Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

To progress from the laboratory to commercial applications, it will be necessary to develop industrially scalable methods to produce large quantities of defect-free graphene. Here we show that high-shear mixing of graphite in suitable stabilizing liquids results in large-scale exfoliation to give dispersions of graphene nanosheets. X-ray photoelectron spectroscopy and Raman spectroscopy show the exfoliated flakes to be unoxidized and free of basal-plane defects. We have developed a simple model that shows exfoliation to occur once the local shear rate exceeds 10(4) s(-1). By fully characterizing the scaling behaviour of the graphene production rate, we show that exfoliation can be achieved in liquid volumes from hundreds of millilitres up to hundreds of litres and beyond. The graphene produced by this method performs well in applications from composites to conductive coatings. This method can be applied to exfoliate BN, MoS2 and a range of other layered crystals.

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Scalable production of large quantities of defect-free few-layer graphene by shear exfoliation in liquids

Polymer-based nanocapsules for drug delivery

Polymer nanoparticles: Preparation techniques and size-control parameters

The flow of homogeneous fluids through porous media: analogies with other physical problems

Solution of population balance equations using the direct quadrature method of moments

Investigation of particulate systems often requires the solution of a population balance, which is a continuity statement written in terms of the number density function. In turn, the number density function is defined in terms of an internal coordinate (e.g., particle length, particle volume) and it generates integral and derivative terms. Different methods exist for numerically solving the population balance equation. For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics (CFD) simulation. Such an approach requires the addition of a large number of scalars and the associated transport equations. This increases the CPU time required for the simulation, and thus it is clear that it is very important to use as few scalars as possible. In this work the quadrature method of moments (QMOM) is used. The QMOM has already been validated for crystal growth and aggregation; here the method is extended to include breakage. QMOM performance is tested for 10 different cases in which the competition between aggregation and breakage leads to asymptotic solutions.

Quadrature method of moments for aggregation-breakage processes.

Although use of computational fluid dynamics (CFD) for simulating precipitation (and particulate systems in general) is becoming a standard approach, a number of issues still need to be addressed. One major problem is the computational expense of coupling a standard discretized population balance (DPB) with a CFD code, as this approach requires the solution of an intractably large number of transport equations. In this work the quadrature method of moments (QMOM) is tested for size-dependent growth and aggregation. The QMOM is validated by comparison with both Monte Carlo simulations and analytical solutions using several functional forms for the aggregation kernel. Moreover, model predictions are compared with a DPB to compare accuracy, computational time, and the number of scalars involved. Analysis of the relative performance of various methods for treating aggregation provides readers with useful information about the range of application and possible limitations.

Quadrature method of moments for population‐balance equations

Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away

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Daniele Marchisio

Papers

Solution of population balance equations using the direct quadrature method of moments

Quadrature method of moments for aggregation-breakage processes.

Quadrature method of moments for population‐balance equations

Computational Models for Polydisperse Particulate and Multiphase Systems

Application of the direct quadrature method of moments to polydisperse gas–solid fluidized beds