R. W. Rollins

Nucleation of Silver on Sodium Chloride

The nucleation rate of silver deposited from the vapor phase onto a sodium chloride substrate has been studied as a function of substrate temperature and incidence rate. The experiments have been performed in an ultra‐high‐vacuum system on a substrate cleaved in situ. The results are found to be in agreement with a model of the nucleation process suggested in previous publications. Using the theory, a value of 0.4 eV has been obtained for the adsorption energy of silver on sodium chloride. It is also estimated that the activation energy for surface diffusion is less than 0.2 eV, and that the dissociation energy of the critical nucleus at the lower supersaturations employed is 2.1 eV.

Magnetic field profiles in type-II superconductors with pinning using a new ac technique

A new ac technique is described which allows the experimental determination of the magnetic field profile near the sample surface in type‐II superconductors with pinning. The technique, like a previous method of Campbell, depends only on the validity of the critical‐state model and can separate the position and magnetic field dependence of the flux‐pinning forces. The entire field profile is obtained from a measurement of the waveform of the response of the sample to a small ac magnetic field superimposed on the dc field. Profiles obtained in cold‐worked Nb and Nb–Ti alloys are reported and the results compared with previous measurements. We have found that the critical‐state model does not adequately describe the results obtained on the Nb–Ti alloys when the magnetic field is less than 0.5Hc2.

Hysteresis in Hard Superconductors

To incorporate the effects of pinning due to defects and predict size- dependence and hysteresis in the magnetization curves of hard superconductors, the AbrikosovCoodman theory is developed. The interaction forces between fluxoid filaments are determined semiempirically. The method developed is illustrated by application to a simple case. (C.E.S.)

Studying chaotic systems using microcomputer simulations and Lyapunov exponents

The study of nonlinear systems in an undergraduate setting has become important, and this article describes the use of an interactive simulation in introducing students to the new techniques used to characterize deterministic chaos. Lyapunov exponents are introduced with emphasis on their physical significance. The results of numerical experiments on the driven, damped, Duffing two‐well oscillator are reported and the global behavior of the Lyapunov exponent spectra is presented. The results confirm an important sum rule satisfied by the Lyapunov exponent spectra. Interesting, structured behavior of the Lyapunov exponent spectra is observed as the Duffing oscillator system follows the period‐doubling route to chaos.

Controlling chaos in a model of thermal pulse combustion

We describe methods for automating the control and tracking of states within or near a chaotic attractor. The methods are applied in a simulation using a recently developed model of thermal pulse combustion as the dynamical system. The controlled state is automatically tracked while a parameter is slowly changed well beyond the usual flame‐out point where the chaotic attractor ceases to exist because of boundary crisis. A learning strategy based on simple neural networks is applied to map‐based proportional feedback control algorithms both with and without a recursive term. Adaptive recursive proportional feedback is found to track farther beyond the crisis (flame‐out) boundary than does the adaptive non‐recursive map‐based control. We also found that a continuous‐time feedback proportional to the derivative of a system variable will stabilize and track an unstable fixed point near the chaotic attractor. The positive results suggest that a pulse combustor, and other nonlinear systems, may be suitably cont...

Periodic and Chaotic Current Oscillations at a Copper Electrode in an Acetate Electrolyte

Periodic and chaotic current oscillations are observed during electrodissolution of copper in a pH 3.5 sodium acetate/ acetic acid buffer under potentiostatic conditions using a rotating copper disk electrode. Periodic or chaotic oscillations are observed depending on the applied potential and electrode rotation rate. The oscillations arise after the formation and dissolution of an acetate salt film precursor to oxide passivation. The nature and composition of the surface films were examined using scanning electron microscopy and x‐ray powder diffraction data. Nonlinear dynamic analysis methods have been used to show the existence of deterministic chaos. Time series data of the chaotic oscillations were used to generate a return map that appears to be one‐dimensional. The chaotic attractor was reconstructed in a three‐dimensional state space using the method of time delays and the largest Lyapunov exponent was calculated and was positive for the chaotic oscillations indicating a sensitive dependence on initial conditions characteristic of deterministic chaos.

Periodic current oscillations in the anodic dissolution of copper in acetate buffer

In this note we describe the oscillations which were observed during the anodic dissolution of copper in an acetate buffer (pH<4) under potentiostatic conditions using a rotating copper disc as the working electrode. The basis of this work is to apply nonlinear dynamics with the techniques of electrochemistry for the purpose of obtaining information on mechanisms related to chemical corrosion

Chaotic dynamics in a model of metal passivation

The dynamic behavior of a model for the passivation of a metal surface in contact with an aqueous solution is investigated. The model, which is characterized by a three-dimensional state space and five-dimensional parameter space, is obtained by combining elements from passivation models developed by Talbot and Oriani and by Sato. A three-dimensional subspace of parameter space has been studied; the remaining two dimensions are not thought to provide any additional interesting dynamics. The model exhibits remarkably rich dynamics, including the period-doubling, intermittency, and crisis routes to chaos, folds and bubbles in periodic portions of the attractor, and multiple attractors with complex, intertwined basins of attraction.

Chaotic dynamics in an atomistic model of environmentally assisted fracture

A simple atomistic model of a crack tip is used to demonstrate the existence of chaotic motion of crack-tip atoms. The model, which has been developed in detail elsewhere in the literature, consists of a linear chain of four atoms. Nearest neighbors interact via Morse-function potentials, with environment-induced lattice decohesion simulated by reducing the strength of the inner bond. Dynamic calculations are carried out by allowing the two inner atoms to move freely, starting from rest in a given initial configuration, with the two end atoms being held rigidly in place, Under certain conditions, associated with large departures from minimum potential energy, the motion of the inner atoms is shown to be chaotic in a manner that is consistent with the Kosloff-Rice description of chaotic dynamics in a classical Hamiltonian system. Possible implications of the results relative to the fracture of actual materials are discussed.

Mixed-mode oscillations in the electrodissolution of copper in acetic acid/acetate buffer

Abstract A sequence of alternating periodic and chaotic current oscillations was found during the electrodissolution of a rotating copper disc in an acetic acid/sodium acetate buffer. The mixed-mode oscillations consist of combinations of large and small amplitude oscillations in peak current that were generated by incrementing the rotation rate of the copper electrode under potentiostatic control at 770 mV versus the saturated calomel electrode. Return maps of the chaotic intermediates were obtained and chaotic attractors were reconstructed in a three dimensional phase space using the method of time delays. The largest Lyapunov exponent was calculated to confirm the existence of deterministic chaos.