Elementary preamble to a theory of granular gases

Granular materials partake almost dramatically at times of the properties of solids and, under different circumstances, of some properties of gases. Here, within the mechanics of mass points, an elementary analysis, involving predominantly velocities rather than places, is shown to lead to a global equation concerning the shuffling motions (in addition to continuity and Cauchy's equations); it involves a stirring tensor and rules the evolution of a Reynolds' tensor.Comment: 17 page

Spin fluids and hyperfluids

The general theory of continua with microstructure reviewed in [2] (and, in particular, the theory of gyrocontinua studied in [1]) is adapted to apply to perfect spin fluids and hyperuids [10]. Obvious changes are needed due to the prevailing interest for solids in [1] and to some extent in [2]; here, in addition, the conservative character of the continuum is exploited. Finally, the roles of metric, coframe, connection, torsion and curvature in fluids are explored.

Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media

In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and other physical objects. Particularly interesting are dynamical models invariant under the group underlying geometry of degrees of freedom. In contrary to the single body case there exist nontrivial potentials invariant under this group (left and right acting). The concept of relative (mutual) deformation tensors of pairs of affine bodies is discussed. Scalar invariants built of such tensors are constructed. There is an essential novelty in comparison to deformation scalars of single affine bodies, i.e., there exist affinely-invariant scalars of mutual deformations. Hence, the hierarchy of interaction models according to their invariance group, from Euclidean to affine ones, can be considered.Comment: 50 pages, 4 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

Cancellation of vorticity in steady-state non-isentropic flows of complex fluids

In steady-state non-isentropic flows of perfect fluids there is always thermodynamic generation of vorticity when the difference between the product of the temperature with the gradient of the entropy and the gradient of total enthalpy is different from zero. We note that this property does not hold in general for complex fluids for which the prominent influence of the material substructure on the gross motion may cancel the thermodynamic vorticity. We indicate the explicit condition for this cancellation (topological transition from vortex sheet to shear flow) for general complex fluids described by coarse-grained order parameters and extended forms of Ginzburg-Landau energies. As a prominent sample case we treat first Korteweg's fluid, used commonly as a model of capillary motion or phase transitions characterized by diffused interfaces. Then we discuss general complex fluids. We show also that, when the entropy and the total enthalpy are constant throughout the flow, vorticity may be generated by the inhomogeneous character of the distribution of material substructures, and indicate the explicit condition for such a generation. We discuss also some aspects of unsteady motion and show that in two-dimensional flows of incompressible perfect complex fluids the vorticity is in general not conserved, due to a mechanism of transfer of energy between different levels.Comment: 12 page

Affine symmetry in mechanics of collective and internal modes. Part I. Classical models

Discussed is a model of collective and internal degrees of freedom with kinematics based on affine group and its subgroups. The main novelty in comparison with the previous attempts of this kind is that it is not only kinematics but also dynamics that is affinely-invariant. The relationship with the dynamics of integrable one-dimensional lattices is discussed. It is shown that affinely-invariant geodetic models may encode the dynamics of something like elastic vibrations

SO(3) invariance and covariance in mixtures of simple bodies

We adapt to mixtures the procedure of invariance of external power under the action of SO(3) to deduce balance equations. The two classical axioms about the growths of momentum and moment of momentum are derived with the help of a rule on the structure of the total power. We discuss also the covariance of the balance equations of each constituent and the nature of the constituent stress.Comment: 12 page

Apports technologiques dans la prévention du risque iatrogène médicamenteux : Exemple de l'actigraphie

La santé et plus particulièrement les médicaments, sont aujourd'hui à la une de l'actualité, non seulement dans le domaine médical mais aussi sociétal et politique. Les professionnels de santé, et plus particulièrement le pharmacien et le médecin, doivent s'assurer de la qualité de leurs divers soins (pharmaceutiques et médicaux) ainsi que de la sécurité de leurs patients. Cette prévention du risque est d'autant plus importante pour certains types de populations, désignées comme populations vulnérables que représentent les personnes âgées et les patients atteints de pathologie chronique. Dans cette démarche, des nouvelles solutions technologiques commencent à apparaître présentées comme des outils d'aide prometteurs. Leur apport réel vis-à-vis du risque iatrogène médicamenteux reste à être démontré par des évaluations précises. Un exemple de protocole est présenté portant sur l'utilisation de l'actigraphie chez la personne âgée