The trace anomaly and low energy phenomenological implications of wormholes

In Coleman's wormhole scenario it is the trace anomaly on S₄ that controls the behavior of fundamental coupling constants, particle masses, mixing angles, etc. We indicate how low energy phenomenology may be derivable from very general properties of wormhole physics and calculable β-functions, etc.     

A general method for the synthesis of 1-substituted (or unsubstituted)-4-carbomethoxy-2-imidazolin-5-ones

A general method for the synthesis of the title compounds by employing the reagent methyl $\text{N}$-(dicarbomethoxymethyl)methanimidate is described. The preparation, properties and reactions of the reagent are also reported.     

Photon correlation spectra of poly(phenylmethyl siloxane) under high pressures

We report polarized photon correlation measurements of bulk poly(phenylmethyl siloxane) (PPMS) with a molecular weight of about 2500 at different pressures from 1 to 1750 bar and temperatures between 269 and 308 K. In the Frequency range accessible by present-day digital correlators, the time correlation function can measure a slow q²-dependent diffusional process due to local concentration fluctuations and a fast α-mode structural relaxation process. The mean characteristic times of the two processes approach each other at low temperatures and high pressures, in contrast to the behavior of the α- and β-relaxation times. We should be cautious in relating the mean characteristic times for the structural relaxation process obtained by different experimental techniques, such as Brillouin scattering and photon correlation spectroscopy, because of the differnces in the probe emphasis and the extremely broad frequency distribution of such relaxation processes.     

Glass transition,crystallization, and morphology relationships in miscible poly(aryl ether ketones) and poly(ether imide) blends

The relationships among glass transition, crystallization, melting, and crystal morphology of poly(aryl ether ketone) (PAEK)/poly(other imide) (PEI) blends was studied by thermal, optical and small-angle x-ray scattering (SAXS) methods. Two types of PAEK were chosen for this work: poly(aryl ether ether ketone), PEEK, and poly(aryl ether ketone ketone), PEKK, which have distinctly different crystallization rates. Both PAEKs show complete miscibility with PEI in the amorphous phase. As PAEK crystallizes, the noncrystallizable PEI component is rejected from the crystalline region, resulting in a broad amorphous population, which was indicated by the broadening and the increase of T_g over that of the purely amorphous mixture. The presence of the PEI component significantly decreases the bulk crystallization and crystal growth rate of PAEK, but the equilibrium melting temperature and crystal surface free energies are not affected. The morphology of the PEI segregation was investigated by SAXS measurements. The results indicated that the inter(lamellar-bundle) PEI trapping morphology was dominant in the PEEK/PEI blends under rapid crystallization conditions, whereas the interspherulitic morphology was dominant in the slow crystallizing PEKK/PEI blends. These morphologies were qualitatively explained by the expression δ=D/G, where G was the crystal growth rate and D was the mutual diffusion coefficient. © 1993 John Wiley & Sons, Inc.     

Equivalence of Two Approaches to Integrable Hierarchies of KdV type

The equivalence between the approaches of Drinfeld-Sokolov and Feigin-Frenkel to the mKdV and KdV hierarchies is established. A new derivation of the mKdV equations in the zero curvature form is given. Connection with the Baker-Akhiezer function and the tau-function is also discussed. Received: Received: 1 July 1996 / Accepted: 21 October 1996     

Solvent dynamics following charge transfer at the liquid-liquid interface

The dynamics of solvent reorganization following charge transfer at the interface between two immiscible liquids, one polar and the other non-polar are investigated by molecular dynamics. Both charge separation and charge recombination processes in two different orientations at the surface are considered and are compared with the same processes in the bulk polar solvent. The relaxation at the surface is significantly slower than in the bulk, in contrast to predictions of continuum models. The linear response approximation works reasonably well in the bulk but fails at the interface. The Langevin model is in poor agreement with the exact equilibrium correlations, especially at short time, but can qualitatively account for the overall rate.     

Three-Dimensional Hückel Theory for closo-Carboranes

We have recently developed a 3-dimensional Hückel method for cluster compounds. The method uses a set of approximations for Coulomb, resonance, and overlap integrals very similar to those employed in the familiar 2-dimensional Hückel theory for the pi electrons of planar conjugated hydrocarbons. The method can be adapted to heteroatomic clusters by introducing heteroatomic Coulomb integrals, alpha(Y) = alpha(X) + hbeta, whereh is a parameter for heteroatom Y. In this paper, we use the 3-dimensional Hückel method to study the properties of the closo-carboranes, C(2)B(n)()(-)(2)H(n)(). We calibrate the method by choosing a value of the heteroatomic parameter h that distinguishes positional isomers by energy and gives them relative energies in rough agreement with those established by observation and ab initio calculations. We obtain modest improvement in matching ab initio relative energies of isomers by means of a three-parameter, first-order perturbation treatment. We use the calibrated method to evaluate various mechanisms proposed for the isomerizations of C(2)B(4)H(6), C(2)B(5)H(7), and C(2)B(6)H(8), all of which have been observed to undergo intramolecular isomerizations. Rearrangements of C(2)B(6)H(8) have been satisfactorily explained by a single-DSD (diamond-square-diamond) process. Those for C(2)B(5)H(7) require at least two DSD processes, concerted, consecutive, or overlapping. Several different mechanisms have been proposed for the rearrangement of C(2)B(4)H(6). In evaluating intermediate and transition state structures, the 3-dimensional Hückel method gives higher energies to those structures with a larger number of nontriangular faces, a plausible conclusion except that occasionally it is wrong. In comparison with ab initio results, the 3-dimensional Hückel method fails to give low energies for classical structures.