Low-molecular-weight poly(alpha-methyl beta,L-malate) of microbial origin: synthesis and crystallization

Low-molecular-weight poly(alpha-methyl beta,L-malate) made of approximately 25-30 units was prepared from microbial poly(beta,L-malic acid) by treatment with diazomethane. The thermal characterization of the polymalate methyl ester was carried out and its crystalline structure was preliminary examined. Its ability to crystallize both from solution and from the melt was comparatively evaluated.     

Realization of Hardy's thought experiment with photons

We present an experimental realization of Hardy's thought experiment [Phys. Rev. Lett. 68, 2981 (1992)], using photons. The experiment consists of a pair of Mach-Zehnder interferometers that interact through photon bunching at a beam splitter. A striking contradiction is created between the predictions of quantum mechanics and local hidden variables. The contradiction relies on nonmaximally entangled position states of two particles. A Clauser-Horne-type inequality is derived and violated.     

Nonlinear Schrödinger equations: concentration on weighted geodesics in the semi-classical limit

We consider the problem

${?}^2\mathrm{\Delta }u?V(x)u+u^p=0,u>0,u\in H^1({\mathbb{R}}^2),$

where $p>1$, $?>0$ is a small parameter and V is a uniformly positive, smooth potential. Let Γ be a closed curve, nondegenerate geodesic relative to the weighted arclength ${\int }_{\Gamma }{V}^{\sigma }$, where $\sigma =\frac{p+1}{p?1}?\frac{1}{2}$. We prove the existence of a solution $u_{\mathrm{\epsilon }}$ concentrating along the whole of Γ, exponentially small in ? at any positive distance from it, provided that ? is small and away from certain critical numbers. This proves a conjecture raised in [A. Ambrosetti, A. Malchiodi, W.-M. Ni, Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I, Commun. Math. Phys. 235 (2003) 427–466] in the two-dimensional case. To cite this article: M. del Pino et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Numerical Analysis of the Behaviour of Tooth Intrarradial Posts by the Finite Element Method

The aim of this work is to study the behaviour of a carbon/epoxi post housed in a canine tooth after endodontic treatment in order to support the typical loads present during mastication. The three-D basic design of the dental piece consisting of tooth + post was carried out with a three-dimensional parametric design program. We study the stresses and displacements of the different elements of the dental piece under normal load conditions, and present the results and conclusions.     

Fourier transform measurement of two-photon excitation spectra: applications to microscopy and optimal control

We report a novel Fourier transform method for measuring two-photon excitation spectra. We demonstrate this method using simple dye molecules and discuss its applications in two-photon fluorescence microscopy and optimal control. This method facilitates an intuitive interpretation of recent control experiments in terms of tuning the nonlinear spectrum of the exciting laser source.     

Coiling, entrainment, and hydrodynamic coupling of decelerated fluid jets

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a conduit of viscously entrained fluid, whose upward recirculation braids the jet, and nearly confines transverse mixing to the narrow conduit. We show that the underlying jet structure and certain scaling relations follow from similarity solutions to the fluid equations and the physics of Kelvin-Helmholtz instabilities.     

Fermi-like behavior of weakly vibrated granular matter

Vertical movement of zirconia-yttria stabilized 2 mm balls is measured by a laser facility at the surface of a vibrated 3D granular matter under gravity. Realizations z(t) are measured from the top of the container by tuning the fluidized gap with a 1D measurement window in the direction of the gravity. The statistics obeys a Fermi-like configurational approach which is tested by the relation between the dispersions in amplitude and velocity. We introduce a generalized equipartition law to characterize the ensemble of particles which cannot be described in terms of a Brownian motion. The relation between global granular temperature and the external excitation frequency is established.     

Heat exchange in a laminar channel flow with temperature gradients at the walls: possibility for heat transfer reversal

This paper presents a detailed numerical study of the heat exchange between two parallel plates with prescribed temperature gradients along the plates and a fluid circulating between them. The interplay between the bulk temperature, the heat flow and the Nusselt number has been clarified.     

The Brezis-Nirenberg problem near criticality in dimension 3

We consider the problem of finding positive solutions of Δu+λu+u^q=0 in a bounded, smooth domain Ω in , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<λ<λ₁. We analyze the role of Green's function of Δ+λ in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or λ are regarded as parameters. As a special case of our results, we find that if , where λ∗ is the Brezis-Nirenberg number, i.e., the smallest value of λ for which least energy solutions for q=5 exist, then this problem is solvable if q>5 and q−5 is sufficiently small.