Collaborative testing of eddy structure identification methods in free turbulent shear flows

 The thrust of this paper is to validate, test and compare several Coherent Structure eduction methods utilizing the same data base. The flow chosen was that of an experimental study of a plane, incompressible, fully developed turbulent two-stream mixing layer. The mixing layer was chosen as the data base because it has been studied extensively from a coherent structures point of view. In addition, its characteristics (similarity, convection velocities, etc.) are well documented. There are also no wall effects so that comparisons between techniques are simplified. The data was collected from hot wire rakes with good spatial resolution thus allowing the contributors to apply and test different structure eduction techniques. The techniques chosen for discussion and used here have found wide utilization over the past decade, and all hold forth the promise of extensive application in the future. These include: Conditional Sampling (Vorticity-based and other methods); Wavelets; Pattern Recognition Analysis; Proper Orthogonal Decomposition; Stochastic Estimation; Topological Concept-based methods; Full Field Methods (e.g., pseudo flow visualization). All are illustrated by application to the mixing layer data base, and comparisons made between the results. This common study has shown that direct comparisons between results of several methods are now possible. Good quantitive and qualitative agreement between the different methods have been observed as well as some differences noted. As an example, the size of the averaged structures computed from the various methods compare to within 6 percent. Received: 15 December 1994/Accepted: 18 December 1997     

On the crystallization of syndiotactic polypropylene (sPP)/high density polyethylene (HDPE) blends

 The crystallization kinetics of syndiotactic polypropylene (sPP)/high-density polyethylene (HDPE) blends were investigated by thermal and microscopical methods. Isothermal crystallization obtained by differential scanning calorimetry (DSC) was used to study the nucleation ability of HDPE on sPP crystallization. Morphological studies with polarized light microscopy (PLM) of solution cast films resulted in a transcrystalline-like overgrowth of the sPP on HDPE spherulites. The arrangement of the HDPE lamellar crystals in the blend were observed in transmission electron microscopy (TEM). But from these results, no straightforward conclusion about the transcrystalline nature of the sPP crystals can be given. Received: 24 November 1997 Accepted: 23 February 1998     

Further characterization of large-scale coherent structure signatures in a turbulent-plane mixing layer

In order to complement a previous collaborative testing of eddy structure identification methods in free turbulent shear flows, a study about the influence of the transverse location of these large-scale vortical structures on their signatures for the same referenced data base is carried out. Using vorticity-based conditional sampling, events which are located on the same transverse locations are selected and averaged. Results show that a coherent structure has its proper identity contained in its core and keeps it whatever its trajectory. In this way, only its signature in comparison with the surrounding environment changes. The comparison with vorticity-based conditional sampling without this transverse selection brings to the fore a bias on the signature of coherent structures. This result throws back into question previous conclusions about the morphology of structures and related energy transfer scenarios. Received: 24 July 2000 / Accepted: 25 June 2001 Published online: 29 November 2001     

On the key factors of angular correlations in complex-forming elementary reactions

In the mid-seventies, Case and Herschbach argued that for complex-forming three-atom reactions governed by long-range forces and performed in supersonic molecular beam experiments, vectorial properties are determined by a single parameter Λ' = 〈L'/(L' + j')〉, L' and j' being respectively the moduli of the orbital and rotational angular momenta of the products. A simple mathematical relation between vectorial properties and Λ' was then proposed. However, Λ' must be determined beforehand by phase space theory calculations. Besides, we have recently shown that scalar properties are mainly controled by two factors ρ'₁ and ρ'₂ respectively called angular excitation and diatomic inertial contribution. We show here that these factors control also vectorial properties. Moreover, the way they control them is summarized in a set of four figures. The advantage of our method is that ρ'₁ and ρ'₂ are related to the mechanical parameters of the reaction by very simple formulas, contrary to Λ'. Last by not least, our parameters appear to be mostly independent, so that vectorial properties cannot be said to strictly depend on Λ'. Nevertheless, it turns out that the rule proposed by Case and Herschbach is reasonable in many realistic situations.     

On Poset Boolean Algebras

Let (P,≤) be a partially ordered set. The poset Boolean algebra of P, denoted F(P), is defined as follows: The set of generators of F(P) is {x _p  : p∈P}, and the set of relations is {x _p ⋅x _q =x _p  : p≤q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and (G,≤ ^B |G) is well-founded. A well-generated algebra is superatomic. THEOREM 1. Let (P,≤) be a partially ordered set. The following are equivalent. (i) P does not contain an infinite set of pairwise incomparable elements, and P does not contain a subset isomorphic to the chain of rational numbers, (ii) F(P) is superatomic, (iii) F(P) is well-generated. The equivalence (i) ⇔ (ii) is due to M. Pouzet. A partially ordered set W is well-ordered, if W does not contain a strictly decreasing infinite sequence, and W does not contain an infinite set of pairwise incomparable elements. THEOREM 2. Let F(P) be a superatomic poset algebra. Then there are a well-ordered set W and a subalgebra B of F(W), such that F(P) is a homomorphic image of B. This is similar but weaker than the fact that every interval algebra of a scattered chain is embeddable in an ordinal algebra. Remember that an interval algebra is a special case of a poset algebra. This revised version was published online in June 2006 with corrections to the Cover Date.     

Solid-phase organic tagging resins for labeling biomolecules by 1,3-dipolar cycloaddition: application to the synthesis of a fluorescent non-peptidic vasopressin receptor ligand

Two novel solid-phase organic tagging (SPOrT) resins were synthesized to facilitate the labeling of peptides and small organic compounds with a fluorescent probe. Both resins were obtained from the commercially available backbone amide linker (BAL) resin. Following the solid-phase synthesis of model compounds, a tripeptide and benzazepine, the fluorescent probe derived from Lissamine Rhodamine B was incorporated through CuI-catalyzed 1,3-dipolar cycloaddition. Final cleavage in acidic media enabled access to both types of molecules in good yield with high purity. The SPOrT resin was successfully applied to the preparation of the first non-peptidic fluorescent compound with a nanomolar affinity for the human vasopressin V2 receptor (V2R) subtype. This molecule will find application in binding assays that use polarization or fluorescence resonance energy-transfer (FRET) techniques. The SPOrT resins are also well suited for other tags and the parallel synthesis of a fluorescently tagged library for protein screening.     

2‐Azido‐2‐deoxycellulose: Synthesis and 1,3‐Dipolar Cycloaddition

Chitosan ( 1 ) was prepared by basic hydrolysis of chitin of an average molecular weight of 70000 Da, ¹H‐NMR spectra indicating almost complete deacetylation. N‐Phthaloylation of 1 yielded the known N‐phthaloylchitosan ( 2 ), which was tritylated to provide 3a and methoxytritylated to 3b . Dephthaloylation of 3a with NH₂NH₂?H₂O gave the 6‐O‐tritylated chitosan 4a . Similarly, 3b gave the 6‐O‐methoxytritylated 4b . CuSO₄‐Catalyzed diazo transfer to 4a yielded 95% of the azide 5a , and uncatalyzed diazo transfer to 4b gave 82% of azide 5b . Further treatment of 5a with CuSO₄ produced 2‐azido‐2‐deoxycellulose ( 7 ). Demethoxytritylation of 5b in HCOOH gave 2‐azido‐2‐deoxy‐3,6‐di‐O‐formylcellulose ( 6 ), which was deformylated to 7 . The 1,3‐dipolar cycloaddition of 7 to a range of phenyl‐, (phenyl)alkyl‐, and alkyl‐monosubstituted alkynes in DMSO in the presence of CuI gave the 1,2,3‐triazoles 8 – 15 in high yields.     

A two-step spin crossover mononuclear iron(II) complex with a [HS-LS-LS] intermediate phase

The two-step spin crossover of a new mononuclear iron(ii) complex is studied by magnetic, crystallographic and calorimetric methods revealing two successive first-order phase transitions and an ordered intermediate phase built by the repetition of the unprecedented [HS-LS-LS] motif.