A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations

The technique of applying form-invariant, spatial coordinate transformations of Maxwell’s equations can facilitate the design of structures with unique electromagnetic or optical functionality. Here, we illustrate the transformation-optical approach in the designs of a square electromagnetic cloak and an omni-directional electromagnetic field concentrator. The transformation equations are described and the functionality of the devices is numerically confirmed by two-dimensional finite element simulations. The two devices presented demonstrate that the transformation optic approach leads to the specification of complex, anisotropic and inhomogeneous materials with well directed and distinct electromagnetic behavior.     

Asymptotic profiles and asymptotic distributions of energy in elastic waves scattering

We compute the asymptotic wave profiles for the exterior problemin elasticity with homogeneous Neumann condition. We give preciseresults on the asymptotic distribution of the elastic energyin various subsets of space. These results are obtained viathe use of a recently developed extension of the scatteringtheory of C. Wilcox (Mabrouk & Helali, 2002).     

Adaptive anisotropic noise filtering for magnitude MR data

Conventional noise filtering schemes applied to magnitude magnetic resonance (MR) images tacitly assume Gauss distributed noise. Magnitude MR data, however, are Rice distributed. Not incorporating this knowledge leads inevitably to biased results, in particular when applying such filters in regions with low signal-to-noise ratio. In this work, we show how the Rice data probability distribution can be incorporated so as to construct a noise filter that is far less biased.     

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS (Ⅱ)——PLANE STRESS PROBLEM

Fundamental theory presented in Part (I)^[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress problems on rectangular area.     

The Space of Inextensional Displacements for a Partially Clamped Linearly Elastic Shell with an Elliptic Middle Surface

We consider a linearly elastic shell with an “elliptic” middle surface, clamped along a portion of its lateral face and subjected to body forces. Under weak regularity assumptions on the middle surface, we prove that the space of linearized inextensional displacements is reduced to zero, by using unique continuation results. Consequently, when the thickness of the shell goes to zero, the limit of the average with respect to the thickness of the three-dimensional displacement vector solves the “generalized membrane” shell model, according to the terminology introduced by P.G. Ciarlet and the first author. This revised version was published online in August 2006 with corrections to the Cover Date.     

Brownian diffusion in a nonuniform gas

An analysis is made of the effects on the diffusion of Brownian particles whose Knudsen number is large compared to unity, of nonuniformities in the host gas. As examples, in one type of nonuniformity of the host gas, the Chapman-Enskog velocity distribution function for the gas molecules is used; in the other, the host gas is a free-molecule Couette flow. In both cases, a new force on the Brownian particles appears. Two techniques are used (extending Kramers' method and utilizing the Chapman-Enskog method) to transform the new Fokker-Planck equation into generalized Smoluchowski and convective diffusion equations. In these equations, the diffusion coefficient appears as a second-order tensor. Thus, it is demonstrated that Brownian diffusion in a nonuniform gas is anisotropic.The work of Slinn was financially supported in part by Battelle Memorial Institute and in part by U.S. Atomic Energy Commission Contract AT(45-1)-1830. The work of Shen was supported in part by U.S. Air Force Office of Scientific Research Contract 49(638)-1346.     

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to “optical” metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.     

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path. Mathematics Subject Classifications (2000) 74R05, 74B05, 74G70.Gerardo E. Oleaga: Supported by EU-Project Front Singularities University of Leipzig and the Max Planck Institute MIS. Partial support was also provided by the Spanish DGES project BFM2000-0605.     

Steady light diffusion application to rheology: a new tool for the characterization of concentrated suspensions

We present new developments of steady light diffusion applied to rheology. Though many techniques allow the structural investigation of diluted or transparent media, very few give direct information on optically dense systems. The technique proposed here is based on the diffusion approximation and is thus valid for sheared, time-dependent flows.After recalling important theoretical results, we show the techniques ability to determine typical sizes and orientation of structures in shear flows for various concentrated suspensions (emulsions, and an industrial softener). In particular, it is able to demonstrate the effect of shear on the orientation of anisotropic objects. Moreover, the use of simple structural models incorporating the measured anisotropy allows good predictions of experimental rheological measurements. This new technique, applicable to a wide range of colloidal systems, is very helpful to characterize the shear induced structural organization of optically dense materials.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.