We report the growth of ${\mathrm{Al}}_2$${\mathrm{O}}_3$ aggregates by precipitation from an ${\mathrm{Al}}_2$${\mathrm{O}}_3$ air suspension at room temperature. The fractal dimension of the larger aggregates is observed to be D∼1.7 and suggests that the growth may represent an example of cluster-cluster aggregation in three dimensions.

We have recently studied experimentally the dielectronic satellite lines from the 1s2$l_a$3$l_b$ doubly excited levels of Li-like ions under dense-plasma, collisional-equilibrium conditions. Herein we extend our study to lower electron densities where satellite lines are produced by dielectronic recombination of the He-like ion and inner-shell excitation of the corresponding Li-like ion. Comparison of the experimental spectra with simulations using our previously published data together with recent Coulomb-Born-exchange calculations of inner-shell-excitation collision cross sections show a satisfactory quantitative agreement.

The helical nature of the magnetic axis induces a curvature component that drives resistive ballooning modes, which scale as the resistivity to the third power in a helical axis stellarator.

The solitary-wave character of the Brochard-Leger wall in liquid crystals is analytically revealed. Such a solitary wave has precisely described the behavior of the phase transition. The results obtained are in good quantitative agreement with experiment. A useful formula to determine the viscosity coefficient ${\gamma }_1$ is proposed. The equation describing the motion of the wall is similar to the Huxley equation, which describes nerve-signal propagation in biology. This similarity is very impressive.

The extended hydrodynamic modes recently discussed by de Schepper, Cohen, and collaborators using an approximate hard-sphere kinetic equation are computed here with use of approximate hard-sphere generalized hydrodynamic equations. The theory presented here is completely analytic and reproduces the results of de Schepper et al. for dense hard-sphere fluids reasonably well. The connection to previous theories based on generalized hydrodynamics is discussed.

In a recent paper of Lee [Phys. Rev. A 31, 1213 (1985)], it was stated that the photon-number distribution in a free-electron laser is always sub-Poissonian. This statement is clearly in contradiction with well-known published results. We show that in the recoilless approximation the photon statistics is Poissonian. However, for electron recoil different from zero, the photon-number distribution presents bunching (antibunching) for positive (negative) detuning parameter.

A nonlinear hydrodynamic model is proposed which reproduces the integral equation of Leutheusser for the density correlation function as the first term in a perturbation expansion. At the transition proposed by this author, our model reduces to a nonlinear oscillator, proving that the transition in this case is an artifact of the approximation.

The criticism by Siggia (in the preceding Comment) of recent work developing a dynamical theory of the liquid-glass transitin is shwn to be based on unphysical and mathematically unjustified mappings onto systems unrelated to those proposed to have a glass transition. His subsequent arguments misrepresent the structure of the transition that has been proposed.

The main conclusion in a recent paper by R.?lmore on thermodynamic length and curvature is shown to be in error.

Contrary to Gilmore’s assertion, Weinhold’s metric is compatible with the second law of thermodynamics.

Previous authors have introduced a Riemannian surface, [(S,V),$U_{\alpha \beta }$(S,V)], and claimed that this surface could be identified with the surface U=U(S,V) for a substance in thermodynamic equilibrium. No proof has ever been offered of this supposed equivalence. The paper commented on showed that such a proof is not possible unless a new class of thermodynamic inequalities were to exist (they do not). The two preceding Comments also fail to provide a proof that these two surfaces can be identified. In the present Comment we prove once again, citing fundamental theorems of differential geometry, that this identification is not possible. We show specifically that any Riemannian metric chosen to measure distances in the equilibrium surface must lead, through the curvature tensor, to a Gaussian sectional curvature which is everywhere positive semidefinite if the convexity condition of the second law of thermodynamics is not to be violated. Two previous choices of metric do not possess this property.

Recent advances in experimental spectroscopy offer the promise of yielding much detailed information about molecular potentials and collisional interactions from a study of the light emitted or absorbed in the far wings of atomic lines. However, readily manipulable, accurate theoretical expressions and methods are needed to extract such knowledge. Straightforward formulas, based on the distorted-wave approximation, for the normalized emission intensity in the far wing of a pumped atomic line are given here. By normalizing theoretical spectra with respect to the strength of the atomic line, one obtains a convenient form for the analysis of experimental differential spectra that are reported in nonarbitrary units. Theoretical and experimental spectra are numerically consistent in the test case of the blue-wing satellite (∼7610 Å) of the Rb $D_2$ line (7800 Å) broadened by Xe perturbers.

The relativistic photoabsorption cross section in the vicinity of the xenon and radon K-absorption edges is calculated using the Dirac-Fock method. The relaxation is included by constructing separate solutions for the initial ground state and for the final 1s-hole state and by including the resulting overlap integrals into the transition amplitude. The relativistic effect is found to lower the cross section with 12% and 35% for xenon and radon, respectively. One-third of this effect results from the change in the K-ionization energy and two-thirds from the change in the ormation on a lattice. A maximum-likelihood growth algorithm is formulated to supplement the integral solution of Laplace’s equation. This allows us to study diffusion-limited aggregation and viscous flow in porous media. Our deterministic solution for the aggregation process displays the same fractal dimension (D≊1.7) as Monte Carlo diffusion-limited aggregation. We also compare our solution to Laplace’s equation with the experimentally observed pattern in one limit of a Hele-Shaw cell experiment. Lastly, we present a second deterministic algorithm which results in a pattern with tips which appear parabolic.