An Essay On Interactive Investigations Of The Zeeman Effect In The Interstellar Medium

The paper presents an interactive module created through the Wolfram Demonstrations Project that visualizes the Zeeman effect for the small magnetic field strengths present in the interstellar medium. The paper provides an overview of spectral lines and a few examples of strong and weak Zeeman splitting before discussing the module in depth. Student discovery is aided with example situations to investigate using the interactive module, which is targeted at the upper undergraduate or early graduate level. This module (http://demonstrations.wolfram.com/TheZeemanEffectInTheInterstellarMedium), which uses free software, can be used in classroom activities or as a means of introducing students to the Wolfram Demonstrations Project as a learning resource.Comment: 6 pages, published in JAES

Physical Dissipation and the Method of Controlled Lagrangians

We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including “balance” systems such as the pendulum on a cart. Since the method involves modifying a system’s kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be “reversed” through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems

Dissipation and Controlled Euler-Poincaré Systems

The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor

Time dependence in perpendicular media with a soft underlayer

In this paper we describe measurements of magnetic viscosity or time dependence in magnetic thin films suitable for use as perpendicular recording media. Generally, such effects cannot be measured using conventional magnetometry techniques due to the presence of a thin (0.1 mum) soft underlayer (SUL) in the media necessary to focus the head field. To achieve our results we have developed an ultrastable MOKE magnetometer, the construction of which is described. This has enabled us to measure nominally identical films with and without the presence of the SUL. We find that the presence of the SUL narrows the energy barrier distribution in the perpendicular film increasing the nucleation field (H-n), reducing the coercivity (H-c) and results in an increase in the squareness of the loop. This in turn results in an increase in the magnitude of the viscosity in the region of the H-c but that the range of fields over which the viscosity occurs is reduced

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