SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limitingfield is the same as that obtained by Dawson (1977). In the recurrent case it is aspatially uniform field. The author also give a central limit theorem for the weightedoccupation time of the super Brownian motion with underlying dimension numberd 3, completing the results of Iscoe (1986).     

The spectral collocation method for efficiently solving PDEs with fractional Laplacian

We derive a spectral collocation approximation to the fractional Laplacian operator based on the Riemann-Liouville fractional derivative operators on a bounded domain Ω = [a, b]. Corresponding matrix representations of (?△) ^α/2 for α ∈ (0,1) and α ∈ (1,2) are obtained. A space-fractional advection-dispersion equation is then solved to investigate the numerical performance of this method under various choices of parameters. It turns out that the proposed method has high accuracy and is efficient for solving these space-fractional advection-dispersion equations when the forcing term is smooth.     

Deactivation of vibrationally excited CD3H using laser-induced fluorescence

Infrared fluorescence observed after exciting to ν₆ (ν=1) of CD₃H with a Q-switched CO₂ laser yields the exponential deactivation rate constant of 0.84 ms^?1 torr^?1. Rate constants for deactivation of CD₃H by rare gases vary from 1.4 (for He) to 0.029 (for Xe) ms^?1 torr^?1.     

Biaxial nematics: computer simulation studies of a generic rod-disc dimer model

One possible route to the elusive biaxial nematic phase is through rod-disc dimers in which the rod and disc mesogenic units are linked via a flexible spacer. We have developed a continuous generic model of such rod-disc dimers in which neighbouring like groups tend to align parallel to each other while unlike groups tend to be orthogonal. A torsional potential controls the relative orientations of the groups within a single dimer; depending on the strength of the torsional potential, the groups may be orthogonal or parallel in the conformational ground state. Monte Carlo simulations show that a rigid rod-disc dimer is most likely to form a biaxial nematic phase if the anisotropies of the two groups are the same. Introduction of flexibility is found to have little effect on the qualitative behaviour of the dimer as the relative anisotropy of the two mesogenic groups is changed. However, when the torsional potential strongly favours the alignment of the rod and disc within a single molecule with their symmetry axes parallel there is a dramatic change. The system then exhibits a strong hysteresis in the molecular shape and biaxiality and the biaxial nematic-isotropic transition becomes strongly first order, in marked contrast to the second-order character usually found for this transition. This first-order transition is observed to occur for a range of relative anisotropies of the two groups rather than at a single point.     

Structure and hydrogen bonding in neat N-methylacetamide: classical molecular dynamics and Raman spectroscopy studies of a liquid of peptidic fragments

The results of classical molecular dynamics (MD) simulations and Raman spectroscopy studies of neat liquid N-methylacetamide (NMA), the simplest model system relevant to the peptides, are reported as a function of temperature and pressure. The MD simulations predict that near ambient conditions, the molecules form a hydrogen bond network consisting primarily of linear chains. Both the links between molecules within the hydrogen-bonded chains and the associations between chains are stabilized by weak methyl-donated "improper" hydrogen bonds. The three-dimensional structural motifs observed in the liquid show some similarity to protein beta-sheets. The temperature and pressure dependence of the hydrogen bond network, as probed by the mode frequency of the experimentally determined amide-I Raman band, blue shifts on heating and red shifts under compression, respectively, suggesting weakened and enhanced hydrogen bonding in response to temperature and pressure increases. Disruption of the hydrogen-bonding network is clearly observed in the simulation data as temperature is increased, whereas the improper hydrogen bonding is enhanced under compression to reduce the energetic cost of increasing the packing fraction. Because of the neglect of polarizability in the molecular model, the computed dielectric constant is underestimated compared to the experimental value, indicating that the simulation may underestimate dipolar coupling in the liquid.     

Rapid interspecies energy flow between vibrationally excited SF6 and the asymmetric stretch of N2O

Rapid, selective collision-dependent excitation of N₂O following pumping of SF₆ with a CO₂ laser is reported. The N₂O fluorescence rise depends on the pressure of each component and is dominated by the SF₆-dependent contribution of 2290 ms^?1 Torr^?1. The subsequent fall is governed by V→V processes among SF₆ vibrational modes.     

Polymeric cross-linked surface treatments for controlling block copolymer orientation in thin films

The orientation of cylinder-forming poly(styrene-block-methyl methacrylate) [P(S-b-MMA)] was investigated on two sets of polymeric surface treatments: 10 para-substituted polystyrene derivatives with <10 mol % poly(4-vinylbenzyl azide) and a series of poly(styrene-random-4-vinylbenzyl azide) [P(S-r-VBzAz)] copolymers with 5-100 mol % poly(4-vinylbenzyl azide). The copolymers were spin-coated to form thin films and then cross-linked by heating. The resulting films exhibited a range of surface tensions from 21 to 45 dyn/cm. Perpendicular orientation of P(S-b-MMA) cylinders was achieved with poly(p-bromostyrene) and all the [P(S-r-VBzAz)] copolymer surface treatments, most notably the homopolymer of poly(4-vinylbenzyl azide). Films made from these simple copolymers are as effective as random terpolymer alignment layers commonly made from both block monomers and a cross-linkable monomer.     

Dinitration studies of 2,4,5-tribromo-3,6-dimethylphenol: the formation of an acyloin rearrangement product

Dinitration of 2,4,5-tribromo-3,6-dimethylphenol(1) gives either the tribromodinitro-compound(2) or its acyloin rearrangement product(3), depending on the reaction conditions: X-ray crystal structure analyses are reported for compounds (2) and (3).     

Intramolecular sulfoxide electrophilic sulfenylation in 2- and 3-indoleanilides

When N-[2-(alkylsulfinyl)phenyl]-1H-indole-2-carboxamides with varying degrees of indolic and amidic N-alkylation are heated in an inert solvent or treated with trifluoroacetic anhydride; only compounds in which the amidic nitrogen is methylated cyclize to indolo[3,2-b]-1,5-benzothiazepinones (9, 10). Successful cyclization is attributed to the ability of N-Me amides to readily adopt a conformation conducive to cyclization, which other derivatives are unable to achieve. The analogous 3-indoleanilide, N,N-dimethyl N-[2-(ethylsulfinyl)phenyl]-1H-indole-3-carboxamide (17a), undergoes SES/rearrangement to produce 10 upon heating in p-xylene. An intermediate 3H-indolinium spirocyclic species is proposed to account for this result.