The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambd...

.......................................................................................................... iv EXECUTIVE SUMMARY .....................................................................................x 1. Rheological Properties of HPAM Solutions ........................................................1 1.

The Archimedean spiral geometry presents a platform for exploration of complex plasmonic mechanisms and applications. Here we show both through simulations and experiment that more complex plasmonic modes with unique near-field structure and larger mode volumes can be realized within a single, topologically robust structure. In the spiral, complex polarization response, resonant interactions an...

Topological winding and unwinding in a quasi-one-dimensional metastable Bose-Einstein condensate are shown to be manipulated by changing the strength of interaction or the frequency of rotation. Exact diagonalization analysis reveals that quasidegenerate states emerge spontaneously near the transition point, allowing a smooth crossover between topologically distinct states. On a mean-field leve...

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in curved spacetime is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solut...