74,739 research outputs found
Partitioning of energy in highly polydisperse granular gases
A highly polydisperse granular gas is modeled by a continuous distribution of
particle sizes, a, giving rise to a corresponding continuous temperature
profile, T(a), which we compute approximately, generalizing previous results
for binary or multicomponent mixtures. If the system is driven, it evolves
towards a stationary temperature profile, which is discussed for several
driving mechanisms in dependence on the variance of the size distribution. For
a uniform distribution of sizes, the stationary temperature profile is
nonuniform with either hot small particles (constant force driving) or hot
large particles (constant velocity or constant energy driving). Polydispersity
always gives rise to non-Gaussian velocity distributions. Depending on the
driving mechanism the tails can be either overpopulated or underpopulated as
compared to the molecular gas. The deviations are mainly due to small
particles. In the case of free cooling the decay rate depends continuously on
particle size, while all partial temperatures decay according to Haff's law.
The analytical results are supported by event driven simulations for a large,
but discrete number of species.Comment: 10 pages; 5 figure
Homogeneous cooling of rough, dissipative particles: Theory and simulations
We investigate freely cooling systems of rough spheres in two and three
dimensions. Simulations using an event driven algorithm are compared with
results of an approximate kinetic theory, based on the assumption of a
generalized homogeneous cooling state. For short times , translational and
rotational energy are found to change linearly with . For large times both
energies decay like with a ratio independent of time, but not
corresponding to equipartition. Good agreement is found between theory and
simulations, as long as no clustering instability is observed. System
parameters, i.e. density, particle size, and particle mass can be absorbed in a
rescaled time, so that the decay of translational and rotational energy is
solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure
How river rocks round: resolving the shape-size paradox
River-bed sediments display two universal downstream trends: fining, in which
particle size decreases; and rounding, where pebble shapes evolve toward
ellipsoids. Rounding is known to result from transport-induced abrasion;
however many researchers argue that the contribution of abrasion to downstream
fining is negligible. This presents a paradox: downstream shape change
indicates substantial abrasion, while size change apparently rules it out. Here
we use laboratory experiments and numerical modeling to show quantitatively
that pebble abrasion is a curvature-driven flow problem. As a consequence,
abrasion occurs in two well-separated phases: first, pebble edges rapidly round
without any change in axis dimensions until the shape becomes entirely convex;
and second, axis dimensions are then slowly reduced while the particle remains
convex. Explicit study of pebble shape evolution helps resolve the shape-size
paradox by reconciling discrepancies between laboratory and field studies, and
enhances our ability to decipher the transport history of a river rock.Comment: 11 pages, 5 figure
25 Years of Self-Organized Criticality: Numerical Detection Methods
The detection and characterization of self-organized criticality (SOC), in
both real and simulated data, has undergone many significant revisions over the
past 25 years. The explosive advances in the many numerical methods available
for detecting, discriminating, and ultimately testing, SOC have played a
critical role in developing our understanding of how systems experience and
exhibit SOC. In this article, methods of detecting SOC are reviewed; from
correlations to complexity to critical quantities. A description of the basic
autocorrelation method leads into a detailed analysis of application-oriented
methods developed in the last 25 years. In the second half of this manuscript
space-based, time-based and spatial-temporal methods are reviewed and the
prevalence of power laws in nature is described, with an emphasis on event
detection and characterization. The search for numerical methods to clearly and
unambiguously detect SOC in data often leads us outside the comfort zone of our
own disciplines - the answers to these questions are often obtained by studying
the advances made in other fields of study. In addition, numerical detection
methods often provide the optimum link between simulations and experiments in
scientific research. We seek to explore this boundary where the rubber meets
the road, to review this expanding field of research of numerical detection of
SOC systems over the past 25 years, and to iterate forwards so as to provide
some foresight and guidance into developing breakthroughs in this subject over
the next quarter of a century.Comment: Space Science Review series on SO
The Two Regime method for optimizing stochastic reaction-diffusion simulations
The computer simulation of stochastic reaction-diffusion processes in biology is often done using either compartment-based (spatially discretized) simulations or molecular-based (Brownian dynamics) approaches. Compartment-based approaches can yield quick and accurate mesoscopic results but lack the level of detail that is characteristic of the more computationally intensive molecular-based models. Often microscopic detail is only required in a small region but currently the best way to achieve this detail is to use a resource intensive model over the whole domain. We introduce the Two Regime Method (TRM) in which a molecular-based algorithm is used in part of the computational domain and a compartment-based approach is used elsewhere in the computational domain. We apply the TRM to two test problems including a model from developmental biology. We thereby show that the TRM is accurate and subsequently may be used to inspect both mesoscopic and microscopic detail of reaction diffusion simulations according to the demands of the modeller
Brownian Dynamics Simulation of Polydisperse Hard Spheres
Standard algorithms for the numerical integration of the Langevin equation
require that interactions are slowly varying during to the integration
timestep. This in not the case for hard-body systems, where there is no
clearcut between the correlation time of the noise and the timescale of the
interactions. Starting from a short time approximation of the Smoluchowsky
equation, we introduce an algorithm for the simulation of the overdamped
Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamics
interactions and briefly discuss the extension to the case of external drifts
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection
Turbulence is argued to play a crucial role in cloud droplet growth. The
combined problem of turbulence and cloud droplet growth is numerically
challenging. Here, an Eulerian scheme based on the Smoluchowski equation is
compared with two Lagrangian superparticle (or su- perdroplet) schemes in the
presence of condensation and collection. The growth processes are studied
either separately or in combination using either two-dimensional turbulence, a
steady flow, or just gravitational acceleration without gas flow. Good
agreement between the differ- ent schemes for the time evolution of the size
spectra is observed in the presence of gravity or turbulence. Higher moments of
the size spectra are found to be a useful tool to characterize the growth of
the largest drops through collection. Remarkably, the tails of the size spectra
are reasonably well described by a gamma distribution in cases with gravity or
turbulence. The Lagrangian schemes are generally found to be superior over the
Eulerian one in terms of computational performance. However, it is shown that
the use of interpolation schemes such as the cloud-in-cell algorithm is
detrimental in connection with superparticle or superdroplet approaches.
Furthermore, the use of symmetric over asymmetric collection schemes is shown
to reduce the amount of scatter in the results.Comment: 36 pages, 17 figure
Dust in Brown Dwarfs IV. Dust formation and driven turbulence on mesoscopic scales
Dust formation in brown dwarf atmospheres is studied by utilising a model for
driven turbulence in the mesoscopic scale regime. We apply a pseudo-spectral
method where waves are created and superimposed within a limited wavenumber
interval. The turbulent kinetic energy distribution follows the Kolmogoroff
spectrum which is assumed to be the most likely value. Such superimposed,
stochastic waves may occur in a convectively active environment. They cause
nucleation fronts and nucleation events and thereby initiate the dust formation
process which continues until all condensible material is consumed. Small
disturbances are found to have a large impact on the dust forming system. An
initially dust-hostile region, which may originally be optically thin, becomes
optically thick in a patchy way showing considerable variations in the dust
properties during the formation process. The dust appears in lanes and curls as
a result of the interaction with waves, i.e. turbulence, which form larger and
larger structures with time. Aiming on a physical understanding of the
variability of brown dwarfs, related to structure formation in substellar
atmospheres, we work out first necessary criteria for small-scale closure
models to be applied in macroscopic simulations of dust forming astrophysical
systems.Comment: A&A accepted, 20 page
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