Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Measuring the effective complexity of cosmological models

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.Comment: 9 pages, 4 figures, revised version accepted for publication in PRD, updated with WMAP3 result

Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps

We develop a Melnikov method for volume-preserving maps with codimension one invariant manifolds. The Melnikov function is shown to be related to the flux of the perturbation through the unperturbed invariant surface. As an example, we compute the Melnikov function for a perturbation of a three-dimensional map that has a heteroclinic connection between a pair of invariant circles. The intersection curves of the manifolds are shown to undergo bifurcations in homologyComment: LaTex with 10 eps figure

Quantum affine Toda solitons

We review some of the progress in affine Toda field theories in recent years, explain why known dualities cannot easily be extended, and make some suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision

Decoherence can be useful in quantum walks

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.Comment: (Imperial College London) 6 (+epsilon) pages, 6 embedded eps figures, RevTex4. v2 minor changes to correct typos and refs, submitted version. v3 expanded into article format, extra figure, updated refs, Note on "glued trees" adde

Depolarization regions of nonzero volume in bianisotropic homogenized composites

In conventional approaches to the homogenization of random particulate composites, the component phase particles are often treated mathematically as vanishingly small, point-like entities. The electromagnetic responses of these component phase particles are provided by depolarization dyadics which derive from the singularity of the corresponding dyadic Green functions. Through neglecting the spatial extent of the depolarization region, important information may be lost, particularly relating to coherent scattering losses. We present an extension to the strong-property-fluctuation theory in which depolarization regions of nonzero volume and ellipsoidal geometry are accommodated. Therein, both the size and spatial distribution of the component phase particles are taken into account. The analysis is developed within the most general linear setting of bianisotropic homogenized composite mediums (HCMs). Numerical studies of the constitutive parameters are presented for representative examples of HCM; both Lorentz-reciprocal and Lorentz-nonreciprocal HCMs are considered. These studies reveal that estimates of the HCM constitutive parameters in relation to volume fraction, particle eccentricity, particle orientation and correlation length are all significantly influenced by the size of the component phase particles

Ancient Egypt 1921 Part 2

Part 2 of the 1921 Ancient Egypt books. Contents include the British school in Egypt, origins of some signs, borders of lotus and grapes, the head of a barbarian, the transmission of history, and a cartouche of Augustus.https://knowledge.e.southern.edu/kweeks_coll/1015/thumbnail.jp

The LuckyCam Survey for Very Low Mass Binaries II: 13 new M4.5-M6.0 Binaries

We present results from a high-angular-resolution survey of 78 very low mass (VLM) binary systems with 6.0 = 0.15 arcsec/yr. 21 VLM binaries were detected, 13 of them new discoveries. The new binary systems range in separation between 0.18 arcsec and 1.3 arcsec. The distance-corrected binary fraction is 13.5% (+6.5%/-4%), in agreement with previous results. 9 of the new binary systems have orbital radii > 10 AU, including a new wide VLM binary with 27 AU projected orbital separation. One of the new systems forms two components of a 2300 AU separation triple system. We find that the orbital radius distribution of the binaries with V-K < 6.5 in this survey appears to be different from that of redder (lower-mass) objects, suggesting a possible rapid change in the orbital radius distribution at around the M5 spectral type. The target sample was also selected to investigate X-ray activity among VLM binaries. There is no detectable correlation between excess X-Ray emission and the frequency and binary properties of the VLM systems.Comment: 11 pages, 8 figures. Submitted to MNRA

Ancient Egypt 1920 Part 1

Part 1 of the 1920 Ancient Egypt books. Contents include the return to research, Nile boats, the treasure of Antinoe, a mace head of Hierakonpolis, and an early portrait.https://knowledge.e.southern.edu/kweeks_coll/1010/thumbnail.jp

Ancient Egypt 1920 Part 2

Part 2 of the 1920 Ancient Egypt books. Contents include a Mentuhetep statue, varnishes in Theban tombs, the kings of Ethiopia, and Nile boats (continued).https://knowledge.e.southern.edu/kweeks_coll/1011/thumbnail.jp