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Laterally driven linear electrostatic micromotors have been fabricated by standard surface micromachining. We attempt to employ mechanical leverage with the aim to increase the force from the order of 1 µN up to the order of 0.1 mN, in combination with walking motion to increase the stroke to virtually unlimited. Three designs have been made and tested. We conclude that mechanical levers with proper stiffness characteristics to be driven by electrostatic actuators are feasible. Friction as a function of the applied electrostatic clamp force has been measured, showing that there is a significant adhesion in the clamps. Walking motion has been successfully generated in one of the designs, generating a stroke of 15 µm and a force of 3 µN. Improvement of the clamping is needed to benefit from the implemented levers to increase the generated force.

We consider the polarization of unstable type-IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large-N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S 3 geometry to that of a fuzzy S 4 .

We consider dynamical systems with a phase space Γ that preserve a measure µ. A partition of Γ into parts of finite µ-measure generates the coarse-grained entropy, a functional that is defined on the space of probability measures on Γ and generalizes the usual (ordinary or fine-grained) Gibbs entropy. We study the approximation properties of the coarse-grained entropy under refinement of the partition and also the properties of the coarse-grained entropy as a function of time.