Chern Numbers, Localisation and the Bulk-edge Correspondence for Continuous Models of Topological Phases

In order to study continuous models of disordered topological phases, we construct an unbounded Kasparov module and a semifinite spectral triple for the crossed product of a separable $C^*$-algebra by a twisted $\mathbb{R}^d$-action. The spectral triple allows us to employ the non-unital local index formula to obtain the higher Chern numbers in the continuous setting with complex observable algebra. In addition, the pairing can be extended to a larger algebra closely related to dynamical localisation, as in the tight-binding approximation. The Kasparov module allows us to exploit the Wiener-Hopf extension and the Kasparov product to obtain a bulk-boundary correspondence for continuous models of disordered topological phases.Comment: 46 pages. V2: results on localisation expanded and clarified. V3: Further revisions. V4: To appear in Mathematical Physics, Analysis and Geometr

The Flag Of My Country

https://digitalcommons.library.umaine.edu/mmb-vp/5396/thumbnail.jp

Applicability of the carbon-dating method of analysis to soil humus studies

Includes bibliographical references.The organic fraction of soil is known to be composed of the soil biomass, partially decomposed plant and animal residues, and the materials commonly referred to as humic substances. Knowledge of the persistence of these fractions in soil is vital to the understanding of their contribution to soil fertility and soil genesis. Much information concerning the biochemistry of the humus materials also could be obtained through a knowledge of the mean residence times of the various organic fractions.This is a non-final version of an article published in final form in Soil Science 104, no. 3 (September 1987): 217-224. Publisher version: http://journals.lww.com/soilsci/Citation/1967/09000/APPLICABILITY_OF_THE_CARBON_DATING_METHOD_OF.10.aspx

A novel technique to repair orbital roof defects: irradiated homologous cadaveric rib (Tutoplast ®) graft in a recurrent frontal sinus ossifying fibroma

Ossifying fibroma in the fronto-ethmoidal sinuses is a rare, benign condition. In symptomatic cases, surgical excision is often undertaken and bony defects may be repaired using alloplastic grafts. We present a novel method of repairing an orbital roof defect using irradiated homologous cadaveric rib (Tutoplast ®) graft, overlaid with a pericranial flap. The patient made an excellent recovery, concluding that it is a viable and safe option with lower morbidity

Almost-Commutative Geometries Beyond the Standard Model II: New Colours

We will present an extension of the standard model of particle physics in its almost-commutative formulation. This extension is guided by the minimal approach to almost-commutative geometries employed in [13], although the model presented here is not minimal itself. The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs model which consists of the standard model and two new fermions of opposite electro-magnetic charge which may possess a new colour like gauge group. As a new phenomenon, grand unification is no longer required by the spectral action.Comment: Revised version for publication in J.Phys.A with corrected Higgs masse

Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets

We will present a new extension of the standard model of particle physics in its almostcommutative formulation. This extension has as its basis the algebra of the standard model with four summands [11], and enlarges only the particle content by an arbitrary number of generations of left-right symmetric doublets which couple vectorially to the U(1)_YxSU(2)_w subgroup of the standard model. As in the model presented in [8], which introduced particles with a new colour, grand unification is no longer required by the spectral action. The new model may also possess a candidate for dark matter in the hundred TeV mass range with neutrino-like cross section

The Dixmier trace and asymptotics of zeta functions

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p \u3e 1 that the asymptotics of the zeta function determines an ideal strictly larger than Lp,∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions

The local index formula in noncommutative geometry revisited

In this review we discuss the local index formula in noncommutative geomety from the viewpoint of two new proofs are partly inspired by the approach of Higson especially that in but they differ in several fundamental aspedcts, in particular they apply to semifinite spectral triples for a *s-subalgebra A of a general semifinite von Neumann algebra. Our proofs are novel even in the setting of the original theorem and reduce the hypotheses of the theorem to those necessary for its statement. These proofs rely on the introduction of a function valued cocycle which is \u27almost\u27 a (b, B)-cocycle in the cyclic cohomology of A. They do not need the \u27discrete dimension spectrum\u27 assumption of jthe original Connes-Moscovici proof only a much weaker condition on the analytic continuation of certain zeta functions, and this only for part of the statement. In this article we also explain the relationship of the pairing between k-theory amd semifinite spectral triples to KK-theory and the Kasparov product. This discussion shows that simifinite spectral triples are a specific kind of representative of a K K-class and the analytically defined index is compatible with the Kasparov product

Self-burial of objects on sandy beds by scour: A synthesis of observations

Factors that influence equilibrium, scour-induced burial depth (B) in sand relative to object diameter (D) are examined through analysis of over 750 observations. The main factors that increase scour-induced B/D under steady currents without waves are found to be an increased Shields parameter () and small D (< 3 cm), with separate power laws applicable to clear-water and live-bed conditions. For larger D, greater cylinder density also increases B/D under steady currents. The main factor that increases scour-induced B/D under wave-dominated conditions is an increased Keulegan-Carpenter number. B/D additionally increases as the mean current component parallel to wave orbitals decreases. For cylinders under waves, B/D also increases as increases and as the angle between wave orbitals and a cylinder’s axis increases. All else being equal, tapered cylinders bury most, followed by cylinders, then spheres, and conical frustums bury least. Parameterized models dependent on the above variables explain 85% of observed variance in B/D

Modification of graphene anode morphologies via wet and dry milling

Graphene, an individual graphite monolayer, is being considered for use in lithium ion anodes as there is a technological drive to make batteries thinner, lighter and more flexible whilst maintaining or increasing cell capacity and cyclability. Due to its mono/few-layer platelet structure graphene may potentially be affected by mechanical processing routes. Here the effects that dry milling and wet milling have on graphene nanoplatelets and graphene anode solutions have been investigated. It was found that dry milling for 15 minutes causes graphene nanoplatelets to form agglomerated graphite, but that wet milling of graphene anode solution results in reduced porosity and smoother electrodes without visibly destroying the nanoplatelets