Alwyn C. Scott

Magnetic‐flux propagation on a Josephson transmission line

The propagation of magnetic flux pulses along the insulating barrier of a long Josephson junction is investigated both theoretically and experimentally. The theoretical study includes applications of both (i) the recently developed ’’inverse‐scattering‐transform method’’ (ISTM) to the corresponding sine‐Gordon equation in characteristic (light cone) coordinates and (ii) Whitham’s method (WM) of averaged Lagrangian analysis to the sine‐Gordon equation in laboratory coordinates. As the number of solitons (flux quanta) in the pulse becomes large, the ISTM becomes numerically unwieldy while WM becomes more accurate; thus these two analytical tools are complementary. WM has the advantage of being readily modified to account for small dissipative effects. Our experimental observations of magnetic‐flux propagation were entirely restricted to the ’’large‐amplitude limit’’ in which the average of the ac Josephson current is effectively zero. In this limit, WM indicates pulse propagation with linear dissipation. Th...

Nonlinear Science at the Dawn of the 21st Century

Nonlinear Science.- Nonlinear Coherent Phenomena in Continuous Media.- Perturbation Theories for Nonlinear Waves.- Josephson Devices.- Josephson Flux-Flow Oscillators in Microwave Fields.- Coupled Structures of Long Josephson Junctions.- Stacked Josephson Junctions.- Dynamics of Vortices in Two-Dimensional Magnets.- Nonlinear Optics.- Spatial Optical Solitons.- Nonlinear Fiber Optics.- Self-Focusing and Collapse of Light Beams in Nonlinear Dispersive Media.- Coherent Structures in Dissipative Nonlinear Optical Systems.- Solitons in Optical Media with Quadratic Nonlinearity.- Lattice Dynamics and Applications.- Nonlinear Models for the Dynamics of Topological Defects in Solids.- 2-D Breathers and Applications.- Scale Competition in Nonlinear Schrodinger Models.- Demonstration Systems for Kink-Solitons.- Quantum Lattice Solitons.- Noise in Molecular Systems.- Biomolecular Dynamics and Biology.- Nonlinear Dynamics of DNA.- From the FPU Chain to Biomolecular Dynamics.- Mutual Dynamics of Swimming Microorganisms and Their Fluid Habitat.- Nonlinearities in Biology: The Brain as an Example.

Exact solutions of the sine‐Gordon equation describing oscillations in a long (but finite) Josephson junction

Readily evaluated exact solutions of the sine‐Gordon equation are presented for nonlinear standing‐wave oscillations on a fixed length of a lossless Josephson transmission line with open‐circuit boundary conditions at the ends. Three distinct species of standing waves are described: (i) plasma oscillation, (ii) breather oscillation, and (iii) fluxon oscillation. Fluxon oscillations can absorb power from an external source of bias current; for this case the volt‐ampere characteristics relating bias current to average junction have been computed.

Coupled Solitary Waves in Neurophysics

An analytic description of single pulse propagation on a single myelinated fiber is presented and multiple pulse solutions on a single fiber are described. A structural perturbation technique is developed to study the formation of condensed pulse states on fiber bundles. It is suggested that such condensed states may serve as a mechanism for the interaction of neural systems with weak (non-ionizing) electromagnetic fields.

Neurodynamics: A critical survey

Abstract Following a brief introduction to the functional complexity of an individual nerve cell, the current status of neural network dynamics is reviewed. This survey is then used as a basis for suggesting some fundamental difficulties in developing a science of the human mind.

Laminar phase flow for an exponentially tapered Josephson oscillator

Exponential tapering and inhomogeneous current feed were recently proposed as means to improve the performance of a Josephson flux flow oscillator. Extensive numerical results backed up by analysis are presented here that support this claim and demonstrate that exponential tapering reduces the small current instability region and leads to a laminar flow regime where the voltage wave form is periodic giving the oscillator minimal spectral width. Tapering also leads to an increased output power. Since exponential tapering is not expected to increase the difficulty of fabricating a flux flow oscillator, we suggest that this feature should be incorporated in future designs.

Sine-Gordon Breather Dynamics

A multisoliton perturbation theory is used to study the dynamics of sine-Gordon breather solitons under the influence of various structural perturbations. Some of the results suggest a distinction that should be made between the clock paradox and the twin paradox of special relativity.

Bäcklund transformations and the inverse method

Abstract For several partial differential equations with important physical applications we show an exact correspondence between the equations of the Backlund transformation and the linear equations of the inverse scattering method.

Effect of the series inductance of a nerve axon upon its conduction velocity

Abstract The reformulation of the Hodgkin-Huxley equations to include the effect of series inductance that has recently been suggested by Lieberstein is examined. An axon model that includes series inductance is employed to obtain an analytic expression for the conduction velocity of an action potential. A recently developed exact transmission line equivalent circuit is then used to estimate the series inductance for a squid axon. It is found to be about five orders of magnitude too small to influence the conduction velocity.

Quantum theory of the small Josephson junction

Abstract A lossless, small area Josephson junction is analyzed from the point of view of quantum dynamics. Schroedingers equation in the flux representation reduces to Mathieus equation.