The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C*-algebras. In particular, our results apply to the largest class of simple C*-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C*-algebras. We also prove in passing that the Cuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for a large class of unital simple C*-algebras.Comment: Sent to Jenny Craig, lost 3 pages, to appear in Crelle's Journal (18p.

Drag Reduction by Polymers in Wall Bounded Turbulence

We address the mechanism of drag reduction by polymers in turbulent wall bounded flows. On the basis of the equations of fluid mechanics we present a quantitative derivation of the "maximum drag reduction (MDR) asymptote" which is the maximum drag reduction attained by polymers. Based on Newtonian information only we prove the existence of drag reduction, and with one experimental parameter we reach a quantitative agreement with the experimental measurements.Comment: 4 pages, 1 fig., included, PRL, submitte

Neck atonia with a focal stimulation-induced seizure arising from the SMA: pathophysiological considerations.

A 28-year-old patient with pharmacoresistant non-lesional right frontal epilepsy underwent extra-operative intracranial EEG recordings and electrical cortical stimulation (ECS) to map eloquent cortex. Right supplementary motor area (SMA) ECS induced a brief seizure with habitual symptoms involving neck tingling followed by asymmetric tonic posturing. An additional feature was neck atonia. During atonia and sensory aura, discharges were seen in the mesial frontal electrodes and precentral gyrus. Besides motor signs, atonia, although rare and not described in the neck muscles, and sensations have been reported with SMA stimulation. The mechanisms underlying neck atonia in seizures arising from the SMA can be explained by supplementary negative motor area (SNMA) - though this was not mapped in electrodes overlying the ictal onset zone in our patient - or primary sensorimotor cortex activation through rapid propagation. Given the broad spectrum of signs elicited by SMA stimulation and rapid spread of seizures arising from the SMA, caution should be taken to not diagnose these as non-epileptic, as had previously occurred in this patient

Stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum brane model

We calculate the vacuum expectation value of the stress-energy tensor for a quantised bulk scalar field in the Randall-Sundrum model, and discuss the consequences of its local behaviour for the self-consistency of the model. We find that, in general, the stress-energy tensor diverges in the vicinity of the branes. Our main conclusion is that the stress-energy tensor is sufficiently complicated that it has implications for the effective potential, or radion stabilisation, methods that have so far been used.Comment: 16 pages, 3 figures. Minor changes made and references added. To appear in Phys. Rev.

Pleistocene landscape evolution in the Avon valley, southern Britain: optical dating of terrace formation and Palaeolithic archaeology

This paper presents the first comprehensive Optically Stimulated Luminescence dating programme from a sequence of Pleistocene river terraces in the Avon valley (Wiltshire-Hampshire-Dorset), southern Britain. These results offer the most complete chronometric framework for Pleistocene landscape evolution and Palaeolithic occupation in the Avon valley, allowing for the first time: (1) an assessment of the timing of terrace formation and landscape evolution, (2) the dating of hominin presence in the area, and (3) an investigation of the relationship between terrace formation and Quaternary climatic change. Analysis of 25 samples collected from terraces 10 and 7 to 4 show that the middle Avon terraces formed in response to the main Pleistocene climatic oscillations (Marine Isotope Stage (MIS) 10, 8, 6) and that fluvial mechanisms changed through time, resulting in three different types of terrace architecture. The highest and oldest deposits are compound terraces deposited during the Early Pleistocene before the Mid Pleistocene Transition. The middle reach of the valley is characterised by well-developed strath terraces overlain with thick fluvial deposits, reflecting the greater degree of incision in response to the increased amplitude of climate cycles in the Middle Pleistocene. The youngest deposits in the confined modern floodplain represent cut-and-fill terraces deposited after MIS5e. The results indicate that the two main Palaeolithic sites in the area, Milford Hill and Woodgreen, date to between at least MIS 10 and 8 with a pre-MIS 10 human occupation at a third main site at Bemerton. This is significant because the sites date to a period previously associated with a decline in hominin presence in Britain. The dating of the Avon valley terrace sequence highlights the complex nature of terrace formation during the Pleistocene and the need to critically reassess the chronological understanding of these fluvial archives in southern Britain. This research demonstrates that with a detailed and multidisciplinary approach shifts in hominin landscape use can be discovered, providing new information on hominin behavioural change during the Pleistocene

One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes

Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the compactification and finite temperature, the renormalized physical parameters of the theory (mass and coupling constant) acquire thermal and topological contributions. In the case of one compactified spatial dimension at finite temperature, we find that the corrections to the mass are positive, but those to the coupling constant are negative. We discuss the possibility of triviality, i.e. that the renormalized coupling constant goes to zero at some temperature or at some radius of the compactified spatial dimension.Comment: 16 pages, plain LATE

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.Comment: 21 pages, 2 figures include