The continental drift convection cell

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 42 (2015): 4301-4308, doi:10.1002/2015GL064480.Continents on Earth periodically assemble to form supercontinents and then break up again into smaller continental blocks (the Wilson cycle). Previous highly developed numerical models incorporate fixed continents while others indicate that continent movement modulates flow. Our simplified numerical model suggests that continental drift is fundamental. A thermally insulating continent is anchored at its center to mantle flow on an otherwise stress-free surface for infinite Prandtl number cellular convection with constant material properties. Rayleigh numbers exceed 107, while continent widths and chamber lengths approach Earth's values. The Wilson cycle is reproduced by a unique, rugged monopolar “continental drift convection cell.” Subduction occurs at the cell's upstream end with cold slabs dipping at an angle beneath the moving continent (as found in many continent/subduction regions on Earth). Drift enhances vertical heat transport up to 30%, especially at the core-mantle boundary, and greatly decreases lateral mantle temperature differences.Funding was provided by NSF grants EAR-1010432 and EAR-1316333.2015-12-0

Orbits and phase transitions in the multifractal spectrum

We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective field exhibits a sharp drop of all D_q with q < 0 at some critical strength of the random field. We introduce the concept of orbits which naturally group the points of the support of the invariant measure. We then show that the pointwise dimension at all points of an orbit has the same value and calculate it for a class of periodic orbits and their so-called offshoots as well as for generic orbits in the non-overlapping case. The sharp drop in the D_q-spectrum is analytically explained by a drastic change of the scaling properties of the measure near the points of a certain periodic orbit at a critical strength of the random field which is explicitly given. A similar drastic change near the points of a special family of periodic orbits explains a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a decisive role in this mechanism is played by a specific offshoot. We furthermore give rigorous upper and/or lower bounds on all D_q in a wide parameter range. In most cases the numerically obtained D_q coincide with either the upper or the lower bound. The results in this paper are relevant for the understanding of random iterated function systems in the case of moderate overlap in which periodic orbits with weak singularity can play a decisive role.Comment: The article has been completely rewritten; the title has changed; a section about the typical pointwise dimension as well as several references and remarks about more general systems have been added; to appear in J. Phys. A; 25 pages, 11 figures, LaTeX2

Adjustment with aphasia after stroke: study protocol for a pilot feasibility randomised controlled trial for SUpporting wellbeing through PEeR Befriending (SUPERB)

Background: Despite the high prevalence of mood problems after stroke, evidence on effective interventions particularly for those with aphasia is limited. There is a pressing need to systematically evaluate interventions aiming to improve wellbeing for people with stroke and aphasia. This study aims to evaluate the feasibility of a peer-befriending intervention. Methods/design: SUPERB is a single blind, parallel group feasibility trial of peer befriending for people with aphasia post-stroke and low levels of psychological distress. The trial includes a nested qualitative study and pilot economic evaluation and it compares usual care (n = 30) with usual care + peer befriending (n = 30). Feasibility outcomes include proportion screened who meet criteria, proportion who consent, rate of consent, number of missing/incomplete data on outcome measures, attrition rate at follow-up, potential value of conducting main trial using value of information analysis (economic evaluation), description of usual care, and treatment fidelity of peer befriending. Assessments and outcome measures (mood, wellbeing, communication, and social participation) for participants and significant others will be administered at baseline, with outcome measures re-administered at 4 and 10 months post-randomisation. Peer befrienders will complete outcome measures before training and after they have completed two cycles of befriending. The qualitative study will use semi-structured interviews of purposively sampled participants (n = 20) and significant others (n = 10) from both arms of the trial, and all peer befrienders to explore the acceptability of procedures and experiences of care. The pilot economic evaluation will utilise the European Quality of life measure (EQ-5D-5 L) and a stroke-adapted version of the Client Service Receipt Inventory (CSRI). Discussion: This study will provide information on feasibility outcomes and an initial indication of whether peer befriending is a suitable intervention to explore further in a definitive phase III randomised controlled trial. Trial registration: ClinicalTrials.gov identifier NCT02947776, registered 28th October 2016

Post-entrapment modification of volatiles and oxygen fugacity in olivine-hosted melt inclusions

The solubilities of volatiles (H_2O, CO_2, S, F, and Cl) in basaltic melts are dependent on variables such as temperature, pressure, melt composition, and redox state. Accordingly, volatile concentrations can change dramatically during the various stages of a magma's existence: from generation, to ascent through the mantle and crust, to final eruption at the Earth's surface. Olivine-hosted melt inclusions have the potential to preserve volatile concentrations at the time of entrapment due to the protection afforded by the host olivine against decompression and changes to the oxidation state of the external magma. Recent studies, however, have demonstrated that rapid diffusive re-equilibration of H_2O and oxygen fugacity (f_(O_2)) can occur within olivine-hosted melt inclusions. Here we present volatile, hydrogen isotope, and major element data from dehydration experiments and a quantitative model that assesses proposed mechanisms for diffusive re-equilibration of H_2O and f_(O_2) in olivine-hosted melt inclusions. Our comprehensive set of data for the behavior of common magmatic volatiles (H_2O, CO_2, F, Cl, and S) demonstrates that post-entrapment modification of CO_2, and to a lesser extent S, can also occur. We show that the CO_2 and S concentrations within an included melt decrease with progressive diffusive H_2O loss, and propose that this occurs due to dehydration-induced changes to the internal pressure of the inclusion. Therefore, deriving accurate estimates for pre-eruptive CO_2 and S concentrations from olivine-hosted melt inclusions requires accounting for the amount of CO_2 and S hosted in vapor bubbles. We find, however, that Cl and F concentrations in olivine-hosted melt inclusions are not affected by diffusive re-equilibration through the host olivine nor by dehydration-induced pressure changes within the melt inclusion. Our results indicate that measured H_2O, CO_2 and S concentrations and Fe^(3+)/ΣFe ratios of included melts are not necessarily representative of the melt at the time of entrapment and thus are not reliable proxies for upper mantle conditions

Relationship between Greenland Ice Sheet surface speed and modeled effective pressure

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Earth Surface 123 (2018): 2258-2278, doi:10.1029/2017JF004581.We use a numerical subglacial hydrology model and remotely sensed observations of Greenland Ice Sheet surface motion to test whether the inverse relationship between effective pressure and regional melt season surface speeds observed at individual sites holds on a regional scale. The model is forced with daily surface runoff estimates for 2009 and 2010 across an ~8,000‐km2 region on the western margin. The overall subglacial drainage system morphology develops similarly in both years, with subglacial channel networks growing inland from the ice sheet margin and robust subglacial pathways forming over bedrock ridges. Modeled effective pressures are compared to contemporaneous regional surface speeds derived from TerraSAR‐X imagery to investigate spatial relationships. Our results show an inverse spatial relationship between effective pressure and ice speed in the mid‐melt season, when surface speeds are elevated, indicating that effective pressure is the dominant control on surface velocities in the mid‐melt season. By contrast, in the early and late melt seasons, when surface speeds are slower, effective pressure and surface speed have a positive relationship. Our results suggest that outside of the mid‐melt season, the influence of effective pressures on sliding speeds may be secondary to the influence of driving stress and spatially variable bed roughness.National Aeronautics and Space Administration (NASA). Grant Number: NXX10AI30G National Science Foundation (NSF) American Geophysical Union Horton Research Grant; National Science Foundation Graduate Research Fellowship; National Science Foundation's Office of Polar Programs (NSF‐OPP) Grant Numbers: PLR‐1418256, ARC‐1023364, ARC‐0520077; Woods Hole Oceanographic Institution's Ocean and Climate Change Institute (OCCI)2019-03-2

Randomly Evolving Idiotypic Networks: Structural Properties and Architecture

We consider a minimalistic dynamic model of the idiotypic network of B-lymphocytes. A network node represents a population of B-lymphocytes of the same specificity (idiotype), which is encoded by a bitstring. The links of the network connect nodes with complementary and nearly complementary bitstrings, allowing for a few mismatches. A node is occupied if a lymphocyte clone of the corresponding idiotype exists, otherwise it is empty. There is a continuous influx of new B-lymphocytes of random idiotype from the bone marrow. B-lymphocytes are stimulated by cross-linking their receptors with complementary structures. If there are too many complementary structures, steric hindrance prevents cross-linking. Stimulated cells proliferate and secrete antibodies of the same idiotype as their receptors, unstimulated lymphocytes die. Depending on few parameters, the autonomous system evolves randomly towards patterns of highly organized architecture, where the nodes can be classified into groups according to their statistical properties. We observe and describe analytically the building principles of these patterns, which allow to calculate number and size of the node groups and the number of links between them. The architecture of all patterns observed so far in simulations can be explained this way. A tool for real-time pattern identification is proposed.Comment: 19 pages, 15 figures, 4 table

Randomly Evolving Idiotypic Networks: Modular Mean Field Theory

We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular architectures, the building principles of which are known. The nodes of the network can be classified into groups of nodes, the modules, which share statistical properties. Each node experiences only the mean influence of the groups to which it is linked. Given the size of the groups and linking between them the statistical properties such as mean occupation, mean life time, and mean number of occupied neighbors are calculated for a variety of patterns and compared with simulations. For a pattern which consists of pairs of occupied nodes correlations are taken into account.Comment: 14 pages, 8 figures, 4 table