Some more problems of geodynamics

This dissertation presents new theoretical methods that could contribute to constraining the deep Earth’s long-wavelength density structure. In Chapter 2 we present a numerically exact method for calculating the internal and external gravitational potential of aspherical and heterogeneous planets. Such calculations are crucial in computing Earth’s long-period deformation. Our approach is based on the transformation of Poisson’s equation into an equivalent equation posed on a spherical computational domain. This new problem is solved in an efficient iterative manner based on a hybrid pseudo-spectral/spectral- element discretisation. The main advantage of our method is that its computational cost reflects the planet’s geometric and structural complexity, being in many situations only marginally more expensive than boundary perturbation theory. Several numerical examples are presented to illustrate the method’s efficacy and potential range of applications. In Chapter 3 we investigate theoretically the dependence of the elastic tensor on the equilibrium stress, our aim being to understand the effect of nonzero stress on seismic wave propagation and Earth’s long-period motion. Using ideas from finite elasticity, it is first shown that both the equilibrium stress and elastic tensor are given uniquely in terms of the equilibrium deformation gradient relative to a fixed choice of reference body. Inversion of the relation between the deformation gradient and stress might, therefore, be expected to lead neatly to the desired expression for the elastic tensor. Unfortunately, the deformation gradient can only be recovered from the stress up to a choice of rotation matrix. Hence it is not possible in general to express the elastic tensor as a unique function of the equilibrium stress. By considering material symmetries, though, it is shown that the degree of non-uniqueness can sometimes be reduced, and in some cases even removed entirely. These results are illustrated through a range numerical calculations, and we also obtain linearised relations applicable to small perturbations in equilibrium stress. Finally, we make a comparison with previous studies before considering implications for geophysical forward- and inverse-modelling. Finally, in Chapter 4 we present a theoretical framework for modelling the rotational dynamics of solid elastic bodies. It takes full account of: Earth’s variable rotation, aspherical topography, and lateral variations in density and wave-speeds. It is based on an exact decomposition of the body’s motion that separates out the motion’s elastic and rotational components, in a way that we make precise in the main text. As a prelude to the elastic problem, we show how Hamilton’s principle provides an elegant means of deriving the exact and linearised equations of rigid body motion, then study the normal modes of a rigid body in uniform rotation. We subsequently build on these ideas to write down the exact equations of motion of a variably rotating elastic body. We linearise the equations and discuss their numerical solution, before showing how to extend these ideas to analyse N elastic bodies interacting through gravity. We conclude in Section 4.7 by discussing the extensions that would be necessary in order to describe layered fluid-solid bodies. Importantly, with those extensions the framework will bypass the numerical difficulties commonly associated with the Earth’s fluid layers, and could therefore readily be used to model diurnal tides. Thus, it would allow the abundant data provided by diurnal tides to be used to constrain lateral variations in mantle density. Furthermore, it would allow for a systematic investigation of the effect of lateral density heterogeneities on the Earth’s rotation; this has never yet been undertaken, and will provide additional constraints on mantle density and other parameters of interest

On the elastodynamics of rotating planets

Equations of motion are derived for (visco)elastic, self-gravitating, and variably-rotating planets. The equations are written using a decomposition of the elastic motion that separates the body's elastic deformation from its net translational and rotational motion as far as possible. This separation is achieved by introducing degrees of freedom that represent the body's rigid motions; it is made precise by imposing constraints that are physically motivated and should be practically useful. In essence, a Tisserand frame is introduced exactly into the equations of solid mechanics. The necessary concepts are first introduced in the context of a solid body, motivated by symmetries and conservation laws, and the corresponding equations of motion are derived. Next, it is shown how those ideas and equations of motion can readily be extended to describe a layered fluid--solid body. A possibly new conservation law concerning inviscid fluids is then stated. Thereafter the equilibria and linearisation of the fluid--solid equations of motion are discussed, along with new equations for use within normal-mode coupling calculations and other Galerkin methods. Finally, the extension of these ideas to the description of multiple, interacting fluid--solid planets is qualitatively discussed

A non-perturbative method for gravitational potential calculations within heterogeneous and aspherical planets

We present a numerically exact method for calculating the internal and external gravitational potential of aspherical and heterogeneous planets. Our approach is based on the transformation of Poisson’s equation into an equivalent equation posed on a spherical computational domain. This new problem is solved in an efficient iterative manner based on a hybrid pseudospectral/spectral element discretization. The main advantage of our method is that its computational cost reflects the planet’s geometric and structural complexity, being in many situations only marginally more expensive than boundary perturbation theory. Several numerical examples are presented to illustrate the method’s efficacy and potential range of applications

Prevalence, timing, and predictors of transitions from inhalant use to Inhalant Use Disorders

BACKGROUND: Few studies of the natural history of DSM-IV inhalant substance use disorders (I-SUDs) have been conducted. This investigation examined the prevalence, timing, and predictors of transitions from inhalant use to formal I-SUDs among inhalant users within a nationally representative sample. METHODS: Participants were 664 U.S. residents participating in the 2000-2001 National Epidemiologic Survey on Alcohol and Related Conditions who reported lifetime inhalant use. Respondents completed structured interviews assessing DSM-IV psychiatric/substance use disorders. Bivariate and Cox regression analyses were conducted to identify risk factors for transitions from inhalant use to I-SUDs. RESULTS: Nearly one in five (19.4%) persons initiating inhalant use developed an I-SUD. Most I-SUD transitions were to inhalant abuse rather than inhalant dependence. Risk for development of I-SUDs was greatest in the first year following initiation of inhalant use and low thereafter. Multivariate proportional hazards models indicated that presence of a mood/anxiety disorder (HR=7.7, CI=3.1-18.9) or alcohol use disorder (HR=11.9, CI=5.46-26.00) antedating initiation of inhalant use predicted significantly elevated risk for I-SUDs, whereas being married conferred a lower risk for onset of I-SUDs. CONCLUSIONS: I-SUDs were relatively common among inhalant users, generally occurred in the year following initiation of inhalant use, and were associated with early-onset mood/anxiety and alcohol use disorders. Given the young average age at onset of inhalant use and the rapidity with which most I-SUDs developed, interventions directed to adolescents who have initiated inhalant use might be effective in reducing the proportion of inhalant users who develop I-SUDs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61908/1/Transition.pd

ATCA Study of Small Magellanic Cloud Supernova Remnant 1E 0102.2-7219

We present new and archival Australia Telescope Compact Array and Atacama Large Millimeter/submillimeter Array data of the Small Magellanic Cloud supernova remnant 1E 0102.2-7219 at 2100, 5500, 9000, and 108000 MHz; as well as Hi data provided by the Australian Square Kilometre Array Pathfinder. The remnant shows a ring-like morphology with a mean radius of 6.2 pc. The 5500 MHz image reveals a bridge-like structure, seen for the first time in a radio image. This structure is also visible in both optical and X-ray images. In the 9000 MHz image we detect a central feature that has a flux density of 4.3 mJy but rule out a pulsar wind nebula origin, due to the lack of significant polarisation towards the central feature with an upper limit of 4 per cent. The mean fractional polarisation for 1E 0102.2-7219 is 7 +- 1 and 12 +- 2 per cent for 5500 and 9000 MHz, respectively. The spectral index for the entire remnant is -0.61 +- 0.01. We estimate the line-of-sight magnetic field strength in the direction of 1E 0102.2-7219 of ~44 microG with an equipartition field of 65 +- 5 microG. This latter model, uses the minimum energy of the sum of the magnetic field and cosmic ray electrons only. We detect an Hi cloud towards this remnant at the velocity range of ~160-180 km s-1 and a cavity-like structure at the velocity of 163.7-167.6 km s-1. We do not detect CO emission towards 1E 0102.2-7219

What Triggers Oxygen Loss in Oxygen Redox Cathode Materials?

It is possible to increase the charge capacity of transition-metal (TM) oxide cathodes in alkali-ion batteries by invoking redox reactions on the oxygen. However, oxygen loss often occurs. To explore what affects oxygen loss in oxygen redox materials, we have compared two analogous Na-ion cathodes, P2-Na0.67Mg0.28Mn0.72O2 and P2-Na0.78Li0.25Mn0.75O2. On charging to 4.5 V, >0.4e– are removed from the oxide ions of these materials, but neither compound exhibits oxygen loss. Li is retained in P2-Na0.78Li0.25Mn0.75O2 but displaced from the TM to the alkali metal layers, showing that vacancies in the TM layers, which also occur in other oxygen redox compounds that exhibit oxygen loss such as Li[Li0.2Ni0.2Mn0.6]O2, are not a trigger for oxygen loss. On charging at 5 V, P2-Na0.78Li0.25Mn0.75O2 exhibits oxygen loss, whereas P2-Na0.67Mg0.28Mn0.72O2 does not. Under these conditions, both Na+ and Li+ are removed from P2-Na0.78Li0.25Mn0.75O2, resulting in underbonded oxygen (fewer than 3 cations coordinating oxygen) and surface-localized O loss. In contrast, for P2-Na0.67Mg0.28Mn0.72O2, oxygen remains coordinated by at least 2 Mn4+ and 1 Mg2+ ions, stabilizing the oxygen and avoiding oxygen loss

Targeting DNA Damage Response and Replication Stress in Pancreatic Cancer

Background and aims: Continuing recalcitrance to therapy cements pancreatic cancer (PC) as the most lethal malignancy, which is set to become the second leading cause of cancer death in our society. The study aim was to investigate the association between DNA damage response (DDR), replication stress and novel therapeutic response in PC to develop a biomarker driven therapeutic strategy targeting DDR and replication stress in PC. Methods: We interrogated the transcriptome, genome, proteome and functional characteristics of 61 novel PC patient-derived cell lines to define novel therapeutic strategies targeting DDR and replication stress. Validation was done in patient derived xenografts and human PC organoids. Results: Patient-derived cell lines faithfully recapitulate the epithelial component of pancreatic tumors including previously described molecular subtypes. Biomarkers of DDR deficiency, including a novel signature of homologous recombination deficiency, co-segregates with response to platinum (P < 0.001) and PARP inhibitor therapy (P < 0.001) in vitro and in vivo. We generated a novel signature of replication stress with which predicts response to ATR (P < 0.018) and WEE1 inhibitor (P < 0.029) treatment in both cell lines and human PC organoids. Replication stress was enriched in the squamous subtype of PC (P < 0.001) but not associated with DDR deficiency. Conclusions: Replication stress and DDR deficiency are independent of each other, creating opportunities for therapy in DDR proficient PC, and post-platinum therapy

Pan-cancer analysis of whole genomes

Cancer is driven by genetic change, and the advent of massively parallel sequencing has enabled systematic documentation of this variation at the whole-genome scale(1-3). Here we report the integrative analysis of 2,658 whole-cancer genomes and their matching normal tissues across 38 tumour types from the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA). We describe the generation of the PCAWG resource, facilitated by international data sharing using compute clouds. On average, cancer genomes contained 4-5 driver mutations when combining coding and non-coding genomic elements; however, in around 5% of cases no drivers were identified, suggesting that cancer driver discovery is not yet complete. Chromothripsis, in which many clustered structural variants arise in a single catastrophic event, is frequently an early event in tumour evolution; in acral melanoma, for example, these events precede most somatic point mutations and affect several cancer-associated genes simultaneously. Cancers with abnormal telomere maintenance often originate from tissues with low replicative activity and show several mechanisms of preventing telomere attrition to critical levels. Common and rare germline variants affect patterns of somatic mutation, including point mutations, structural variants and somatic retrotransposition. A collection of papers from the PCAWG Consortium describes non-coding mutations that drive cancer beyond those in the TERT promoter(4); identifies new signatures of mutational processes that cause base substitutions, small insertions and deletions and structural variation(5,6); analyses timings and patterns of tumour evolution(7); describes the diverse transcriptional consequences of somatic mutation on splicing, expression levels, fusion genes and promoter activity(8,9); and evaluates a range of more-specialized features of cancer genomes(8,10-18).Peer reviewe

Oxygen redox chemistry without excess alkali-metal ions in Na2/3_{2/3}[Mg0.28_{0.28}Mn0.72_{0.72}]O2_2

The search for improved energy-storage materials has revealed Li- and Na-rich intercalation compounds as promising high-capacity cathodes. They exhibit capacities in excess of what would be expected from alkali-ion removal/reinsertion and charge compensation by transition-metal (TM) ions. The additional capacity is provided through charge compensation by oxygen redox chemistry and some oxygen loss. It has been reported previously that oxygen redox occurs in O 2$p$ orbitals that interact with alkali ions in the TM and alkali-ion layers (that is, oxygen redox occurs in compounds containing Li$^+$–O(2$p$)–Li$^+$ interactions). Na$_{2/3}$[Mg$_{0.28}$Mn$_{0.72}$]O$_2$ exhibits an excess capacity and here we show that this is caused by oxygen redox, even though Mg$^{2+}$ resides in the TM layers rather than alkali-metal (AM) ions, which demonstrates that excess AM ions are not required to activate oxygen redox. We also show that, unlike the alkali-rich compounds, Na$_{2/3}$[Mg$_{0.28}$Mn$_{0.72}$]O$_2$ does not lose oxygen. The extraction of alkali ions from the alkali and TM layers in the alkali-rich compounds results in severely underbonded oxygen, which promotes oxygen loss, whereas Mg$^{2+}$ remains in Na$_{2/3}$[Mg$_{0.28}$Mn$_{0.72}$]O$_2$, which stabilizes oxygen