Data for the surface tension of pure fluids near critical points and for the interfacial tension between coexisting liquid phases of binary mixtures near consolute points are reviewed using recent theoretical values for the critical exponents and the concept of two-scale-factor universality [D. Stauffer, M. Ferer, and M. Wortis, Phys. Rev. Lett. 29→, 345 (1972)]. The data are used to estimate the universal amplitude ratios relating the interfacial tension amplitude ${\sigma }_0$ to the specific-heat divergence and to the correlation length near $T_c$. The amplitude ratios for a wide variety of fluid systems including polymer solutions are consistent and, in the most favorable cases, have an accuracy approaching ±5% of ${\sigma }_0$. The experimental amplitude ratios do not agree with recent theoretical estimates from either Monte Carlo simulations of the Ising model or the ε expansion. The theoretical values of ${\sigma }_0$ are about 65% of the experimental values. I have no explanation for this inconsistency. In the process of reviewing surface-tension data for pure fluids, it was observed that the capillary-length data for many fluids deviate by less than 2% from the expression $a^2$=$a_0^2$(1-T/$T_c$${)}^{0.93}$ ${}_{}{}^5{}_{}{}^{}$ when T varies from the triple point to 0.99$T_c$. (The exponent 0.935 is expected to be accurate only asymptotically close to $T_c$.) This observation implies that the scale factors for the critical anomaly in the free energy of these liquid-vapor systems can be estimated from measurements of the densities of the coexisting phases at all temperatures and a measurement of the capillary rise near the triple point.

The neutron scattering cross section (density-correlation function) for a harmonic oscillator subject to small, frequent impulsive forces (Brownian motion) is calculated. We find that the impulse approximation is not correct in the limit that the momentum transfer approaches infinity, as there is no time scale on which the particle can be regarded as free.

The Fermi-Pasta-Ulam β model has been studied by integrating numerically the equations of motion for a system of N nonlinearly coupled oscillators with N ranging from 64 to 512. Multimode excitations have been considered as initial conditions; the number Δn of initially excited modes is such that the ratio Δn/N is kept constant. We can consider the system as a gas of weakly coupled phonons (normal modes), so that if we keep the ratio Δn/N constant we find an analogy with the thermodynamical limit of statistical mechanics where the ratio M/V is constant when both the volume V and the number of particles M are increased up to infinity. The relaxation towards stationary states is followed through the time evolution of a suitably defined ‘‘spectral entropy’’ which depends on the shape of the space Fourier spectrum; this spectral entropy is a good equipartition indicator: Strong evidence is reported in favor of the existence of an equipartition threshold. Its persistence at very different values of N is also clearly shown. The main result concerns the occurrence of the threshold at the same value of the energy density (i.e., of the ‘‘control parameter’’) when the number of degrees of freedom is changed. More general initial conditions are also considered and the same result is found using as a control parameter a pseudo-Reynolds-number R: The threshold occurs at the same critical value $R_c$ when N is varied. It turns out that a fully chaotic regime (equipartition) is obtained with an ‘‘average nonlinearity’’ of the system of about 3%.

A numerical solution of a hydrodynamic second-order model shows that the propagation of the first ionizing wave arises from an overgrowth of hot electrons in the wave front in a zone of a greatly disturbed electric field. This gives rise, in the electron shock zone ahead of the wave, to a precursor phenomenon, whose effect is to accelerate the channel propagation. Inside the shock zone, the electronic energy differs from the characteristic energy; the nonequilibrium between the electrons and the electric field, as a result of the electron pressure gradient, induces a heating of electrons in this zone. The space-charge electric field is calculated assuming that the discharge evolves in a variable ellipsoidal envelope with revolution symmetry around the propagation axis. The electron shock-wave structure is shown to maintain itself and to propagate during the evolution of the discharge. The results obtained from this second-order model are compared to those obtained from a classical first-order model in which the electron temperature is a function of the reduced electric field alone. This comparison allows us to define the concept of electron nonequilibrium in an electron shock wave and to show that it is the source of the high-speed propagation of the streamer. The close agreement of the results obtained from the second-order model with the experimental data justifies the formulation of the model, particularly that of the interaction operators of the energy equation.

This paper reports the result of a calculation which shows the effect of damping on the quantum interference of two Gaussian wave packets in a harmonic potential. We use the influence-functional method, which seems to be the most appropriate one for this kind of calculation. It is shown that quantum interference effects are severely diminished by the presence of damping even when its influence on the system is only light. The corrections to the undamped formulas are always expressible in terms of the phenomenological damping constant γ, the temperature T (in the high-temperature limit), the cutoff frequency (Ω) of the reservoir oscillators, and the mean number (N) of quanta of energy initially present in the system. Both weakly and strongly damped systems are analyzed in the regime of low and high temperatures.

The dynamically exactly solvable system of a local oscillator coupled harmonically to a finitely extended one-dimensional string (continuum transmission line field) is studied in detail. An earlier recognized quantum-mechanical logarithmic ultraviolet divergence in the oscillator’s kinetic fluctuations is shown to originate in the infinitely strong (rigid) coupling limit. For any finite coupling strength the fluctuations are finite. Inter alia attention is given to such aspects as mode stability, nonorthogonality of the eigenfunctions, the essential singular nature of the eigenmatrix, completeness relations, the initial-value problem, infinite-system limit, quantum exponential decay, coherent-state evolution, and the thermal string model.

We have measured the power spectra of a periodically driven p-n junction in the vicinity of a dynamical instability. The addition of external noise introduces new lines in the spectra, which become more prominent as a bifurcation point is approached. The scaling of the peak, width, area, and line shape of these lines is measured near the onset of two different codimension-one instabilities: the period doubling and Hopf bifurcations. The results are in excellent agreement with recent theoretical predictions.

Light-scattering measurements are reported for densities and temperatures close to the critical point of ${\mathrm{CO}}_2$ in the range ‖(T-$T_c$)/$T_c$‖≲${10}^{\mathrm{-}4}$. A contour of constant scattering was determined in the z-T plane, where z is the vertical distance from the point of maximum scattering or from the meniscus at the given temperature. The contour was found to be fitted by a cubic model parametric equation with a=22.3, γ=1.22, β=0.347, $b^2$=3/(3-2β)=1.30, $T_c$=31.011 55 °C, and r=6.45×${10}^{\mathrm{-}5}$. The measured contour was also compared with predictions of a parametric equation of state representing interferometric measurements made very close to the critical point and with linear model equations that have been used to describe thermodynamic measurements made farther from the critical point. Disagreements amounted to as much as 4%, a portion of which may be attributed to the difficulty of completely eliminating vertical temperature gradients in the scattering cell. Data are also presented for several profiles of scattering intensity versus height and for maximum scattered intensity versus temperature near the critical point.

We assume that the formal results of the maximum-entropy approach for the description of some quantal systems remain valid in the presence of a perturbation that cannot be formulated in terms of a Hamiltonian, if the dynamical laws for a convenient set of observables are known. As an example we study the harmonic motion of a quantal object coupled to a heat reservoir (a) reversibly and (b) irreversibly. In case (b), the data concerning the evolution of the individual fluctuations permit the construction of a density matrix for all times.

The effect of inertia on droplet growth in a d-dimensional (simple) fluid mixture is investigated. Four typical growth laws of average droplet radius are obtained: two conventional ones ($t^{1/d}$ and t) and two new ones ($t^{2/(d+2)}$ and $t^{2/3}$). The regions of the applicabilities of these growth laws are investigated. Far away from the critical point, or for earlier or later stages of phase separation, new growth laws ($t^{2/(d+2)}$ and $t^{2/3}$) are dominant. These new laws represent droplet growth in the case of high Reynolds numbers where the inertia of the fluid is important and the system may be turbulent.

The weak-noise limit of Fokker-Planck models is studied for the case where the steady-state probability density in that limit cannot be represented by a continuously differentiable nonequilibrium potential. In a previous paper [J. Stat. Phys. 35, 729 (1984)], we have shown that this corresponds to the general case in systems outside thermodynamic equilibrium. By using an extremum principle, the nondifferentiable potential is constructed, which generalizes the differentiable case. The relation of approximate differentiable potentials to the exact nondifferentiable potential is considered and discussed for two examples with attracting limit cycles, a periodically forced nonlinear oscillator, and two phase-coupled nonlinear oscillators. The relevance of nondifferentiable potentials for non- equilibrium thermodynamics is pointed out.

We briefly review the results of experimental investigations into the effect of noise on electrohydrodynamic instabilities in nematic liquid crystals. So far, no satisfactory theoretical treatment of the observed noise-induced effects exists, apparently due to the fact that the noise is coupled to the system through two different mechanisms. By considering a simpler, but related instability, namely the Fréedericksz transition, we are able to isolate one of the mechanisms. We present a theoretical treatment of the effect of colored noises on the full nonlinear problem, and make quantitative predictions concerning the behavior of the system as a function of the correlation time and the intensity of the noise.

The problem of a particle trapped in a sinusoidal potential well in the presence of a monochromatic external field is studied. The critical amplitudes of external field at which the particle can be driven out of the well are calculated. Predictions based on renormalization-group techniques using the pendulum approximation are found to deviate from the results of numerical experiment. Good agreement is obtained by studying the overlap of resonance zones obtained from full nonlinear one-resonance-approximation Hamiltonians. Even though no external noise is present, the particle once driven from a well exhibits a random walk between wells.

The Fokker-Planck equation describing the dynamics of fluctuations near instability has been solved for a class of oscillatory bifurcations. A generalized case and two other cases are discussed. Exact solutions are obtained.

A rotation by 2π around an Aharanov-Bohm solenoid is shown to change the wave function of a charged spinless particle by a phase factor χ=exp(ieφ/ħ). For fermions the effect manifests itself as a phase shift in addition to the well-known sign change. A gedanken experiment is proposed for observation.

K-x-ray production cross sections have been measured in (nearly symmetric) ${}_{16}{}^{}{}_{}{}^{}$S${+\mathrm{}}_{18}$Ar and (very asymmetric) ${}_{16}{}^{}{}_{}{}^{}$S${+\mathrm{}}_2$He collisions as a function of the projectile charge state q (q=3–16) at low incident energies of 10 and 20 MeV. The charge-state dependence is very similar in the two cases, confirming results obtained at higher incident energies. The sensitivity of such studies to different K-vacancy-production mechanisms is discussed.

An electron and photon atomic-recoil technique has been used to measure absolute total cross sections for electrons scattered by $3^2$$P_{3/2}$ sodium atoms in the 6–25-eV energy range, with the use of a new, high-resolution crossed-beam apparatus. A single-mode tunable ring dye laser is used to selectively excite the F=3 hyperfine level. Excited-state populations are determined by using the atomic recoil in resonant photon absorption. At 6 eV there is very good agreement with a previous measurement [B. Jaduszliwer, R. Dang, P. Weiss, and B. Bederson, Phys. Rev. A 21, 808 (1980)].

Rotational-level mixing by anisotropic intermolecular forces is found to be important to the mechanism which produces intracollisional interference effects in the pure rotational spectrum of HD and HD–inert-gas mixtures. The major contribution involves the anisotropic repulsive term in the potential and the anisotropic overlap-induced dipole moment. Improved agreement between calculation and experiment results when the mixing is included in the analysis.

The impact-parameter-dependent K-shell-vacancy-production probability for ${\mathrm{F}}^{8+}$+Ne and ${\mathrm{S}}^{15+}$+Ar collisions is studied with use of the modified atomic-orbital (AO+) expansion model. It is shown that the AO+ model predicts results in good agreement with experimental data. The discrepancies at low energies are discussed and further experimentation is suggested.

In accordance with the plane-wave Born approximation, contribution of atomic bremsstrahlung (AB) in heavy-ion–atom collisions has been estimated and compared with experimental results. It is found that AB is negligibly small in symmetric or nearly symmetric collisions, whereas it becomes predominant in asymmetric collisions. Thus continuum x rays produced in asymmetric heavy-ion–atom collisions, which have not fully been interpreted yet, can be understood by taking account of the atomic bremsstrahlung.