using our optimized Forest-Ruth-like algorithms allows
us to increase the efficiency of the computations more than in ten times with
respect to that of the original integrator by Forest and Ruth, and
approximately in five times with respect to Suzuki's approach. The theoretical
predictions are confirmed in molecular dynamics simulations of a Lennard-Jones
fluid. A special case of the optimization of the proposed Forest-Ruth-like
algorithms to celestial mechanics simulations is considered as well.Comment: 12 pages, 3 figures; submitted to Computer Physics Communication
Coarse-graining the dynamics of coupled oscillators
We present an equation-free computational approach to the study of the
coarse-grained dynamics of {\it finite} assemblies of {\it non-identical}
coupled oscillators at and near full synchronization. We use coarse-grained
observables which account for the (rapidly developing) correlations between
phase angles and oscillator natural frequencies. Exploiting short bursts of
appropriately initialized detailed simulations, we circumvent the derivation of
closures for the long-term dynamics of the assembly statistics.Comment: accepted for publication in Phys. Rev. Let
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