Modelling the fate of surface melt on the Larsen C Ice Shelf

Surface melt lakes lower the albedo of ice shelves, leading to additional surface melting. This can substantially alter the surface energy balance and internal temperature and density profiles of the ice shelf. Evidence suggests that melt lakes also played a pivotal role in the sudden collapse of the Larsen B Ice Shelf in 2002. Here a recently developed, high-physical-fidelity model accounting for the development cycle of melt lakes is applied to the Larsen C Ice Shelf, Antarctica’s most northern ice shelf and one where melt lakes have been observed. We simulate current conditions on the ice shelf using weather station and reanalysis data and investigate the impacts of potential future increases in precipitation and air temperature on melt lake formation, for which concurrent increases lead to an increase in lake depth. Finally, we assess the viability in future crevasse propagation through the ice shelf due to surface meltwater accumulation

Mars' Atmosphere: Comparison of Entry Profiles with Numerical Models

This presentation was part of the session : Poster SessionsSixth International Planetary Probe WorkshopAs planetary probes enter an atmosphere, they capture measurements which provide thermodynamic information about the atmosphere, but only within a narrow vertical column within that atmosphere over a limited extent of time. In order to place this in situ information into context, it needs to be correlated with other less spatially resolved but more temporally extensive measurements, which can be provided by orbiters as well as numerical models. Before the entry probe is designed and developed, there needs to be some foreknowledge of conditions the probe will experience. Data from previous probes and orbiters can help, and models can aid by permitting investigation of conditions the orbiters may not have observed. Focusing on Mars, there are now six entry profiles available for analysis and interpretation, as well as a decade's worth of remotely sensed atmospheric thermal and aerosol characterization from orbiting platforms. Additionally, there are one-dimensional (vertical) and three-dimensional numerical models of the atmosphere available to provide predictions for entry probes [1,2,3] (and aerobraking spacecraft [4]) and to aid in interpretations of entry probe measurements. This presentation focuses upon the atmospheric variability that can be experienced by a probe, which has a dependency on atmospheric dust load, season, location (latitude and longitude), and "weather" (baroclinic waves, thermal tides, dust storms, etc.) The primary tool is a numerical model of the Martian atmosphere with significant heritage (NASA AMES GCM), with additional comparison to a new model in development with collaboration with the University of Michigan. Haberle, R. M., J.R. Barnes, J.R. Murphy, M. M Joshi, and J. Schaeffer, Meteorological Predictions for the Mars Pathfinder Lander. J. Geophys. Res., 102, 13301-13311, 1997. Tyler Jr., D., J.R. Barnes, E.D. Skyllingstad, Mesoscale and LES Model Studies of the Martian Atmosphere in Support of Phoenix, Submitted, J. Geophys. Res., Spring 2008. Michaels, T. I., and S.C.R. Rafkin, (2008), Meteorological Predictions for Candidate 2007 Phoenix Mars Lander Sites using MRAMS, Submitted, J. Geophys. Res., Spring 2008. Bougher, S.W., J.R. Murphy, J.M. Bell, R.W. Zurek, Prediction of the Structure of the Martian Upper Atmosphere for the Mars Reconnaissance Orbiter (MRO) Mission, Mars, 2, 10-20, 2006.NASA ; New Mexico Space Grant Fellowship ; NSF Atmospheres Program ; International Planetary Probe Worksho

Monitoring crack extension in fracture toughness tests by ultrasonics

An ultrasonic method was used to observe the onset of crack extension and to monitor continued crack growth in fracture toughness specimens during three point bend tests. A 20 MHz transducer was used with commercially available equipment to detect average crack extension less than 0.09 mm. The material tested was a 300-grade maraging steel in the annealed condition. A crack extension resistance curve was developed to demonstrate the usefulness of the ultrasonic method for minimizing the number of tests required to generate such curves

A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

Model-Based Analysis for Qualitative Data: An Application in Drosophila Germline Stem Cell Regulation.

Discovery in developmental biology is often driven by intuition that relies on the integration of multiple types of data such as fluorescent images, phenotypes, and the outcomes of biochemical assays. Mathematical modeling helps elucidate the biological mechanisms at play as the networks become increasingly large and complex. However, the available data is frequently under-utilized due to incompatibility with quantitative model tuning techniques. This is the case for stem cell regulation mechanisms explored in the Drosophila germarium through fluorescent immunohistochemistry. To enable better integration of biological data with modeling in this and similar situations, we have developed a general parameter estimation process to quantitatively optimize models with qualitative data. The process employs a modified version of the Optimal Scaling method from social and behavioral sciences, and multi-objective optimization to evaluate the trade-off between fitting different datasets (e.g. wild type vs. mutant). Using only published imaging data in the germarium, we first evaluated support for a published intracellular regulatory network by considering alternative connections of the same regulatory players. Simply screening networks against wild type data identified hundreds of feasible alternatives. Of these, five parsimonious variants were found and compared by multi-objective analysis including mutant data and dynamic constraints. With these data, the current model is supported over the alternatives, but support for a biochemically observed feedback element is weak (i.e. these data do not measure the feedback effect well). When also comparing new hypothetical models, the available data do not discriminate. To begin addressing the limitations in data, we performed a model-based experiment design and provide recommendations for experiments to refine model parameters and discriminate increasingly complex hypotheses

An interpolation theorem for proper holomorphic embeddings

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging

Plug-and-Play Priors (PnP) is one of the most widely-used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data-fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly-successful applications of PnP algorithms include bio-microscopy, computerized tomography, magnetic resonance imaging, and joint ptycho-tomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. We also point the way towards further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms