Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian–Eulerian (ALE) framework with the constraint that the mesh velocity and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy and, it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm.     

Approximation by Multipoles of the Multiple Acoustic Scattering by Small Obstacles in Three Dimensions and Application to the Foldy Theory of Isotropic Scattering

The asymptotic analysis carried out in this paper for the problem of a multiple scattering in three dimensions of a time-harmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by point sources. Among other issues, this asymptotic expansion of the wave furnishes a mathematical justification with optimal error estimates of Foldy’s method that consists in approximating each small obstacle by a point isotropic scatterer. Finally, it is shown how this theory can be further improved by adequately locating the center of phase of the point scatterers and the taking into account of self-interactions. In this way, it is established that the usual Foldy model may lead to an approximation whose asymptotic behavior is the same than that obtained when the multiple scattering effects are completely neglected.     

Reducing shear thickening of cement-based suspensions

Rheological measurements were made on concrete and mortars to characterize the shear thickening behavior of certain concrete mix designs. Shear thickening reduction levers were found by selecting and designing admixtures. Since the shear-thickening phenomena occur at the scale of the finest particles, industrial limestone fillers were studied that behave like cementitious materials. Theories based on previous academic works were relevant. The shear stress-dependent effects of shear thickening and size scaling were very helpful to distinguish between surface interactions, such as lubrication and volumetric contributions and also including the packing effects. The suspension viscosity curves vary accordingly to the Newtonian viscosity of the solvent medium. In both the shear thinning and shear thickening regimes, viscosity is controlled by adjusting the amount of two specific admixtures. The reduction of friction between polymer-coated materials appears to be a key phenomenon to delay onset shear thickening in industrial processes.     

Speeding-up structured probabilistic inference using pattern mining

In many domains where experts are the main source of knowledge, e.g., in reliability and risk management, a framework well suited for modeling, maintenance and exploitation of complex probabilistic systems is essential. In these domains, models usually define closed-world systems and result from the aggregation of multiple patterns repeated many times. Object Oriented-based Frameworks such as Probabilistic Relational Models (PRM) thus offer an effective way to represent such systems. They define patterns as classes and substitute large Bayesian networks (BN) by graphs of instances of these classes. In this framework, Structured Inference avoids many computation redundancies by exploiting class knowledge, hence reducing BN inference times by orders of magnitude. However, to keep modeling and maintenance costs low, object oriented-based framework’s classes often encode only generic situations. More complex situations, even those repeated many times, are only represented by combinations of instances. In this paper, we propose to determine online such combination patterns and exploit them as classes to speed-up Structured Inference. We prove that determining an optimal set of patterns is NP-hard. We also provide an efficient algorithm to approximate this set and show numerical experiments that highlight its practical efficiency.     

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods

We present a new hybrid conservative remapping algorithm for multimaterial Arbitrary Lagrangian–Eulerian (ALE) methods. The hybrid remapping is performed in two steps. In the first step, only nodes of the grid that lie inside subdomains occupied by single materials are moved. At this stage, computationally cheap swept-region remapping is used. In the second step, nodes that are vertices of mixed cells (cells containing several materials) and vertices of some cells in a buffer zone around mixed cells are moved. At this stage, intersection-based remapping is used. The hybrid algorithm results in computational expense that lies between swept-region and intersection-based remapping We demonstrate the performance of our new method for both structured and unstructured polygonal grids in two dimensions, as well as for cell-centered and staggered discretizations.     

Influence of bromine substitution pattern on the singlet oxygen generation efficiency of two-photon absorbing chromophores

A molecular engineering strategy based on rational variations of the bromine substitution pattern in two-photon absorbing singlet oxygen sensitizers allows studying the relations that exist between the positioning of an inter-system crossing promoter on the charge-transfer chromophore and its ability to generate singlet oxygen.     

Kinetic theory of long-range interacting systems with angle–action variables and collective effects

We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a Lenard–Balescu-type kinetic equation written in angle–action variables. We confirm the result obtained by Heyvaerts [Heyvaerts, Mon. Not. R. Astron. Soc. 407, 355 (2010)] who started from the Liouville equation and used the BBGKY hierarchy truncated at the level of the two-body distribution function (i.e., neglecting three-body correlations). When collective effects are ignored, we recover the Landau-type kinetic equation obtained in our previous papers [P.H. Chavanis, Physica A 377, 469 (2007); J. Stat. Mech., P05019 (2010)]. We also consider the relaxation of a test particle in a bath of field particles. Its stochastic motion is described by a Fokker–Planck equation written in angle–action variables. We determine the diffusion tensor and the friction force by explicitly calculating the first and second order moments of the increment of action of the test particle from its equations of motion, taking collective effects into account. This generalizes the expressions obtained in our previous works. We discuss the scaling with N$N$ of the relaxation time for the system as a whole and for a test particle in a bath.