667 research outputs found

    Precision mass measurements for the astrophysical rp-process and electron cooling of trapped ions

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    Precision mass measurements of rare isotopes with decay half-lives far below one second are of importance to a variety of applications including studies of nuclear structure and nuclear astrophysics as well as tests of fundamental symmetries. The first part of this thesis discusses mass measurements of neutron-deficient gallium isotopes in direct vicinity of the proton drip line. The reported measurements of 60-63Ga were performed with the MR-TOF-MS of TRIUMF's Ion Trap for Atomic and Nuclear Science (TITAN) in Vancouver, Canada. The measurements mark the first direct mass determination of 60Ga and yield a 61Ga mass value three times more precise than the literature value from AME2020. Our 60Ga mass value constrains the location of the proton dripline in the gallium isotope chain and extends the experimentally evaluated IMME for isospin triplets up to A=60. The improved precision of the 61Ga mass has important implications for the astrophysical rapid proton capture process (rp-process). Calculations in a single-zone model demonstrate that the improved mass data substantially reduces uncertainties in the predicted light curves of Type I X-ray bursts. TITAN has demonstrated that charge breeding provides a powerful means to increase the precision and resolving power of Penning trap mass measurements of radioactive ions. However, the charge breeding process deteriorates the ion beam quality, thus mitigating the benefits associated with Penning trap mass spectrometry of highly charged ions (HCI). As a potential remedy for the beam quality loss, a cooler Penning trap has been developed in order to investigate the prospects of electron cooling the HCI prior to the mass measurement. The second part of this thesis reports exploratory studies of electron cooling of singly charged ions in this cooler Penning trap. Comparison of measured ion energy evolutions to a cooling model provides a detailed understanding of the underlying cooling dynamics. Extrapolation of the model enables the deduction of tentative estimates of the expected cooling times for radioactive HCI

    Bi-invariant types, reliably invariant types, and the comb tree property

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    We introduce and examine some special classes of invariant types\unicode{x2014}bi-invariant, strongly bi-invariant, extendibly invariant, and reliably invariant types\unicode{x2014}and show that they are related to certain model-theoretic tree properties. We show that the comb tree property (recently introduced by Mutchnik) is equivalent to the failure of Kim's lemma for bi-invariant types and is implied by the failure of Kim's lemma for reliably invariant types over invariance bases. We show that every type over an invariance base extends to a reliably invariant type\unicode{x2014}generalizing an unpublished result of Kruckman and Ramsey\unicode{x2014}and use this to show that, under a reasonable definition of Kim-dividing, Kim-forking coincides with Kim-dividing over invariance bases in theories without the comb tree property. Assuming a measurable cardinal, we characterize the comb tree property in terms of a form of dual local character. We also show that the antichain tree property (introduced by Ahn and Kim) seems to have a somewhat similar relationship to strong bi-invariance. In particular, we show that NATP theories satisfy Kim's lemma for strongly bi-invariant types and (assuming a measurable cardinal) satisfy a different form of dual local character. Furthermore, we examine a mutual generalization of the local character properties satisfied by NTP2_2 and NSOP1_1 theories and show that it is satisfied by all NATP theories. Finally, we give some related minor results\unicode{x2014}a strengthened local character characterization of NSOP1_1 and a characterization of coheirs in terms of invariant extensions in expansions\unicode{x2014}as well as a pathological example of Kim-dividing.Comment: 27 page

    Exploring barriers to green space use and how these differ by chronic health condition

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    Background: Using green space has been shown to improve health and wellbeing. However, use is unequal across many groups, such as those defined by age and income. Poor health is one of the most commonly reported barriers to green space use, despite individuals with poor health having the most potential benefit. Further research is required to understand the health-related barriers to green space use and how these differ by type of chronic condition, including physical and mental health conditions. The Covid-19 pandemic may have further exacerbated barriers to green space use and therefore requires further investigation to understand the influence of the novel restrictions/lockdowns on green space use. Aims: The thesis aims to explore how general barriers to use of green space, those specifically related to physical health, and those related to the Covid-19 pandemic, vary between people with different chronic health conditions and socio-demographic characteristics. Methods: Two nationally representative surveys were used to explore general and health related barriers to green space use: Natural England’s People and Nature Survey (PANS) and a new survey administered through YouGov. In PANS, data were collected between November 2020-March 2021 (N=10,415 English adults aged 16+), and the YouGov survey consisted of three survey waves in April 2020, November 2020, and April 2021 (N=6,713 UK adults aged 18+). A question capturing the types of chronic health condition experienced by individuals was included in both surveys. Data were also collected on frequency of green space use, barriers to green space use, and demographic characteristics including sex, age, and income. The surveys also collected data on barriers to green space use introduced or exacerbated by the Covid-19 pandemic. Associations between the outcome variables (the barriers to green space use) and predictors (the health conditions and socio-demographic variables) were assessed using Structural Equation Modelling (SEMs) and multiple binary logistic regression models. Findings: The most commonly reported barrier to green space use for those with chronic health conditions was ‘poor physical health’. The findings indicated that those with physical disabilities and progressive illnesses reported physical health-related barriers (mobility and health, lack of disabled facilities, unsuitable/poorly maintained sites, and having no-one to go with/help them) as important in stopping them from visiting green spaces in the last 14 days. A lack of disabled facilities was found to be a particularly important issue for respondents with heart/circulatory conditions, physical disabilities, and progressive illnesses. Poor mental health was more likely to be reported as a barrier by those with mental health conditions, diabetes, and respiratory conditions, as well as by respondents aged 16-24 years. The Covid-19 pandemic was found to have exacerbated existing inequalities in both green space use and reporting of barriers with the introduction of new issues, such as worrying about social distancing and green spaces being too busy. Conclusions: Overall, there were differences by type of health condition and socio demographic characteristics when reporting barriers to green space use. The findings outlined in this study emphasise that a ‘one size fits all’ approach to increasing green space use and mitigating barriers to use for individuals with chronic health conditions will not work, with a more targeted approach required to ensure that green spaces are accessible and provide health and well-being benefits for all

    Teaching G{\"o}del's incompleteness theorems

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    The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science departments, to graduate and to undergraduate students. Many textbooks now present these notions, in particular the incompleteness theorems. Having taught these notions for several decades, our community can now stand back and analyze the choices faced when designing such a course. In this note, we attempt to analyze the choices faced when teaching the incompleteness theorems

    Forking and invariant measures in NIP theories

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    We give an example of an NIP theory TT in which there is a formula that does not fork over \varnothing but has measure 00 under any global \varnothing-invariant Keisler measure, and we show that this cannot occur if TT is also first-order amenable

    Banach LpL^p lattices with an automorphism

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    We study the theory of Banach LpL^p lattices with a distinguished automorphism, in the framework of continuous logic. Using a functional version of the Rokhlin lemma, we prove that it admits a model companion, which is stable and has quantifier elimination. We show that the types of this theory that are not trivial cannot be isolated. We then use this result to obtain a proof of the absence of comeagre conjugacy classes in Aut(μ)\operatorname{Aut}^*({\mu}), the Polish group of non-singular transformations of a standard probability space

    Zilber's notion of logically perfect structure: Universal Covers

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    We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we discuss in a systematic and unified way several examples indicating the main ideas of the proofs and the necessary changes in method for different situations: exponential covers, modular and Shimura curves, Shimura and abelian varieties, and coherent families of smooth covers.Comment: 1 figur

    The face of the city

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