Lie point symmetries of the Lane-Emden systems

It is shown that a Lie point symmetry of the Lane-Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.     

First observations of a spiral instability at the smectic A—cholesteric transition under an electric field

Abstract

Archimedian spiral wave instabilities have been discovered in chemical [1] and biological systems [2]. We present here the first example of such an instability pattern, encountered in a physical medium [3]. This instability is directly observed by polarized optical microscopy, on a positive dielectric anisotropy smectic A sample with homeotropic organization between parallel glass slides. The arm of the spiral is probably constituted of a 180° Bloch wall, separating indistinguishable smectic domains, and incorporating progressively the helicity of the cholesteric phase, excluded from the smectic.     

Crystal structure of 5-benzoylamino-5-isopropyl-4-oxo-1,3-dioxane

C₁₄H₁₇NO₄ crystallizes in the monoclinic space groupP2₁/n (Z=4) witha=10.208(2),b=10.888(2),c=11.909(2) Å, and=90.89(2)°. The structure was solved by direct methods and refined by full-matrix LSQ to anR factor of 0.036. The 4-oxo-1,3-dioxane ring is in a slightly distorted O(1)-sofa conformation flattened at the C(4) end with the 5-isopropyl substituent in a pseudoaxial position and planar lactone group. The molecules form dimers by means of intermolecular N-HO(4) hydrogen bonds of 3.091(2) Å. The¹H NMR spectrum of the title compound shows unusual features.     

Solution Properties of the Exopolysaccharide Produced by Pseudomonas Marginalis Strain HT041B 1

Abstract

The solution properties of the exopolysaccharide marginalan produced by Pseudomonas marginalis HT041B were investigated by means of low-angle laser light-scattering, capillary viscometry, and rheology. Potentiometric and viscosimetric data indicated the absence of a cooperative transition of the disorder-to-order type. The experimental findings obtained in dilute solution (Mark-Houwink coefficients, rigidity coefficient, characteristic ratio) suggested that the polymer behaves like a semiflexible chain which adopts a disordered conformation. The rheological behaviour of more concentrated marginalan solutions, as determined by means of both steady shear and oscillatory measurements, further confirmed the disordered conformational state of the polymer in solution.

     

Bluff-body drag reduction using a deflector

A passive flow control on a generic car model was experimentally studied. This control consists of a deflector placed on the upper edge of the model rear window. The study was carried out in a wind tunnel at Reynolds numbers based on the model height of 3.1 × 10⁵ and 7.7 × 10⁵. The flow was investigated via standard and stereoscopic particle image velocimetry, Kiel pressure probes and surface flow visualization. The aerodynamic drag was measured using an external balance and calculated using a wake survey method. Drag reductions up to 9% were obtained depending on the deflector angle. The deflector increases the separated region on the rear window. The results show that when this separated region is wide enough, it disrupts the development of the counter-rotating longitudinal vortices appearing on the lateral edges of the rear window. The current study suggests that flow control on such geometries should consider all the flow structures that contribute to the model wake flow.     

X-ray diffraction study of a polybutadiene, side chain, mesomorphic polymer

A side chain, mesomorphic polymer has been synthesized, starting from a commercial polybutadiene main chain. A preliminary X-ray diffraction study shows the influence of the degree of substitution and the spacer length on the interdigited S_A layer thickness, particularly for strongly polar alkoxycyanobiphenyl mesogens. Some hypotheses are deduced about the particular odd-even effect observed with this backbone and on the conformation of the main and side chains.     

Optimal enough?

An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular application, portfolio optimisation. We demonstrate that the randomness of the ‘optimal’ solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the remaining uncertainty in the out-of-sample period. The relationship between in-sample fit and out-of-sample performance is not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample. Beyond this point there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample only to financially meaningless improvements and unpredictable changes (noise) in performance.