Nonconservative forcing and diffusion in refractive optical traps

Refractive optical trapping forces can be nonconservative in the vicinity of a stable equilibrium point even in the absence of radiation pressure. We discuss how nonconservative 3D force fields, in the vicinity of an equilibrium point, reduce to circular forcing in a plane; a simple model of such forcing is the refractive trapping of a sphere by a four rays. We discuss in general the diffusion of an anisotropically trapped, circularly forced particle and obtain its spectrum of motion. Equipartition of potential energy holds even though the nonconservative flow does not follow equipotentials of the trap. We find that the dissipated nonconservative power is proportional to temperature, providing a mechanism for a runaway heating instability in traps.Comment: To appear in the Journal of the Optical Society of America

Locating the source of projectile fluid droplets

The ill-posed projectile problem of finding the source height from spattered droplets of viscous fluid is a longstanding obstacle to accident reconstruction and crime scene analysis. It is widely known how to infer the impact angle of droplets on a surface from the elongation of their impact profiles. However, the lack of velocity information makes finding the height of the origin from the impact position and angle of individual drops not possible. From aggregate statistics of the spatter and basic equations of projectile motion, we introduce a reciprocal correlation plot that is effective when the polar launch angle is concentrated in a narrow range. The vertical coordinate depends on the orientation of the spattered surface, and equals the tangent of the impact angle for a level surface. When the horizontal plot coordinate is twice the reciprocal of the impact distance, we can infer the source height as the slope of the data points in the reciprocal correlation plot. If the distribution of launch angles is not narrow, failure of the method is evident in the lack of linear correlation. We perform a number of experimental trials, as well as numerical calculations and show that the height estimate is insensitive to aerodynamic drag. Besides its possible relevance for crime investigation, reciprocal-plot analysis of spatter may find application to volcanism and other topics and is most immediately applicable for undergraduate science and engineering students in the context of crime-scene analysis.Comment: To appear in the American Journal of Physics (ms 23338). Improved readability and organization in this versio

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the Stokes-Einstein relation as a special case of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this non-equilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging. This is the clearest change in material properties of the system with aging.Comment: 5 pages,4 figure