We investigate the impact of geometric constriction on viscous flow electron liquid through quantum point contacts. provide analysis electric potential distribution given setup a slit configuration and use method conformal mapping to obtain analytical results. The profile can be tested contrasted experimentally with scanning tunneling potentiometry technique. discuss intricate physics that unde...

In classical Kirchhoff flow, an ideal incompressible fluid flows past an obstacle and around a motionless wake bounded by free streamlines. Since 1869 it has been known that in principle, the two-dimensional Kirchhoff flow over a polygonal obstacle can be determined by constructing a conformal map onto a polygon in the log-hodograph plane. In practice, however, this idea has rarely been put to ...

The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled surfaces. The finite energy case yields a limit of images, under a suitable topology, with a union of discs and straight line segments. Generalization to highe...

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has continuous homeomorphic extension to the closures of domains. Our involve notions cofat and ...

Abstract We analyze the properties of Padé and conformal map approximants for functions with branch points, in situation where expansion coefficients are only known finite precision or subject to noise. prove that there is a universal scaling relation between strength noise order at which breaks down. illustrate this behavior some physically relevant model test two non-trivial physical examples...