Glen J. Culler

Wall‐Pinning Model of Magnetic Hysteresis

A simple model for the motion of a domain wall in most magnetic materials is presented. The real flexible wall is represented by an equivalent rigid plane wall. The motion of the plane is impeded by springs which are attached to the wall and to defects in the material in the wake of the plane. A spring breaks when the force it exerts on the wall reaches a value characteristic of the defect, and the energy stored in it is lost to the motion. The model is similar to one developed earlier but is based on a more plausible view of the interaction of a wall with a defect. In common with the earlier model, it describes both reversible and irreversible flux changes; it predicts a small‐signal hysteresis loop which is similar to, but significantly different from, the Rayleigh loop; it explains the frictional nature of magnetic hysteresis without invoking any ad hoc energy‐loss mechanisms. It is sufficiently simple to be applied to complex problems. It agrees with the results of exact dynamic calculations to good a...

PLASMA OSCILLATIONS IN AN EXTERNAL ELECTRIC FIELD

The fluctuation longitudinal electric field, Ek, is studied for a two component plasma immersed in a uniform, external electric field E0. Since the time dependence of the space‐averaged part of the distribution functions precludes the usual Laplace transform approach, computational techniques are developed to solve the integral equation for Ek directly in the time domain. Solutions are given for the case where E0 is large compared to the critical field for runaway and compared with the familiar constant‐drift solutions. Growth in the vicinity of resonance (vdrift ≈ ωp/k) is observed, followed by Landau damping at longer times.

Mathematical laboratories: a new power for the physical and social sciences

The concept of a mathematical laboratory has been developing throughout the lifetime of computers. The capabilities made available in systems supporting these laboratories range from symbolic integration, differentiation, polynomial and power series manipulation; through mathematical simulation; to direct control experimental systems. About 1961 two trends, one toward what has become known as on-line computation, the other toward time sharing gained enough recognition to develop national support and subsequently have come to represent what is now known as modern computation. An on-line system provides interactive facilities by which a user can exert deterministic influence over the computation sequence; a time-sharing system provides a means by which partial computations on several different problems may be interleaved in time and share facilities according to predetermined sharing algorithms. For reasons of economy it is hard to put a single user in direct personal control (on-line, that is) of a large scale computer. It is equally or more difficult to get adequate computation power for significant scientific applications out of any small scale economical computer. Consequently, on-line computing has come to depend upon time-sharing as its justifiable mode of implementation. On the other hand, valuable on-line applications have formed one of the major reasons for pushing forward the development of time-sharing systems. At present, both efforts have reached such a stage of fruition that one finds many systems incorporating selective aspects of the early experimental systems of both types. In this chapter, we will bring out some of the key features of highly interactive direct control systems that have implications for continuing design effort aimed at furthering the development of experimental mathematical laboratories. We then present a brief description of the foundations of an existing facility at the University of California at Santa Barbara and illustrate its use in a typical application. Finally, we discuss some extension of the system which will provide deeper power for future experimental applications.