The dynamics of active particles is of interest at many levels and is the focus of theoretical and experimental research. There have been many attempts to describe the dynamics of particles affected by random active forces in terms of an effective temperature. This kind of description is tempting due to the similarities (or lack thereof) with systems in or near thermal equilibrium. However, the generality and validity of the effective temperature is not yet fully understood. Here, we studied the dynamics of trapped particles subjected to both thermal and active forces. The particles were not overdamped. Expressions for the effective temperature due to the potential and kinetic energies were derived, and they differ from each other. A third possible effective temperature can be derived from the escape time of the particle from the trap, using a Kramers-like expression for the mean escape time. We found that over a large fraction of the parameter space, the potential energy effective temperature is in agreement with the escape temperature, while the kinetic effective temperature only agrees with the former two in the overdamped limit. Moreover, we show that the specific implementation of the random active force, and not only its first two moments and the two point auto-correlation function, affects the escape time distribution.

This sketch describes the computer graphics techniques used to render the out-of-focus areas of a picture. We propose a simple, phenomenological model that provides control to the artist and achieves a realistic look. Abstract"Bokeh" is a Japanese word used to describe the quality of the out-of-focus areas as rendered on film by a physical lens. In areas that are out of focus, the circle of confusion (i.e., the distribution of light absorbed onto film from a single point of light in the scene) is bigger than in areas that are focused. Different lenses distribute light within the circle of confusion differently, depending on a number of factors, like the shape and number of diaphragm blades and the optical design of the lens itself. For example, lenses that are designed to correct for optical aberrations tend to render a circle of confusion that is more intense on the edges and slightly less so in the center. Other lenses, like the so called "mirror" lenses, which include reflective elements besides refractive ones, typically produce donut-shaped circles of confusion since some of the light paths are cut from the center by the reflective element.

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