Joshua A. Anderson

General purpose molecular dynamics simulations fully implemented on graphics processing units

Graphics processing units (GPUs), originally developed for rendering real-time effects in computer games, now provide unprecedented computational power for scientific applications. In this paper, we develop a general purpose molecular dynamics code that runs entirely on a single GPU. It is shown that our GPU implementation provides a performance equivalent to that of fast 30 processor core distributed memory cluster. Our results show that GPUs already provide an inexpensive alternative to such clusters and discuss implications for the future.

Rigid body constraints realized in massively-parallel molecular dynamics on graphics processing units

Abstract Molecular dynamics (MD) methods compute the trajectory of a system of point particles in response to a potential function by numerically integrating Newtonʼs equations of motion. Extending these basic methods with rigid body constraints enables composite particles with complex shapes such as anisotropic nanoparticles, grains, molecules, and rigid proteins to be modeled. Rigid body constraints are added to the GPU-accelerated MD package, HOOMD-blue, version 0.10.0. The software can now simulate systems of particles, rigid bodies, or mixed systems in microcanonical (NVE), canonical (NVT), and isothermal-isobaric (NPT) ensembles. It can also apply the FIRE energy minimization technique to these systems. In this paper, we detail the massively parallel scheme that implements these algorithms and discuss how our design is tuned for the maximum possible performance. Two different case studies are included to demonstrate the performance attained, patchy spheres and tethered nanorods. In typical cases, HOOMD-blue on a single GTX 480 executes 2.5–3.6 times faster than LAMMPS executing the same simulation on any number of CPU cores in parallel. Simulations with rigid bodies may now be run with larger systems and for longer time scales on a single workstation than was previously even possible on large clusters.

Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newtons equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.

Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods

We report large-scale computer simulations of the hard-disk system at high densities in the region of the melting transition. Our simulations reproduce the equation of state, previously obtained using the event-chain Monte Carlo algorithm, with a massively parallel implementation of the local Monte Carlo method and with event-driven molecular dynamics. We analyze the relative performance of these simulation methods to sample configuration space and approach equilibrium. Our results confirm the first-order nature of the melting phase transition in hard disks. Phase coexistence is visualized for individual configurations via the orientational order parameter field. The analysis of positional order confirms the existence of the hexatic phase.

Nanoparticle assembly: made to order.

The DNA-mediated assembly of anisotropic gold nanoparticles shows the importance of particle shape in the controlled formation of DNA–nanoparticle superlattices.

Nanoparticle Ordering via Functionalized Block Copolymers in Solution

We consider nanoparticles and functionalized copolymers, block copolymers with attached end groups possessing a specific affinity for nanoparticles, in solution. Using molecular dynamics, we show that nanoparticles are able to direct the self-assembly of the polymer/nanoparticle composite. We perform a detailed study for a wide range of nanoparticle sizes and concentrations. We show that the nanoparticles order in a number of distinct phases: simple cubic, layered hexagonal, hexagonal columnar, gyroid, and a novel square columnar. Our results show that nanoparticles ordered with functionalized block copolymers can provide a simple and efficient tool for assembling novel materials with nanometer scale resolution.

Micellar crystals in solution from molecular dynamics simulations

Polymers with both soluble and insoluble blocks typically self-assemble into micelles, which are aggregates of a finite number of polymers where the soluble blocks shield the insoluble ones from contact with the solvent. Upon increasing concentration, these micelles often form gels that exhibit crystalline order in many systems. In this paper, we present a study of both the dynamics and the equilibrium properties of micellar crystals of triblock polymers using molecular dynamics simulations. Our results show that equilibration of single micelle degrees of freedom and crystal formation occur by polymer transfer between micelles, a process that is described by transition state theory. Near the disordered (or melting) transition, bcc lattices are favored for all triblocks studied. Lattices with fcc ordering are also found but only at lower kinetic temperatures and for triblocks with short hydrophilic blocks. Our results lead to a number of theoretical considerations and suggest a range of implications to experimental systems with a particular emphasis on Pluronic polymers.

Optimal Filling of Shapes

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

Efficient neighbor list calculation for molecular simulation of colloidal systems using graphics processing units

Abstract We present an algorithm based on linear bounding volume hierarchies (LBVHs) for computing neighbor (Verlet) lists using graphics processing units (GPUs) for colloidal systems characterized by large size disparities. We compare this to a GPU implementation of the current state-of-the-art CPU algorithm based on stenciled cell lists. We report benchmarks for both neighbor list algorithms in a Lennard-Jones binary mixture with synthetic interaction range disparity and a realistic colloid solution. LBVHs outperformed the stenciled cell lists for systems with moderate or large size disparity and dilute or semidilute fractions of large particles, conditions typical of colloidal systems.

Self-assembled ordered polymer nanocomposites directed by attractive particles

We theoretically investigate general conditions under which an inorganic phase can direct the self-assembly of an ordered polymer nanocomposite. For this purpose, we consider a solution of triblock copolymers forming a hexagonal phase of micelles and investigate the effect of adding attractive particles. We show that if the triblock is functionalized at its ends by attaching groups with specific affinity for the particles, thus effectively becoming a pentablock, the particles direct the self-assembly of the system into phases where both the polymers and the particles exhibit mesoscopic order. Different lamellar and gyroid phases (both with Ia3d and I4(1)32 space symmetries) are presented in detail. Our results show that functionalization is a very powerful route for directing self-assembly of polymer nanocomposites. We briefly discuss the connections with recent theoretical and experimental results in diblock melts with nanoparticles as well as for problems where polymers are used to template the growth of an inorganic phase in solution.