Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC's), in which all future-directed CTC's traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in $L_2$ on {\cI}^{-}, we prove existence of smooth solutions which are regular at null and spatial infinity (have finite energy and finite $L_2$-norm) and have the given initial data on \cI^-. A restricted uniqueness theorem is obtained, applying to solutions that fall off in time at any fixed spatial position. For a complementary class of spacetimes in which CTC's are confined to a compact region, we show that when solutions exist they are unique in regions exterior to the CTC's. (We believe that more stringent uniqueness theorems hold, and that the present limitations are our own.) An extension of these results to Maxwell fields and massless spinor fields is sketched. Finally, we discuss a conjecture that the Cauchy problem for free fields is well defined in the presence of CTC's whenever the problem is well-posed in the geometric-optics limit. We provide some evidence in support of this conjecture, and we present counterexamples that show that neither existence nor uniqueness is guaranteed under weaker conditions. In particular, both existence and uniqueness can fail in smooth, asymptotically flat spacetimes with a compact nonchronal region.Comment: 47 pages, Revtex, 7 figures (available upon request

The Near-Infrared Broad Emission Line Region of Active Galactic Nuclei -- I. The Observations

We present high quality (high signal-to-noise ratio and moderate spectral resolution) near-infrared (near-IR) spectroscopic observations of 23 well-known broad-emission line active galactic nuclei (AGN). Additionally, we obtained simultaneous (within two months) optical spectroscopy of similar quality. The near-IR broad emission line spectrum of AGN is dominated by permitted transitions of hydrogen, helium, oxygen, and calcium, and by the rich spectrum of singly-ionized iron. In this paper we present the spectra, line identifications and measurements, and address briefly some of the important issues regarding the physics of AGN broad emission line regions. In particular, we investigate the excitation mechanism of neutral oxygen and confront for the first time theoretical predictions of the near-IR iron emission spectrum with observations.Comment: 45 pages, 17 figures, accepted by ApJ

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Preferences for Prenatal Tests for Cystic Fibrosis: A Discrete Choice Experiment to Compare the Views of Adult Patients, Carriers of Cystic Fibrosis and Health Professionals

As new technologies enable the development of non-invasive prenatal diagnosis (NIPD) for cystic fibrosis (CF), research examining stakeholder views is essential for the preparation of implementation strategies. Here, we compare the views of potential service users with those of health professionals who provide counselling for prenatal tests. A questionnaire incorporating a discrete choice experiment examined preferences for key attributes of NIPD and explored views on NIPD for CF. Adult patients (n = 92) and carriers of CF (n = 50) were recruited from one children’s and one adult NHS specialist CF centre. Health professionals (n = 70) were recruited via an e-mail invitation to relevant professional bodies. The key attribute affecting service user testing preferences was no miscarriage risk, while for health professionals, accuracy and early testing were important. The uptake of NIPD by service users was predicted to be high and includes couples that would currently decline invasive testing. Many service users (47%) and health professionals (55.2%) thought the availability of NIPD for CF would increase the pressure to undergo prenatal testing. Most service users (68.5%) thought NIPD for CF should be offered to all pregnant women, whereas more health professionals (68.2%) thought NIPD should be reserved for known carrier couples. The implications for clinical practice are discussed

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Minimal-resource computer program for automatic generation of ocean wave ray or crest diagrams in shoaling waters

A computer program for studying linear ocean wave refraction is described. The program features random-access modular bathymetry data storage. Three bottom topography approximation techniques are available in the program which provide varying degrees of bathymetry data smoothing. Refraction diagrams are generated automatically and can be displayed graphically in three forms: Ray patterns with specified uniform deepwater ray density, ray patterns with controlled nearshore ray density, or crest patterns constructed by using a cubic polynomial to approximate crest segments between adjacent rays

Survival with Treated and Well-Controlled Blood Pressure: Findings from a Prospective Cohort Study.

AIM: To compare survival and incident cardiovascular disease between normotensive, untreated hypertensive, treated and poorly-controlled hypertensive and treated and well-controlled hypertensive adults. METHODS AND RESULTS: Data from the British Regional Heart Study (men) and British Women's Heart and Health Study (women) were used (N = 6476). Blood pressure and treatment were assessed at baseline (1998-2001) when participants were aged 60-79 years and participants were followed up for a median of 8 years. Date and cause of death were obtained from death certificates and non-fatal cardiovascular disease events were obtained from repeat detailed medical record reviews. Of the whole cohort 52% of women and 49% of men had untreated hypertension and a further 22% and 18%, respectively, had poorly treated hypertension. Just 3% of women and 4% of men had treated and well controlled hypertension and 23% and 29%, respectively, were normotensive. Compared to normotensive individuals, incident cardiovascular disease (fatal and non-fatal) was increased in those with poorly-controlled hypertension (Hazard Ratio (HR): 1.88; 95%CI: 1.53, 2.30), those with untreated hypertension (HR 1.46; 95%CI 1.22, 1.75) and those who were well-controlled hypertension (HR 1.38; 95%CI 0.94, 2.03). Adjustment for baseline differences in mean blood pressure between the groups resulted in attenuation of the increased risk in the poorly-controlled (1.52 (1.18, 1.97) and untreated groups (1.21 (0.97, 1.52), but did not change the association in the well-controlled group. All-cause mortality was also increased in all three hypertension groups but estimates were imprecise with wide confidence intervals. CONCLUSIONS: Half of women and men aged 60-79 in Britain had untreated hypertension and only a very small proportion of those with diagnosed and treated hypertension were well controlled. Those with hypertension, irrespective of whether this was treated and controlled or not, were at greater risk of future cardiovascular disease than those who are normotensive

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca