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

http://research.engr.oregonstate.edu/immiscibles/sites/research.engr.oregonstate.edu.immiscibles/files/Papers/Wildenschild_Sheppard_AWR_2012.pdf

X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems

Local structure characterization with the bond-orientational order parameters q4, q6,  introduced by Steinhardt et al has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions and cluster formation Here we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater influence on both the numerical values and qualitative trend of ql than a change of the physical parameters, such as packing fraction Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by ql, leads to a lack of robustness of the ql as structure metrics Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics ql' These ql' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys Lett 90, 34001 (2010); Phys Rev E 85, 030301 (2012)]

/pdf/shortcomings-of-the-bond-orientational-order-parameters-for-1hkhjxzdyl.pdf

Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter

Local structure characterization with the bond-orientational order parameters q(4), q(6), ... introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)] has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions, and cluster formation. Here, we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of nearest neighboring (NN) spheres, NN(p), around a given central particle p; we show that the choice of neighborhood definition can have a bigger influence on both the numerical values and qualitative trend of q(l) than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by q(l), leads to a lack of robustness of the q(l) as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics q(l)'. These q(l)' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [G. E. Schroder-Turk et al., Europhys. Lett. 90, 34001 (2010); S. Kapfer et al., Phys. Rev. E 85, 030301(R) (2012)].

/pdf/shortcomings-of-the-bond-orientational-order-parameters-for-4dg8rqk7uq.pdf

Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure-property relationships for tensor-valued or orientation-dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor-valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear-time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co-polymer films by an electric field imaged by surface force microscopy; (b) local cell anisotropy of spherical bead pack models for granular matter and of closed-cell liquid foam models; (c) surface orientation in open-cell solid foams studied by X-ray tomography; and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.

Minkowski tensor shape analysis of cellular, granular and porous structures.

Microstructural evolution during deformation of tin dioxide nanoparticles in a comminution process

Mechanically induced phase transformation of zinc sulfide

In this work, the results of a series of molecular statics simulations to investigate the size dependence of the elastic properties of metallic nanoparticles are presented. The per-atom stiffness tensor was calculated from the derivative of the used embedded atom method potentials and, from it, lower order elastic parameters, such as the Young’s modulus or the Poisson ratio. The Young’s modulus decayed up to 30 % relative to the bulk values for 2.5 nm small particles, whereas the Poisson ratio showed an increase with decreasing particle size for most materials. Particles with a diameter of 30 nm approached the continuum values to around 1 %, marking the transition to continuum theory. The size-dependent Young’s modulus and several other material properties can be described by a simple algebraic function of the number of atoms per particle. By plotting the radial distribution of the local Young’s modulus within particles of different size, it is shown that only the outermost 2–3 atomic layers are responsible for the size-dependent change of elastic properties. Within these layers, the average atomic stiffness was found to decay linearly and independent of the particle size.

Size effects in the elastic deformation behavior of metallic nanoparticles

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Papers

Minkowski tensor shape analysis of cellular, granular and porous structures.

Microstructural evolution during deformation of tin dioxide nanoparticles in a comminution process

Mechanically induced phase transformation of zinc sulfide

Size effects in the elastic deformation behavior of metallic nanoparticles