A Simple Model for Faraday Waves

We show that the linear-stability analysis of the birth of Faraday waves on the surface of a fluid is simplified considerably when the fluid container is driven by a triangle waveform rather than by a sine wave. The calculation is simple enough to use in an undergraduate course on fluid dynamics or nonlinear dynamics. It is also an attractive starting point for a nonlinear analysis.Comment: 8 pages, revtex, with included, embedded eps figs; to appear in Am. J. Phys. (but don't hold your breath

Nanoscale virtual potentials using optical tweezers

We combine optical tweezers with feedback to impose arbitrary potentials on a colloidal particle. The feedback trap detects a particle's position, calculates a force based on an imposed "virtual potential," and shifts the trap center to generate the desired force. We create virtual harmonic and double-well potentials to manipulate particles. The harmonic potentials can be chosen to be either weaker or stiffer than the underlying optical trap. Using this flexibility, we create an isotropic trap in three dimensions. Finally, we show that we can create a virtual double-well potential with fixed well separation and adjustable barrier height. These are accomplished at length scales down to 11 nm, a feat that is difficult or impossible to create with standard optical-tweezer techniques such as time sharing, dual beams, or spatial light modulators

Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form

Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here, for the first time, we measure experimentally this function. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.Comment: 9 pages, 3 figures, and supplemental materia