Unsteady laminar flow developing in a curved duct

The flow developing in a tightly curved U-bend of square cross section has been investigated experimentally and via numerical simulation. Both long-time averages and time histories of the longitudinal (streamwise) component of velocity were measured using a laser-Doppler velocimeter. The Reynolds number investigated was Re = 1400. The data were obtained at different bend angles, θ, and were confined to the symmetry plane of the bend. At Re = 1400, the flow entering the bend is steady, but by θ = 90° it develops an oscillatory component of motion along the outer-radius wall. Autocorrelations and energy spectra derived from the time histories yield a base frequency of approximately 0.1 Hz for these oscillations. Flow-visualization studies showed that the proximity of the outer-radius wall served to damp the amplitude of the spanwise oscillations.

Numerical simulations of the flow were performed using both steady and unsteady version of the finite-difference elliptic calculation procedure of Humphrey et al. (1977). Although the unsteadiness observed experimentally does not arise spontaneously in the calculations, numerical experiments involving the imposition of a periodic time-dependent perturbation at the inlet plane suggest that the U-bend acts upon the incoming flow so as to damp the amplitude of the imposed oscillation while altering its frequency.

The oscillations observed experimentally, and numerically as a result of the periodic perturbation, have been linked to the formation of Goertler-type vortices of the outer-radius wall in the developing flow. The vortices, which develop as a result of the centrifugal instability of the flow on the outer-radius wall, undergo a further transition to an unsteady regime at higher flow rates.     

WHITE ASPARAGUS HARVEST DATE DISCRIMINATION USING NIRS TECHNOLOGY

Asparagus is still an important resource for mid-size and small farms. It has been traditionally believed that factors such as the asparagus harvesting date have an influence on its quality. This research sought to identify the harvesting dates of different fruits by using Near Infrared Spectroscopy (NIRS) technology as quality indicators and the best zone a long of the asparagus to acquire the spectrum. All the asparagus tested came from the same manufacturer but had been canned on three different dates, giving a total of nine lots. There were one hundred asparagus per lot and the experiment data were taken from three different parts (tip, middle, and base) of each spear. Reflectance spectrum in the near infrared between 800–1700 nm was determined. Differences NIRS among the asparagus harvested on different dates were found. NIRS technology was able to classify the asparagus correctly in terms of harvest dates (71% well classified). The base of the asparagus turned out to be the best part to use in order to establish the harvest date.     

Déformations covariantes sur les orbites polarisées d''un groupe de Lie

We prove the existence of covariant star-products on the orbits of the coadjoint representation of a Lie group which admits polarisations.     

Algebraic deformation program on minimal nilpotent orbit

We construct an algebraic star product on the minimal nilpotent coadjoint orbit of a simple complex Lie group with a Lie algebra which is not of typeA _n. According to the deformation program, we study the representations of the Lie algebra associated to this orbit.     

Symmetric nonself-adjoint operators in an enveloping algebra

Nelson and Stinespring proved that in any unitary representation of a Lie group with compact Lie algebra the representation of Hermitian elements in the enveloping algebra are essentially self-adjoint. If the Lie algebra is noncompact, we construct in its enveloping algebra a Hermitian element u such that in any locally faithful unitary representation the representative of u has no self-adjoint extension.     

Weak quadratic overgroups for a class of Lie groups

Let $G$ be a connected and simply connected Lie group with Lie algebra $\mathfrak g $ . We say that a subset $X$ in the set $\mathfrak g ^\star / G$ of coadjoint orbits is convex hull separable when the convex hulls differ for any pair of distinct coadjoint orbits in $X$ . In this paper, we define a class of solvable Lie groups, and we give an explicit construction of an overgroup $G^+$ and a quadratic map $\varphi $ sending each generic orbit in $\mathfrak g ^\star $ to a $G^+$ -orbit in $\mathfrak{g ^+}^\star $ , in such a manner that the set $\varphi (\mathfrak g ^\star _{gen}){/ G^+}$ is convex hull separable. We then call $G^+$ a weak quadratic overgroup for $G$ . Thanks to this construction, we prove that any nilpotent Lie group, with dimension at most 7 admits such a weak quadratic overgroup. Finally, we produce different examples of solvable Lie groups, having weak quadratic overgroups, but which are not in our class of Lie groups and for which usual constructions fail to hold.     

The Poincare-Dulac theorem for nonlinear representations of nilpotent lie algebras

The aim of this Letter is to show that the Poincare-Dulac theorem for holomorphic finite-dimensional representation, is valid for any nilpotent Lie algebrag. We reduce the classification problem of representations with a semisimple linear part satisfying the Poincaré condition to an algebraic problem. We develop a complete computation in a particular case.     

Applications of Successive Self-Nucleation and Annealing (SSA) to Polymer Characterization

A new technique to thermally fractionate polymers using DSC has been recently developed in our laboratory. The applications of the novel successive self-nucleation and annealing (SSA) technique to characterize polyolefins with very dissimilar molecular structures are presented as well as the optimum conditions to thermally fractionate any suitable polymer sample with SSA. For ethylene/-olefin copolymers, the SSA technique can give information on the distribution of short chain branching and lamellar thickness. In the case of functionalized polyolefins, detailed examinations of SSA results can help to establish possible insertion sites of grafted molecules. The application of the technique to characterize crosslinked polyethylene and crystallizable blocks within ABC triblock copolymers is also presented.This revised version was published online in November 2005 with corrections to the Cover Date.     

Star products for SL(2)

The deformation program (the use of star products in harmonic analysis) leads to the definition of an adapted Fourier transform, unitary transformation between spaces of square integrable functions of the group G and on the dual of its Lie algebra, describing the unitary dual of G and its Plancherel transform. This Letter is an application of this program to the universal covering group of SL(2).