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

Thermosetting (bio)materials derived from renewable resources: A critical review

Physics of Flow through Porous Media

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

The theory of the dynamic bulk modulus, K(ω), of a porous rock, whose saturation occurs in patches of 100% saturation each of two different fluids, is developed within the context of the quasi-static Biot theory. The theory describes the crossover from the Biot–Gassmann–Woods result at low frequencies to the Biot–Gassmann–Hill result at high. Exact results for the approach to the low and the high frequency limits are derived. A simple closed-form analytic model based on these exact results, as well as on the properties of K(ω) extended to the complex ω-plane, is presented. Comparison against the exact solution in simple geometries for the case of a gas and water saturated rock demonstrates that the analytic theory is extremely accurate over the entire frequency range. Aside from the usual parameters of the Biot theory, the model has two geometrical parameters, one of which is the specific surface area, S/V, of the patches. In the special case that one of the fluids is a gas, the second parameter is a different, but also simple, measure of the patch size of the stiff fluid. The theory, in conjunction with relevant experiments, would allow one to deduce information about the sizes and shapes of the patches or, conversely, to make an accurate sonic-to-seismic conversion if the size and saturation values are approximately known.

Theory of Frequency Dependent Acoustics in Patchy-Saturated Porous Media

https://hal-upec-upem.archives-ouvertes.fr/hal-00684305/document

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

This work is concerned with the characterization of the statistical dependence between the components of random elasticity tensors that exhibit some given material symmetries. Such an issue has historically been addressed with no particular reliance on probabilistic reasoning, ending up in almost all cases with independent (or even some deterministic) variables. Therefore, we propose a contribution to the eld by having recourse to the Information Theory. Speci cally, we ci rst introduce a probabilistic methodology that allows for such a dependence to be rigorously characterized and which relies on the Maximum Entropy (MaxEnt) principle. We then discuss the induced dependence for the highest levels of elastic symmetries, ranging from isotropy to orthotropy. It is shown for instance that for the isotropic class, the bulk and shear moduli turn out to be independent Gamma-distributed random variables, whereas the associated stochastic Young modulus and Poisson ratio are statistically dependent random variables.

/pdf/on-the-statistical-dependence-for-the-components-of-random-226tz20hlk.pdf

On the Statistical Dependence for the Components of Random Elasticity Tensors Exhibiting Material Symmetry Properties

This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-Gaussian random fields which may take its values in some subset of the set of real symmetric positive-definite matrices presenting sparsity and invariance with respect to given orthogonal transformations. Within the context of linear elasticity, this situation is typically faced in the multiscale analysis of heterogeneous microstructures, where the constitutive elasticity matrices may exhibit some material symmetry properties. The representation introduced involves a parametrization which offers some flexibility for forward simulations and inverse identification by uncoupling the level of statistical fluctuations of the random field and the level of fluctuations associated with a stochastic measure of anisotropy. A novel numerical strategy for random generation is subsequently proposed and consists of solving a family of Ito stochastic differential equations. A Stormer-Verlet algorithm is used for the discretization of the stochastic differential equation.

/pdf/stochastic-model-and-generator-for-random-fields-with-hc9op1q9qp.pdf

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

This work is concerned with the construction of an equivalent continuum model for random interphases, based on a set of atomistic simulations. A stochastic representation for the tensor-valued random field modeling the elasticity field in the interphase region is first presented. Sampling issues are then discussed and a new numerical scheme based on stochastic differential equations is provided. Finally, a statistical inverse problem involving the atomistic computations is introduced in order to identify the stochastic continuum model.

https://hal-upec-upem.archives-ouvertes.fr/hal-01158280/document

Stochastic continuum modeling of random interphases from atomistic simulations

https://hal.archives-ouvertes.fr/hal-01223801/document

Johann Guilleminot

Papers

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

On the Statistical Dependence for the Components of Random Elasticity Tensors Exhibiting Material Symmetry Properties

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

Stochastic continuum modeling of random interphases from atomistic simulations

Stochastic continuum modeling of random interphases from atomistic simulations. Application to a polymer nanocomposite