Structure of solutions of the Skyrme model on three-sphere. Numerical results

The hedgehog Skyrme model on three-sphere admits very rich spectrum of solitonic solutions which can be encompassed by a strikingly simple scheme. The main result of this paper is the statement of the tripartite structure of solutions of the model and the discovery in what configurations these solutions appear. The model contains features of more complicated models in General Relativity and as such can give insight into them.Comment: 20 pages, 13 figures in, with emai

Plasmonic Hot Spots in Triangular Tapered Graphene Microcrystals

Recently, plasmons in graphene have been observed experimentally using scattering scanning near-field optical microscopy. In this paper, we develop a simplified analytical approach to describe the behavior in triangular samples. Replacing Coulomb interaction by a short-range one reduces the problem to a Helmholtz equation, amenable to analytical treatment. We demonstrate that even with our simplifications, the system still exhibits the key features seen in the experiment.Comment: 4 pages, 3 figure

Results from the CASTLES Survey of Gravitational Lenses

We show that most gravitational lenses lie on the passively evolving fundamental plane for early-type galaxies. For burst star formation models (1 Gyr of star formation, then quiescence) in low Omega_0 cosmologies, the stellar populations of the lens galaxies must have formed at z_f > 2. Typical lens galaxies contain modest amounts of patchy extinction, with a median differential extinction for the optical (radio) selected lenses of E(B-V) = 0.04 (0.07) mag. The dust can be used to determine both extinction laws and lens redshifts. For example, the z_l=0.96 elliptical lens in MG0414+0534 has an R_V=1.7 +/- 0.1 mean extinction law. Arc and ring images of the quasar and AGN source host galaxies are commonly seen in NICMOS H band observations. The hosts are typically blue, L < L_* galaxies.Comment: 12 pages, 10 figures, from Proceedings of the 9th Annual Astrophysics Conference in Maryland, After the Dark Ages: When Galaxies Were Youn

Infrared nano-spectroscopy and imaging of collective superfluid excitations in conventional and high-temperature superconductors

We investigate near-field infrared spectroscopy and superfluid polariton imaging experiments on conventional and unconventional superconductors. Our modeling shows that near-field spectroscopy can measure the magnitude of the superconducting energy gap in Bardeen-Cooper-Schrieffer-like superconductors with nanoscale spatial resolution. We demonstrate how the same technique can measure the c-axis plasma frequency, and thus the c-axis superfluid density, of layered unconventional superconductors with a similar spatial resolution. Our modeling also shows that near-field techniques can image superfluid surface mode interference patterns near physical and electronic boundaries. We describe how these images can be used to extract the collective mode dispersion of anisotropic superconductors with sub-diffractional spatial resolution.Comment: 11 pages, 8 figure

Unicyclic Components in Random Graphs

The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a result, the total number of unicyclic components grows logarithmically with the system size.Comment: 4 pages, 2 figure