Topological Transitions in Metamaterials

The ideas of mathematical topology play an important role in many aspects of modern physics - from phase transitions to field theory to nonlinear dynamics (Nakahara M (2003) in Geometry, Topology and Physics, ed Brewer DF (IOP Publishing Ltd, Bristol and Philadelphia), Monastryskiy M (1987) in Riemann Topology and Physics, (Birkhauser Verlag AG)). An important example of this is the Lifshitz transition (Lifshitz IM (1960) Anomalies of electron characteristics of a metal in the high-pressure region, Sov Phys JETP 11: 1130-1135), where the transformation of the Fermi surface of a metal from a closed to an open geometry (due to e.g. external pressure) leads to a dramatic effect on the electron magneto-transport (Kosevich AM (2004) Topology and solid-state physics. Low Temp Phys 30: 97-118). Here, we present the optical equivalent of the Lifshitz transition in strongly anisotropic metamaterials. When one of the components of the dielectric permittivity tensor of such a composite changes sign, the corresponding iso-frequency surface transforms from an ellipsoid to a hyperboloid. Since the photonic density of states can be related to the volume enclosed by the iso-frequency surface, such a topological transition in a metamaterial leads to a dramatic change in the photonic density of states, with a resulting effect on every single physical parameter related to the metamaterial - from thermodynamic quantities such as its equilibrium electromagnetic energy to the nonlinear optical response to quantum-electrodynamic effects such as spontaneous emission. In the present paper, we demonstrate the modification of spontaneous light emission from quantum dots placed near the surface of the metamaterial undergoing the topological Lifshitz transition, and present the theoretical description of the effect

Deformation Energy Minima at Finite Mass Asymmetry

A very general saddle point nuclear shape may be found as a solution of an integro-differential equation without giving apriori any shape parametrization. By introducing phenomenological shell corrections one obtains minima of deformation energy for binary fission of parent nuclei at a finite (non-zero) mass asymmetry. Results are presented for reflection asymmetric saddle point shapes of thorium and uranium even-mass isotopes with A=226-238 and A=230-238 respectively.Comment: 5 pages, 2 Postscript figures, REVTeX, Version 4.

Similarity classes of 3x3 matrices over a local principal ideal ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr

Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies

Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight vectors are represented in terms of Schur's $Q$-functions. The method to get the polynomial solutions to the reduced BKP hierarchies is shown to be equivalent to a certain rule in Maya game.Comment: January 1994, 11 page

Individual and Multi Vortex Pinning in Systems with Periodic Pinning Arrays

We examine multi and individual vortex pinning in thin superconductors with periodic pinning arrays. For multi-vortex pinning we observe peaks in the critical current of equal magnitude at every matching field, while for individual vortex pinning we observe a sharp drop in the critical current after the first matching field in agreement with experiments. We examine the scaling of the critical current at commensurate and incommensurate fields for varied pinning strength and show that the depinning force at incommensurate fields decreases faster than at the commensurate fields.Comment: 4 figuure

Nucleosynthesis in Massive Stars With Improved Nuclear and Stellar Physics

We present the first calculations to follow the evolution of all stable nuclei and their radioactive progenitors in stellar models computed from the onset of central hydrogen burning through explosion as Type II supernovae. Calculations are performed for Pop I stars of 15, 19, 20, 21, and 25 M_sun using the most recently available experimental and theoretical nuclear data, revised opacity tables, neutrino losses, and weak interaction rates, and taking into account mass loss due to stellar winds. A novel ``adaptive'' reaction network is employed with a variable number of nuclei (adjusted each time step) ranging from about 700 on the main sequence to more than 2200 during the explosion. The network includes, at any given time, all relevant isotopes from hydrogen through polonium (Z=84). Even the limited grid of stellar masses studied suggests that overall good agreement can be achieved with the solar abundances of nuclei between 16O and 90Zr. Interesting discrepancies are seen in the 20 M_sun model and, so far, only in that model, that are a consequence of the merging of the oxygen, neon, and carbon shells about a day prior to core collapse. We find that, in some stars, most of the ``p-process'' nuclei can be produced in the convective oxygen burning shell moments prior to collapse; in others, they are made only in the explosion. Serious deficiencies still exist in all cases for the p-process isotopes of Ru and Mo.Comment: 53 pages, 17 color figures (3 as separate GIF images), slightly extended discussion and references, accepted by Ap

ZOBOV: a parameter-free void-finding algorithm

ZOBOV (ZOnes Bordering On Voidness) is an algorithm that finds density depressions in a set of points, without any free parameters, or assumptions about shape. It uses the Voronoi tessellation to estimate densities, which it uses to find both voids and subvoids. It also measures probabilities that each void or subvoid arises from Poisson fluctuations. This paper describes the ZOBOV algorithm, and the results from its application to the dark-matter particles in a region of the Millennium Simulation. Additionally, the paper points out an interesting high-density peak in the probability distribution of dark-matter particle densities.Comment: 10 pages, 8 figures, MNRAS, accepted. Added explanatory figures, and better edge-detection methods. ZOBOV code available at http://www.ifa.hawaii.edu/~neyrinck/vobo

Large-Scale Power Spectrum and Structures from the ENEAR Galaxy Peculiar Velocity Catalogue

We estimate the mass density fluctuations power spectrum (PS) on large scales by applying a maximum likelihood technique to the peculiar velocity data of the recently completed redshift—distance survey of early-type galaxies (hereafter ENEAR). Parametric cold dark matter (CDM)-like models for the PS are assumed, and the best-fitting parameters are determined by maximizing the probability of the model given the measured peculiar velocities of the galaxies, their distances and estimated errors. The method has been applied to CDM models with and without COBE normalization. The general results are in agreement with the high-amplitude power spectra found from similar analyses of other independent all-sky catalogue of peculiar velocity data such as MARK III and SFI, in spite of the differences in the way these samples were selected, the fact that they probe different regions of space and galaxy distances are computed using different distance relations. For example, at k = 0.1 h Mpc−1 the power spectrum value is P(k)Ω1.2 = (6.5 ± 3) × 103(h−1 Mpc)3 and η8 ≡ σ8Ω0.6 = 1.1−0.35+0.2; the quoted uncertainties refer to 3σ error level. We also find that, for ΛCDM and OCDM COBE-normalized models, the best-fitting parameters are confined by a contour approximately defined by Ω h1.3 = 0.377 ± 0.08 and Ω h0.88 = 0.517±0.083 respectively. Γ-shape models, free of COBE normalization, result in the weak constraint of Γ≥0.17 and in the rather stringent constraint of η8 = 1.0 ± 0.25. All quoted uncertainties refer to 3σ confidence level (c.l.). The calculated PS has been used as a prior for Wiener reconstruction of the density field at different resolutions and the three-dimensional velocity field within a volume of radius ≈80 h−1 Mpc. All major structures in the nearby Universe are recovered and are well matched to those predicted from all-sky redshift surveys. The robustness of these features has been tested with constrained realizations (CR). Analysis of the reconstructed three-dimensional velocity field yields a small bulk-flow amplitude (∼160±60 km s−1 at 60 h−1 Mpc) and a very small rms value of the tidal field (∼60 km s−1). The results give further support to the picture that most of the motion of the Local Group arises from mass fluctuations within the volume considered