2,035 research outputs found
Molecular dynamics simulation: a tool for exploration and discovery using simple models
Emergent phenomena share the fascinating property of not being obvious
consequences of the design of the system in which they appear. This
characteristic is no less relevant when attempting to simulate such phenomena,
given that the outcome is not always a foregone conclusion. The present survey
focuses on several simple model systems that exhibit surprisingly rich emergent
behavior, all studied by MD simulation. The examples are taken from the
disparate fields of fluid dynamics, granular matter and supramolecular
self-assembly. In studies of fluids modeled at the detailed microscopic level
using discrete particles, the simulations demonstrate that complex hydrodynamic
phenomena in rotating and convecting fluids, the Taylor-Couette and
Rayleigh-B\'enard instabilities, can not only be observed within the limited
length and time scales accessible to MD, but even quantitative agreement can be
achieved. Simulation of highly counterintuitive segregation phenomena in
granular mixtures, again using MD methods, but now augmented by forces
producing damping and friction, leads to results that resemble experimentally
observed axial and radial segregation in the case of a rotating cylinder, and
to a novel form of horizontal segregation in a vertically vibrated layer.
Finally, when modeling self-assembly processes analogous to the formation of
the polyhedral shells that package spherical viruses, simulation of suitably
shaped particles reveals the ability to produce complete, error-free assembly,
and leads to the important general observation that reversible growth steps
contribute to the high yield. While there are limitations to the MD approach,
both computational and conceptual, the results offer a tantalizing hint of the
kinds of phenomena that can be explored, and what might be discovered when
sufficient resources are brought to bear on a problem.Comment: 21 pages, 20 figures (v2 - minor text addition
Hexagonal convection patterns in atomistically simulated fluids
Molecular dynamics simulation has been used to model pattern formation in
three-dimensional Rayleigh--Benard convection at the discrete-particle level.
Two examples are considered, one in which an almost perfect array of
hexagonally-shaped convection rolls appears, the other a much narrower system
that forms a set of linear rolls; both pattern types are familiar from
experiment. The nature of the flow within the convection cells and quantitative
aspects of the development of the hexagonal planform based on automated polygon
subdivision are analyzed. Despite the microscopic scale of the system,
relatively large simulations with several million particles and integration
timesteps are involved.Comment: 4 pages, 6 figures (color figures have low resolution, high
resolution figures available on author's website) Minor changes to text. To
appear in PRE (Rapid Comm
Simulated three-component granular segregation in a rotating drum
Discrete particle simulations are used to model segregation in granular
mixtures of three different particle species in a horizontal rotating drum.
Axial band formation is observed, with medium-size particles tending to be
located between alternating bands of big and small particles. Partial radial
segregation also appears; it precedes the axial segregation and is
characterized by an inner core region richer in small particles. Axial bands
are seen to merge during the long simulation runs, leading to a coarsening of
the band pattern; the relocation of particles involved in one such merging
event is examined. Overall, the behavior is similar to experiment and
represents a generalization of what occurs in the simpler two-component
mixture.Comment: 7 pages, 11 figures (low resolution color figures only; originals at
author's website http://www.ph.biu.ac.il/~rapaport/research/granular.html)
[revised version contains extra figures
Evaluating cumulative ascent: Mountain biking meets Mandelbrot
The problem of determining total distance ascended during a mountain bike
trip is addressed. Altitude measurements are obtained from GPS receivers
utilizing both GPS-based and barometric altitude data, with data averaging used
to reduce fluctuations. The estimation process is sensitive to the degree of
averaging, and is related to the well-known question of determining coastline
length. Barometric-based measurements prove more reliable, due to their
insensitivity to GPS altitude fluctuations.Comment: 10 pages, 9 figures (v.2: minor revisions
Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems
For percolating systems, we propose a universal exponent relation connecting
the leading corrections to scaling of the cluster size distribution with the
dynamic corrections to the asymptotic transport behaviour at criticality. Our
derivation is based on a cluster-resolved scaling theory unifying the scaling
of both the cluster size distribution and the dynamics of a random walker. We
corroborate our theoretical approach by extensive simulations for a site
percolating square lattice and numerically determine both the static and
dynamic correction exponents.Comment: 6 pages, 5 figures, 1 tabl
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