147 research outputs found
The role of symmetry in driven propulsion at low Reynolds number
We theoretically and experimentally investigate low-Reynolds-number
propulsion of geometrically achiral planar objects that possess a dipole moment
and that are driven by a rotating magnetic field. Symmetry considerations
(involving parity, , and charge conjugation, )
establish correspondence between propulsive states depending on orientation of
the dipolar moment. Although basic symmetry arguments do not forbid individual
symmetric objects to efficiently propel due to spontaneous symmetry breaking,
they suggest that the average ensemble velocity vanishes. Some additional
arguments show, however, that highly symmetrical (-even) objects
exhibit no net propulsion while individual less symmetrical
(-even) propellers do propel. Particular magnetization
orientation, rendering the shape -odd, yields
unidirectional motion typically associated with chiral structures, such as
helices. If instead of a structure with a permanent dipole we consider a
polarizable object, some of the arguments have to be modified. For instance, we
demonstrate a truly achiral (- and -even)
planar shape with an induced electric dipole that can propel by
electro-rotation. We thereby show that chirality is not essential for
propulsion due to rotation-translation coupling at low Reynolds number.Comment: 5 pages, 5 figure
Opposites Attract: A Theorem about the Casimir Force
We consider the Casimir interaction between (nonmagnetic) dielectric bodies or conductors. Our main result is a proof that the Casimir force between two bodies related by reflection is always attractive, independent of the exact form of the bodies or dielectric properties. Apart from being a fundamental property of fields, the theorem and its corollaries also rule out a class of suggestions to obtain repulsive forces, such as the two hemisphere repulsion suggestion and its relatives
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