We report measurements on the aggregation processes in a colloidal solution of polystyrene particles performed by elastic (intensity) and quasielastic light scattering. In order to observe the different kinetics of aggregation of the system, reversible flocculation, and the slow and the fast irreversible coagulation, the experiment was made varying the concentration of a simple electrolyte (NaCl) in the 0.01–3 mol/liter range. Intensity data give direct information that aggregated clusters are built with fractal structure and different kinetics; in the slow regime the aggregation process is reaction limited, whereas in the raft regime we have a diffusion-limited cluster-cluster aggregation. Dynamical data, showing well-defined scaling behavior in the measured mean linewidth, confirm such a picture and give a rough estimate of the cluster dimension. Experimental results are consistent with the Derjaguin-Landau-Verwey-Overbeek theory on colloidal stability [Derjaguin and Landau, Acta Phys. Chim. Debricina 14, 633 (1941); Verwey and Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948)].

We study a family of equivalent models which includes the polymer in a random medium, the stochastically growing interface with spatially random deposition of particles, and the diffusion in a random catalytic environment ${\partial }_t$ψ(x,t)=D${\nabla }^2$ψ+U(x)ψ. $U( x vec—) denotes a frozen Gaussian random potential of strength $u_0$ and correlation length a. The intrinsic length scales of the problem, $l_0$=(D/$u_0$${)}^{2/\left(4\mathrm{-}d\right)}$ and a, are both assumed to be small in comparison with the diffusion length √Dt and the system size L (L${<10\mathrm{}}^8$a). Flory-Imry-Ma–type arguments show that for dimensions d<4 the polymer of contour length t→∞ is both collapsed (ν=0) and localized, in agreement with previous results for a≪$l_0$ [Edwards and Muthukumar, J. Chem. Phys. 89, 2435 (1988); and Cates and Ball, J. Phys. (Paris) 49, 2009 (1988)]. The sample-to-sample variations of the polymer free-energy scale as $t^{\chi }$ with χ=1. For d>4, a collapsed, localized or a Gaussian, delocalized polymer is found for strong or weak disorder, respectively. The disorder becomes irrelevant for self-avoiding polymers. For growing interfaces, the roughness exponent χ/ν and dynamical exponent 1/ν are both equal to unity, but scaling is modified by logarithmic corrections.

The results are supported by a renormalization-group (RG) approach. Vertex corrections destroy the relation χ=2ν-1. For d>4 we find a phase transition as a function of disorder strength. For d<4 there is no stable fixed point. In particular, for d≤2 the fixed point found is unstable with respect to infinitely many nonlinear terms generated under the RG. It is argued that this corresponds to the appearance of a nonanalytic elastic term in the polymer Hamiltonian. The results are substantiated by mapping the problem onto the localization of a quantum particle in a random potential. When considering activated dynamics for the polymer we find that it cannot relax to the absolutely optimal environment present in the medium during observational time scales τ but will be localized in a typical well. Due to this effect, the lnL terms occurring in the static theory have to be replaced by ln$L_{\tau }$ with an additional dynamical length scale $L_{\tau }$≪L.

The renormalization-group method recently applied to Kawasaki dynamics in the Ising chain is generalized to periodically distributed interactions. Our results confirm those recently obtained by a different technique, for the special case of alternating interactions. However, our method can be applied to the general one-dimensional situation, with arbitrary periods.

The predictions of a recent theoretical analysis developed by Weiss, DiMarzio, and Gaylord [J. Stat. Phys. 42, 567 (1986)] on the mean first-passage time for a random-walk span in a ‘‘free’’ system to reach a given target span S are compared with the results of numerical simulation. Although the results are in good agreement qualitatively, a systematic quantitative discrepancy is found between theoretical predictions and experimental results in the ‘‘large but finite’’ S region, thus indicating the need for further theoretical analysis of the problem. Numerical results are also obtained in the case of a random-walk process driven by Gaussian colored noise.

The structural properties of random fractals embedded in a d-dimensional Euclidean space are studied by means of transfer-matrix formalism of fractal sets. For d=1, both global and local approaches have been investigated, leading to the definition of a subdimension that is different from the fractal dimension and depends on the probability distribution. This subdimension is shown to be identical for the global and local approaches; then, the scaling corrections involved in this subdimension are the same for both these approaches. For d>1, only the local approach can be generalized, characterizing the connectivity properties of these structures. There are exactly d subdimensions called connectivity dimensions that prove to be useful to describe percolation properties of these fractals. Several percolation thresholds are shown, and the fractal dimension of the sets at the percolation threshold are related to the connectivity dimensions.

We have studied numerically the basin of attraction of learned patterns and the phase-space fraction available to them in a layered feed-forward model with iterated learning rule. We observe a new transition at α≃0.03, apart from the discontinuous one at α≃0.18 reported earlier for the model (α is the fraction of the number of learned patterns to the number of neurons in a layer). These two transitions are speculated to be identical to the corresponding transitions at α≃0.05 and α≃0.14 (discontinuous) in the Hopfield model, which occurs in the first few layers, and finally shift in position due to amplification (and filtration) effect of the layered systems. The robustness of such a layered network against the loss of neurons in some intermediate layers is also studied.

The voltage drop distribution in the random-resistor networks constituted by all nearest-neighbor bonds connecting points visited by a lattice self-avoiding walk (SAW) is studied by accurate numerical techniques in d=2. An analysis of the moments of the distribution allows one to establish the value ζ=1.333±0.007 for the resistance exponent and to exclude the possibility of multifractal behavior. These results are also consistent with a topological investigation of the connection properties of SAW, which independently yields ζ=1.33±0.01. This clearly supports ζ=(4/3 and a spectral dimension d̃=1 for these walks, solving an old controversy. A possible extension of such an analysis to SAW at the FTHETA point is also discussed.

Numerical simulations have shown that a parametrically damped, but otherwise undriven pendulum possesses many of the dynamical modes characteristic of a simple driven pendulum, yet with notable differences. Over most of the parameter space only a stationary steady state is possible. A single domain exists within which are situated three distinct subregions of periodic, multiperiodic, or chaotic motion. The periodic orbits generally occur at half the damping modulation frequency. All of these phenomena have been experimentally observed on an actual pendulum in which parametric damping is generated electronically.

The structure and dynamics of an aggregation have been studied when the aggregate grows from a lattice gas with a nonzero gas density $n_g$. At low $n_g$ and for a short length scale up to ξ, the structure of the aggregation is fractal and similar to the diffusion-limited aggregation (DLA). For a large length scale it is compact and has a nonzero asymptotic density. The steady growth rate V in d-dimensional space is inversely proportional to the characteristic length ξ, and depends on the density as V∼${\xi }^{\mathrm{-}1}$∼$n_g^{1/\left(d\mathrm{-}{D}_f\right)}$, with $D_f$ being the fractal dimension of DLA. Extensive Monte Carlo simulations in two dimensions confirm the above theoretical hypothesis of the velocity selection mechanism with $D_f$=1.71. The interfacial width w is also found to be compatible with the expectation w∝$n_g^{\mathrm{-}1/2\left(d\mathrm{-}{D}_f\right)}$. .AE

The ordering in bipolar liquid-crystal droplets close to the nematic-paranematic phase translation is studied. Here, ‘‘paranematic’’ refers to the phase above the nematic-isotropic transition temperature. The structure of spherical droplets is obtained after the minimization of the Landau–de Gennes-type free energy assuming a constant value of the surface order parameter and strong anchoring of the molecules parallel to the surface. Disordered defect regions caused by elastic deformations are found close to the poles. The defect regions grow into the droplet as the coexistence temperature between the paranematic and nematic phases is approached from below. The temperature-radius phase diagram shows the first-order coexistence curve terminating in the critical point and a pronounced decrease of the coexistence temperature on approaching the critical radius.

Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann’s entropy H=lnW, as well as Shannon’s information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon’s formula and (ii) of the algorithmic information content—algorithmic randomness—present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ‘‘decide’’ on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite. The limits on the thermodynamic efficiency arise not from the ensemble considerations, but rather reflect basic laws of computation. Thus inclusion of algorithmic randomness in the definition of physical entropy allows one to formulate thermodynamics from the Maxwell demon’s point of view.

An expression for the electrophoretic mobility of polyelectrolytes in gels is proposed, using configuration averages. It includes the lifetime associated with each configuration of a stretched tube in the biased reptation model

An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Péclet number for small values of the surface-tension parameter. The velocity selection is caused by the effect of transcendentally small terms that are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small-Péclet-number analytical results of other investigators, although there are some discrepancies in details. It also addresses questions raised by a recent investigator on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.

Studies of electron transmission through Ca vapor reveal two prominent resonances in the range 0–4 eV. The energies and widths of these temporary anion states suggest that they may be assigned to the strongly mixed (4$s^2$3d${)}^2$D and (4s4$p^2$${)}^2$D states of ${\mathrm{Ca}}^{\mathrm{-}}$. This interpretation is supported by ab initio configuration-interaction calculations and is consistent with previously unassigned structure observed in the photodetachment cross section.

We map the eigenvalue problem of a periodically driven quantum system with N-dimensional Hilbert space to a Hamiltonian N-particle system connected with an infinite-dimensional Lie algebra. This N-particle system is integrable and its equations of motion can be written in Lax form. It is a natural generalization of the so-called generalized Calogero-Moser and Sutherland models, which can be derived from eigenvalue problems of autonomous and kicked quantum systems, respectively. We show that, contrary to common opinion, the generalization of the Weierstrass potential dynamics no longer fulfills all Lax equations and is therefore not expected to be integrable.

The finite-element method has been applied to the problem of hydrogen in a superstrong magnetic field. Binding energies have been calculated for the low-lying states (1$s_0$, 2$s_0$, 2$p_0$, and 2$p_{\mathrm{-}1}$) for a range of magnetic fields from ${10}^5$ to ${10}^{12}$ G. This calculation establishes highly accurate lower bounds for the binding energy of the excited states.

We consider an absorption process in a two-level atom for which the driving pulse is controlled in both its frequency modulation (FM) and its amplitude modulation (AM), or temporal shape. In the weak-signal limit, we find that a variety of FM-AM combinations can provide either broadening or narrowing of the absorption line shape, along with an enhancement or suppression of the atomic absorptivity. We develop a simple analytic criterion for the driving pulses which induce absorptive line broadening or narrowing, and give examples of each type. The absorptivity increments can be exploited in spectroscopic and signal broadcast applications.

Coordinate wave functions for the one-mode squeezed states produced by the quantum analog of the general linear transformation in phase space are calculated. The probability density [‖ψ(q)${\Vert }^2$] for these states is Gaussian with center predicted by the classical transformation. The quantum image (which includes the traditional two-mode squeeze operator) of a three-parameter symplectic map in two-mode phase space equally generates squeezed states having Gaussian ‖ψ($q_1$,$q_1$)${\Vert }^2$. The center of the two-mode Gaussian is again predicted by the classical mapping.

Swept gain superfluorescent operation is reported in a mode-locked laser. We quantitatively compare theoretical predictions and experimental results for the laser output, which show drastically reduced pulse lengths together with increased bandwidth corresponding to the generation of near-π pulses. The attainment of this operating mode depends on the intracavity power level and the relevant homogeneous lifetimes. The effect has been observed for several mode-locked argon laser lines.

We show that the resonant interaction between a field mode and a pair of vibronic levels is influenced by dynamical coupling to nonresonant states. The dependence of the occupation probability of vibronic states on dipole coupling, displacement, and resonance condition is discussed.