Simulations have been carried out to investigate the structures generated by a nonequilibrium Laplacian-random-walk model for the growth of polymer chains which was recently developed by Lyklema et al. Instead of solving the Laplace equation numerically to obtain the growth probabilities at the active end of the growing polymer chain, random walkers are used to simulate a random growth process controlled by a harmonic field. The results from two-dimensional simulations are in good agreement with those of Lyklema et al., Bradley and Kung, and Debierre and Turban. The growth of single chains on square lattices or cubic lattices leads to structures which can be described in terms of a single geometric scaling exponent (fractal dimensionality) for both absorbing and reflecting boundary conditions at the inactive (nongrowing chain sites). The main objective of this work was the investigation of models in which many chains grow from a line or plane of active sites to represent growth from a surface. For these models at least two effective exponents are needed to describe the structure of the system. The distribution of chain length can be described in terms of a power law (with an exponential cutoff) and the total density profile can also be described by a power law. The two-point density-density correlation function $C^h$(r) for those sites located at a distance h from the original surface of active sites can be described in terms of the scaling form $C^h$(r)∼$h^{\mathrm{-}\mu }$f(r/$h^{\omega }$), where f(x) is a scaling function. These results indicate that the structure of the surface deposits grown by the models should be described in terms of a non-self-similar (possibly self-affine) fractal geometry.

A model-layered feed-forward neural network with an iterated learning stage is described. The system is capable of self-organizing its ‘‘internal representations’’ so that a large number of patterns can be perfectly stored and retrieved. The performance of the network is found to be robust against various degrading operations. Comparison of performance with an exactly solvable model is made.

Real-space renormalization-group arguments are used to derive scaling relations for the mean displacement 〈R〉 and the variance 〈(R-〈R〉${)}^2$〉 of a tracer particle in a fluid flowing through a heterogeneous material which is near a percolation threshold $p_c$; both small- and large-Peclet-number regions are studied. The existence of a noninteger-power-law dependence of 〈R〉 and 〈(R-〈R〉${)}^2$〉 on time and the strength of flow, which cannot be described by a convection-diffusion equation, is revealed. Particularly at large Peclet numbers, the variance exhibits anomalously fast time dependence and an associated divergence near $p_c$. As p→$p_c$, the region dominated by convection extends prominently, while the region controlled by diffusion shrinks.

We consider a system of N identical bosons which interact in one dimension via attractive pair potentials and obey nonrelativistic quantum mechanics. This system is studied from two complementary viewpoints. The equivalent two-body method approximates the system as a collection of (N-1) independent two-particle systems with coupling constants enhanced by the factor N/2, and this yields energy lower bounds. The collective-field method approaches the problem from the standpoint of the limit as N→∞ and leads to energy upper bounds. We find that Gaussian trial functions for the N-particle Hamiltonian and Gaussian trial densities in the collective-field theory lead to precisely the same energy upper bounds. The upper bounds provided by field theory allow for systematic improvement via a variational principle. Details are worked out for two exactly soluble problems, namely, the harmonic oscillator and the attractive δ potential.

Positive Lyapunov exponents provide an unambiguous signature of chaotic behavior. Using a sinusoidally driven semiconductor diode circuit, we have determined Lyapunov exponents describing the behavior of the system in the chaotic regime near the period-doubling accumulation point. The measured parameter dependence of the values of the exponents is in excellent agreement with the universal scaling law predicted by Huberman and Rudnick.

We consider squeezed light described as an SU(1,1) coherent state interacting with a two-photon Jaynes-Cummings model of a two-level atom. We study the time variation of the mean photon number and also the variance of the field quadratures with particular regard to the squeezing.

We obtained the path-integral solution of a three-dimensional pseudoharmonic potential by applying a suitably chosen point canonical transformation.

Total scattering cross sections for the Ar${(}^3$${\mathrm{P}}_2$,0)+${\mathrm{N}}_2$(X) are reported over a relative velocity range from 0.55 to 1.75 km/s. The data are compared with cross sections calculated from a spherically symmetric potential with four adjustable parameters. The best fit gave $r^{\mathrm{-}5}$ and $r^{\mathrm{-}6}$ potential constants of 6.7±1.2 and 37.8±11.6 a.u., respectively.

Quantal calculations of the proton-impact excitation of the n=2 fine-structure levels of ${\mathrm{Ar}}^{17+}$ in a dense plasma are carried out and compared to recent semiclassical impact-parameter calculations. The agreement is satisfactory and confirms the usefulness of the semiclassical approximation. The sensitivity of the cross sections to the form of the screening potentials is also investigated.

A computationally fast approximate method for the calculation of large atomic-dipole transition arrays is proposed using an adaptation of Wigner’s random-matrix theory. Unlike the Gaussian orthogonal ensemble, off-diagonal matrix elements are populated statistically according to a bi-Gaussian distribution function where elements are correlated according to the term value of the parent shell.

We performed molecular-dynamics simulation experiments for a hard-sphere fluid at four high densities and determined the spatial Fourier transform of the three-particle equilibrium correlation function with two of the three particles at contact.

The growth rate and threshold for the stimulated scattering process in which magnetic-electron-drift vortex waves are scattered off plasma ions are given. The process can be important in a plasma with nearly equal electron and ion temperatures.

The dc protonic conductivity of powders of lysozyme was calculated from capacitance data measured for the frequency range 10 KHz to 10 MHz and for varied levels of hydration. Analysis of the hydration dependence of the conductivity close to the percolation threshold gave the value for the critical exponent t=1.29±0.05. This value is in close agreement with expectation from theory for a two-dimensional percolative process. These results support the idea that the threshold for hydration-induced protonic conduction (and, quite possibly, for enzymatic activity) corresponds to the formation of a percolation network of absorbed water molecules on the surface of this protein macromolecule.

We discuss the theory of Z. Deng and J. H. Eberly [Phys. Rev. A 34, 2492 (1986)] and present our point of view regarding coherent trapping and continua, which is not in agreement with that put forward by these authors.

We emphasize our finding of both trapping and antitrapping in solutions to a coupled-continuum model without any discrete states.

Recently, Karwowski, Duch, and Valdemoro have developed a method for constructing a matrix representation of a spin-adapted reduced Hamiltonian based on evaluation of traces of occupation number operators over finite spaces of many electrons being coupled to a definite spin S. We show that the spectral-distribution method, used in nuclear physics, leads to a unified and general reduction formula for the fixed-S traces.

In the preceding comment Nomura derived a general formula for traces of products of occupation number operators over finite-dimensional, N-electron, and spin-adapted spaces within the spectral-distribution method of nuclear physics. We supplement and generalize his result by giving recurrent relations which determine the traces in an alternative way. The relations are derived using simple techniques of atomic and molecular physics.

Aluminum cluster anions are produced in a laser vaporization source, cooled spectrometer. Pulsed uv light is used for electron detachment; the photoelectrons undergo energy analysis in a magnetic-bottle–type spectrometer. The resulting electron spectra reflect the band-structure development of aluminum clusters.