James A Flaten

Pendulum waves: A lesson in aliasing

A set of uncoupled pendula may be used to exhibit “pendulum waves,” patterns that alternately look like traveling waves, standing waves, and chaos. The pendulum patterns cycle spectacularly in a time that is large compared to the oscillation period of the individual pendula. In this article we derive a continuous function to explain the pendulum patterns using a simple extension to the equation for traveling waves in one dimension. We show that the cycling of the pendulum patterns arises from aliasing of this underlying continuous function, a function that does not cycle in time.

Curves of constant width

Curves of constant width have the same breadth regardless of how they are rotated. Highly noncircular curves with this property may be constructed geometrically. Such curves make good rollers, manhole covers, and allow one to drill nearly square holes.

The Interpretation of Phase-Slip and Critical-Velocity Data from the Flow of Superfluid 4He through a 2 μm by 2 μm Aperture

An analysis has been made of phase-slip and critical-velocity data for both the ac and dc flow of superfluid4He through a 2 μm by 2 μm aperture in a 0.1-μm-thick titanium foil between 0.36 and 2.10 K. Single-2π phase slips were resolvable over the entire range of temperature in the ac flow measurements, carried out between 10 and 20 Hz, making it possible to determine the width of the critical-velocity distribution throughout the temperature range from these measurements. These data have been interpreted in terms of the thermal nucleation of vortex half-rings at the walls of the aperture, involving a velocity- and temperature-dependent energy barrier. The barrier can be modeled with moderate success using an approach close to that of Avenel and Varoquaux and coworkers.

Studies of the critical velocity of superfluid4he in a 2 μm by 2 μm aperture in a thin foil at various frequencies

Measurements of the critical velocity behavior of oscillatory superfluid4He flow through a 2 μm by 2 μm square aperture in a 0.1 μm thick titanium foil are being made at temperatures between 0.36 K and 2.1 K and at pressures of less than 0.4 bar at various frequencies between 50 Hz and 1000 Hz. The purpose of this work is to study a micron-size aperture for possible frequency-dependent deviations from the critical velocity behavior seen in submicron-size apertures. Preliminary results show a nearly linear decrease of critical velocity with increasing temperature that is similar to the temperature dependences seen in smaller apertures and that is approximately independent of frequency. However, at frequencies above 500 Hz, a region appears at the lowest temperatures in which supercritical behavior is dominated by large energy-loss events requiring a number of half-cycles for completion, a region that extends up to 1.1 K at 970 Hz.

Improving Upon Mach's Wave Machines to Demonstrate Traveling Waves

This note describes how to demonstrate traveling wave patterns, as opposed to standing wave patterns, with sets of uncoupled pendula using an apparatus known as Machs wave machine. Both transverse and longitudinal variants of the wave machine are discussed, as are ways to independently adjust wave speed, amplitude, and frequency (and hence wavelength) of the traveling wave patterns.