Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure

An estimation of overall properties of heterogeneous Cosserat materials

In this work, we try to answer the following question : What is the effective characteristic length of a mixture of Cosserat continua ? More generally, homogenization methods for heterogeneous Cosserat media are proposed and applied to the case of linear elasticity. They first application deals with a beam network regarded as a discrete Cosserat medium and the second with a continuous heterogeneous Cosserat continuum

The time-dependent expected reward and deviation matrix of a finite QBD process

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we focus on the special case of a finite quasi-birth-and-death (QBD) process, motivated by the desire to compute the expected revenue lost in a MAP/PH/1/C queue. We use two different approaches in this context. The first is based on the solution of a finite system of matrix difference equations; it provides an expression for the blocks of the expected reward vector, the deviation matrix, and the mean first passage time matrix. The second approach, based on some results in the perturbation theory of Markov chains, leads to a recursive method to compute the full deviation matrix of a finite QBD process. We compare the two approaches using some numerical examples

Relating cellular structure of open solid food foams to their Young's modulus: Finite element calculation

International audienc

Experimental investigation and discrete simulation of fragmentation in expanded breakfast cereals

International audienceThe fragmentation behaviour of brittle airy cereal product is studied both numerically and experimentally. A cereal food item is subjected to severe compression up to the densification stage. Experimental evidence of typical airy food behaviour is pointed out including elasticity, cell collapse and densification regimes. In order to better explain the observed behaviour, especially the resulting fragmentation, a numerical approach is proposed based on the discrete element method. Predicted results show good agreement with experimental mechanical responses. In particular, the maximum force values for fragmentation and the size of resulting fragments are in good accordance with experiments. Our numerical results show that the observed fragment size distribution is the consequence of a small number of rupture events of cell walls. This result highlights the role of the airy structure associated with a particular tendency to form a bimodal size distribution of fragments

Application of the Discrete Element Method to crack propagation and crack branching in a vitreous dense biopolymer material.

Hedjazi, L. Martin, C. L. Guessasma, S. Della Valle, G. Dendievel, R. 18 PERGAMON-ELSEVIER SCIENCE LTDInternational audienceCrack propagation in a vitreous biopolymer material is simulated using the Discrete Element Method (DEM), which models the brittle material as an assembly of particles bonded together. The simulations are compared to experiments combining a high-speed camera monitoring of crack branching together with a micromechancial testing of samples where local mixture mode is generated by introducing a stress concentrator. Our experimental results show unstable crack propagation and branching occurring upon crack deviation by the action of the stress concentrator. The validity of the DEM simulations is checked by comparing its result to the Finite Element Method (FEM) and to an analytical expression under similar conditions. DEM results show a higher sensitivity to mixed mode compared to FEM and a better match with the analytical formulation. Finally, crack branching is correctly predicted using DEM without any specific criterion for the initiation of secondary cracks

Study of the cellular structure of extruded starches and its relations with expansion phenomenon and foam mechanical properties by X-ray tomography

International audienceThe cellular structure of extruded starch foams, with different amylose content (0–70%) has been determined by X-ray tomography (10 and 40 μm), leading to highly contrasted 3D images. These foam structures were analysed using a 3D granulometric approach. Their cellular features were determined for relative density (D*) values in the interval [0.11, 0.34]. Their mean cell size (MCS) and mean cell wall thickness (MWT) varied in the range [0.2, 5 mm] and [75, 630 μm], respectively, and were strongly correlated. For the same value of D*, the finest structures (MCS < 2 mm and MWT < 300 μm) were found the most resistant to rupture. These finest cellular structures were mainly obtained for larger moisture content (24%) during extrusion. The influence of the extrusion variables on the phenomena occurring at die expansion, such as nucleation, bubble growth and coalescence, was discussed. Finally, the influence of amylose content was attributed to elongational viscosity, in relation with the storage modulus in the rubbery domain