Joshua A. Anderson, Ph.D.

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Melting in two dimensions

Melting behavior of polygons

We study the melting behavior of all regular polygons from triangles to tetradecagons. Triangles, squares, and hexagons melt continuously with x-atic phases; pentagons have a first order, one-step melting transition, and regular polygons with seven or more edges follow the same two-step behavior as disks.

Melting behavior of polygons

Hard disk hexatic phase

We apply Massively Parallel Monte Carlo to systems of hard disks. Combined with results from Event Chain Monte Carlo and Event Driven Molecular Dynamics, we confirm the existence of the hexatic phase and the first order fluid to hexatic phase transition for hard disks.

Melting in two dimensions

Hard particle self assembly

Shape allophiles

Shape allophiles

We investigate a class of "shape allophiles" that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. We examine the assembly characteristics of this system via the potential of mean force and torque, and the fraction of particles that entropically bind.

Optimization Problems

Shape filling

Optimal filling of shapes

We propose filling as a type of placement problem similar to covering and packing. Filling is the optimal placement of N overlapping objects entirely inside an arbitrary shape so as to cover the most interior volume. We attack the problem with a Genetic Algorithm and develop heuristics to efficiently find solutions in polygons.

GPU Computing


Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We implement this method in HOOMD-blue intended for simulation of hard, faceted nanoparticles, with a conservative WCA interparticle potential, coupled to a thermodynamic ensemble.

AABB tree

Hard particle Monte Carlo


We implement multi-CPU and multi-GPU parallel hard particle Monte Carlo (HPMC) methods in HOOMD-blue v2.0. HPMC supports a wide variety of shape classes, including spheres/disks, unions of spheres, convex polygons, convex spheropolygons, concave polygons, ellipsoids/ellipses, convex polyhedra, convex spheropolyhedra, spheres cut by planes, and concave polyhedra.

BVH trees for neighbor lists

We implement a bounding volume hierarchy (BVH) acceleration structure for efficient neighbor searching in molecular dynamics simulations. The BVH structure allows fast lookup of neighbors even when particle size disparity is very large, enabling research that was previously inconceivable due to slow cell list performance.

AABB tree

Strong scaling MD on GPUs

Strong scaling of a monolayer

We implement multi-GPU scaling in HOOMD-blue, available open source starting in v1.0. Strong scaling is enabled with GPU optimized communication routines, including optional use of GPUDirect RDMA. We demonstrate scaling of a 108 million particle system to more than 3000 nodes on Titan.

Massively Parallel Monte Carlo

We develop a massively parallel method to perform Monte Carlo simulations of off-lattice particles. Our GPU implementation is 18 times faster on an NVIDIA K20 GPU than on an 8-core Intel CPU. In our initial work, we apply our method to large scale simulations of hard disks in 2D and confirm the existence of the hexatic phase.

Massively parallel Monte Carlo

GPU Accelerated Rigid Body MD

GPU Accelerated Rigid Body MD

We expand HOOMD-blue with the capability to group particle together into rigid bodies. All steps of the computation are implemented on the GPU, offering significant speed ups over serial CPU implementations. Performance on a single GPU is significantly faster than possible even with a parallel CPU domain decomposition scheme.

GPU Accelerated DPD

We expand HOOMD-blue with Dissipative Particle Dynamics (DPD) thermostats. Hash-based random number generators provide excellent performance for this algorithm on the GPU.

GPU Accelerated Dissipative Particle Dynamics

GPU Accelerated MD

GPU Accelerated MD

We develop HOOMD-blue, a general purpose particle simulation tool written from the ground up for maximum performance on massively parallel GPUs.

Polymer Self-assembly

Nanoparticle Telechelics


We use a polymer tether to geometrically constrain a pair of nanoparticles into a nanoparticle telechelic. Our simulation results show how architectural features control the self-assembled morphologies. HOOMD-blue powers these simulations on NVIDIA GPUs.

Polymer Nanocomposites

We perform a systematic investigation of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution. Functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system without inorganic components. HOOMD-blue powers these simulations on NVIDIA GPUs.


Pluronic Micelles


We study cubic phases of Pluronic F127 in solution using coarse-grained Molecular Dynamics.