Disjoining pressure of planar adsorbed films

Frumkin-Derjaguin theory of interfacial phase transitions and in particular the concept of the disjoining pressure of a planar adsorbed film is reviewed and then discussed in terms of statistical mechanical formulations of interfacial phase transitions beyond mean-field.Comment: 11 pages including the two figure

Renormalized Path Integral in Quantum Mechanics

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.Comment: 13 pgs, plain TEX fil

Solitons in a Bilocal Field Theory

We obtain a bilocal classical field theory as the large $N$ limit of the chiral Gross--Neveu (or non--abelian Thirring) model. Exact classical solutions that describe topological solitons are obtained. It is shown that their mass spectrum agrees with the large $N$ limit of the spectrum of the chiral Gross--Neveu model.Comment: Tex, 18 pages, no figure

Renormalized Contact Potential in Two Dimensions

We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before attempting to solve the system, and leads to an interesting eigenvalue problem in N-2 degrees of freedom (in the center of momentum frame) when there are N particles. The effective Hamiltonian for N-2 particles has a nonlocal attractive interaction, and the Schrodinger equation becomes an eigenvalue problem for the logarithm of this Hamiltonian. The 3-body case is examined in detail, and in this case a variational estimate of the ground-state energy is given.Comment: Plain Te

Non-analytic curvature contributions to solvation free energies: influence of drying

We investigate the solvation of a hard spherical cavity, of radius $R$, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation $\delta \mu\equiv \mu - \mu_{co}(T)$ is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale $R_c=2 \gamma_{gl}^\infty/(\Delta \rho \delta \mu)$, where $\gamma_{gl}^\infty$ is the planar gas-liquid surface tension and $\Delta \rho$ is the difference in coexisting densities at temperature $T$. For $R>R_c$, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature $R^{-1}$, in keeping with the analysis of Stillinger and Cotter, J. Chem. Phys. {\bf 55}, 3449 (1971). In the other regime, $R<R_c$, the interfacial free energy and its derivatives acquire terms depending on $\ln R$. Since $R_c^{-1}$ can be made arbitrarily small this implies non-analytic behavior, as $R^{-1}\to 0$, of the work of formation of a hard spherical cavity and of the Gibbs adsorption and the fluid density at contact with the wall. Our analysis, which is based on an effective interfacial Hamiltonian combined with exact statistical mechanical sum rules, is confirmed fully by the results of microscopic density functional calculations for a square-well fluid.Comment: 17 pages, 3 figures; accepted for publication in J. Chem. Phy

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this

A comparison of measured and theoretical predictions for STS ascent and entry sonic booms

Sonic boom measurements have been obtained during the flights of STS-1 through 5. During STS-1, 2, and 4, entry sonic boom measurements were obtained and ascent measurements were made on STS-5. The objectives of this measurement program were (1) to define the sonic boom characteristics of the Space Transportation System (STS), (2) provide a realistic assessment of the validity of xisting theoretical prediction techniques, and (3) establish a level of confidence for predicting future STS configuration sonic boom environments. Detail evaluation and reporting of the results of this program are in progress. This paper will address only the significant results, mainly those data obtained during the entry of STS-1 at Edwards Air Force Base (EAFB), and the ascent of STS-5 from Kennedy Space Center (KSC). The theoretical prediction technique employed in this analysis is the so called Thomas Program. This prediction technique is a semi-empirical method that required definition of the near field signatures, detailed trajectory characteristics, and the prevailing meteorological characteristics as an input. This analytical procedure then extrapolates the near field signatures from the flight altitude to an altitude consistent with each measurement location

The first total synthesis of (+)-mucosin

The first total synthesis of (+)-mucosin has been completed allowing assignment of the absolute stereochemistry of the natural product. A zirconium induced co-cyclisation was utilised to install the correct stereochemistry of the four contiguous stereocentres around the unusual bicyclo[4.3.0]nonene core

Results of the flight noise measurement program using a standard and modified SH-3A helicopter

A field noise measurement program has been conducted using both a standard SH-3A helicopter and an SH-3A helicopter modified to reduce external noise levels. Modifications included reducing rotor speed, increasing the number of rotor blades, modifying the blade-tip shapes, and acoustically treating the engine air intakes and exhaust. The purpose of this study was to document the noise characteristics recorded on the ground of each helicopter during flyby, hover, landing, and take-off operations. Based on an analysis of the measured results, the average of the overhead, overall, ontrack noise levels was approximately 4 db lower for the modified helicopter than for the standard helicopter. The improved in-flight noise characteristics, and associated small footprint areas and time durations, were judged to be mainly due to tail-rotor noise reductions. The noise reductions were obtained at the expense of required power increases at airspeeds greater than 70 knots for the modified helicopter