Pattern formation in annular convection

This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold tropopause, modeled by the two dimensional Boussinesq equations. The second is annular electroconvection in a thin semetic film, where experiments reveal the birth of convection-like vortices in the plane as the electric field intensity is increased. This is modeled by two dimensional Navier-Stokes equations coupled with a simplified version of Maxwell's equations. The two models share fundamental mathematical properties and satisfy the prerequisites for application of O(2)-equivariant bifurcation theory. We show this can give predictions of interesting dynamics, including stationary and spatio-temporal patterns

Transience of Simple Random Walks With Linear Entropy Growth

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at a vertex $x_0$, if the entropy after $n$ steps, $E_n$ is at least $Cn$ where the $C$ is independent of $x_0$, then the random walk is transient. We also give an example which demonstrates that the condition of $C$ being independent of $x_0$ is necessary.Comment: 8 pages, 1 figur

Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS).Comment: 37 pages, 2 figures, 5 tables; notation revised and clarified, some sections (particularly 4.3 and 5) made more rigorous, some derivations moved into the appendix, typos fixed, some wording change

Individual Nurse Productivity in Preparing Patients for Discharge Is Associated with Patient Likelihood of 30-Day Return to Hospital

Objective: Applied to value-based health care, the economic term “individual productivity” refers to the quality of an outcome attributable through a care process to an individual clinician. This study aimed to (1) estimate and describe the discharge preparation productivities of individual acute care nurses and (2) examine the association between the discharge preparation productivity of the discharging nurse and the patient’s likelihood of a 30-day return to hospital [readmission and emergency department (ED) visits]. Research Design: Secondary analysis of patient-nurse data from a cluster-randomized multisite study of patient discharge readiness and readmission. Patients reported discharge readiness scores; postdischarge outcomes and other variables were extracted from electronic health records. Using the structure-process-outcomes model, we viewed patient readiness for hospital discharge as a proximal outcome of the discharge preparation process and used it to measure nurse productivity in discharge preparation. We viewed hospital return as a distal outcome sensitive to discharge preparation care. Multilevel regression analyses used a split-sample approach and adjusted for patient characteristics. Subjects: A total 522 nurses and 29,986 adult (18+ y) patients discharged to home from 31 geographically diverse medical-surgical units between June 15, 2015 and November 30, 2016. Measures: Patient discharge readiness was measured using the 8-item short form of Readiness for Hospital Discharge Scale (RHDS). A 30-day hospital return was a categorical variable for an inpatient readmission or an ED visit, versus no hospital return. Results: Variability in individual nurse productivity explained 9.07% of variance in patient discharge readiness scores. Nurse productivity was negatively associated with the likelihood of a readmission (−0.48 absolute percentage points, P\u3c0.001) and an ED visit (−0.29 absolute percentage points, P=0.042). Conclusions: Variability in individual clinician productivity can have implications for acute care quality patient outcomes

Chief Justice James Prendergast and the administration of New Zealand colonial justice, 1862-1899

The New Zealand legal system during the nineteenth-century was in a state of rapid change and constant turmoil. After the signing of the Treaty of Waitangi between Maori and the British Crown in 1840, British immigration to New Zealand began in earnest. As a British colony, New Zealand gradually acquired the British legal system and adapted it to suit the colonial environment. These adaptations resulted in conflict with Maori and eventually the supremacy of British law in New Zealand. This thesis explores the role of James Prendergast in helping to create the colonial New Zealand legal system. Prendergast served as Attorney-General of New Zealand from 1865 to 1875 and Chief Justice of New Zealand from 1875 to 1899. Firstly, the English background of Prendergast is analysed and provided as a context for his actions in New Zealand. Then, Prendergast’s rise to power in New Zealand is explored, focusing primarily on his roles as Attorney-General and Chief Justice. Particular attention is paid to Prendergast’s relationship with Maori, his enduring legacy in New Zealand statute and case law and the relationship between English law and the colonial New Zealand legal system. The recent vilification of Prendergast by modern scholars is detailed, especially in relation to Prendergast’s decision in the case, Wi Parata v Bishop of Wellington (1877). Finally, an assessment is made of Prendergast’s life, legacy and influence in New Zealand legal history. Several important conclusions are reached through the study of the life of James Prendergast. Through his words, actions and judgments, Prendergast played a highly influential role in the development of the New Zealand legal system. Prendergast is more than just the two-dimensional figure that he has become in modern scholarship. Many of Prendergast’s actions that were considered successful by contemporary colonial society are also the actions for which Prendergast is now criticised by modern New Zealand society. A clash has occurred between the standards of the past and the views of the present. This thesis also proffers the argument that the English legal system was of overwhelming importance in the development of the New Zealand legal system and the administration of colonial justice. The central problem in adapting the English system to the New Zealand environment was the inflexibility of the law in the face of indigenous people’s rights. Prendergast was a product of Victorian England and failed to come to terms with Maori society. While he was a competent judge who left a legacy of common law precedent, Prendergast’s main success was as an administrator and leader of the colonial legal environment. While the Wi Parata decision of 1877 was legally dubious, it is misleading to judge Prendergast's career solely by this one decision. James Prendergast is a pivotal figure in the study of nineteenth-century New Zealand legal history. He has left a legacy of legal precedent and jurisprudential controversy. This judicial biography provides an account of his successes and failures throughout his long and eventful life

The Practice and Potential of Renewable Energy Localisation: Results from a UK Field Trial

open access articleThe adaptation of electricity demand to match the non-despatchable nature of renewable generation is one of the key challenges of the energy transition. We describe a UK field trial in 48 homes of an approach to this problem aimed at directly matching local supply and demand. This combined a community-based business model with social engagement and demand response technology employing both thermal and electrical energy storage. A proportion of these homes (14) were equipped with rooftop photovoltaics (PV) amounting to a total of 45 kWp; the business model enabled the remaining 34 homes to consume the electricity exported from the PV-equipped dwellings at a favourably low tariff in the context of a time-of-day tariff scheme. We report on the useful financial return achieved by all participants, their overall experience of the trial, and the proportion of local generation consumed locally. The energy storage devices were controlled, with user oversight, to respond automatically to signals indicating the availability of low cost electricity either from the photovoltaics or the time of day grid tariff. A substantial response was observed in the resulting demand profile from these controls, less so from demand scheduling methods which required regular user configuration. Finally results are reported from a follow-up fully commercial implementation of the concept showing the viability of the business model. We conclude that the sustainability of the transition to renewable energy can be strengthened with a community-oriented approach as demonstrated in the trial that supports users through technological change and improves return on investment by matching local generation and consumption

Three Essays in Health Economics

State governments play a major role in the United States health care market. Moreover, states administer much of the regulation, budgeting, and policy for their own markets, which creates idiosyncratic differences across states. This dissertation contributes to the literature by evaluating those differences to analyze the effectiveness of certain regulations and policies and to explore the relationship between state health care markets and other state obligations. The first chapter uses state differences in the nurse practitioner (NP) market to evaluate the effects of state laws allowing NPs to prescribe controlled substances on prescription opioid use. I study these effects by merging nationwide data from the Medical Expenditure Panel Survey (MEPS) over 18 years (1996-2013) with data on state laws. I then exploit variation in these laws over time to create a quasi-natural experiment and to estimate the causal impact of NP deregulation on prescription opioid use. I find, relative to patients living in more restrictive states, that patients who live in states with more flexible NP laws emph{reduce} their prescription opioid use by 7 percent to 9 percent. I also find that health outcomes either slightly improve or remain unaffected by the enactment of these laws. Taken together, these results indicate that NP deregulation slows the trend in prescription opioid growth while potentially improving patient outcomes. Furthermore, suggestive evidence implies that these effects may be even larger for the least restrictive states, opening the door for future reforms. The second chapter (co-authored with Andrew Litten) seeks to identify the causal relationship between increased state Medicaid obligations and higher education spending. After several decades of federal mandates and high rates of health cost inflation, Medicaid spending has taken an increasingly larger share of state budgets, forcing states to make offsetting cuts elsewhere. We argue that state governments are likely to cut higher education in response to these changes, as institutions of higher education have the capacity to find additional revenues elsewhere. We use federally administered Supplemental Security Income (SSI) enrollments to instrument for state Medicaid spending. We find that a one dollar increase in Medicaid costs leads to a decrease in higher education subsidies of 20 cents to 37 cents. Our approach provides estimates which are both more credible and more precise than those which have previously been used in the literature. The third chapter studies the effectiveness of Prescription Drug Monitoring Programs (PDMPs). These programs are widely considered to be a promising tool for preventing prescription opioid misuse. Using a nationally representative sample that spans the majority of PDMP implementation, I find little evidence that PDMP implementation is effective in preventing prescription opioid misuse. Nonetheless, I find that when states pair PDMPs with policies mandating health care provider use ("must access" laws), they can successfully reduce high-volume opioid prescriptions. States that add "must access" laws reduce high-volume prescriptions by about 20 percent. In addition, these states do not appear to affect overall prescribing behavior, suggesting that PDMPs with "must access" laws can target potential misuse without hindering medically appropriate access.PHDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138556/1/hamiltmr_1.pd

Making Legacy Thermal Storage Heating fit for the Smart Grid

Collaborative paper with Oxford University Environmental Change Institute and Energy Local Ltd. The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Thermal storage heaters, charged using overnight off-peak electricity, have been used for domestic space heating in the UK and other countries since the 1980s. However, they have always been difficult for consumers to manage efficiently and, with the advent of a high proportion of renewables in the electricity generation mix, the time of day when they are charged needs to be more flexible. There is also a need to reduce peaks in the demand profile to allow distribution networks to support new sources of demand such as electric vehicles. We describe a trial of a smart control system that was retrofitted to a group of six dwellings with this form of heating, with the objectives of providing more convenient and efficient control for the users while varying the times at which charging is performed, to flatten the profile of demand and make use of locally-generated renewable electricity. The trial also employs a commercially-realistic combination of a static time-of-day tariff with a real time tariff dependent on local generation, to provide consumers with the opportunity and incentive to reduce their costs by varying times of use of appliances. Results from operation over the 2015-16 heating season indicate that the objectives are largely achieved. It is estimated that on an annualised and weather-adjusted basis most of the users have consumed less electricity than before intervention and their costs are less on the trial tariffs. Critical factors for success of this form of system are identified, particularly the need to facilitate hands-on control of heating by thrifty users and the importance of an effective and sustained user engagement programme when introducing the technology, to ensure users gain confidence through a readily-accessible source of support and advice

Toward an Empirical Theory of Pulsar Emission. IX. On the Peculiar Properties and Geometric Regularity of Lyne & Manchester's "Partial Cone" Pulsars

Lyne & Manchester (1988) identified a group of some 50 pulsars they called "partial cones" which they found difficult to classify and interpret. They were notable for their asymmetric average profiles and asymmetric polarization position-angle (PPA) traverses, wherein the steepest gradient (SG) point fell toward one edge of the total intensity profile. Over the last two decades, this population of pulsars has raised cautions regarding the core/cone model of the radio pulsar-emission beam which implies a high degree of order, symmetry and geometric regularity. In this paper we reinvestigate this population "partial cone" pulsars on the basis of new single pulse polarimetric observations of 39 of them, observed with the Giant Meterwave Radio Telescope in India and the Arecibo Observatory in Puerto Rico. These highly sensitive observations help us to establish that most of these "partial cones" exhibit a core/cone structure just as did the "normal" pulsars studied in the earlier papers of this series. In short, we find that many of these "partial cones" are partial in the sense that the emission above different areas of their polar caps can be (highly) asymmetric. However, when studied closely we find that their emission geometries are overall identical to core/double cone structure encountered earlier-that is, with specific conal dimensions scaling as the polar cap size.Comment: Accepted for publication in ApJ, 42 pages with 45 figures, notes to table 2 and 3 are in the beginning of the appendix sectio

Photocatalytic air-purification: A low-cost, real-time gas detection method

This research demonstrates the use of a gas detector as a feasible alternative to the standardized analytical methods typically found in photocatalytic air-purification ISO standard tests and academic literature. A methyl mercaptan detector is calibrated and validated (for linearity) using a standard gas generator. The detector can be directly connected to the photoreactor exit allowing real-time span gas measurement with data-logging at one minute intervals. The detector successfully differentiated samples with different photocatalytic performance. The use of such detectors offers an easy-to-use, low-cost alternative to gas measurement with applications in academic research, proof-of-concept photocatalytic tests and also as an educational tool