Visualizing the geometry of state space in plane Couette flow

Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a dynamical, 10^5-dimensional state-space representation of plane Couette flow at Re = 400 in a small, periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Reynolds number and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Reynolds turbulence. The invariant manifolds tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of continuous and discrete symmetry-induced heteroclinic connections.Comment: 32 pages, 13 figures submitted to Journal of Fluid Mechanic

Essays on Climatic Disruptions and Monetary Policy

This thesis consists of four research papers that examine the macroeconomic effects of climate change and the implications for the conduct and design of optimal monetary policy. The first paper (joint with Warwick McKibbin) examines alternative monetary regimes and evaluates the performance of the conventional inflation targeting framework from the standpoint of Australia. Specifically, the paper examines (i) how well each monetary regime can handle supply shocks; (ii) the challenges associated with the measurement and communication of target variables under alternative monetary regimes, particularly for indicators whose real-time measurements are subject to relatively larger errors in a climatically disrupted world; (iii) the forecastability of the target variables under each monetary regime; and (iv) the ability of the conventional inflation targeting regime to credibly anchor price expectations under conditions of persistent supply-side disruptions. The second and third papers build on the arguments from the first paper by revisiting the measurement and forecastability problems facing inflation-targeting central banks in a carbon-constrained and climatically disrupted macroeconomy. The second paper tests the hypothesis that the inclusion of climate effects in the estimation of potential output can improve real-time estimates of the output gap, with Australia as a case study. Using variations in temperature and precipitation 'anomalies' as proxies for climatic conditions over time, the paper employs an unobserved component model estimated by the data-driven Maximum Likelihood technique in the state-space context to derive climate-neutral measures of potential output and the output gaps. The results show that potential output and output gap measures that are adjusted for climatic disruptions are relatively more accurate in real time than those obtained from conventional approaches that do not take climate effects into consideration The third paper employs a Bayesian-estimated structural multivariate filtering model calibrated to data for Australia and the United States, innovatively incorporating climate hysteresis into the estimation of potential output and the output and unemployment gaps. The results suggest non-trivial implications for monetary policy in a climatically disrupted world, with different implications for inflation signals during the upturn or downturn of the business cycle. Specifically, macroeconomic slacks are smaller when both actual conditions and potential supply capacity are modelled to change simultaneously, with recessions that may be less disinflationary, and booms that may be less inflationary. The final paper, forthcoming in the Oxford Review of Economic Policy (joint with Warwick McKibbin, Adele Morris and Peter Wilcoxen) explores the interaction of climate change and monetary policy as they jointly influence macroeconomic outcomes, employing a general equilibrium model with full sectoral disaggregation of the energy generation sectors and strong global linkages in capital and trade. The results show that a central bank that targets the growth in nominal income outperforms one that is focused on flexibly balancing price and output stability goals in a carbon-constrained environment. Overall, the interaction between climate policy and monetary policy strongly suggests that the two policy frameworks should be jointly evaluated. Managing each regime separately can easily lead to policies that seem optimal in isolation, but that perform very poorly in practice

Therapy for Auditory Processing Impairment in Aphasia: An evaluation of two approaches

Purpose: This study evaluated two forms of discrimination therapy for auditory processing impairment in aphasia. It aimed to determine whether therapy can improve speech perception and/or help participants use semantic information to compensate for their impairment. Changes in listening were also explored by recording the level of facilitation needed during therapy tasks. Finally the study examined the effect of therapy on an everyday listening activity: a telephone message task. Method: The study employed a repeated measures design. Eight participants received 12 sessions each of phonological and semantic-phonological therapy. Both programmes used minimal pair judgement tasks, but the latter embedded such tasks within a meaningful context, so encouraged the strategic use of semantic information (semantic bootstrapping). Experimental measures of auditory discrimination and comprehension were administered twice before therapy, once after each programme, and again six weeks later. The telephone message task was also administered at each time point. Test data were subjected to both group and individual analyses. Records of progress during therapy (i.e changes in support needed to carry out therapy tasks) were completed during treatment and analysed across the group. Results: Group analyses showed no significant changes in tests of word and nonword discrimination as a result of therapy. One comprehension task improved following therapy, but two did not. There was also no indication that therapy improved the discrimination of treated words, as assessed by a priming task. The facilitation scores indicated that participants needed less support during tasks as therapy progressed, possibly as a result of improved listening. There was a significant effect of time on the telephone message task. Across all tasks there were few individual gains. Conclusions: The results offer little evidence that therapy improved participants’ discrimination or semantic bootstrapping skills. Some changes in listening may have occurred, as indicated by the facilitation scores. Reasons for the null findings are discussed

The stability of dense oceanic crust near the core‐mantle boundary

The large low‐shear‐velocity provinces (LLSVPs) are thought to be thermo‐chemical in nature, with recycled oceanic crust (OC) being a contender for the source of the chemical heterogeneity. The melting process which forms OC concentrates heat producing elements (HPEs) within it which, over time, may cause any collected piles of OC to destabilize, limiting their suitability to explain LLSVPs. Despite this, most geodynamic studies which include recycling of OC consider only homogeneous heating rates. We perform a suite of spherical, three‐dimensional mantle convection simulations to investigate how buoyancy number, geochemical model and heating model affects the ability of recycled OC to accumulate at the core‐mantle boundary. Our results agree with others that only a narrow range of buoyancy numbers allow OC to form piles in the lower mantle which remain stable to present day. We demonstrate that heterogeneous radiogenic heating causes piles to destabilize more readily, reducing present day CMB coverage from 63% to 47%. Consequently, the choice of geochemical model can influence pile formation. Geochemical models which lead to high internal heating rates can cause more rapid replenishment of piles, increasing their longevity. Where piles do remain to present day, first order comparisons suggest that old (hot) OC material can produce seismic characteristics, such as Vs anomalies, similar to those of LLSVPs. Given the range of current density estimates for lower mantle mineral phases, subducted OC remains a contender for the chemical component of thermo‐chemical LLSVPs

ESBL-producing Enterobacteriaceae in 24 neonatal units and associated networks in the south of England: no clustering of ESBL-producing Escherichia coli in units or networks.

OBJECTIVES: The objectives of this study were to characterize ESBL-producing Enterobacteriaceae present in 24 neonatal units (NNUs) in eight networks participating in a multicentre probiotic study and to test the hypothesis that specific strains would cluster within individual units and networks. METHODS: We performed analysis of stool samples for the presence of ESBL-producing Enterobacteriaceae at 2 weeks post-natal age and 36 weeks post-menstrual age. ESBL-producing Enterobacteriaceae were characterized and typed using molecular methods. RESULTS: ESBL-producing Enterobacteriaceae (n = 71) were isolated from 67/1229 (5.5%) infants from whom we received a sample at either sampling time or both sampling times, and from infants in 18 (75%) of the 24 recruiting NNUs. Thirty-three Escherichia coli, 23 Klebsiella spp. and 6 Enterobacter spp. strains were characterized. ESBL-producing E. coli were all distinguishable within individual NNUs by antibiotic resistance genotype, serogroup (O25b), phenotype, phylotype or ST. Ten of the 33 were ST131 and 9 of the 10 ST131 isolates were ciprofloxacin resistant. Seven of the 10 ST131 isolates carried genes encoding CTX-M group 1 enzymes. ST131 isolates were isolated from centres within five of the eight NNU networks. There were clusters of indistinguishable ESBL-producing Klebsiella and Enterobacter isolates associated with specific NNUs. CONCLUSIONS: Strains of E. coli ST131 were distributed across neonatal networks in the south of England. There was no evidence of clustering of clonally related ESBL-producing E. coli strains, by contrast with Klebsiella spp. and Enterobacter spp., which did cluster within units. The possibility that ESBL-producing E. coli strains are spread by vertical transmission requires further investigation