The thermodynamic geometries of Gibbs, Weinhold, and Gilmore are compared and the benefits of each are pointed out along with the structures which must be abandoned in order to reap the benefits. While the measurement of distances is not required (or even meaningful) in a traditional Gibbsian picture, Weinhold’s metric can be used to measure distances in the equation-of-state surface. Using Weinhold’s metric for more than a single state of equilibrium necessitates abandoning a Gibbsian picture of convex surfaces of thermodynamic states. Gilmore’s metric, on the other hand, is compatible with standard Gibbsian thermodynamics. This metric measures distance in the potential surface of statistical mechanics rather than the equation-of-state surface of equilibrium thermodynamics.

We show that Weinhold’s metric cannot be induced on the equation-of-state surface from a Euclidean metric in the ambient space of all extensive state variables, whereas it can be induced if the ambient space is assumed to have only a Riemannian metric. This metric, however, is not unique.

By solving a self-consistent integral equation numerically, we have obtained the equations-of-state and thermodynamic properties of equilibrium supercooled liquids with soft-sphere potentials plus the Kac potential (generalized van der Waals model). The equations of state obtained deviate from those of molecular-dynamics simulations below the liquid-glass transition predicted. The static pair structures differ significantly along two branches, i.e., molecular-dynamics glasses and equilibrium supercooled liquids. From entropy curves obtained from the solutions of integral equations, we indicate the stability limit of the equilibrium supercooled liquid for the softness parameter n=4, 6, 9, 12, and ∞. We also discuss the effect of the softness on the thermodynamic properties of supercooled liquids.

Linear stability results for convection in binary fluid mixtures are given for experimental boundary conditions and parameter values. Normal ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He and ethanol-water mixtures are considered with no-slip boundary conditions on the velocity and no outward mass flux. Two cases are considered in detail: fixed temperature at top and bottom, and fixed temperature at the top and fixed thermal flux at the bottom. The role played by the Biot number is emphasized. The results are presented in a manner most useful to experimentalists. The errors incurred in determining the separation ratio S from experimental observations using scaled results with free boundaries are quantified. Neutral curves for both oscillatory and steady-state instabilities together with the corresponding critical wave numbers $k_c$ are determined as functions of S. For the latter, $k_c$ vanishes as S increases. The critical values of S for which this first occurs are determined analytically. Growth rates and frequencies for supercritical Rayleigh numbers are also given. The codimension-two point is found to be masked by steady-state instabilities that set in at smaller Rayleigh numbers, but the masking vanishes in the limit of small Lewis numbers and large Prandtl numbers. The lowest observable frequency along the Hopf curve is determined.

Noise effects on various properties of fully developed chaotic maps are studied. For the weak-noise case a perturbation method is developed. It yields the stationary density, eigenvalues, eigenfunctions, and null functions of the Frobenius-Perron operator in powers of the moments of the noise. The linear response of the noisy map to a deterministic perturbation is defined and calculated perturbatively. Correlation functions and Lyapunov exponents are also investigated. The examples are the tent map and the logistic map in the fully developed chaotic state with multiplicative white noise. The results for the Lyapunov exponents are in good agreement with those determined numerically.

As a possible mechanism for energy storage and transport in proteins, Davydov has proposed soliton formation and propagation. In this paper we investigate the stability of Davydov solitons at biological temperatures. From Davydov’s original theory evolution equations are derived quantum mechanically without approximations, and their numerical solutions at different temperatures are presented. Our conclusion is that the Davydov soliton is stable at 310 K.

Recent studies by Edwards, Davis, Swicord, and Saffer have indicated resonant absorption of microwave radiation by DNA in solution. Previous theoretical calculations had indicated that such resonances should be overdamped. We present a more realistic model that provides a parametrization for the overcoming of the overdamping. The refinements include the electrically active nature of the solvent and the binding of the first hydration layer. Our results show that the hydration layer binding is the single most important aspect of the phenomenon. The parametrization indicates that the ability of bound layers to transmit shear must be greatly reduced. This is a behavior that can be qualitatively explained in terms of bond orientation by the structured water and reduced bond density for the DNA-water interface as opposed to corresponding surface in pure water. Conclusive results, however, await a discrete molecular modeling of the hydration layer binding.

Orientational properties of a quantum rotor interacting with a classical substrate are investigated by dynamical simulated annealing. At zero temperature a transition in the molecular orientation is observed when the molecule-substrate coupling exceeds a critical value ${\alpha }_c$. For very light molecules we find a smooth transition and a decrease in ${\alpha }_c$ with an increase in the moment of inertia I. Above a certain value of I the molecule undergoes a sharp reorientational transition that shifts to higher values of ${\alpha }_c$ with an increase in I. The observed continuous transition is always mean field in nature. At finite temperatures the molecule-substrate interaction has a significant thermal broadening effect on the reorientational transition. The rms fluctuations in the rotor energy increase dramatically while those in the order parameter exhibit a peak around ${\alpha }_c$.

Recent work regarding stochastic motion in a bistable potential is critiqued. Emphasis is placed on mean first-passage time analysis and the effects of colored noise. Controversy has arisen regarding general theory, particular calculations, and numerical simulations. Each of these aspects of the problem is addressed in this paper.

The importance of the three-body dispersion interaction (Axilrod-Teller potential) in liquid Xe near its triple point is investigated by numerical simulations. Although large for the heavy rare gas Xe, its effect on collective dynamical properties such as the dynamical structure factor and transport coefficients is very small. When used in conjunction with an accurate pair potential, good agreement is obtained with experiment for both the pressure and transport coefficients.

Using geometric arguments of nonlinear dynamics we determine parameter regions for which the resistively shunted Josephson equation is assuredly nonchaotic, with or without an inductive shunting term, and with anyforcing. These results can account for the observed stability and voltage-to-frequency fidelity of the Kamper-Soulen resistively shunted Josephson thermometer, in the region of low inductive shunting.

Rayleigh-Bénard convection is studied under the influence of an external driving force due to a time-dependent Rayleigh number and sidewall heating. Using the Melnikov method we show that if the ratio of dissipation to forcing is sufficiently small, chaotic behavior occurs. The chaotic threshold is studied as a function of the frequency of the driving terms. It is shown that the limits ω→∞,0 reduce the size of the chaotic region in parameter space. ${\omega }_{\max }$, the most chaotic frequency, is computed and discussed.

The existence of anomalous Saffman-Taylor fingers when a localized disturbance is applied at their tip has been demonstrated by several recent experiments. We show that they form a well-defined family with strong similarities with crystalline dendrites. They are narrower and more stable than normal fingers, their tip is parabolic, and its radius of curvature ρ is proportional to the capillary length $l_0$. For very large velocities, saturation occurs when ρ becomes of the order of the plate spacing. Using localized disturbance and periodic forcing we characterize the amplification of waves on their lateral fronts and we then discuss some implications for dendritic crystalline growth.

The problem of diffusion in modulated and random media as described by a master equation is reduced to a discrete Schrödinger equation, and further transformed into a recursive nonlinear map. Short- and long-time diffusion is then discussed in terms of dynamical properties of such a map. Analytical expressions for scaling behavior of the integrated density of states are derived for the top and bottom of the spectrum. The numerical results allow estimation of the scaling region and the corrections to the leading behavior.

We study the effect of disorder on the superfluidity of the hard-sphere Bose gas in one dimension. This system is equivalent to the spin-(1/2 XY model with a random transverse field, which in turn can be mapped onto a disordered spinless-fermion model. We show that the localization of all fermionic states implies an exponential decay in the spin-spin correlation function and hence the instability of the superfluid against any amount of disorder. We point out a fundamental difference in the characteristics of the Jordan-Wigner transformation between the pure and disordered systems. Generalization of our results beyond the present model and implications to disordered superconductivity are discussed.

The rate for thermally activated escape from a cubic metastable well is investigated. The escape rate can become substantially smaller than its transition-state-theory limit either for strong damping, where the slow spatial diffusion across the barrier top diminishes the rate, or for very weak damping, where the rate is reduced because of the slow repopulation of the highly excited states in the well. It is shown that for a system with time-delayed friction the two regions can clearly be distinguished. For spatial-diffusion-limited decay, the rate shows a monotonic dependence on the delay time, while for energy-diffusion-limited decay the rate exhibits oscillatory behavior. Calculations are performed for a specific model which is suitable to describe the decay of the zero-voltage state of a Josephson junction shunted by a transmission line with variable effective length.

A particle in a one-dimensional δ-function potential possesses both discrete and continuum solutions. The configuration-space Green’s function and propagator for this problem are derived by explicit summation over the spectrum of eigenstates. The momentum-space Green’s function is also obtained. The propagator does not contain the classical action function in any simple way, in contrast to the usual structure in Feynman’s path-integral formalism. Various analogies between the δ-function and Coulomb problems are discussed.

We exhibit a solution to the Lorentz-Dirac equations for two classical point particles in circular orbits, each interacting with the retarded field of the other. The fields produce the exact tangential force required to balance the loss of energy by radiation.

The mass-polarization shift in the energy levels of 1sNL states of helium contains a term of second order in the ratio of the electron mass to that of the nucleus that is independent of L. Although inherent in an earlier work [Phys. Rev. A 33, 2780 (1986)], it was not pointed out there since only L-dependent splittings were of interest. The derivation is very simple and yields a correction of significance for the calculation of absolute ionization energies.

It has been suggested that ‘‘short’’ pulses of intense laser radiation can modify atomic collision dynamics in new and interesting ways. Recent experimental results in sodium-argon vapor with 1.6-psec pulses verify the existence of such an effect, although smaller in magnitude and at somewhat higher field intensities than had been predicted from theoretical arguments. Using quantum-mechanical wave-packet propagation on a realistic potential-energy curve under the parameters of the experiment, we determine that the time between curve crossings, the standard against which pulse durations should be measured, is on the order of 0.8 psec or less. The experimental results can then be understood in the context of having used too long a pulse to have clearly observed short-pulse effects.