We study the growth rate of a dendritic crystal in two and three dimensions in the symmetric model of solidification. We clarify the question of the variation of the ‘‘stability constant’’ with the Péclet number in the regime of moderate to large values. A careful WKB treatment shows that the eigenvalues selected by anisotropy of surface tension are strongly Péclet-number dependent in contradiction with some earlier treatments. We also perform a numerical analysis of this problem and our results are compared with recent experimental data.

Dynamic light scattering is used to study the dependence of the aggregation kernel homogeneity λ on the aggregant concentration [HCl] for aqueous gold sols. We find the cluster growth kinetics are well described by a powerlaw, $R_{\mathrm{app}\mathrm{\sim }{t}^{z/D}}$, where $R_{\mathrm{app}}$ is the measured apparent radius, D the cluster fractal dimension, and z=1/(1-λ) for all aggregant concentrations. The values for the dynamic exponent z, and hence the homogeneity λ, are functions of HCl concentration. We find the larger HCl concentrations yield a fast-aggregation regime characterized by λ≃-0.6. Smaller HCl concentrations yield a continuum of aggregation regimes characterized by homogeneities evolving from λ≃-0.6 towards 1.0. Our results do not support the view that aggregation in gold colloids is based on two limiting regimes, diffusion-limited and reaction-limited aggregation.

Analytical solutions for the time-dependent cluster concentrations and nucleation rate in homogeneous nucleation are obtained by the singular perturbation approach. The effect of cluster scavenging by free molecule particles on the kinetics of nucleation is also investigated through analogous analytical solutions in this case. Apparent conflicting suggestions in the literature concerning the time lag of nucleation are resolved.

We have developed a reversible diffusion-limited aggregation model for self-assembling polymers, which contain an associating site at each end of the chain. The simulations show that the associating sites form finite-sized clusters that are interconnected by intervening chains in a three-dimensional network. The average cluster size is seen to decrease with an increase in $\tau$ (the residence time of the chain in the cluster).

Monte Carlo simulation of transient, diffusion-controlled annihilation (A+A→0) and fusion (A+A→A) reactions have been performed on one- and two-dimensional lattices and on the fractal, critical percolation cluster of a square lattice (applying a breadth-first search algorithm). Fast self-ordering is demonstrated via analyses of the interparticle distributions and the nearest-neighbor distance distributions (NNDD). Good agreement is obtained with the few existing analytical results in one dimension. For the higher dimensions (where there are no analytical results and where the interparticle distances are not uniquely defined), we find the NNDD via a ‘‘taxicab’’ approach. We obtain the kinetically self-ordered particle distributions and relate them to the global rate laws.

Monte Carlo simulations of transient, diffusion-controlled A+B→0 reactions are performed on one-, two-, and three-dimensional Euclidean lattices and on a fractal lattice (two-dimensional critical percolation cluster). The particle distributions are analyzed by partial nearest-neighbor distance distributions (NNDD), taxicab NNDD, and linearized NNDD. Comparisons are made with NNDD and interparticle distributions of the A+A→0 and A+A→A reactions (extending some of the simulations of the preceding paper [Phys. Rev. A 41, 2113 (1990)]), revealing some empirical connections. The aggregation of like particles and the segregation of unlike particles are monitored in time, for the various diffusion topologies. The relations between the partial NNDD, the microscopic and mesoscopic ordering, and the global rate laws are discussed.

We investigate possible mechanisms for the recently observed selective quenching of spontaneous emission coefficients of carbon and nitrogen ions (C iv, C iii, and N v) in laser-produced plasmas. Various effects of the plasma electrons on the spontaneous emission of the ions are considered. We suggest (by exclusion) that the cause of the phenomenon is the weak trapping of plasma electrons by the radiating ions (producing C iii, C ii, and N iv ions in highly excited states). These highly excited electrons so strongly shift and change some low-frequency lines that they are not observed. The branching ratio of line intensities from the same upper level then becomes proportional to the fraction of ions not having any trapped electrons.

The heating of plasma electrons by two laser fields in the presence of a uniform strong static magnetic field via the inverse bremsstrahlung process is considered. A kinetic equation is derived, and the change in kinetic energy of the Landau electrons is calculated. For laser radiation propagating parallel to the magnetic field and incident on cold electrons, it is found that the heating rate increases as the laser frequencies approach the electron cyclotron frequency.

An experimental analysis of collective effects, depending on the electron-ion mutual interactions, which occur during the ionization of a gas jet by impact with an incident monochromatic pulsed electron beam, is presented. The dependences on the gas pressure of the transmitted current and of the ion yields show a marked deviation, in the same range of gas pressure, i.e., of produced charges, from the expected behavior in the absence of interactions between incident and produced charges. The phenomenon is described by an approximate solution of the two-fluid equation system that takes into account the transient phase, during the impact ionization, and the symmetry of the experiment. The theoretical model well explains the observed dependences.

We report measurements on time-resolved spectra of the 2${\omega }_0$ (and, indirectly, 1${\omega }_0$) emission from plasmas produced by focusing 70–400-psec duration Nd-laser pulses to intensities above ≊${10}^{14}$ W/${\mathrm{cm}}^2$ onto planar targets. We observe repeated bursts of the emission lasting only 10–20 psec and typically separated by 30–50 psec. During these bursts the emitted frequency was observed to sweep rapidly across the wavelength band (≊50 Å wide), indicating the operation of processes that modulate the emission via phase. The results support our previous work [Dragila, Maddever, and Luther-Davies, Phys. Rev. A 36, 5292 (1987)], where we concluded that such phase modulation must occur in order to explain the observation that time-integrated spectra obtained in the same conditions were modulated.

It is demonstrated that stimulated Brillouin scattering (SBS) saturated by a nonlinear shift of the wave number of the ion-acoustic wave can be responsible for temporal oscillations of the radiation reflected from an expanding laser-produced plasma. Repetitive amplification and quenching of the SBS result in rapid motion of the reflection point, thus causing large sweeps of the phase of the emitted light. Both temporal pulsations and modulation of time-integrated spectra of the back-reflected radiation and its harmonics are in accord with experimental observations.

The stability of oblique modulation of ion-acoustic waves in an unmagnetized plasma due to nonlinear interaction with a slow-response quasistatic plasma is studied. A nonlinear Schrödinger equation is derived for the system. It is found that there exists a wide domain in the k-θ plane in which the ion-acoustic waves would be modulationally unstable. It is also found that when θ>60°, the waves are unstable for all values of k. However, for θ<60°, the waves are unstable only for 0$k_{\max }$, where $k_{\max }$ is given by tanθ/(3-${\tan }^2$θ${)}^{1/2}$.

A method for numerically modeling hot plasma over a wide range of densities is described. The model generalizes the essential aspects of the Stewart-Pyatt model to plasmas comprising mixtures of elements and extends the treatment to include the effects of electron polarization and screening. A practical numerical prescription is provided that is a straightforward generalization of the ion-sphere cell model. In addition, exact closed-form expressions are given for the continuum lowering. The model also addresses the problem of the microfield, i.e., the plasma-potential fluctuations that perturb the upper electronic states, and provides a suitable framework for improved practical approaches to this.

The nonequilibrium driven lattice gas with repulsive interactions is studied via dynamic mean-field theory. The resulting phase diagram for stationary states is in good agreement with recent simulation results of Leung, Schmittmann, and Zia [Phys. Rev. Lett. 62, 1772 (1989)]. Interesting new predictions for the current at first- and second-order phase transitions also emerge.

In the Fröhlich model of energy transport from a source to a heat bath via a system of oscillators, a nonlinear coupling of the oscillator modes with the bath can produce at high-energy flux a nonthermal excitation of a single mode, proportional to the total number of excitations S in all modes. The remaining modes have a modified thermal distribution, independent of S. In the normal model, the predominant mode is that with lowest frequency, regardless of the manner in which the energy is introduced into the system. In the extended model, any of the modes can be selected for nonthermal excitation by introduction of slightly more than half of the excitations into that mode. The energy introduced by the source into the remaining thermalized modes is then channeled into the selected mode as a consequence of the nonlinearity. The details of this process in the extended model are exhibited. It is shown that, as the selection of the mode for nonthermal excitation is changed from one to another, the change from the linear dependence on S to independence of S progresses through fractional values of S in a manner that depends on the competition between the most highly excited modes.

We work out the thermodynamic curvature resulting from a Riemannian geometric approach to thermodynamics for the general multicomponent ideal gas. This Riemannian geometry is based on including fluctuation theory in thermodynamics. We find that the Riemannian curvature scalar for this system is small, on the order of the average volume per molecule, no matter how many components. This result fits in well with expectations developed earlier that the thermodynamic curvature gives a measure of the volume where classical thermodynamic fluctuation theory fails.

A logistic map generates multifractal sets in its periodic windows. Using the thermodynamic formalism of Halsey et al. [Phys. Rev. A 33, 1141 (1986)], we present two methods of calculating their generalized dimensions $D_q$, and we show that there is a phase transition in a period-6 window, i.e., $D_q$ is a nonanalytic function of q.

We measure the surface order parameter $S_s$ at the interface between the nematic liquid crystal p-methoxy-benzylidine-p-n-butyl-aniline and a rough glass plate. Roughness is induced by oblique evaporation of SiO. We observe a critical decrease of $S_s$ when the surface roughness increases, just above the transition from planar to oblique orientation. This experiment supports the ordoelectric model to explain the oblique orientation of the nematic liquid crystal.

The expansion of hot, near-solid-density plasmas produced by subpicosecond laser pulses has been measured by monitoring the spectral modifications imposed on the specularly reflected heating pulse. The spectral changes are attributable to Doppler shifts arising from mass motion driven by the heated electrons; a simple model for the expansion is used to estimate electron temperatures in the range 1–100 eV, corresponding to incident laser intensities ${10}^{12}$–${10}^{15}$ W/${\mathrm{cm}}^2$. .AE

It is shown that radiation due to impurities can cause an instability involving short-wavelength (compared to the ion gyroradius) electrostatic waves. The instability is closely associated with the electron-temperature-gradient-driven electron-acoustic and ion drift modes. Dissipative effects are shown also to play an important role.