Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.     

Self-organized minimum-energy structures for dielectric elastomer actuators

When a stretched elastomer is laminated to a flat plastic frame, a complex shape is formed, which is termed a minimum-energy structure. It is shown how self-organized structures can be applied in the development of actuators with complex, out-of-plane actuationmodes. This unusual concept is then demonstrated in the case of dielectric elastomer actuators. Among advantages of this approach are the simplicity in manufacturing, the potential complexity and sophistication of the manufactured structures, and the general benefits of the concept when applied to other electro-mechanically active materials. PACS 46.32.+x; 77.65.-j; 83.80.Va     

Conjecture de Franchetta forte

Sans résumé