Higher-order constraints for higher kinematic pairs and their application to mobility and shakiness analysis of mechanisms

The mobility analysis of mechanisms rests on an adequate formulation of the constraints defining its configuration space (c-space). Whereas there is no general method for a global analysis, the higher-order mobility analysis, which locally approximates the c-space, is applicable to general mechanisms. It requires an efficient method for the evaluation of higher-order constraints, i.e. constraints on velocity, acceleration, jerk, etc. Such a method is known for linkages comprising lower pair joints only. In this paper a method for the efficient evaluation of higher-order constraints for mechanisms comprising higher pair joints is proposed. The method builds on the results for the lower pair linkages. It leads to a computationally simply recursive algorithm. This is applied to the mobility analysis that allows to determine the local finite mobility, to detect singularities, and to identify shaky mechanisms.     

Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations

This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.     

Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic propertiesPolycristaux poreux constitués d'aiguilles orientées de façon uniforme ou axisymétrique : homogénéisation des propriétés élastiques

Porous polycrystal-type microstructures built up of needle-like platelets or sheets are characteristic for a number of biological and man-made materials. Herein, we consider (i) uniform, (ii) axisymmetrical orientation distribution of linear elastic, isotropic as well as anisotropic needles. Axisymmetrical needle orientation requires derivation of the Hill tensor for arbitrarily oriented ellipsoidal inclusions with one axis tending towards infinity, embedded in a transversely isotropic matrix; therefore, Laws' integral expression of the Hill tensor is evaluated employing the theory of rational functions. For a porosity lower 0.4, the elastic properties of the polycrystal with uniformly oriented needles are quasi-identical to those of a polycrystal with solid spheres. However, as opposed to the sphere-based model, the needle-based model does not predict a percolation threshold. As regards axisymmetrical orientation distribution of needles, two effects are remarkable: Firstly, the sharper the cone of orientations the higher the anisotropy of the polycrystal. Secondly, for a given cone, the anisotropy increases with the porosity. Estimates for the polycrystal stiffness are hardly influenced by the anisotropy of the bone mineral needles. Our results also confirm the very high degree of orientation randomness of crystals building up mineral foams in bone tissues. To cite this article: A. Fritsch et al., C. R. Mecanique 334 (2006).     

The permutation class group of a finite group

Analogously to the projective class group, the permutation class group of a finite group π can be defined as the group of equivalence classes of direct summands of integral permutation modules modulo permutation modules. It is shown that this group behaves nicely with respect to localization and completion, which then is used to prove that contrary to the projective class group - it is not always a torsion group. More precisely, the rank of the permutation class of group is computed.     

Additive functionals with application to sojourn times in infinite-server and processor sharing systems

We deal with additive functionals of stationary processes. It is shown that under some assumptions a stationary model of the time-changed process exists. Further, bounds for the expectation of functions of additive functionals are derived. As an application we analyze virtual sojourn times in an infinite-server system where the service speed is governed by a stationary process. It turns out that the sojourn time of some kind of virtual requests equals in distribution an additive functional of a stationary time-changed process, which provides bounds for the expectation of functions of virtual sojourn times, in particular bounds for fractional moments and the distribution function. Interpreting the GI(n)/GI(n)/∞ system or equivalently the GI(n)/GI system under state-dependent processor sharing as an infinite-server system where the service speed is governed by the number n of requests in the system provides results for sojourn times of virtual requests. In the case of M(n)/GI(n)/∞, the sojourn times of arriving and added requests equal in distribution sojourn times of virtual requests in modified systems, which yields several results for the sojourn times of arriving and added requests. In case of positive integer moments, the bounds generalize earlier results for M/GI(n)/∞. In particular, the mean sojourn times of arriving and added requests in M(n)/GI(n)/∞ are proportional to the required service time, generalizing Cohen’s famous result for M/GI(n)/∞.     

Reflection groups on Riemannian manifolds

We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the orbit space M/G is isometric to a Weyl chamber C which is a Riemannian manifold with corners and certain angle conditions along intersections of faces. We can also reconstruct the manifold and its action from the Riemannian chamber and its equipment of isotropy group data along the faces. We also discuss these results from the point of view of Riemannian orbifolds. Mathematics Subject Classification Primary 51F15, 53C20, 20F55, 22E40     

The Stokes operator in weighted Lq-spaces II: weighted resolvent estimates and maximal Lp-regularity

In this paper we establish a general weighted L ^q -theory of the Stokes operator in the whole space, the half space and a bounded domain for general Muckenhoupt weights . We show weighted L ^q -estimates for the Stokes resolvent system in bounded domains for general Muckenhoupt weights. These weighted resolvent estimates imply not only that the Stokes operator generates a bounded analytic semigroup but even yield the maximal L ^p -regularity of in the respective weighted L ^q -spaces for arbitrary Muckenhoupt weights . This conclusion is archived by combining a recent characterisation of maximal L ^p -regularity by -bounded families due to Weis [Operator-valued Fourier multiplier theorems and maximal L _p -regularity. Preprint (1999)] with the fact that for L ^q -spaces -boundedness is implied by weighted estimates.