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Parsa S.,Wesleyan University | Calzavarini E.,Lille Laboratory of Mechanics | Toschi F.,TU Eindhoven | Voth G.A.,Wesleyan University
Physical Review Letters | Year: 2012

The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape. © 2012 American Physical Society. Source

Zhu Q.-Z.,University Paris Est Creteil | Zhu Q.-Z.,Lille Laboratory of Mechanics
International Journal for Numerical Methods in Engineering | Year: 2012

This paper presents mathematical derivation of enrichment functions in the extended finite element method for numerical modeling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by one interface across which displacement field suffers a jump. The main steps towards the derivation of enrichment functions are as follows: (1) extension of the subfields separated by the interface to the whole element domain and definition of complementary nodal variables; (2) construction of characteristic functions for describing the geometry and physical field; (3) determination of the sets of basic nodal variables; (4) domain decompositions according to Step 3 and then reproduction of the physical field in terms of characteristic functions and nodal variables; and (5) comparison of the piecewise interpolations formulated at Steps 3 and 4 with the standard extended finite element method form, which yields enrichment functions. In this process, the physical meanings of both the basic and complementary nodal variables are clarified, which helps to impose Dirichlet boundary conditions. Enrichment functions for weak discontinuities are constructed from deeper insights into the structure of the functions for strong discontinuities. Relationships between the two classes of functions are naturally established. Improvements upon basic enrichment functions for weak discontinuities are performed so as to achieve satisfactory convergence and accuracy. From numerical viewpoints, a simple and efficient treatment on the issue of blending elements is also proposed with implementation details. For validation purposes, applications of the derived functions to heterogeneous problems with imperfect interfaces are presented. © 2012 John Wiley & Sons, Ltd. Source

Pavlov V.I.,Lille Laboratory of Mechanics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

We analytically study the evolution of gravitational instability of self-gravitating dark matter within the framework of a nonrelativistic "hydrodynamical" model of the Universe, valid for scales that are small compared to the Hubble scale and for distances far away from black holes. We propose a particular form for parametrization of the particle distribution function via macroscopic quantities, such that the initial dispersion of microscopic velocities is not neglected, but plays a determinant role. Thus our model may be called a modified cold dark matter model. We found an analytical solution which indicates that a spontaneous spatially localized fluctuation of velocity generates density perturbations relative to initially unperturbed background. For the instability to arise, we do not need to assume any initial density (metric) fluctuations. The evolving perturbation is hydrodynamically unstable in the self-gravitating expanding Universe and can produce both-regions where no dark matter accumulates and halolike regions where dark matter does accumulate. The perturbation region boundary propagates as a shock wave with a speed that is time varying, until eventually reaching its steady state. We also derive an explicit analytical expression for the correlation function R(x 1-x 2) of density fluctuations, which can be compared by experimentalists with data from astrophysical observations. © 2012 American Physical Society. Source

Jiang T.,Multiscale Design Systems, LLC | Shao J.F.,Lille Laboratory of Mechanics
Computers and Geotechnics | Year: 2012

Micromechanical analysis based on the fast Fourier transform (FFT) is presented as applied to the nonlinear behavior of porous geomaterials. In this micromechanical model, a simple classical constitutive model is employed for the solid phase, such that the distinct mechanical properties of porous geomaterials can be subsequently and satisfactorily predicted without the use of additional parameters. Furthermore, the FFT-based model automatically satisfies the periodic boundary condition of the micromechanics scheme. The efficacy of the model is shown by applications to Lixhe chalk and Vosges sandstone. © 2012 Elsevier Ltd. Source

Liu J.,Lille Laboratory of Mechanics | Qi T.,Southwest Jiaotong University | Wu Z.,Southwest Jiaotong University
Tunnelling and Underground Space Technology | Year: 2012

Using expanding excavation based on shield tunnel can be regarded as a new approach to construct a metro station, especially when traditional methods cannot be implemented. This paper focuses on the ground movement property caused by shield tunneling and expanding construction. Ground movement property and construction influence scope, which happens during the construction process, are obtained by large numbers of numerical calculations and monitoring measurements. Results show that expanding excavation is the main factor which affects ground movement, and its influence will increase as the stability of surrounding rock deteriorates. Besides, horizontal displacement and vertical displacement (uneven settlement) are the two important factors which lead to building deformation and cracks; therefore, more attention should be given to these areas where the maximum displacement may occur during the construction process. Analysis of the two parameters, length to diameter ratio and depth to diameter ratio, indicates their relationship with safety of tunnel and building. Influence degree and scope of ground settlement are obtained due to change of the two parameters. The practical importance of this analysis is that we can judge whether building and tunnel are in a dangerous zone and thereby adopt relevant pre-reinforcements to ensure their safety. Later with the comparison of numerical simulation and in-situ data, we verify the accuracy of simulation. © 2011 Elsevier Ltd. Source

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