Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Ricci flows with bursts of unbounded curvature

Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling by a factor 1/2t ) to this hyperbolic metric [GT11], i.e. our Ricci flow geometrises the surface. In this paper we show that there exist complete, bounded curvature initial metrics, including those conformal to a hyperbolic metric, which have subsequent Ricci flows developing unbounded curvature at certain intermediate times. In particular, when coupled with the uniqueness from [Top13], we find that any complete Ricci flow starting with such initial metrics must develop unbounded curvature over some intermediate time interval, but that nevertheless, the curvature must later become bounded and the flow must achieve geometrisation as t → ∞, even though there are other conformal deformations to hyperbolic metrics that do not involve unbounded curvature. Another consequence of our constructions is that while our Ricci flow from [GT11] must agree initially with the classical flow of Hamilton and Shi in the special case that the initial surface is complete and of bounded curvature, by uniqueness, it is now clear that our flow lasts for a longer time interval in general, with Shi’s flow stopping when the curvature blows up, but our flow continuing strictly beyond in these situations. All our constructions of unbounded curvature developing and then disappearing are in two dimensions. Generalisations to higher dimensions are then immediate

Re-identification of c. 15 700 cal yr BP tephra bed at Kaipo Bog, eastern North Island: implications for dispersal of Rotorua and Puketarata tephra beds.

A 10 mm thick, c. 15 700 calendar yr BP (c. 13 100 14C yr BP) rhyolitic tephra bed in the well-studied montane Kaipo Bog sequence of eastern North Island was previously correlated with Maroa-derived Puketarata Tephra. We revise this correlation to Okataina-derived Rotorua Tephra based on new compositional data from biotite phenocrysts and glass. The new correlation limits the known dispersal of Puketarata Tephra (sensu stricto, c. 16 800 cal yr BP) and eliminates requirements to either reassess its age or to invoke dual Puketarata eruptive events. Our data show that Rotorua Tephra comprises two glass-shard types: an early-erupted low-K2O type that was dispersed mostly to the northwest, and a high-K2O type dispersed mostly to the south and southeast, contemporary with late-stage lava extrusion. Late-stage Rotorua eruptives contain biotite that is enriched in FeO compared with biotite from Puketarata pyroclastics. The occurrence of Rotorua Tephra in Kaipo Bog (100 km from the source) substantially extends its known distribution to the southeast. Our analyses demonstrate that unrecognised syn-eruption compositional and dispersal changes can cause errors in fingerprinting tephra deposits. However, the compositional complexity, once recognised, provides additional fingerprinting criteria, and also documents magmatic and dispersal processes

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Stratigraphy and chronology of a 15ka sequence of multi-sourced silicic tephras in a montane peat bog, eastern North Island, New Zealand.

We document the stratigraphy, composition, and chronology of a succession of 16 distal, silicic tephra layers interbedded with lateglacial and Holocene peats and muds up to c. 15 000 radiocarbon years (c. 18 000 calendar years) old at a montane site (Kaipo Bog) in eastern North Island, New Zealand. Aged from 665 +/- 15 to 14 700 +/- 95 14C yr BP, the tephras are derived from six volcanic centres in North Island, three of which are rhyolitic (Okataina, Taupo, Maroa), one peralkaline (Tuhua), and two andesitic (Tongariro, Egmont). Correlations are based on multiple criteria: field properties and stratigraphic interrelationships, ferromagnesian silicate mineral assemblages, glass-shard major element composition (from electron microprobe analysis), and radiocarbon dating. We extend the known distribution of tephras in eastern North Island and provide compositional data that add to their potential usefulness as isochronous markers. The chronostratigraphic framework established for the Kaipo sequence, based on both site-specific and independently derived tephra-based radiocarbon ages, provides the basis for fine-resolution paleoenvironmental studies at a climatically sensitive terrestrial site from the mid latitudes of the Southern Hemisphere. Tephras identified as especially useful paleoenvironmental markers include Rerewhakaaitu and Waiohau (lateglacial), Konini (lateglacial-early Holocene), Tuhua (middle Holocene), and Taupo and Kaharoa (late Holocene)

Harmonic maps from degenerating Riemann surfaces

We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity. We find conditions that are both necessary and sufficient for the compactness in $W^{1,2}$ and $C^{0}$ modulo bubbles of sequences of such maps.Comment: 27 page

Predicting the public health benefit of vaccinating cattle against Escherichia coli O157

Identifying the major sources of risk in disease transmission is key to designing effective controls. However, understanding of transmission dynamics across species boundaries is typically poor, making the design and evaluation of controls particularly challenging for zoonotic pathogens. One such global pathogen is Escherichia coli O157, which causes a serious and sometimes fatal gastrointestinal illness. Cattle are the main reservoir for E. coli O157, and vaccines for cattle now exist. However, adoption of vaccines is being delayed by conflicting responsibilities of veterinary and public health agencies, economic drivers, and because clinical trials cannot easily test interventions across species boundaries, lack of information on the public health benefits. Here, we examine transmission risk across the cattle–human species boundary and show three key results. First, supershedding of the pathogen by cattle is associated with the genetic marker stx2. Second, by quantifying the link between shedding density in cattle and human risk, we show that only the relatively rare supershedding events contribute significantly to human risk. Third, we show that this finding has profound consequences for the public health benefits of the cattle vaccine. A naïve evaluation based on efficacy in cattle would suggest a 50% reduction in risk; however, because the vaccine targets the major source of human risk, we predict a reduction in human cases of nearly 85%. By accounting for nonlinearities in transmission across the human–animal interface, we show that adoption of these vaccines by the livestock industry could prevent substantial numbers of human E. coli O157 cases

Ricci Flow Gravity

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar system the effects of Ricci flow gravity cannot be distinguished from Einstein gravity and therefore it passes all classical tests. However for cosmology significant deviations from standard Einstein cosmology will appear.Comment: 15 pages. V2: improved presentation, in particular Jordan vs. Brans-Dicke and on viability. Added section on physical interpretation. V3: more references. Reworked to agree with published versio

Controlling magnetic order and quantum disorder in molecule-based magnets.

We investigate the structural and magnetic properties of two molecule-based magnets synthesized from the same starting components. Their different structural motifs promote contrasting exchange pathways and consequently lead to markedly different magnetic ground states. Through examination of their structural and magnetic properties we show that [Cu(pyz)(H 2 O)(gly) 2 ](ClO 4 ) 2 may be considered a quasi-one-dimensional quantum Heisenberg antiferromagnet whereas the related compound [Cu(pyz)(gly)](ClO 4 ) , which is formed from dimers of antiferromagnetically interacting Cu 2+ spins, remains disordered down to at least 0.03 K in zero field but shows a field-temperature phase diagram reminiscent of that seen in materials showing a Bose-Einstein condensation of magnons