This Comment aims to bring attention to the following fact: whenever a stratified fluid in a gravitational field g is supported from below by a free surface, the growth rate of the dominating Rayleigh-Taylor (RT) instability mode for sufficiently large wave numbers k is equal to (gk${)}^{1/2}$ and independent of the fluid density profile. The paper we comment upon [D. H. Munro, Phys. Rev. A 38, 1433 (1988)] appears to state otherwise, but this is evidently a misunderstanding. This should be taken into account to avoid the same sort of misunderstanding that can occur when the known simple formula from the elementary theory of the RT instability is used to interpret the results of numerical simulations carried out for laser and electromagnetic acceleration of plasmas.

Recent claims of solitonic excitations in a nonlinear model of the DNA double helix are critically examined. It is found that the parameters used in a previous analysis are not physical and that the excitations presented in that previous analysis are not solitons. Using more realistic parameters, the excitations do not propagate and remain pinned on the lattice.

The criticized aspects of our original paper [Phys. Rev. A 40, 6134 (1989)] are considered; comparisons are made between the two calculations: the original and that described in the preceding Comment [Techera, Daemen, and Prohofsky, Phys. Rev. A 42, 5033 (1990)]. We show that when a complete account of all differing features of the two calculations is made, the criticized parameter value corresponds almost perfectly with that of the Comment. Furthermore, we display a rerun of the disputed calculation in which the parameter values have been changed in accord with those advised in the Comment. The results are fully consistent with our earlier calculation, rather than those of the Comment. We have also rerun our calculation to study the case described in the Comment, that of two solitons crossing each other. Contrary to the assertions of the Comment, we find that the simulation produces the expected solitonlike crossing behavior. We point out that the differences in computed behavior seem to arise from faulty programming in one or the other of the two calculations. We give the results of certain tests run for checking our program. We also discuss the accuracy criterion used by the authors of the preceding Comment.

It is shown that the motion of an individual test electron in a low-density relativistic electron beam propagating through a realizable planar wiggler magnetic field is nonintegrable and can become chaotic. The presence of chaos, which is induced by the transverse spatial inhomogeneities in the wiggler field, poses limits on the wiggler field amplitude and the beam size for beam propagation and free-electron-laser operation. An approximate condition that determines the onset of chaos-induced beam degradation is derived analytically and found to be in good qualitative agreement with the numerical simulations using the Poincaré map.

We present an extension of Nosé’s method of generating canonical distributions from pseudocanonical dynamics for standard Hamiltonians as well as for classical systems, where one cannot use a global set of canonical variables (e.g., a system of classical spins) and Nosé’s formulation does not apply.

An experimental study of the temporal evolution of two-dimensional drained soap froths is presented. The long-time behavior of the froth shows a linear dependence of the average bubble area on time. By keeping nearly constant and thin plateau borders at all times, deviations from 120° in the angle between adjacent films at a vertex are not observed. In addition, evidence of dynamical scaling of area distributions is presented.

We investigate the linear stability of steady-state needle crystals in dendritic growth in the presence of anisotropies in both surface tension and interfacial kinetics. The needle crystals are linearly unstable for certain ranges of values of the surface tension and kinetic coefficients. This instability results in complex tip-splitting and sidebranching events that lead to morphological transitions.

Ideas from the theory of constitutional supercooling, as well as an approximate linear-stability analysis for small wavelength perturbation, lead to a simple stability criterion for the periodic cellular patterns seen in the directional solidification of alloys with a small partition coefficient. There is good qualitative agreement with the limited experimental data available in the cellular regime. This criterion suggests that solutions found by using the analogy between directional solidification and Saffman-Taylor fingers may be unstable.

A relativistic Fermi-Segre formula, which gives the behavior of Dirac single-particle bound-state wave functions near the origin in terms of the derivative dɛ(n,κ)/dn of the energy with respect to principal quantum number, is derived utilizing a generalized WKB approximation. Simple quadrature integrals are obtained for the binding energies and for the normalization coefficients. Excellent agreement is obtained in comparison with exact numerical calculations.

Using the kicked rotator as an example, we show how to apply the formalism of Wigner symbols to the study of quantum dynamics. This approach provides a simple and direct method of comparing quantum and classical dynamics. We investigate in detail the leading quantum effects for small values of ħ and discuss the time scales at which quantum effects appear.

A method for analytical calculation of energy levels using perturbation theory is developed. Convergence of the perturbation theory directly follows from the method itself. An example of this method is given for the anharmonic oscillator.

A four-parameter potential function is introduced for bond-stretching vibration of diatomic molecules. It may fit the experimental RKR (Rydberg-Klein-Rees) curve more closely than the Morse function, especially when the potential domain extends to near the dissociation limit. The corresponding Schrödinger equation is solved exactly for zero total angular momentum and approximately for nonzero total angular momentum.

The Thomas-Fermi-Dirac (TFD) electronic structure model with the Weizsacker gradient corrections (TFD-λW) is employed to calculate the cold equation of state in the Wigner-Seitz spherical-cell approximation. We demonstrate how inclusion of the Weizsacker term removes many of the unphysical features of the TFD lattice model. Results are summarized for seven elements: ${}_6{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{12}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{26}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{47}{}^{108}{}_{}{}^{}\mathrm{Ag}$, ${}_{79}{}^{197}{}_{}{}^{}\mathrm{Au}$, ${}_{82}{}^{207}{}_{}{}^{}\mathrm{Pb}$, and ${}_{92}{}^{236}{}_{}{}^{}\mathrm{U}$. Our equation of state (computed using several values of the Weizsacker coupling coefficient) is compared with previous computations and with experimental data. The Weizsacker correction substantially improves the theoretical TFD equation of state at low densities. We also calculate low-mass, equilibrium stellar models constructed from the TFD-λW equation of state for carbon. We find that for λ=1/9 the maximum radius of a carbon white dwarf star is R/${\mathit{R}}_{\mathrm{\odot }}$=3.9×${10}^{\mathrm{-}2}$ at a mass M/${\mathit{M}}_{\mathrm{\odot }}$=2.3×${10}^{\mathrm{-}3}$.

It is shown that the exact total-energy eigenvalue of the Schrödinger equation is a functional of the Hartree-Fock charge density. Furthermore, the exact correlation energy, defined as the correction to the Hartree-Fock energy, is a universal functional of the Hartree-Fock charge density. Similarly, the exact total energy is a functional of the Xα, Hartree-Fock-Slater, or approximate-density-functional charge density. The correction to the energies of these models is again a universal functional of the model charge density.

The connections of O(4,2) coherent states, as defined by Perelomov, with hydrogenic atoms are investigated according to a previous work by Mostowski (Lett. Math. Phys. 2, 1 (1977)]. It is shown that these coherent states are well localized near the momentum-space point of classical mechanics corresponding to any elliptical Kepler motion. They are localized in the direction of the Coulomb force in configuration space but are delocalized radially along this direction. The decomposition of these coherent states with respect to Sturmian bases is given. The explicit expression of the configuration-space wave functions for the case of zero eccentricity is also given. Finally, the explicit expression of the momentum-space wave functions is given for all cases.

The structure and dynamics of the doubly excited metastable states of the helium atom have been investigated. Using wave functions determined by the complex coordinate method, we have calculated the energies, the lifetimes, and the average interparticle distances and the mass polarization energy of the three lowest resonant states of ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}^{\mathit{e}}$ symmetry.

A differential equation in l for hydrogenic radial dipole matrix elements is generated from the recursion relations of Infeld and Hull [Rev. Mod. Phys. 23, 31 (1951)]. The equation is valid for all (n,n’)≫1, for all ‖Δn‖ieq‖n’-n‖, and for bound-free transitions from excited states. Approximate solutions are obtained for the case l≪n and are found to be equivalent to those of other workers when ‖Δn‖≫1. We also present a power-series solution in l good for all ‖Δn‖. General features of the dependence of the matrix elements on l are explained.

The 2s2p ${}_{}{}^1{}_{}{}^{}$P and ${}_{}{}^3{}_{}{}^{}$P autoionizing states of heliumlike ions are studied via an implementation of the Feshbach projection method within the framework of Z-dependent perturbation theory. These same states are also studied by a more straightforward (nonprojected) application of Z-dependent perturbation theory that has features similar to those of the stabilization method. The computational and theoretical advantages of applying the Feshbach method within Z-dependent perturbation theory are emphasized. Results for all two-electron ions with Z=2 to 10 are tabulated and compared with experiment and with other very accurate theoretical results for these systems. Included in these results are estimates of the resonance positions, energy ‘‘shifts,’’ and widths of these autoionizing states.