It is proven that the Runge-Gross version of the Hohenberg-Kohn theorem is valid for arbitrary time-dependent ensembles.

With the help of a commutativity condition, we construct Kadomtsev-Petviashvili equations which depend explicitly on x and t.

Comments are made on the wave-number selection when a ramp changes the conditions in Taylor-Couette flow from locally subcritical to supercritical as z increases. It is argued that under certain well-defined circumstances the wave number is uniquely determined by the geometry.

An electron-photon coincidence technique was used to probe the coherence of the excitation of the 3 ${\mathrm{}}^2$P state in sodium by 22.1-eV electrons. The observed coherence implied that spin-dependent interactions could be neglected for forward-angle scattering at this energy. The magnitude and phase of the scattering amplitudes are compared with those derived from experiments which are the time and parity inverse of the present experiments.

Laser ionization was used to measure the state-selective angular and velocity distributions of NO molecules scattered from a graphite surface. The data showed that at sufficiently low surface temperatures, the scattered molecules were generally composed of quasispecular reflected part and a diffusive scattered part with different translational and rotational behavior.

A systematic difference between the x-ray energies emitted by the daughter atom produced in electron-capture radioactive decay and the usual ‘‘characteristic’’ x-ray energies produced by electron bombardment or photoemission is noted. Particularly, enhanced differences are predicted for certain elements, and some measurements demonstrating this effect are presented.

We show that photoelectron angular distributions in the 2${\sigma }_u$ channel of ${\mathrm{N}}_2$ are significantly distorted by continuum-continuum coupling with the f-wave (l=3) shape resonance in the 3${\sigma }_g$ photoionization channel. This distortion is clearly seen in measured 2${\sigma }_u$ angular distributions. The effect is demonstrated using K-matrix methods to couple the one-electron 2${\sigma }_u$ε${\sigma }_g$ and 3${\sigma }_g$ε${\sigma }_u$ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ channels. Non-Franck-Condon ${\mathrm{N}}_2$${\mathrm{}}^{+}$ B ${\mathrm{}}^2$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$ vibrational branching ratios and vibrationally dependent 2${\sigma }_u$ε${\sigma }_g$ photoelectron asymmetry parameters are predicted as additional effects.

A semiclassical expansion for the quantum partition function of solids is presented. With respect to the usual Wigner method, the temperature range where the expansion is significant is broadened owing to the correct quantum-statistical treatment of the harmonic modes, while a Wigner-like expansion is retained only for the anharmonic part. As an application, the lowest quantum correction to the specific heat of a one-dimensional sine-Gordon model is calculated analytically.

Time-resolved conductivity measurements on nanosecond pulse-ionized xenon gas confirm the prediction of McMahon and Shizgal that initially formed hot electrons can undergo a net displacement in the reverse field direction. This negative mobility situation persists for 30 ns after the pulse at 10 atm (E/N≲${10}^{\mathrm{-}19}$ V ${\mathrm{cm}}^2$) and gradually disappears as the field strength is increased.

A random-walk model is proposed to simulate Darcy-law two-dimensional flows in hydrodynamics in the limit of zero-surface tension. The simulation is compared with the analytic and numerical results of the latter in steady-state and dynamic cases, respectively. The instabilities of the model in a flat interface are studied in the linear region. It is clear that the mean-field limit of diffusion-limited aggregation is a Saffman-Taylor problem.

We consider the distribution of the velocity difference between two points separated by an inertial range distance in a high Reynolds number turbulent flow. The pth moment of this distribution is assumed to vary as the ((1/3)p)+$y_p$ power of the separation. We propose a new one-parameter model for the dependence of $y_p$ on p based on a dynamical scaling argument. We find that $y_p$=0 for p<$p_c$, and is proportional to (p-$p_c$) for p>$p_c$. The model fits experiment reasonably well for $p_c$≊5, suggesting that the Kolmogorov (5/3) law for the energy spectrum is exact.

Recent experiments have shown that the stirring rate strongly affects the bistable region exhibited by certain chemical systems in continuous stirred tank reactors. An interpretation of these results is presented in terms of the competition between turbulent mixing and the inhomogeneities generated by the feeding of the reactor.

Various domain-growth mechanisms in phase-separating binary fluids are discussed. A tube hydrodynamic instability for concentrated mixtures is studied through a linear stability analysis. A quantitative discussion of the three-dimensional linear growth law is given. For two-dimensional concentrated mixtures we argue that domains grow in time with a diffusive growth law $t^{1/2}$. No crossover to a linear growth law is expected, in contrast to d=3. This is in apparent agreement with a molecular-dynamics simulation of a d=2 pure fluid. For two-dimensional dilute mixtures we argue that a $t^{1/2}$ diffusive behavior crosses over to a $t^{1/3}$ Lifshitz-Slyozov growth in the latter stages of phase separation.

We have made power-spectral measurements in both laboratory and rotating reference frames on fluid flow between rotating concentric cylinders. The oscillating modes identified in previous experiments were traveling azimuthal waves; in contrast, three of the oscillatory modes observed in the present experiment were found to be nonpropagating. One of the modes gives an instrumentally sharp component in the spectra, while the other two produce broad spectral components; hence the latter two flows are nonperiodic.

Because of the high symmetry of a cubic lattice, the interpretation of Bragg-scattering results may be complicated by the presence of multiple-scattering effects. We calculate here the polarization properties of light that is multiply Bragg scattered from chiral cubic structures with a view to interpreting the (111) backscatter from blue-phase lattices. We find that doubly and triply scattered light from (100)- and (110)-like Bragg planes having m=2 symmetry (using the notation of Hornreich and Shtrikman) has the same polarization as singly backscattered light from the (111), m=0 plane. The results are used to interpret the scattering measurements of Tanimoto and Crooker.

The eigensolutions of the Maxwell equations for light propagation in a perfect cholesteric liquid crystal are considered. They are Bloch waves having, in principle, infinitely many Fourier components. The relative amplitudes of these components are studied as a function of the angular frequency ω and of the incidence angle ${\theta }_i$, in order to determine the conditions under which the actual eigensolutions can be suitably approximated by a superposition of only a few plane waves. When these conditions are satisfied, the wave vectors and the amplitudes of the components are given by simple analytical expressions. The main results are the following: (a) Far from the Bragg reflection bands, only one or two plane-wave components need be retained. Regions of the (ω,${\theta }_i$) plane are found, in which a very good approximation is represented by a linearly polarized wave (π- and σ- polarized-wave approximation) or by a nearly circular wave (quasinormal approximation). This allows selecting the optical conditions for which practically a single plane wave is excited in a cholesteric sample, a fact which is very important when dielectric inhomogeneities due to thermal fluctuations or defects and Brownian motions or fluorescence of guest molecules are studied. (b) Simple dispersion relations are obtained, which give the correct values of both real and imaginary parts of the wave vectors near the first-order reflection band. (c) It is shown that for the higher-order reflection bands, reasonably simple analytical expressions can be obtained, which give good qualitative results but which are not useful for a quantitative analysis. However, an exact dispersion relation simpler than the ones given in the literature is found. In all these cases, each approximation is discussed in detail. The approximate expressions found are in general simpler and more accurate than the ones previously given for similar cases. Their limits of validity for any practical purposes are found. The ensemble of the regions of validity of given approximations covers the largest portion of the (ω,${\theta }_i$) plane.