We present results of an experimental study of Saffman-Taylor fingers in dilute solutions of polystyrene in dioctyl phthalate (DOP). While fingers in pure DOP obey classical scaling laws, we observe transitions to narrow fingers in polysterene solutions of concentrations as low as 1 part per million. The onset of narrowing occurs at a shear rate which roughly equals the inverse of the polymer Zimm relaxation time and depends only weakly on concentration. The onset of instability occurs earlier than in Newtonian fluids and is often initiated by small-amplitude oscillations.

We have used light transmission to follow for four decades in time the annealing of defects generated by pressure jumps in a uniaxial liquid crystal. Two distinct scaling regimes for the light intensity as a function of time were observed: an early-time regime in which light propagates diffusively to the detector, and a late-time regime in which unscattered light dominates the signal reaching the detector. The measured values for the scaling exponent ν for the string density ${\mathrm{\rho }}_{\mathit{s}}$∝${\mathit{t}}^{\mathrm{-}\nu }$ are within 10% of the expected value ν=1 over the time interval 10 msec<t<100 sec.

Starting from the Smoluchowski equation we derive exact microscopic expressions for the self-diffusion and the self-mobility coefficients of a sheared suspension of interacting colloidal particles in a semidiluted regime. We find that the usual Einstein relation between the self-mobility and the self-diffusion matrices is no longer valid for this nonequilibrium situation. The self-mobility and self-diffusion matrices are explicitly calculated in a low-shear-rate regime for a charge-stabilized colloidal suspension.

It is argued that diffusion-limited aggregation with disaggregation leads to an equilibrium regime that can be exactly related to the ensemble of branched-polymer configurations. Thus diffusion-limited aggregation with disaggregation and lattice animals belong to the same universality class.

We calculate the power transfer from an intense modulated electron beam to an external load. The simple model fully incorporates various effects such as nonlinear beam loading, finite transit time, ac and dc space charges, and the beam’s initial velocity modulation. We show that a fully modulated beam may deliver up to a maximum of 57% of its power to a load without forming a virtual cathode.

A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions, demonstrating its capability in describing large-scale properties of short-term memory and electroencephalographic systematics. This methodology also defines an algorithm to construct a mesoscopic neural network, based on realistic neocortical processes and parameters, to record patterns of brain activity and to compute the evolution of this system. Furthermore, this algorithm is quite generic and can be used to similarly process information in other systems, especially, but not limited to, those amenable to modeling by mathematical physics techniques alternatively described by path-integral Lagrangians, Fokker-Planck equations, or Langevin rate equations. This methodology is made possible and practical by a confluence of techniques drawn from SMNI itself, modern methods of functional stochastic calculus defining nonlinear Lagrangians, very fast simulated reannealing, and parallel-processing computation.

One-dimensional pattern-forming systems with a quadratic nonlinearity and a long-wave zero mode in the governing equations are considered. The pattern-generating instability, which may be both steady and oscillatory, is assumed to set in at a finite wave number. Physical examples are the instability of a front of the laser-sustained evaporation of a solid and the instability of seismic waves in a viscoelastic medium. A system of generalized Ginzburg-Landau equations for the complex envelope of a fundamental harmonic and for the real slowly relaxing zero mode are derived in a general form [for the case of the steady instability, essentially the same equations have been proposed earlier by Coullet and Fauve, Phys. Rev. Lett. 55, 2857 (1985)]. Using these equations, stability of spatially periodic patterns is investigated. The main result is that the stability band is anomalously narrow in comparison with the classical Eckhaus band. For the case of the steady instability, the evolution of long-wave modulations of the patterns is investigated in the geometric-optics approximation. It is demonstrated that, unlike the usual Ginzburg-Landau equation, the equations derived in the present work allow for modulation profiles of a permanent shape. The profiles may be transient layers moving at a constant velocity, or quiescent periodic ‘‘superstructures,’’ including a ‘‘soliton’’ as a limiting case. At least some of those profiles can be stable.

An accurate spin-polarized exchange-only Kohn-Sham (KS) potential is constructed from a consideration of the optimized-effective-potential (OEP) method. A detailed analysis of the OEP integral equation for the exchange-only case results in a set of conditions which are manifestly satisfied by the exact OEP; these conditions are employed to construct an approximate OEP, ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}$, and therefore an approximate KS exchange-only potential as a functional of KS orbitals. Further, it is shown that this ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}$ can be derived analytically based on a simple approximation of the Green’s functions in the OEP integral equation. The constructed potential, although approximate, contains many of the key analytic features of the exact KS potential: it reduces to the exact KS result in the homogeneous-electron-gas limit, approaches -1/r as r→∞, yields highest occupied-orbital energy eigenvalues ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$ that satisfy Koopmans’s theorem, and exhibits an integer discontinuity when considered as a function of fractional occupancy of the highest-energy occupied single-particle state of a given spin projection σ. In addition ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$ nearly exactly satisfies Janak’s theorem. The approximate OEP is a simple but remarkably accurate representation of the exact, numerically derived exchange-only OEP.

Detailed numerical results obtained by employing ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}$ as the exchange-only potential for ten atoms with closed subshells yield total energies, Hartree potentials, single-particle expectation values, and ${\mathrm{\varepsilon }}_{\mathit{m}}$ which are in excellent agreement with both exact OEP and Hartree-Fock (HF) results and represent a significant improvement over the results obtained by employing other exchange-only potentials. Similarly, the properties of alkali-metal atoms are calculated including the separate spin-up and spin-down densities to obtain results in excellent agreement with those of spin-unrestricted OEP and HF methods. Finally, we demonstrate the accuracy of ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}$ by calculating the total energy, ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\uparrow }}$, and ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\downarrow }}$ as a function of fractional filling f, of the highest occupied single-particle orbital for the magnesium atom (Z=12) from N=9–12 electrons and find excellent agreement with both spin-unrestricted OEP and HF results even when ${\mathrm{\varepsilon }}_{\mathit{m}\mathrm{\sigma }}$ is strongly dependent on f. In addition we display the integer discontinuity in ${\mathit{V}}_{\mathit{x}\mathrm{\sigma }}$ when the highest-energy spin subshell begins to be filled.

We investigate the kinetics and fractal morphology of aggregating polystyrene latex in an intermediate region between diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). The measurements are made by means of a low-angle elastic-light-scattering setup covering two decades in scattering wave vectors. For each aggregation run, the salt concentration c is changed and the samples are prepared under isopycnic conditions, to avoid differential sedimentation. The average cluster mass is found to grow according to a power law with an exponent z varying in a continuous fashion in the range of salt concentration used. At high c (DLCA), we find for the fractal morphology ${\mathit{d}}_{\mathit{f}}$=1.65. For lower concentrations, ${\mathit{d}}_{\mathit{f}}$ is at first larger than 2 and therefore close to the typical RLCA fractal dimension, but then it gradually reverts to lower values not far from those typical of DLCA. This behavior is also exhibited at the lowest values of c explored, although the decay to DLCA is much slower. An interpretation of the results is presented on the basis of the available theories and simulation work on the cluster morphology in the intermediate regimes.

We describe numerical investigations of the dynamics of interfaces in two dimensions, using a Monte Carlo algorithm that combines elements of both the microcanonical and the canonical methods. We employ a lattice-gas Hamiltonian which corresponds to a system with a first-order phase transition, so that we can study interfaces between distinct thermodynamic phases. Results include the first numerical observation of roughening dynamics for Hohenberg and Halperin’s model C of critical dynamics, and the first numerical observation of the Mullins-Sekerka instability which results from the presence of a thermal gradient.

We present an analytic solution of the growth-site probability distribution for a family of hierarchical models for the structure of diffusion-limited aggregation (DLA) clusters. These models are characterized by self-similar voids that are delineated by narrow channels. The growth-site probability distributions for all the models are shown to have the same form, n(α,M)∼exp{-(A/lnM)[α-${\mathrm{\alpha }}_0$(M)${]}^2$}, where n(α,M)dα is the number of growth sites with α<-ln${\mathit{p}}_{\mathit{i}}$/lnM<α+dα, ${\mathit{p}}_{\mathit{i}}$ is the growth probability at site i, M is the cluster mass, ${\mathrm{\alpha }}_0$(M)==B lnM, and A,B are constants. We find the same form of the distribution for all members of the family of models, suggesting the possibility that it is a consequence of the channels and self-similar voids, and is independent of other details of the model. Our result is in accord with the recent calculations for DLA clusters by Schwarzer et al. [Phys. Rev. A 43, 1134 (1991)].

Motivated by the connection to diffusion-limited aggregation (DLA), we study the Saffman-Taylor problem in an axisymmetric tube geometry. We find that the surface tension selects an allowed set of finger widths from the continuous set present at zero surface tension, as is expected by analogy with the channel geometry. However, the solution branches merge and disappear in pairs as surface tension is lowered. This behavior was first seen in self-similar solutions for sector-shaped cells in two dimensions, but this is the first occurrence of this effect for steady-state patterns. The implications of our results for DLA and for flow in porous media are discussed.

We extend our study of a recently proposed mean-field theory (MFT) for diffusion-limited aggregation (DLA) to radial geometries. These include growth from a point in a fully open space and also growth in sectors with a range of opening angles. We find that the MFT accurately predicts the shape, angular width, and anisotropy dependence of the ensemble-averaged DLA pattern. For systems such that there is no stable solution of the related Saffman-Taylor problem, the mean-field theory exhibits an extreme flattening of the tip region which is also present in averaged DLA. The latter fact has not been noticed previously due to the stabilizing effect of lattice anisotropy present in previous simulations.

Using a hierarchical ordering scheme, many off-lattice diffusion-limited-aggregation (DLA) clusters containing ${10}^6$ particles are separated into branches of different orders. For each order we measure the number, mass, length, and width of the branches. All of these branch properties depend, with an exponential law, on the branch order. This means that for all of them the ratios between properties of subsequent branch orders are constant. By relating length, width, and mass to each other we find that the length and width of the whole branches both depend, with the same exponents ${\nu }_{\mathrm{?}}$=${\nu }_{\mathrm{\perp }}$=0.60≃β=1/D, on the mass of the branch. By measuring the ramification matrix ${\mathit{R}}_{\mathit{i}\mathit{k}}$ of the clusters we find that the branches and stems are distributed in a self-similar way. Furthermore, we measure the angles enclosed by two branches. We find that this angle saturates to a finite value around 38°. All of these results indicate a statistical self-similarity between branches of different orders. This result is supported by a direct comparison of off-lattice DLA clusters of ${10}^5$, ${10}^6$, and ${10}^7$ particles.

We study the kinetics of an irreversible monomer-monomer model of heterogeneous catalysis. In this model, two reactive species, A and B, adsorb and stick to single sites of a catalytic substrate. Surface reactions are assumed to occur only between dissimilar species that are nearest neighbors on the substrate. The kinetics of the process are studied in the reaction-controlled limit. We map the monomer-monomer model of heterogeneous catalysis onto a kinetic Ising model and find that the dynamics of the process is a superposition of zero-temperature spin-flip dynamics and infinite-temperature spin-exchange dynamics. We solve the kinetics analytically and determine the rate at which the catalyst becomes ‘‘saturated,’’ i.e., completely covered by only one species. We show that the saturation time is proportional to N ln(N), where N is the number of catalyst sites. We also discuss the monomer-monomer process with desorption.

The nonlinear second-order echo effects are investigated for a magnetized inhomogenous plasma by means of ideal magnetohydrodynamic equations. Externally excited perturbations of such a system are damped out due to phase mixing but their initial existence remains ‘‘memorized’’ in terms of oscillations with a continuous Alvén spectrum. It is shown that an appropriate spatial and/or temporal dependence of external disturbances results in a spatial, a temporal, and a spatial-temporal echo effect. The relevant analytical expressions are obtained for the echo-signal shape and a possible application of the obtained results to plasma diagnostics is considered.

We derive the third-frequency-moment (${\mathrm{\omega }}^3$) sum rule and exact high-frequency dielectric response function for the layered electron liquid in zero magnetic field. The latter is examined in the kd→0 and kd→∞ limits characteristic of bulk behavior and two-dimensional (2D) single-layer behavior, respectively (k is the 2D wave number, d is the distance between any two adjacent layers). We incorporate the correlational part of the ${\mathrm{\omega }}^3$ sum rule into a mean-field-theory description of the long-wavelength dispersion of the in-phase and out-of-phase plasmon modes in the presence of very strong correlations.

Analysis of the circular polarization of a spectral line emission inside plasmas provides a measurement of the poloidal magnetic field on the Texas experimental tokamak (TEXT). Three sets of different polarimeters, using, respectively, the Ti XVII 3834-Å line of the intrinsic titanium impurity and the Li I 6708-Å line of a monoenergetic lithium beam, were developed and operated on TEXT. The safety factor q on the magnetic axis, determined from the measured magnetic field, was found to be near unity in all cases of Ohmically heated sawtoothing and nonsawtoothing discharges, and significantly below unity in the case of electron-cyclotron-resonance heating at the plasma center for high edge q discharges.

The behavior of an rf discharge can be modeled by using a fluid approach. For this approach, the values of the mobility and diffusion coefficients as well as the ionization rate are necessary. These values are often obtained by extrapolating the data of dc Townsend discharges. To check whether this is justified we computed the coefficients for electrons in an rf discharge by using a kinetic model based on a two-term approximation of the electron energy distribution function. The calculated electron mobility and electron diffusion coefficients agree reasonably well with the extrapolated Townsend values. Significant deviations were found between the extrapolated Townsend ionization rate and the computed rf ionization rate as a function of the reduced electric field.

The acceleration and heating of charged particles by electromagnetic fields has been extensively investigated by the standard map. The question arises as to how the relativistic effects change the dynamical behavior described with the classical standard map. The relativistic standard map is a two-parameter (K,β=ω/kc) family of dynamical systems reduced to the standard map when β→0. For β≠0 the relativistic mass increase suppresses the onset of stochasticity. It is shown that the speed of light limits the rate of advance of the phase in the relativistic standard map and introduces Kolmogorov-Arnold-Moser surfaces persisting in the high-momentum region. An intricate structure in the higher-order periodic orbits and chaotic orbits is analyzed using the symmetry properties of the relativistic standard map. An interchange of the stability of the periodic orbits is observed and explained by the local linear stability of the periodic orbits.