Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Electric-field-induced patterns in thin polymer films: weakly nonlinear and fully nonlinear evolution

A thin polymer melt on a substrate can be unstable to an electric field normal to the interface, a phenomenon that can be harnessed as a patterning technique with a range of potential applications. Motivated by the variety of patterns observed in experiments for polymers under both unpatterned and patterned masks, we describe here, from theoretical and numerical analyses, how nonlinear effects govern the growth of the instability and determine the final patterns. In particular, we discuss the nonlinear growth in terms of interactions among different Fourier modes and show that the second- and third-order nonlinearities favor the growth of hexagonal patterns under a featureless mask, in agreement with experimental observations. Also, numerical simulations based on the fully nonlinear model validate the prediction of the weakly nonlinear analysis: hexagonal patterns do emerge under an unpatterned mask. Furthermore, in one-dimensional simulations, we demonstrate the energetic evolution of this patterning process and reveal several "kinetically stable structures" along the path to the thermodynamically stable state. Two-dimensional simulations allow us to study the effects of both mask patterns and the initial film thickness. Generally, patterns on the mask guide the growth such that the pattern conforms to the geometric shapes. Interestingly, a small cylindrical protrusion at the center of the mask can produce exactly the same pattern as a large, flat, circular protrusion. The initial film thickness or the thickness ratio of the polymer layer to the air gap plays an important role in determining the final pattern formed. Finally, we demonstrate, by two simple examples, that the simulations can provide insights on "smart" mask designs for producing large areas of well-ordered patterns.     

The influence of macrocyclic polyether constitution upon ammonium ion/crown ether recognition processes

Secondary dialkylammonium (R2NH2+) ions are bound readily by dibenzo[24]crown-8 (DB24C8) to form threaded complexes, namely [2]pseudo-rotaxanes. The effect of replacing one or both of the catechol rings in DB24C8 with resorcinol rings upon the crown ether's ability to bind R2NH2+ ions has now been investigated. When only one aromatic ring is changed from catechol to resorcinol, a crown ether with a [25]crown-8 constitution is created-namely benzometaphenylene[25]crown-8 (BMP25C8). A [2]pseudorotaxane is formed in the solid state when BMP25C8 is co-crystallized with dibenzylammonium hexafluorophosphate, as evidenced by its X-ray crystal structure. Furthermore, this crown ether has been shown to bind R2NH2+ ions in solution, an observation which has been exploited in the synthesis of the first BMP25C8-containing [2]rotaxane. The methodology employed to generate this [2]rotaxane--the reaction of an amine with an isocyanate to form a urea--was tested initially on a system incorporating DB24C8 and was shown to work efficiently. Both [2]rotaxanes have been fully characterized by 1H and 13C NMR spectroscopies, FAB mass spectrometry and X-ray crystallography. Interestingly, the unsymmetrical nature of the dumbbell-shaped component in each of the two [2]rotaxanes renders each face of the encircling macrocyclic polyether diastereotopic, a feature that is apparent upon inspection of their 1H NMR spectra. The resonances associated with the diastereotopic protons on each face of the macrorings are well enough resolved to enable the faces of the crown ethers to be readily identified with respect to their protons by 1H NMR spectroscopy. Unambiguous assignments can be made as a result of the fact that the protons on each face of the macrocyclic polyether experience a unique set of through-space interactions, as evidenced by T-ROESY experiments. Additionally, the two-dimensional NMR analyses are in agreement with the X-ray crystallographic studies performed on these [2]rotaxanes, indicating that the crown ethers are located intimately around the NH2+ centers as expected. Replacement of both catechol rings in the DB24C8 constitution with resorcinol rings results in a crown ether with a [26]crown-8 constitution--namely bismetaphenylene[26]crown-8 (BMP26CS). All the evidence to date points to the fact that this further change in constitution results in a crown ether that does not bind R2NH2+ ions in either the solution or solid states.     

Dynamic hemicarcerands and hemicarceplexes

The reversible nature of the imine bond formation in CDCl(3) solution has been exploited to exchange substituted for unsubstituted m-phenylenediamine (MPD) units in hemicarcerand octaimines. Moreover, acid-catalyzed imine exchange has been shown to provide a novel mechanism whereby ferrocene (Fc) can be released as an entrapped guest from the hemicarceplex C(2)B(4)&crcldt;Fc dissolved in CDCl(3) to give the hemicarcerand C(2)B(4) when excess of both MPD and trifluoroacetic acid are present.     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

New homochiral binaphthol-modified organolanthanide reagents for the enantioselective addition to aldehydes

Optically active secondary alcohols were obtained in high chemical yield and optical purity (up to 85% ee) from the lanthanide-mediated enantioselective addition of alkyl nucleophiles to aromatic aldehydes.     

Non-planar smoulder propagation governed by diffusion

The steady propagation of a thin smouldering front in a half-spacehas been considered. A suitable coordinate transformation hasallowed the region near the leading edge of the front to beexamined for both a maintained planar surface and with surfacecollapse due to material shrinkage. The change in the oxidizerconcentration for a small increment in the propagation speedfor large time and surface collapse has been determined. Theinfluence of two types of nonlinear diffusion on the shape ofthe smouldering front has been found; other cases can be dealtwith in a similar manner.     

Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)

Representation determines how we can reason about a specific problem. Sometimes one representation helps us to find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used tools from Isabelle’s Transfer package to automate the use of these transformations in proofs. We give an overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show a few reasoning tactics we developed in Isabelle to improve the use of transformations, including the automation of search in the space of representations. We present and analyse some results of the use of these tactics.     

Microradiographic strain measurement using markers

A method for measuring strain on interior planes of some real structural materials is presented. X-ray images are formed of small (10–40 micron) gold markers placed on selected interior planes of optically opaque X-ray transparent materials. The use of well collimated monochromatic synchrotron radiation makes possible high contrast images of the small markers. Images of the particles before and after straining are recorded photographically. Photographs are enlarged 33X and measured using a simple electro-optical setup. In calibration experiments using approximately a 300-micron gage length, the strain measured by this method agreed with extensometer measured strains to within 100 microstrain. Example applications in a graphite-epoxy composite are presented, including measurement of the strain drop off near the free edge, strain concentration around a hole, and the strain field on a particular plane near a hole after local delamination. The technique is currently limited to materials no less X-ray transparent than titanium.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.