Molecular dynamics study of T=3 capsid assembly

Molecular dynamics simulation is used to model the self-assembly of polyhedral shells containing 180 trapezoidal particles that correspond to the T=3 virus capsid. Three kinds of particle, differing only slightly in shape, are used to account for the effect of quasi-equivalence. Bond formation between particles is reversible and an explicit atomistic solvent is included. Under suitable conditions the simulations are able to produce complete shells, with the majority of unused particles remaining as monomers, and practically no other clusters. There are also no incorrectly assembled clusters. The simulations reveal details of intermediate structures along the growth pathway, information that is relevant for interpreting experiment.Comment: 18 pages, 10 figures (minor changes

A new mechanism for granular segregation

A novel process is described that produces horizontal size segregation in a vertically vibrated layer of granular material. The behavior is a consequence of two distinct phenomena that are unique to excited granular media: vibration which causes the larger particles to rise to the top of the layer, and a vibrating base with a sawtooth surface profile which can produce stratified flows in opposite directions at different heights within the layer. The result of combining these effects is that large and small particles are horizontally driven in opposite directions. The observations reported here are based on computer simulations of granular models in two and three dimensions.Comment: 4 pages, 5 figures, revised (slightly longer) version, to be published in PR

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

Modeling capsid self-assembly: Design and analysis

A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms. The fact that different viruses adopt similar structural forms is an indication of a common underlying design, motivating the use of simplified, low-resolution models in exploring the assembly process. Several versions of a molecular dynamics approach are described. Polyhedral shells of different sizes are involved, the assembly pathways are either irreversible or reversible, and an explicit solvent is optionally included. Model design, simulation methodology and analysis techniques are discussed. The analysis focuses on the growth pathways and the nature of the intermediate states, properties that are hard to access experimentally. Among the key observations are that efficient growth proceeds by means of a cascade of highly reversible stages, and that while there are a large variety of possible partial assemblies, only a relatively small number of strongly bonded configurations are actually encountered.Comment: 27 pages, 18 fig

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

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

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

Close-packed structures and phase diagram of soft spheres in cylindrical pores

It is shown for a model system consisting of spherical particles confined in cylindrical pores that the first ten close-packed phases are in one-to-one correspondence with the first ten ways of folding a triangular lattice, each being characterized by a roll-up vector like the single-walled carbon nanotube. Phase diagrams in pressure-diameter and temperature-diameter planes are obtained by inherent-structure calculation and molecular dynamics simulation. The phase boundaries dividing two adjacent phases are infinitely sharp in the low-temperature limit but are blurred as temperature is increased. Existence of such phase boundaries explains rich, diameter-sensitive phase behavior unique for cylindrically confined systems

Computational study of the thermal conductivity in defective carbon nanostructures

We use non-equilibrium molecular dynamics simulations to study the adverse role of defects including isotopic impurities on the thermal conductivity of carbon nanotubes, graphene and graphene nanoribbons. We find that even in structurally perfect nanotubes and graphene, isotopic impurities reduce thermal conductivity by up to one half by decreasing the phonon mean free path. An even larger thermal conductivity reduction, with the same physical origin, occurs in presence of structural defects including vacancies and edges in narrow graphene nanoribbons. Our calculations reconcile results of former studies, which differed by up to an order of magnitude, by identifying limitations of various computational approaches

Stratified horizontal flow in vertically vibrated granular layers

A layer of granular material on a vertically vibrating sawtooth-shaped base exhibits horizontal flow whose speed and direction depend on the parameters specifying the system in a complex manner. Discrete-particle simulations reveal that the induced flow rate varies with height within the granular layer and oppositely directed flows can occur at different levels. The behavior of the overall flow is readily understood once this novel feature is taken into account.Comment: 4 pages, 6 figures, submitte