Fausto Malvagi

Finite-size effects and percolation properties of Poisson geometries

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of d-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d=3. We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.

Benchmark solutions for transport in d-dimensional Markov binary mixtures

Abstract Linear particle transport in stochastic media is key to such relevant applications as neutron diffusion in randomly mixed immiscible materials, light propagation through engineered optical materials, and inertial confinement fusion, only to name a few. We extend the pioneering work by Adams, Larsen and Pomraning [1] (recently revisited by Brantley [2] ) by considering a series of benchmark configurations for mono-energetic and isotropic transport through Markov binary mixtures in dimension d. The stochastic media are generated by resorting to Poisson random tessellations in 1 d slab, 2 d extruded, and full 3 d geometry. For each realization, particle transport is performed by resorting to the Monte Carlo simulation. The distributions of the transmission and reflection coefficients on the free surfaces of the geometry are subsequently estimated, and the average values over the ensemble of realizations are computed. Reference solutions for the benchmark have never been provided before for two- and three-dimensional Poisson tessellations, and the results presented in this paper might thus be useful in order to validate fast but approximated models for particle transport in Markov stochastic media, such as the celebrated Chord Length Sampling algorithm.

Monte Carlo particle transport in random media: The effects of mixing statistics

Abstract Particle transport in random media obeying a given mixing statistics is key in several applications in nuclear reactor physics and more generally in diffusion phenomena emerging in optics and life sciences. Exact solutions for the ensemble-averaged physical observables are hardly available, and several approximate models have been thus developed, providing a compromise between the accurate treatment of the disorder-induced spatial correlations and the computational time. In order to validate these models, it is mandatory to use reference solutions in benchmark configurations, typically obtained by explicitly generating by Monte Carlo methods several realizations of random media, simulating particle transport in each realization, and finally taking the ensemble averages for the quantities of interest. In this context, intense research efforts have been devoted to Poisson (Markov) mixing statistics, where benchmark solutions have been derived for transport in one-dimensional geometries. In a recent work, we have generalized these solutions to two and three-dimensional configurations, and shown how dimension affects the simulation results. In this paper we will examine the impact of mixing statistics: to this aim, we will compare the reflection and transmission probabilities, as well as the particle flux, for three-dimensional random media obtained by using Poisson, Voronoi and Box stochastic tessellations. For each tessellation, we will furthermore discuss the effects of varying the fragmentation of the stochastic geometry, the material compositions, and the cross sections of the background materials.

Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

Abstract Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called ’Poisson Box Sampling’, PBS) aimed at improving the accuracy of the CLS approach for transport in d -dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

Pre-exascale Architectures: OpenPOWER Performance and Usability Assessment for French Scientific Community

Exascale implies a major pre-requisite in terms of energy efficiency, as an improvement of an order of magnitude must be reached in order to stay within an acceptable envelope of 20 MW. To address this objective and to continue to sustain performance, HPC architectures have to become denser, embedding many-core processors (to several hundreds of computing cores) and/or become heterogeneous, that is, using graphic processors or FPGAs. These energy-saving constraints will also affect the underlying hardware architectures (e.g., memory and storage hierarchies, networks) as well as system software (runtime, resource managers, file systems, etc.) and programming models. While some of these architectures, such as hybrid machines, have existed for a number of years and occupy noticeable ranks in the TOP 500 list, they are still limited to a small number of scientific domains and, moreover, require significant porting effort. However, recent developments of new paradigms (especially around OpenMP and OpenACC) make these architectures much more accessible to programmers. In order to make the most of these breakthrough upcoming technologies, GENCI and its partners have set up a technology watch group and lead collaborations with vendors, relying on HPC experts and early adopted HPC solutions. The two main objectives are providing guidance and prepare the scientific communities to challenges of exascale architectures.