Monotone strain-stress models for shape memory alloys hysteresis loop and pseudoelastic behaviorx

To describe the behavior of Shape Memory Alloy we use a thermomechanical model, founded on a free energy which is a convex function with respect to the strain and to the martensitic volume fraction, and a concave one with respect to the temperature. The material parameters of the model are experimentally determined.Received: November 26, 2001; revised: March 20, 2002     

Symmetry of the restricted 4 + 1 body problem with equal masses

We consider the problem of symmetry of the central configurations in the restricted 4 + 1 body problem when the four positive masses are equal and disposed in symmetric configurations, namely, on a line, at the vertices of a square, at the vertices of a equilateral triangle with a mass at the barycenter, and finally, at the vertices of a regular tetrahedron [1–3]. In these situations, we show that in order to form a non collinear central configuration of the restricted 4 + 1 body problem, the null mass must be on an axis of symmetry. In our approach, we will use as the main tool the quadratic forms introduced by A. Albouy and A. Chenciner [4]. Our arguments are general enough, so that we can consider the generalized Newtonian potential and even the logarithmic case. To get our results, we identify some properties of the Newtonian potential (in fact, of the function ϕ(s) = −s ^k, with k < 0) which are crucial in the proof of the symmetry.     

The depth of ultraproducts of Boolean algebras

We show that if μ is a compact cardinal then the depth of ultraproducts of less than μ many Boolean algebras is at most μ plus the ultraproduct of the depths of those Boolean algebras. Received May 18, 2004; accepted in final form December 9, 2004.     

Effect of magnetic field on the TC and magnetic properties for the aligned MnBi compound

In the compound MnBi, a first-order transition from the paramagnetic to the ferromagnetic state can be triggered by an applied magnetic field and the Curie temperature increases nearly linearly with an increase in magnetic field by ∼2 K/T. Under a field of 10 T, T_C increases by 20 and 22 K during heating and cooling, respectively. Under certain conditions a reversible magnetic field or temperature induced transition between the paramagnetic and ferromagnetic states can occur. A magnetic and crystallographic H-T phase diagram for MnBi is given. Magnetic properties of MnBi compound aligned in a Bi matrix have been investigated. In the low temperature phase MnBi, a spin-reorientation takes place during which the magnetic moments rotate from being parallel to the c-axis towards the basal plane at ∼90 K. A measuring Dc magnetic field applied parallel to the c-axis of MnBi suppresses partly the spin-reorientation transition. Interestingly, the fabricated magnetic field increases the temperature of spin-reorientation transition T_s and the change in magnetization for MnBi. For the sample solidified under 0.5 T, the change in magnetization is ∼70% and T_s is ∼91 K.     

The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in and the gradient flow to the harmonic map to the sphere are discussed. Namely the Serrin-Ohyama type regularity criteria are improved in the terms of the Besov spaces. Received: 21 September 2000; in final form: 16 Feburary 2001 / Published online: 18 January 2002     

Pfaffian graphs, <Emphasis Type="Italic">T</Emphasis>-joins and crossing numbers

We characterize Pfaffian graphs in terms of their drawings in the plane. We generalize the techniques used in the proof of this characterization, and prove a theorem about the numbers of crossings in T-joins in different drawings of a fixed graph. As a corollary we give a new proof of a theorem of Kleitman on the parity of crossings in drawings of K _2j+1 and K _2j+1,2k+1. Partially supported by NSF grants DMS-0200595 and DMS-0701033.     

Annulation de la cohomologie cuspidale de sous-groupes de congruence deGL n (ℤ)

Sans résumé

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Je remercie Jean-François Mestre, mon directeur de thèse, dont les idées sont à l'origine de ce travail, ainsi que Laurent Clozel, Guy Henniart et Jean-Pierre Labesse qui ont contribué par leur aide précieuse à son bon déroulement     

Tangent measure distributions of hyperbolic Cantor sets

Tangent measure distributions were introduced byBandt [2] andGraf [8] as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure distributions of hyperbolic Cantor sets generated by certain contractive mappings, which are not necessarily similitudes. We show that the tangent measure distributions of these sets equipped with either Hausdorff- or Gibbs measure are unique almost everywhere and give an explicit formula describing them as probability distributions on the set of limit models ofBedford andFisher [5].     

A Variational Principle in Krein Space II

Let A be a self-adjoint operator in a Krein space Under certain natural assumptions, it is shown precisely which real eigenvalues of A can be given a max-inf characterization generalizing the usual one in Hilbert space. This result unifies several approaches in the recent literature.