An asymptotic formula is proved analytically for the effect on the generalized dimensions due to the finite size of the partition. For the special case of the $2^{\mathrm{\infty }}$ attractor the amplitude of this effect is expressed in terms of the dimensions.

We study a realistic model for the absorption of colloid particles or latex spheres from solution on a solid surface. The adsorbing particles are represented by hard spheres that undergo Brownian motion in the vicinity of the surface. Once a sphere touches the surface, it becomes permanently fixed in place. We show that the mean coverage and structure of the jammed configurations that result from this irreversible adsorption process are indistinguishable from those of their counterparts generated by a random sequential adsorption (RSA) algorithm. This result demonstrates, posteriori, the importance of the RSA model in the study of static properties of systems of absorbed particles.

Behavior of a Brownian particle confined in a harmonic potential that is disturbed by a random environment is considered. The effect of the environment on the mean-square displacement, the relaxation time, and the equilibrium distribution function are studied within the renormalization-group method to the first order of ε=2-d (where d is the space dimensionality).

As noted in the first applications of the renormalization-group method, a major simplification of this method lies on the assumption that the effective interactions obtained after the small-scales elimination are nonlocal in Fourier space. This seems in complete contradiction with the usually accepted description of the turbulent Kolmogorov-Richardson cascade. We show, however, that if this nonlocal assumption is relaxed, the renormalized propagator of the Navier-Stokes equation exhibits unphysical behaviors for the large scales. We also discuss the results of numerical renormalization-group methods.

High-precision molecular-dynamics (MD) data are reported for the shear viscosity η of the Lennard-Jones liquid at its triple point, as a function of the shear rate ε̇ for a large system (N=2048). The Green-Kubo (GK) value η(ε̇=0)=3.24±0.04 is estimated from a run of 3.6×${10}^6$ steps (40 nsec). We find no numerical evidence of a ${\mathit{t}}^{\mathrm{-}3/2}$ long-time tail for the GK integrand (stress-stress time-correlation function). From our nonequilibrium MD results, obtained both at small and large values of ε̇, a consistent picture emerges that supports an analytical (quadratic at low shear rate) dependence of the viscosity on ε̇.

We report local concentration measurements of electrolyte in electrochemical deposition using a schlieren method. The intensity contrast of schlieren images is used to obtain concentration information. The images reveal active regions of the growth and thus provide excellent records to study the dynamics of electrochemical deposition processes. Quantitative results of local concentration measurements in the early stages of the growth agree well with recent model calculations.

Magnetosonic solutions, which are a generalization of the recently discovered relativistic zero-temperature soliton in including a self-consistent temperature, are found to exist, and are also highly electrically charged. The maximally allowed potential drop across the half-width of a relativistically propagating soliton is approximately 1/12(${\gamma }_{\mathrm{\infty }}$${)}^{1/2}$${\gamma }_{\mathit{t}\mathrm{\infty }}$${\mathrm{\beta }}_{\mathit{t}\mathrm{\infty }}$ GV when (${\gamma }_{\mathrm{\infty }}$${)}^{1/2}$${\gamma }_{\mathit{t}\mathrm{\infty }}$${\mathrm{\beta }}_{\mathit{t}\mathrm{\infty }}$≫1, where ${\gamma }_{\mathrm{\infty }}$ and ${\gamma }_{\mathit{t}\mathrm{\infty }}$ are the Lorentz factors of the soliton speed and background ion thermal speed, respectively. The soliton is reduced to the previously found cold one, which is charged up to 1 GV, when the above inequality is reversed.

The Stark broadening parameters of several C ii and C i lines have been measured with the help of a pulsed discharge operating with a He+${\mathrm{CO}}_2$ mixture.

We demonstrate the feasibility of x-ray resonant nonlinear effects (absorption saturation and nonlinear refractive index) for the radiation of some of existing x-ray lasers (XRL’s) when it propagates in relatively low-temperature discharge plasmas different from those used in the respective XRL. We identified 12 resonant ‘‘XRL-plasma’’ couples suitable for such effects.

Interaction of slightly overlapping solitary pulses (SP’s) is considered in the cubic nonlinear Schrödinger equation with small pumping and dissipation terms, and in the quintic Ginzburg-Landau equation with small dispersion terms. In both cases, the small perturbing terms render the asymptotic wave form of a SP spatially oscillating. Using the description of the interaction of SP’s in terms of an effective potential, it is demonstrated that this fact may give way to formation of two-pulse and multipulse bound states, which are weakly stable.

We study a model of coupled limit-cycle oscillators that was introduced in order to model the synchronization observed in the firing of mammalian cortical cells. This Brief Report is devoted to the study of a time-delayed feedback. We show, by both numerical simulations and analytical arguments, that the delay has a desynchronizing influence on the oscillations.

A time-of-flight photoelectron spectrometer is oriented coaxially with a pulsed molecular beam to detect high Rydberg states of HCl with lifetimes as long as 7 μs. Two classes of such states are found. Delayed extraction following double-resonant excitation field-ionizes Rydberg states of very high principal quantum number (n≥100) that converge to successive rotational limits for producing ${\mathrm{HCl}}^{+}$, effectively yielding a rotationally resolved threshold photoelectron spectrum. Surprisingly, excitation under more rigorously field-free conditions (<100 mV/cm) produces additional resonances which can be assigned to series of long-lived Rydberg states extending to principal quantum numbers as low as 10. The lower-principal-quantum-number resonances isolated by their long field-free lifetimes appear to constitute a high-angular-momentum nonpenetrating subset of the autoionizing Rydberg series that converge both to accessible rotational levels of the upper ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{1/2}^{}{}_{}{}^{}$ threshold and excited rotational limits of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{3/2}^{}{}_{}{}^{}$ ground state of ${\mathrm{HCl}}^{+}$.

Measurements of velocity-changing collision kernels have recently been reported. Here we describe the results of calculations which demonstrate that interatomic potentials can accurately be derived from such data. It is important to analyze the kernel directly in terms of an interatomic potential and not in terms of a traditional energy-averaged differential cross section. We use experimental results to determine the Rb-He potential and compare it to calculated potentials.

The density matrices of excited H atoms (n=2 and 3 manifolds) resulting from electron capture in collisions of ${\mathrm{H}}^{+}$ ions with He atoms in the energy region from 1 to 100 keV/amu are investigated on the basis of the atomic-orbital–molecular-orbital matching approach. Two electrons in the system are explicitly included in the calculation. The present results for the electric dipole moment, electron current density distributions, and alignment parameters compare favorably with recent measurements by Cline (unpublished), Hippler et al. [Phys. Rev. A 43, 2587 (1991)], and Ashburn et al. [Phys. Rev. A 41, 2407 (1990)] in the entire energy regions studied, and reveal similarities of these quantities for n=2 and n=3. Some insights of the similarities are discussed.

We report a solution of the Gavrila-Kaminski coupled-channel system of equations describing the continuum states of an electron in the combined field of a Coulomb potential and a linearly polarized intense radiation field. Convergence was achieved in the number of Floquet states and partial waves for intensities up to 3×${10}^{14}$ W/${\mathrm{cm}}^2$ at a photon energy of 7.35 eV. In addition, we observed the one- and two-photon capture-escape resonances.

A numerical technique for the solution of the time-dependent Schrödinger equation in three spatial dimensions is proposed to study the time evolution of hydrogen atoms subject to ultraintense short laser pulses. The method makes use of the Kramers-Henneberger transformation, and through a variable substitution, all of position space is discretized and the correct boundary condition at infinity is implemented. Calculations for 6-fs pulses with a ${\sin }^2$-shaped envelope show that stabilization of the atom against ionization does occur at high laser frequency and intensity, but that it is much less efficient than predicted by one-dimensional model calculations.

The dynamics of a bistable optical system suddenly brought in a domain of multimode instability is studied both experimentally and numerically. The sine-wave self-pulsing is shown to start with an initial amplitude dramatically depending on the switching conditions.

We have observed optical precursors by studying propagation of ultrashort optical pulses with a steeply rising and an exponentially decaying trailing edge through a 0.2-μm-thick GaAs crystal near the exciton resonance. The appearance of a fast pulse front—the precursor—independent of the detuning with respect to the resonance, was accompanied by a delayed main pulse. The delay of the main pulse varies with detuning in according with theoretical predictions.

We analyze the distribution of eigenfrequencies of microwave resonators which correspond to pseudointegrable billiards. The statistical properties of the measured spectra are explained by means of a model of additive random matrices.

A cellular-automaton model for a surface reaction is introduced that describes the chemical reactions correctly. The phase-transition points and the order of the phase transitions agree well with the results of Ziff, Gulari, and Barshad via a Monte Carlo simulation [Phys. Rev. Lett. 56, 2553 (1986)]. The high performance of the cellular automaton leads to a more precise determination of the critical exponent β at the second-order phase transition (β=0.58), which thus appears to belong to the universality class of Reggeon field theory.