Density of monodromy actions on non-abelian cohomology

In this paper we study the monodromy action on the first Betti and de Rham non-abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski dense monodromy orbit. In particular we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.Comment: LaTeX2e, 48 pages, Version substantially revised for publication. A gap in the proof of the density for Lefschetz pencils is fixed. The case of hyperelliptic monodromy is also treated in detai

Embedded Eigenvalues and the Nonlinear Schrodinger Equation

A common challenge to proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues can inhibit the dispersive estimates key to proving stability. Following the work of Marzuola & Simpson, we prove the absence of embedded eigenvalues for a collection of nonlinear Schrodinger equations, including some one and three dimensional supercritical equations, and the three dimensional cubic-quintic equation. Our results also rule out nonzero eigenvalues within the spectral gap and, in 3D, endpoint resonances. The proof is computer assisted as it depends on the sign of certain inner products which do not readily admit analytic representations. Our source code is available for verification at http://www.math.toronto.edu/simpson/files/spec_prop_asad_simpson_code.zip.Comment: 29 pages, 27 figures: fixed a typo in an equation from the previous version, and added two equations to clarif

The cosmic evolution of radio-AGN feedback to z=1

This paper presents the first measurement of the radio luminosity function of 'jet-mode' (radiatively-inefficient) radio-AGN out to z=1, in order to investigate the cosmic evolution of radio-AGN feedback. Eight radio source samples are combined to produce a catalogue of 211 radio-loud AGN with 0.5<z<1.0, which are spectroscopically classified into jet-mode and radiative-mode (radiatively-efficient) AGN classes. Comparing with large samples of local radio-AGN from the Sloan Digital Sky Survey, the cosmic evolution of the radio luminosity function of each radio-AGN class is independently derived. Radiative-mode radio-AGN show an order of magnitude increase in space density out to z~1 at all luminosities, consistent with these AGN being fuelled by cold gas. In contrast, the space density of jet-mode radio-AGN decreases with increasing redshift at low radio luminosities (L_1.4 < 1e24 W/Hz) but increases at higher radio luminosities. Simple models are developed to explain the observed evolution. In the best-fitting models, the characteristic space density of jet-mode AGN declines with redshift in accordance with the declining space density of massive quiescent galaxies, which fuel them via cooling of gas in their hot haloes. A time delay of 1.5-2 Gyr may be present between the quenching of star formation and the onset of jet-mode radio-AGN activity. The behaviour at higher radio luminosities can be explained either by an increasing characteristic luminosity of jet-mode radio-AGN activity with redshift (roughly as (1+z) cubed) or if the jet-mode radio-AGN population also includes some contribution of cold-gas-fuelled sources seen at a time when their accretion rate was low. Higher redshifts measurements would distinguish between these possibilities.Comment: Accepted for publication in MNRA

The Oyster River Culvert Analysis Project

Studies have already detected intensification of precipitation events consistent with climate change projections. Communities may have a window of opportunity to prepare, but information sufficiently quantified and localized to support adaptation programs is sparse: published literature is typically characterized by general resilience building or regional vulnerability studies. The Fourth Assessment Report of the IPCC observed that adaptation can no longer be postponed pending the effective elimination of uncertainty. Methods must be developed that manage residual uncertainty, providing community leaders with decision-support information sufficient for implementing infrastructure adaptation programs. This study developed a local-scale and actionable protocol for maintaining historical risk levels for communities facing significant impacts from climate change and population growth. For a coastal watershed, the study assessed the capacity of the present stormwater infrastructure capacity for conveying expected peak flow resulting from climate change and population growth. The project transferred coupled-climate model projections to the culvert system, in a form understandable to planners, resource managers and decision-makers; applied standard civil engineering methods to reverse-engineer culverts to determine existing and required capacities; modeled the potential for LID methods to manage peak flow in lieu of, or combination with, drainage system upsizing; and estimated replacement costs using local and national construction cost data. The mid-21st century, most likely 25-year, 24-hour precipitation is estimated to be 35% greater than the TP-40 precipitation for the SRES A1b trajectory, and 64% greater than the TP-40 value for the SRES A1fi trajectory. 5% of culverts are already undersized for the TP-40 event to which they should have been designed. Under the most likely A1b trajectory, an additional 12% of culverts likely will be undersized, while under the most likely A1fi scenario, an additional 19% likely will be undersized. These conditions place people and property at greater risk than that historically acceptable from the TP-4025-year design storm. This risk level may be maintained by a long-term upgrade program, utilizing existing strategies to manage uncertainty and costs. At the upper-95% confidence limit for the A1fi 25-year event, 65% of culverts are adequately sized, and building the remaining 35%, and planned, culverts to thrice the cross-sectional area specified from TP-40 should provide adequate capacity through this event. Realizable LID methods can mitigate significant impacts from climate change and population growth, however effectiveness is limited for the more pessimistic climate change projections. Results indicate that uncertainty in coupled-climate model projections is not an impediment to adaptation. This study makes a significant contribution toward the generation of reliable and specific estimates of impacts from climate change, in support of programs to adapt civil infrastructures. This study promotes a solution to today\u27s arguably most significant challenge in civil infrastructure adaptation: translating the extensive corpus of adaptation theory and regional-scale impacts analyses into localscale action

Nuclear quadrupole resonances in compact vapor cells: the crossover from the NMR to the NQR interaction regimes

We present the first experimental study that maps the transformation of nuclear quadrupole resonances from the pure nuclear quadrupole regime to the quadrupole-perturbed Zeeman regime. The transformation presents an interesting quantum-mechanical problem, since the quantization axis changes from being aligned along the axis of the electric-field gradient tensor to being aligned along the magnetic field. We achieve large nuclear quadrupole shifts for I = 3/2 131-Xe by using a 1 mm^3 cubic cell with walls of different materials. When the magnetic and quadrupolar interactions are of comparable size, perturbation theory is not suitable for calculating the transition energies. Rather than use perturbation theory, we compare our data to theoretical calculations using a Liouvillian approach and find excellent agreement.Comment: 4 pages, 4 figure

Case management models and the care programme approach: how to make the CPA effective and credible.

The care programme approach (CPA), a form of case management, is a key mental health policy in England. Yet after over 10 years, it remains poorly and unevenly implemented with few benefits for service users, carers or mental health staff. This paper reviews the wider literature on case management and identifies and considers the principal models that might have informed the development of the CPA. After discussing the evidence for each of the clinical, strengths, intensive and assertive case management models, the paper identifies the key components that appear to be central to effective case management across these models. These components are then considered in relation to the CPA. It is argued that the CPA has been undermined by a failure to incorporate and build on certain important features of the major models of case management. The paper concludes by suggesting the key developments required to make the CPA more effective and to underpin the policy with a unifying philosophy while endorsing it with much needed credibility among both clinicians and service users