On the boundary-layer structure of patterns of convection in rectangular-planform containers

This paper considers the structure of steady-state solutions of the Swift–Hohenberg equation describing convection in shallow rectangular-planform containers heated from below. The lateral dimensions of the planform are assumed to be much larger than the characteristic wavelength of convection. Results are restricted to patterns composed of rolls orthogonal to the sides of the rectangle in which case convection sets in at a critical value of the Rayleigh number in the form of rolls parallel to the shorter sides. This primary bifurcation from the conductive state of no motion produces a solution which subsequently undergoes a secondary bifurcation in which the low-amplitude motion near the shorter sides is replaced locally by cross-rolls perpendicular to the sides. This results in the formation of grain boundaries (or domain boundaries) within the fluid which mark the division between the different roll orientations.With increasing Rayleigh number the grain boundaries approach the sides of the rectangle and a boundary-layer structure is formed. In the present paper the method of matched asymptotic expansions is used to determine this boundary-layer structure and to predict the location of the grain boundaries. An interesting feature of the solution is that the grain boundaries develop significant curvature and bend into the corners of the rectangle, where the local solution is also determined.The results are compared with numerical computations of the secondary solution branch and with previous numerical and experimental work.</jats:p

Schwannomatosis of the Spinal Accessory Nerve: A Case Report.

Schwannomatosis is a distinct syndrome characterized by multiple peripheral nerve schwannomas that can be sporadic or familial in nature. Cases affecting the lower cranial nerves are infrequent. Here, the authors present a rare case of schwannomatosis affecting the left spinal accessory nerve. Upon genetic screening, an in-frame insertion at codon p.R177 of the Sox 10 gene was observed. There were no identifiable alterations in NF1, NF2, LZTR1, and SMARCB1. This case demonstrates a rare clinical presentation of schwannomatosis in addition to a genetic aberration that has not been previously reported in this disease context

Majorana Fermion Induced Resonant Andreev Reflection

We describe experimental signatures of Majorana fermion edge states, which form at the interface between a superconductor and the surface of a topological insulator. If a lead couples to the Majorana fermions through electron tunneling, the Majorana fermions induce \textit{resonant} Andreev reflections from the lead to the grounded superconductor. The linear tunneling conductance is $0$ ($2 e^2/h$) if there is an even (odd) number of vortices in the superconductor. Similar resonance occurs for tunneling into the zero mode in the vortex core. We also study the current and noise of a two-lead device.Comment: 4 pages, 3 figures. Discussion on STM tunneling into the Majorana zero mode in the vortex core is adde

Vortex description of the fractionalized phase in exciton bose condensate

As a sequel to the previous work [Phys. Rev. B 72, 235104 (2005)] we present a vortex description of the fractionalized phase in exciton bose condensate. Magnetic flux line and monopole of the 3+1D emergent U(1) gauge theory are identified in the exciton picture. A bundle of vortex/anti-vortex pairs of all flavors of excitons corresponds to the magnetic flux line and a point at which the vortices and anti-vortices recombine is identified as magnetic monopole. This completes the magnetic sector of the low energy excitation in the fractionalized phase.Comment: 8 pages, 6 figures; clarification made in introductio

Cuprates as doped U(1) spin liquids

We explore theoretically the notion that the underdoped cuprates may be viewed as doped U(1) spin liquid Mott insulators. We pursue a conceptually clear version of this idea that naturally incorporates several aspects of the phenomenology of the cuprates. We argue that the low doping region may be fruitfully discussed in terms of the universal physics associated with a chemical potential tuned Mott transition between a U(1) spin liquid insulator and a d-wave superconductor. A precise characterization of the deconfinement in the U(1) spin liquid is provided by the emergence of a conserved gauge flux. This extra conservation law should hold at least approximately in the underdoped materials. Experiments that could possibly detect this conserved gauge flux are proposed.Comment: 11 pages, 7 figure

Overscreened Kondo fixed point in S=1 spin liquid

We propose a possible realization of the overscreened Kondo impurity problem by a magnetic s=1/2 impurity embedded in a two-dimensional S=1 U(1) spin liquid with a Fermi surface. This problem contains an interesting interplay between non-Fermi-liquid behavior induced by a U(1) gauge field coupled to fermions and a non-Fermi-liquid fixed point in the overscreened Kondo problem. Using a large-N expansion together with an expansion in the dynamical exponent of the gauge field, we find that the coupling to the gauge field leads to weak but observable changes in the physical properties of the system at the overscreened Kondo fixed point. We discuss the extrapolation of this result to a physical case and argue that the realization of overscreened Kondo physics could lead to observations of effects due to gauge fields.Comment: 10 pages, 5 figure