Brownian Computation Is Thermodynamically Irreversible

Brownian computers are supposed to illustrate how logically reversible mathematical operations can be computed by physical processes that are thermodynamically reversible or nearly so. In fact, they are thermodynamically irreversible processes that are the analog of an uncontrolled expansion of a gas into a vacuum.     

Denjoy's theorem with exponents

If is the (unique) minimal set for a diffeomorphism of the circle without periodic orbits, , then the upper box dimension of is at least . The method of proof is to introduce the exponent into the proof of Denjoy's theorem.

     

A hybrid model for the acoustic response of a two-dimensional rough surface to an impulse incident from a refracting medium

A numerical model to calculate the impulse response of a two-dimensional, impenetrable, rough surface directly in the time domain has been recently introduced [J. Acoust. Soc. Am. (2000) 107, 27]. This model is based on wedge diffraction theory and assumes that the half-space containing the source and receiver is homogeneous. In this work, the model is extended to handle media where the index of refraction varies with the distance to the surface by merging the scattering model with a ray-based propagation model. The resulting hybrid model is tested against a Finite-Difference Time-Domain (FDTD) method for the problem of backscattering from a corrugated surface in the presence of a refractive layer. This new model can be applied, for example, to calculate acoustic reverberation from the sea surface in cases where the water mass is inhomogeneous and in the presence of a subsurface bubble layer at low frequencies where dispersion is negligible. It can also be used for atmospheric propagation problems where there is a sound speed gradient overlying rough terrain.     

A mass spectral rearrangement of 2-(alkylamino)benzoic acid derivatives and related heterocyclic systems

The behavior of a series of 2-(alkylamino)benzoic acid derivatives and related heterocylic systems has been investigated using electron impact mass spectrometry and fragmentation pathways have been formulated. Deuterium-labeled and ¹³C-labeled compounds were used in this study. An interesting rearrangement of the alkylamino compounds, in which the alkyl substituent is incorporated into a fulvene ion, was observed. This rearrangement had previously been observed for 1-alkylisatins and l-alkyl-3-arylimino-2-indolinones.     

Mechanistic observations in the gewald syntheses of 2-aminothiophenes

The Gewald syntheses were employed to prepare a series of 2-amino-3-carboethoxythiophenes, and the syntheses of two of these, namely, the 3,4-trimethylene ( 1f ) and 3,4-tetramethylene ( 1g ) derivatives, were examined in detail. In two preparations of 1f , octahydro-6a-(4-morpholinyl)-2-thioxocyclopenta[b]pyrrole-3-carboxylic acid ( 7 ) was a co-product. The structure of 7 was ascertained from its 300 MHz ¹H nmr and ¹³C nmr spectra, and by its conversion to 1,4,5,6-tetrahydro-2-mercaptocyclopenta[b]pyrrole-3-carboxylic acid ethyl ester ( 8 ). Isolation of 7 and other observations led to postulated mechanisms for three of the Gewald thiophene syntheses.     

The solvent extraction of some thallium(I) chelates

Fourteen different chelating reagents have been investigated, as possible extradants for radioiabelled 10^-6M thallium(I) from aqueous solutions into chloroform. The data have beun analyzed theoretically to identify the predominant species involved and to estimate association and distribution constanta.     

Design and synthesis of type-III mimetics of omega-conotoxin GVIA

Our interest lies in the rational design and synthesis of type-III mimetics of protein and polypeptide structure and function. Our approach involves interactive design of conformationally defined molecular scaffolds that project certain functional groups in a way that mimics the projection of important binding residues as determined in the parent structure. These design principles are discussed and applied to the structurally defined polypeptide, -conotoxin GVIA, which blocks voltage-gated, neuronal N-type calcium channels. These ion channels represent therapeutic targets for the development of new analgesics that can treat chronic pain. It is shown how a discontinuous, 3-residue pharmacophore of GVIA can be mimicked by different molecular scaffolds. It is illustrated how such 1^st generation leads must necessarily be weak and that optimisability must therefore be built-in during the design process.     

Polybrominated oxydiphenol derivatives from the sponge dysidea herbacea: Structure determination by analysis of 13C spin-lattice relaxation data for quaternary carbons and 13C-1H coupling constants

Five polybrominated oxydiphenol derivatives have been isolated from various Great Barrier Reef collections and one Fijian collection of the sponge Dysidea herbacea: 3,4',5,6,6'-hexabromo-2, 2'-oxydiphenol (11), 3,4',5,6,6'-pentabromo-2,2'-oxydiphenol (12), 3.4',5,6,6'-pentabromo-2,2'-oxydiphenol 1-methyl ether (13), 3,4,4',5,6'-pentabromo-2,2'-oxydiphenol 1,1'-dimethyl ether (14) and 3,4',5,6'-tetrabromo-2,2'-oxydiphenol 1'-methyl ether (15).The structure of the first member of this series is determined by a new method involving ¹³C spin-lattice relaxation data. The contributions of nearby hydrogens to quaternary carbon spin-lattice relaxation times are calculated for various possible structures and compared with the experimental data, leading to an unequivocal proof of structure. The structures of the remaining compounds in the series are established principally by analysis of ¹³C chemical shifts and ¹³C-¹H coupling constants.     

Thermal dealkylations of quaternized methoxyquinolinium and methoxyisoquinolinium iodides in the mass spectrometer

Dealkylations of N-alkyl 6- and 7-methoxy quinolinium and isoquinolinium iodides in the mass spectrometer proceeded to give predominantly O-demethylation when resonance stabilized ions were produced. When O-demethylation did not provide a resonance stabilized ion, N-dealkylation predominated.     

Kinetics and thermodynamics of H. transfer from (eta5-C5R5)Cr(CO)3H (R = Ph,Me, H) to methyl methacrylate and styrene

The rates of H/D exchange have been measured between (a) the activated olefins methyl methacrylate-d(5) and styrene-d(8), and (b) the Cr hydrides (eta(5)-C(5)Ph(5))Cr(CO)(3)H (2a), (eta(5)-C(5)Me(5))Cr(CO)(3)H (2b), and (eta(5)-C(5)H(5))Cr(CO)(3)H (2c). With a large excess of the deuterated olefin the first exchange goes to completion before subsequent exchanges begin, at a rate first order in olefin and in hydride. (Hydrogenation is insignificant except with styrene and CpCr(CO)(3)H; in most cases, the radicals arising from the first H. transfer are too hindered to abstract another H. .) Statistical corrections give the rate constants k(reinit) for H. transfer to the olefin from the hydride. With MMA, k(reinit) decreases substantially as the steric bulk of the hydride increases; with styrene, the steric bulk of the hydride has little effect. At longer times, the reaction of MMA or styrene with 2a gives the corresponding metalloradical 1a as termination depletes the concentration of the methyl isobutyryl radical 3 or the alpha-methylbenzyl radical 4; computer simulation of [1a] as f(t) gives an estimate of k(tr), the rate constant for H. transfer from 3 or 4 back to Cr. These rate constants imply a DeltaG (50 degrees C) of +11 kcal/mol for H. transfer from 2a to MMA, and a DeltaG (50 degrees C) of +10 kcal/mol for H. transfer from 2a to styrene. The CH(3)CN pK(a) of 2a, 11.7, implies a BDE for its Cr-H bond of 59.6 kcal/mol, and DFT calculations give 58.2 kcal/mol for the Cr-H bond in 2c. In combination the kinetic DeltaG values, the experimental BDE for 2a, and the calculated DeltaS values for H. transfer imply a C-H BDE of 45.6 kcal/mol for the methyl isobutyryl radical 3 (close to the DFT-calculated 49.5 kcal/mol), and a C-H BDE of 47.9 kcal/mol for the alpha-methylbenzyl radical 4 (close to the DFT-calculated 49.9 kcal/mol). A solvent cage model suggests 46.1 kcal/mol as the C-H BDE for the chain-carrying radical in MMA polymerization.