The inf-sup constant for the divergence on corner domains

The inf-sup constant for the divergence, or LBB constant, is related to the Cosserat spectrum. It has been known for a long time that on non-smooth domains the Cosserat operator has a non-trivial essential spectrum, which can be used to bound the LBB constant from above. We prove that the essential spectrum on a plane polygon consists of an interval related to the corner angles and that on three-dimensional domains with edges, the essential spectrum contains such an interval. We obtain some numerical evidence for the extent of the essential spectrum on domains with axisymmetric conical points by computing the roots of explicitly given holomorphic functions related to the corner Mellin symbol. Using finite element discretizations of the Stokes problem, we present numerical results pertaining to the question of the existence of eigenvalues below the essential spectrum on rectangles and cuboids

Modeling the electron with Cosserat elasticity

We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose a coframe and a density. We then add an extra (third) spatial dimension, extend our coframe and density into dimension 1+3, choose a conformally invariant Lagrangian proportional to axial torsion squared, roll up the extra dimension into a circle so as to incorporate mass and return to our original (1+2)-dimensional spacetime by separating out the extra coordinate. The main result of our paper is the theorem stating that our model is equivalent to the Dirac equation in dimension 1+2. In the process of analyzing our model we also establish an abstract result, identifying a class of nonlinear second order partial differential equations which reduce to pairs of linear first order equations

Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids

Transformation elasticity, by analogy with transformation acoustics and optics, converts material domains without altering wave properties, thereby enabling cloaking and related effects. By noting the similarity between transformation elasticity and the theory of incremental motion superimposed on finite pre-strain it is shown that the constitutive parameters of transformation elasticity correspond to the density and moduli of small-on-large theory. The formal equivalence indicates that transformation elasticity can be achieved by selecting a particular finite (hyperelastic) strain energy function, which for isotropic elasticity is semilinear strain energy. The associated elastic transformation is restricted by the requirement of statically equilibrated pre-stress. This constraint can be cast as \tr {\mathbf F} = constant, where $\mathbf{F}$ is the deformation gradient, subject to symmetry constraints, and its consequences are explored both analytically and through numerical examples of cloaking of anti-plane and in-plane wave motion.Comment: 20 pages, 5 figure

A mathematical model for phase separation: A generalized Cahn-Hilliard equation

In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced for an incompressible fluid, so the resulting differential system couples a generalized Cahn-Hilliard equation with the Navier-Stokes equation. Its consistency with the second law of thermodynamics in the classical Clausius-Duhem form is finally proved.Comment: 9 pages, 1 figure, Published online in Wiley Online Librar

Weyl's Lagrangian in teleparallel form

The main result of the paper is a new representation for the Weyl Lagrangian (massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e. an orthonormal tetrad of covector fields. We write down a simple Lagrangian - wedge product of axial torsion with a lightlike element of the coframe - and show that this gives the Weyl Lagrangian up to a nonlinear change of dynamical variable. The advantage of our approach is that it does not require the use of spinors, Pauli matrices or covariant differentiation. The only geometric concepts we use are those of a metric, differential form, wedge product and exterior derivative. Our result assigns a variational meaning to the tetrad representation of the Weyl equation suggested by J. B. Griffiths and R. A. Newing

Hyperfluid - a model of classical matter with hypermomentum

A variational theory of a continuous medium is developed the elements of which carry momentum and hypermomentum (hyperfluid). It is shown that the structure of the sources in metric-affine gravity is predetermined by the conservation identities and, when using the Weyssenhoff ansatz, these explicitly yield the hyperfluid currents.Comment: plain Tex, 11 pages, no figure

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Covariant Balance Laws in Continua with Microstructure

The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas

Les 100 médicaments essentiels. Une approche de médecine interne = 100 essential drugs. An internal medicine approach

Déclaration d'intérêts : B. Grosbois : expert pour Actélion, Celgene, Octapharma, Shire. Recherche subventionnée par LFB, Janssen, Genzyme. L. Guillevin : conseiller scientifique Actélion, expert pour (et conférences rémunérées par) GSK, CSL, Roche. L. Guillevin estime cependant n'avoir pas de conflit d'intérêt concernant le présent travail. C. Le Jeunne : expert pour Roche, Sanofi, Novartis, BSM, UCB. Essais thérapeutiques en cours pour Bayer, Pfizer, BMS. P. Morlat : expert pour Gilead, ViiV Health Care, BMS, Abbott, MSD. Ph. Morlat estime cependant n'avoir pas de conflit d'intérêt concernant le présent travail. P. Arlet, O. Aumaitre, J. Cosserat, A. Kettaneh, C. Massot et M. Thomas : aucun conflit d'intérêt.International audiencePURPOSE: Up to 4600 drugs in about 15,000 pharmaceutical forms are available in France which may be a source of misuse with increased occurrence of side effects and costs. While the World Health Organization is encouraging each developed country to work out its own list of essential drugs. The list provided in 2008 by the French Office for the safety of health products has had so far limited impact on practice, so it became obvious to a group of internists to work out a "wise list" of 100 essential medicines covering 95% of the disorders observed in France. METHODS: In June 2011, 10 internists agreed to each provide a list of 100 essential medicines, according to individual experience. In December 2011, a meeting of the participants provided a list as initial consensus and mandated five among them to make proposals for those areas neglected by too many participants or in which needless dispersion of medicines was stated. After internet-facilitated exchanges, an additional list was validated in mild-January 2012. RESULTS: Fifty-four drugs were included in the list of initial consensus (including nine selected by all 10 participants), and 46 in the additional list. So the final "wise list" included 100 drugs. In June 2012, 56 of these drugs were available as generics. This list was compared to those lists set out by five countries in the European Union. CONCLUSION: Generating such a list is feasible. Undoubtedly still non-comprehensive, this list will benefit from the expertise of 14 general practitioners who are currently working out a similar list across France. The final list will be submitted for validation by the French associations of generalist teachers and Internists