Marc Spiegelman - US grants

Variations in trace element distributions at mid-ocean ridges have often been used to constrain parameters such as melting source compositions, depth and degree of melting, and size and shape of source regions. Traditional trace element models assume some model of the melting process that, in general, do not include either the physics of magma migration or trace element transport. The purpose of this research is to investigate and quantify to what degree observable trace elements to varying parameters such as flow regime, sensitive is the behavior of trace element distribution can distinguish between different potential mantel processes. The behavior of arbitrary initial trace element distributions can be calculated for a range of physically consistent models governing the flow of melt and solid in the mantle. The following questions will be addresses. How sensitive is the behavior of trace elements to varying parameters such as flow regime, degree of melting, source characteristics, porosity/permeability structure? Can these parameters be recovered from trace element distribution observed at the surface? What are the errors in the parameters recovered using more traditional melting models?

9220106 Spiegelman The role of subduction and magmatism in the growth of the continental crust and the evolution of the crust/mantle system has long been recognized, but a detailed, process-oriented under- standing of the subduction cycle has been elusive. In this project the principal investigators will combine experimental petrology and geochemistry, observational seismology, isotope and trace element geochemistry and laboratory convection experiments with numerical approaches to the thermal structure and large-scale convection of the slab and mantle wedge, and porous flow models for melt and fluid migration in the arc environment. Heat flow and various analyses of seismic data, from primarily the Japan arc, will constrain the thermal structure and rheological properties used in the initial calculations (2-D and some 3-D) of flow in the slab and mantle, using a temperature-dependent viscosity. Models developed for Japan, where seismic constraints are strongest, will be used as a base for Central America and for the Cascades, where a young hot plate is subducting and conditions are far from steady state. Models for transport of hydrous fluids in the vicinity of the slab, and of melts through the mantle will be calculated using the stress and flow fields from the thermal and convection modeling. Plate scale mass transport delivers chemical elements derived from the continental crust, hydrosphere and lithosphere to the deep source of arc magmas; fluid and melt transport processes translate some fraction of these elements back to the surface in crust building magmas. Documentably slab-derived elements such as 10Be (1.5 Ma half-life), B and U (75 ka half-life in disequilibria series) will be incorporated as chemical tracers in fluid/melt migration models, with fluxes, transport paths and characteristic transport times constrained from chemistry of subconducting sediments and erupting lavas. Fluid partitioning studies on key elements will further constrain input to migration models. Predictions from coupled thermal, convection and transport models regarding spatial distribution, character and chemistry of lavas along the length and across the width of arcs will be compared with observed values, and evaluated against observed variations in subduction parameters from arc to arc to arrive at an integrated model of the subduction cycle and its role in crustal growth and evolution of the mantle. ***

9402922 Sparks In this project the PIs will investigate magma migration and various scales of mantle flow. They will perform 2- and 3-D numerical modelling to address questions concerned with melt channelling and focusing. They will use a time-efficient gridding technique (Fast Adaptive Composite gridding) to obtain high resolution at various scales that may be needed.

Kinzler 9314626 Motivated by the concern how melting near sp/gt lherzolite transition and magma extraction processes will control major and trace elements in magmas, the PIs propose a 4-step approach in this project to study magma generation processes at mid-oceanic ridges. The PIs will perform simple phase equilibrium experiments at 17-40 kbar, parameterize the results, use simple 2-D and 3-D transport models to examine how trace element abundances in magmas will be affected, and, finally, work out the mass and energy conservation of the models.

OCE-9530307 Geochemical and field evidence suggest that melt transport in the mantle is localized into some form of meso-scale channels; however, the mechanism for the formation of such channels from a grain-scale distribution of melt is poorly understood. Two possible mechanisms will be investigated: (1) reactive inflitration instability, which is an interaciton between the fluid-mechanics of melt motion and chemical dissolution, and (2) purely mechanical flow segregations due to local pressure graneints. A series of numerical model problems will be used to quantify the behavior and effects of both of these processes.

Magmatism and mantle convection at subduction zones and island arcs are some of the principal processes affecting the geochemical and physical evolution of our planet. The purpose of the proposed work is to develop a set of quantitative computer models that can relate these processes at depth to observations available at the surface, particularly the composition and volume of volatiles and magmas that erupt at island arcs. This requires developing codes that can consistently solve for reactive magma-transport in a deforming convecting mantle. Based on an extensive set of models designed for melting at mid-ocean ridges these new codes will be extended to include the impact of volatiles on melting at island arcs. Both sets of models will provide a consistent framework for investigating the coupled geophysical/geochemical dynamics of the Earth's mantle.

EAR-0002533
Marc Spiegelman


This proposal requests funds to help support travel costs of U.S. participants to the 23rd International Conference on Mathematical Geophysics. This year's conference is titled Extreme Earth Events. The conference focuses on systems that display sudden transitions from quiescent states to crises, extreme events, catastrophic or disastrous instabilities. Examples range from large natural catastrophes such as earthquakes, volcanic eruptions, hurricanes and tornadoes, landslides, avalanches, mass extinctions and catastrophic events of environmental degradation, to the failure of engineering structures, crashes in the stock market, social unrest and economic disruptions on national and global scales, regional power blackouts, traffic gridlock, diseases and epidemics. The purpose of this conference is to provide a forum that allows scientists from a full range of scientific disciplines to interact with each other and with experts in the math and physics community.

Spiegelman
EAR-0221406

The distribution of melt and solid within partially molten regions of the Earth's mantle is one of the key parameters controlling the dynamics, properties and compositions of these regions. Field observations, experiments and theory all suggest that melt should be distributed in some form of channelized network at depth but the physical mechanisms for producing these networks are still not well understood. This project will develop new tools to investigate mechanical instabilities for flow localization based on fluid flow in deformable permeable media with strongly variable solid shear viscosity. These tools will complement existing models for flow localization due to reactive melt transport. Developing accurate flow solvers in heterogeneous media is numerically quite challenging, however, the investigation will be guided by recent experiments from David Kohlstedt's laboratory (U. Minnesota) on flow induced melt localization that provide clear and diagnostic tests for the theory. The opportunity to directly combine theory and experiment is rare and the investigators plan to work closely in consultation with the Kohlstedt group. However, the initial objective of this project is the development of the needed numerical tools. Once developed and validated with the experimental results, they will be used to extrapolate the experimental results to larger scales and investigate geologically relevant systems such as melt transport beneath mid-ocean ridges and island arcs.

Columbia University is establishing a new, multi-departmental graduate program in Applied Mathematics and the Earth & Environmental Sciences. The aim of this new IGERT Joint Program is to train a new generation of scientists whose level of mathematical sophistication will be considerably higher than that of typical students currently graduating from earth and environmental science programs and, at the same time, whose familiarity with the important issues and major open research questions in the earth and environmental sciences will be much deeper that what is usually expected of students trained uniquely within applied mathematics departments. To achieve this goal, five departments at Columbia - Mathematics, Statistics, Applied Physics & Applied Mathematics, Earth & Environmental Sciences, and Earth & Environmental Engineering - under the coordinating role of the Columbia Earth Institute, will collaboratively train graduate students under this new IGERT Joint Program. While students in the IGERT Joint Program will be individually admitted by each department, their progress will be monitored by a Steering Committee of faculty associated with the Joint Program. In addition to satisfying the requirements of the departments into which they are admitted, all students in the Joint Program will take a new integrated two-semester sequence in Applied Mathematics specifically tailored to issues and problems in the global environmental sciences, and will be expected to earn a minimum number of credits in both mathematical and earth science courses. In addition, they will be expected to attend a weekly colloquium organized by the Joint Program, give a formal presentation of their research results once a year to the faculty and other students affiliated with the Joint Program, attend special series of invited lectures, assist in the mentoring of undergraduates, and complete a one summer internship during their graduate training at a research institution, national laboratory, or industrial research center.

IGERT is an NSF-wide program intended to meet the challenges of educating U.S. Ph.D. scientists and engineers with the multidisciplinary backgrounds and the technical, professional, and personal skills needed for the career demands of the future. The program is intended to catalyze a cultural change in graduate education by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. In the fifth year of the program, awards are being made to twenty-one institutions for programs that collectively span the areas of science and engineering supported by NSF.

Spiegelman
EAR-0207851

The distribution of melt and solid within partially molten regions of the Earth's mantle is one of the key parameters controlling the dynamics, properties and compositions of these regions. Field observations, experiments and theory all suggest that melt should be distributed in some form of channelized network at depth but the physical mechanisms for producing these networks are still not well understood. This project will develop new tools to investigate mechanical instabilities for flow localization based on fluid flow in deformable permeable media with strongly variable solid shear viscosity. These tools will complement existing models for flow localization due to reactive melt transport. Developing accurate flow solvers in heterogeneous media is numerically quite challenging, however, the investigation will be guided by recent experiments from David Kohlstedt's laboratory (U. Minnesota) on flow induced melt localization that provide clear and diagnostic tests for the theory. The opportunity to directly combine theory and experiment is rare and the investigators plan to work closely in consultation with the Kohlstedt group. However, the initial objective of this project is the development of the needed numerical tools. Once developed and validated with the experimental results, they will be used to extrapolate the experimental results to larger scales and investigate geologically relevant systems such as melt transport beneath mid-ocean ridges and island arcs.
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In this proposed study the PIs will investigate the interaction between channelized and porous flow of melt in the mantle and chemical heterogeneities that might be present at various length scales. Using theoretical models constrained by geologic and petrologic observations, they will examine the basic behavior of systems undergoing melting and their predictions. The research will primarily be undertaken by a graduate student, with close supervision by the PIs in a staged manner, progressing from simple to more complex (realistic) models. It is expected that the new models can be used to test emerging ideas and observations of chemical heterogeneity in melts and mantle residues in a variety of melting regimes (ridges, arc, plumes).

This proposal requests funds to help support meeting costs and travel expenses of U.S.
participants to the 25th International Conference on Mathematical Geophysics to be held
at Columbia University in New York City from June 16-18, 2004. The Conference on
Mathematical Geophysics meets every two years and is sponsored by the Committee on
Mathematical Geophysics of the International Union of Geodesy and Geophysics.

Intellectual merits This year's conference is titled Frontiers in Theoretical Earth Science
and brings together earth scientists, physicists, applied mathematicians, and others who
seek to develop new ideas for better understanding the processes and properties of the
Earth. This year, the meeting will survey the current and future state of theoretical Earth
sciences ranging from the core and mantle to the surface, oceans, and life. In particular
the meeting emphasizes advances in theory, techniques such as advanced computation and
data analysis and new problems and observations in need of theoretical understanding.
This meeting provides a single multi-disciplinary forum for the exchange of ideas and
techniques across the disciplinary boundaries in the Earth Sciences The conference web
site can be found at http://www.ldeo.columbia.edu/~mspieg/CMG2004/.

Broader Impacts This meeting provides a rare opportunity for students and early-career
scientists from across the earth sciences and applied mathematics to interact with senior
scientists in a small informal setting. This meeting also forms a principal activity of
Columbia's NSF IGERT Joint Program in Applied Mathematics and Earth & Environ-mental
Sciences. It will be staffed by current IGERT graduate students and will provide
excellent exposure for these students to a wide range of research opportunities, new peers
and senior scientists. Space permitting, the oral sessions of this meeting will be open to the
general public.

Fluid transport in volcanic arcs is perhaps the most extreme expression of a larger class of problems in reactive fluid transport that has important applications to problems such as ground water flow and contaminant transport. This research focuses on developing computational and theoretical methods to construct a consistent framework for investigating the transport of fluid, melts and chemistry across the mantle wedge in subduction zones. The model will be tested by comparing model predictions with geophysical and geochemical observations from subducting slabs and volcanic arcs. The completed model will permit insights into the behavior of channelized hydrous magmatic systems and the transport of magmatic and hydrothermal geochemical tracers. The primary objective of the work is to provide computational and theoretical tools to facilitate collaboration between observationalists and

ABSTRACT (Spiegleman - 0452457)
This research will develop a fully coupled theory and mathematical basis to explain fluid flow, dike emplacement, and crustal deformation in deformable/permeable and reactive media using seismic strain data and hydrothermal observations. The approach adopted is based on the recently developed theory of evolving damaged materials generated by one of the investigators that has recently been validated at small scales against laboratory experiments. The research involves development of a set of numerical and conceptual models of increasing complexity that address coupled deformation and hydrothermal circulation in brittle/fractured/fracturing ocean crust at mid-ocean ridges. To constrain and verify these models, there will be collaborations between researchers at the Lamont Doherty Earth Observatory of Columbia University in New York who have data and first-hand knowledge of the geography of fractured-seafloor hydrothermal systems at intensively studied RIDGE 2000 integrated study sites and the corresponding chemical, hydrological, and geophysical characteristics in these areas. These observational data will be used to parameterize the final models and simulations will be carried out and ground truthed using data from natural systems.

Broader Impacts: This project provides cross-disciplinary training for a young scientist and fosters international and interdisciplinary collaboration in the marine geology and geophysics community. It also develops a more general framework for understanding the behavior of fluids in deformable brittle media, which is a fundamental problem in engineering with potential applications to earthquake dynamics, volcanic eruptions, landslides and other natural hazards.

The investigators are focused on developing a deeper understanding of the behavior of the dynamics of
partially molten rock (magma) in the Earth's mantle. This problem has important implications for the dynamics of large scale mantle convection and plate tectonics as well as the geochemical evolution of the planet. Magma migration is also an intrinsically interesting problem in coupled fluid/solid mechanics as it requires understanding the non-linear interactions of low viscosity reactive fluids in a strongly deformable
and permeable matrix. For the past 20 years, the predominant theory for magma migration in the mantle has been a system of mathematical models (partial differential equations or PDEs), which describe the evolution of macroscopic quantities, e.g. the porosity or proportion of molten rock at a given position and time. These equations have proved useful for exploring the behavior of magmatic systems through both simplified model problems and more complex geoscience specific applications. However, more recent experimental work suggests that there exist some important quantitative discrepancies between the experiments and predictions of these models. In particular, these models become singular as the porosity becomes small. These and other results suggest that a modeling and mathematical understanding of the behavior of the current equations is necessary to gauge the utility of these models and to develop improved mathematical descriptions (e.g. by introducing physically reasonable regularizations) for partially molten regions in large scale mantle dynamics. The purpose of this proposal is to combine expertise in the analysis of non-linear PDE's with the physics and computation of magma dynamics to develop better insight and better models for complex coupled fluid/solid systems. This work is collaborative effort between Michael I. Weinstein (Columbia Applied Mathematics) and Marc Spiegelman (Columbia Joint appointment between Earth and Env. Sciences and Applied Math) and will be the primary Ph. D. research of Gideon Simpson who is jointly supervised by Weinstein and Spiegelman. This project will attack two separate problems that arise at different scales in partially molten regions. At large scales, variations in porosity can propagate as dispersive non-linear waves with a poorly understood non-linear dispersion term. At smaller scales, laboratory experiments demonstrate that shear deformation of the solid matrix can drive localization of melt-rich bands We will consider a series of analytic and numerical model problems to develop a better understanding of the current models as well as exploring ways to improve the formulation.

This project will form the primary source of funding for a promising graduate student (Gideon Simpson) to work at the intersection of Applied Mathematics and Earth Science. This work should also have general applications in science and engineering to problems involving the flow of fluids in permeable deformable solids such as those arising in petroleum engineering, hydrology and nuclear/toxic waste confinement.

Intellectual Merit. A fundamental challenge for geochemists and geophysicists is to understand how to use observed chemical variability to infer both properties and processes occurring in the Earth's mantle. The Uranium-series decay chains hold enormous promise for inferring mantle processes because these nuclides are sensitive to the rates of melting and melt transport as well as the geometry of melt and solid distribution (i.e. porosity/channeling etc.). Realizing this promise, however, remains extremely challenging. New observations of correlations between U-series nuclides, other trace elements and geophysical parameters place strong constraints on models and, together with other studies, suggest that melt transport in the mantle is highly localized into some form of channelized network. Thus, to quantitatively relate observed U-series excesses to mantle processes requires models that integrate coupled melt and solid dynamics with chemical transport. The purpose of this proposal is to develop and systematically explore the next generation of models for stable and radiogenic tracers in magmatic systems to understand their implications for mantle processes.

Specifically, it is proposed to 1) Extend current models for stable and U-series transport in reactive channelized flows to include realistic major element melting and trace element partitioning behavior so that the models can be compared directly to observations. 2) Use these models to systematically explore the sensitivity of coupled REE and U-series behavior to possible mantle processes. 3) Extend the models to investigate other mechanisms for melt localization such as shear-induced mechanical instabilities. 4) Develop comprehensive U-series models for mid-ocean ridge geometries.
For accuracy, the computational models require extremely fine spatial and temporal resolution, which becomes important when solving for U-series response in large-scale geological systems. Thus, another component of this research is to develop the next generation of high-performance computational models for high-resolution melt and chemical transport. We have begun this process by porting major components to the Portable Extensible Toolkit for Scientific Computation (PETSc) which is a core technology in the Computational Infrastructure for Geodynamics (CIG). We will work closely with CIG to develop publicly accessible chemical transport models that are interoperable within the larger CIG framework. If successful, this proposal will develop both a better understanding of the dynamic implications of U-series observations as well as flexible modeling tools that can benefit the entire geochemical and geophysical community.

Broader Impacts. This project will form the primary source of funding to finish the graduate work of Yanming Fang to work at the intersection of Applied Mathematics and Earth Science. This work should also have general applications in science and engineering to problems involving the flow of fluids in permeable, reactive and deformable solids such as petroleum engineering, hydrology and nuclear waste production and disposal. All codes and algorithms developed through this work will be made available as open source components to the public through the CIG.

0624648
Spiegelman

26th International Conference on Mathematical Geophysics: Request
for student travel support

Marc Spiegelman (LDEO/Columbia), David Yuen (U. Minn) and Peter Fox (NCAR)
This proposal requests funds to help support travel and meeting costs for students and
early career scientists at U.S. institutions to the 26th International Conference on Mathematical
Geophysics Coupling in Earth Systems: Solids, Fluids, Life to be held in
June 4 - 8, 2006 near Tiberias, Israel on the Sea of Galilee. The conference website is
http://www.weizmann.ac.il/conferences/CMG2006/.
Intellectual merits This conference brings together Earth scientists from across the disciplines
with physicists, applied mathematicians, and computational scientists to discuss
advances in mathematical and computational techniques for understanding properties and
processes in the earth. This years meeting emphasizes understanding coupled systems
such as coupled convective systems (ocean-atmosphere, mantle-lithosphere), coupled fluidsolid
mechanics, interactions between the biosphere and geosphere, and in particular, interactions
between humans and the earth through natural hazards. Many, if not all, of
these problems require techniques for investigating, multi-scale, multi-physics problems
and the meeting will emphasize both analytical and advanced computational methods for
such problems. This meeting provides a single multi-disciplinary forum for the exchange
of ideas and techniques across the disciplinary boundaries in the Earth Sciences. Funds
are requested to support travel costs for 20 students, post-docs and early career scientists
which is approximately half the number attending past meetings.
Broader Impacts This meeting is highly interdisciplinary and international in nature and
provides an important opportunity for U.S. students and early-career scientists from across
the earth sciences and applied mathematics to interact with senior scientists in a small informal
setting. This year there will also be an increased emphasis on mathematical aspects
of natural hazards in an attempt to understand how to merge fundamental knowledge of
earth processes with risk management and societal needs.

A combined microstructural and modeling investigation of mantle shear zones using outcrop scale relationships, tests and explores (a) extrapolation of experimental flow laws, development of lattice preferred orientation, and grain size evolution; and (b) models that predict strain localization and viscous shear heating instabilities. Research focuses on well-exposed shear zones in the Josephine peridotite (Klamath Mountains, Oregon) where shear zone boundaries can be easily identified and finite strain can be quantified by measuring the deflection of pre-existing pyroxene-rich bands. Field and laboratory studies assess models for lattice preferred orientation development and calibrate indicators of shear sense, viscous flow trajectory, and finite strain preserved in peridotite microstructures. Numerical modeling will reproduce strain distribution around shear zones in the Josephine peridotite, using viscoelastic rheology. Olivine flow laws and parameterizations of grain size evolution as a function of stress, strain, strain rate, and grain growth will be incorporated. Rheological properties constrained by observation of the shear zones are compared to the results of the numerical models that incorporate the same rheology. Forward models that approximately reproduce basic field observations will be used to: (a) investigate processes responsible for strain localization and, by analogy, tectonic plate boundaries; and (b) evaluate the hypothesis that viscous shear heating instabilities cause intermediate depth earthquakes in subduction zones, and perhaps other earthquakes in the shallow mantle, such as along oceanic fracture zones.

Results from laboratory deformation experiments of peridotite and its constituent minerals are widely used in geodynamical models of the upper mantle. Laboratory studies, however, use samples that are very small in comparison to upper mantle dimensions and are conducted at strain rates much higher than expected in the upper mantle. This study bridges the gap in size and time between laboratory studies and mantle-scale processes, which is essential for understanding upper mantle rheology. This not only further constrains geodynamical modeling, but will also improve understanding of processes controlling intermediate depth earthquakes, post-seismic deformation, preservation of cratonic roots, and the evolution of plate boundaries.

The purpose of this workshop is to bring together solid-earth geoscientists, mathematicians, computational and computer scientists to focus on specific
issues arising from a range of solid-Earth dynamics problems that have proven both difficult and critical for progress in studying and modeling the dynamics of the planet. These problems form the core activities for the Computational Infrastructure for Geodynamics (CIG) and provide new challenges and opportunities in multi-scale/multiphysics modeling and inference.

This workshop will focus on three related ?grand challenge problems? and their attendant mathematical/computational issues:

1. Mantle Convection and Lithospheric Deformation (large scale solid deformation with complex rheologies)
2. Magma Dynamics (multi-physics problems: Coupled fluid/solid flow in strongly deformable, reactive media)
3. Crustal Dynamics and the Earthquake Cycle (Multi-scale brittle mechanics
and fault evolution) The geophysical models at the heart of this workshop are developed further below and provide a common set of mathematical and computational problems that are essential for studying coupled natural systems. These include linear and nonlinear solvers and pre-conditioners for coupled problems, multi-scale methods for systems with space-time localization, multi-scale material modeling, and data-assimilation and inversion for integrating observations and dynamics.

These problems complement, but have significant differences from other application areas such as subsurface flow or climate modeling. Thus a primary goal of this workshop is to foster new collaborations between solid Earth scientists, mathematicians, computer scientists, and computational scientists that can make significant progress on these critical problems. The proposed meeting format is two and a half days of talks and discussion that closely connect the Earth science applications and mathematical/computational
problems and methods. In addition, the workshop will discuss critical issues in developing, disseminating and supporting advanced, collaborative modeling software for the general community, which is central to the CIG mission.

This workshop provides new opportunities for collaborative research
for students, early career scientists and senior scientists across a range of disciplines. The focus on developing advanced computational methods and software for exploring coupled systems should be useful for a wide range of related problems including subsurface fluid flow, earthquake engineering and hazards.

Intellectual Merit
The work proposed is to develop quantitative tools to model fluid flow and magmatism at subduction zones. The focus of the work will be on the top of the downgoing slab where fluids are released by metamorphic dehydration reactions, and the mantle wedge where fluids interact with high temperature solids to form magma. The work will start with 2-D models and extend to more challenging 3-D models.

Broader Impacts
This project will contribute to the modeling infrastructure of the marine geology and geophysics community and other communities as well. It will also address the need for the synthesis of geochemical and geophysical observations as the MARGINS program enters its final stages. Finally, it will support a full-time post-doc.

This project will provide both analysis and functioning open-source
software to evaluate the utility and applicability of the Extended
Finite Element Method (XFEM) to the problem of dynamic Earthquake
rupture on complex non-planar faults. While standard finite element
methods are applicable to many earthquake physics problems, the
requirement that the mesh be conformal to a complex, non-volume
forming network of faults is a fundamental difficulty, particularly in
3-dimensions. The XFEM, provides a potentially powerful alternative
by encoding discontinuous basis functions into the approximation space
without requiring faults to coincide with mesh edges, an approach that
naturally fits the earthquake rupture problem.

Preliminary work, however, demonstrates several complications that
arise in this application. Standard techniques for frictional failure
do not work with the XFEM, so new weak formulations of failure must be
developed. In addition, discrete singularities, which are effectively
removed in quasi-static engineering rupture problems, become crucial
in dynamic repeated rupture. These discrete problems can
fundamentally affect event statistics, and must be avoided.

The investigators will address these complications via analysis,
computation, and physical intuition. Specifically, they propose two
possibilities for weak failure criteria, and plan to test them with a
series of benchmark problems. Additionally, they propose analysis of
numerical accuracy of the weak frictional criteria, with the goal of
better understanding error in rupture propagation in these discrete
systems. In a second component, they plan to derive bounds for the
existence of mesh-fault interaction artifacts. Using these bounds, they
will either determine enrichment schemes that eliminate the artifacts
or develop meshing schemes to avoid them. Finally, the above work
will culminate in a proof of concept for the XFEM in repeated rupture
problems, and they will work to better understand event complexity in
complex fault systems. These problems provide an excellent
opportunity for collaboration between computational and applied
mathematicians and earthquake physicists.


Broader Significance:
Understanding the dynamics and probability of
Earthquakes on realistically complex fault networks is a fundamental
science and engineering problem that has direct consequences for
improved estimates of Earthquake hazards. Advanced computational
models, combined with observations, provide an important tool for
exploring and understanding these systems. A critical component of
such models, however is the geometric description and accurate
modeling of failure on non-planar faults which poses significant
challenges for traditional finite-element methods. This project will
investigate an alternative method that allows the description of the
fault network to be only loosely coupled to the computational mesh.
If this method is successful, it promises to significantly increase
the ease of describing and composing these problems and is better
suited to exploring the dynamics of fault networks, particularly under
the uncertainty of fault location. The proposed research will also
contribute to the computational infrastructure for modeling the
dynamics of brittle systems and earthquake genesis. The resulting open
source software will be distributed through the Computational
Infrastructure for Geodynamics (CIG: www.geodynamics.org), and be
accessible to a broad community of researchers with impact beyond the
immediate realm of Earthquake physics.

Have you ever wondered at the variety of self assembled deposit structures that can be obtained by evaporating liquids containing nanoparticles on top of a solid substrate. Deposit shapes vary from rings around a coffee drop, to hexagonal cells and fractal patterns. An interdisciplinary team of Columbia University scientists will study the related fascinating multiscale physics, using a combination of experimental, theoretical and numerical techniques. The team has the following skills: multiphase flow (Attinger, PI), colloids (Somasundaran), pattern recognition (Chang) and open-source computational fluid dynamics (Spiegelman). The complex self-assembly of nanoparticles will be studied by using first physical principles to explain the resulting selfassembled patterns (what we call a top-down approach), and by identifying features in the patterns that are signs of specific basic laws or transport rules (bottom-up approach).

Intellectual Merit:

Experiments will involve the spotting of microdrops of complex fluids on various substrates, fluorescence microscopy and laser profilometry to scan the three dimensional deposits. The first intellectual merit will be to describe with a phase diagram the self-assembly of nanoparticles during liquid evaporation on a solid substrate. The use of a phase diagram in that context is novel and allows a simple but powerful comparison of the magnitude of competing transport phenomena, such as evaporation at the wetting line, Marangoni recirculation, electrostatic and van der Waals forces, buoyancy, and dielectrophoresis. The phase diagram will provide an insight and an overview of the complex interplay between multiphase processes, influenced by the geometry of the liquid drop or film: fluid mechanics, heat transfer, mass transfer, colloidal interactions. Second, an available proprietary 2D-axisymmetric numerical code with a moving mesh able to very accurately track the free surface will be extended to 3D (see Chandra collaboration letter). This will allow the simulation of a wider ranges of boundary conditions, permitting the consideration of thin films and complex geometries. Explaining the self-assembly of nanoparticles from evaporating drops and liquid films from first principles is a challenging approach, given the multiple transport phenomena and time/length scales. Therefore, we will also develop a bottom-up approach based on pattern recognition of selfassembled features. We will test the hypothesis that the patterns tell us the about the physics that created them.

Broader Impact:

The proposed research will deliver innovative solutions to pattern nanoparticles on solid substrates, with applications in organic electronics and patterning of biomolecules for biosensors. Methods to increase printing resolution by two orders of magnitude (see Sonoplot letter), and to pattern uniform layers of particles will be investigated. The pattern recognition algorithms developed in this proposal will be tested to identify biomolecules (see Zenhausern letter) and enhance the accuracy of bloodstain pattern analysis, in collaboration with forensics expert MacDonell (see collaboration letter). Also, the 3D code developed in this proposal will be distributed freely as an open-source code, allowing every interested scientist to study problems involving drop and film transport phenomena such as drop impact, drop evaporation, film drying. Funding will support one graduate student.

Lava flows are abundant throughout the solar system, and are the most common fashion in which erupted magmas are emplaced. Lava flows hold key information about fundamental processes of planetary evolution, but at the same time present a great risk to the communities residing near some active volcanoes. Despite their clear importance in shaping the planet and affecting society, there are many open questions regarding the properties and behavior of lava flows. This project aims to combine a novel observational technique for measuring lava deformation in the field with a comprehensive flow modeling program in order to develop a better understanding of lava physical properties and the behavior and dynamics of active flows. Gaining more accurate descriptions of the mechanical properties of lavas in their natural environment and of the processes controlling flow emplacement will help address fundamental scientific questions, such as the way oceanic crust is formed or how the faces of volcanically-active moons and planets are shaped. The proposed work is applicable to lava flows in a wide range of environments.

The researchers will employ a new experimental, observational and analytical methodology designed to measure lava velocity in active channelized flows in great detail and to infer a rheology model from it. They will capture, in-situ, the entire surface velocity and temperature fields of the flowing lava using both visible and infrared high-resolution cameras. They make observations on both natural lava flows in active volcanoes (e.g., in Hawai'i or Italy) and man-made lava flows at the Lava Project experimental facility in Syracuse University (http://lavaproject.syr.edu). The theoretical aspects of this work will employ modern computer-vision techniques to extract the velocity field from the captured imagery. Data obtained in the experiments and in the field will be used to narrow down the most appropriate rheological model and parameters that are needed to describe flowing lava. This will be done by systematically examining numerical forward-models of channelized flow with varying rheologies and geometries. This work will be the first time that lava rheology and deformation are studied at such detail and close range. In parallel to the observational effort, it is planned to advance the computational tools used to model lava flows, in order to allow models that account for complex rheologies and flow structures. For example, they will strive to develop a modeling tool that will include the field-based rheological model and will support self- channelization, an important capability currently not available to the community. They will make their modeling tool general and flexible, to accommodate a wide set of eruption environments, including terrestrial, submarine and volcanic terrains on other planets.

Plate tectonics remains the over-arching context for solid earth geophysics and describes the motion of the solid Earth's surface by the relative movement of ~14 rigid plates that interact along weak boundaries. These boundaries provide the locus for most of the planet's earthquakes and volcanoes and while their location and relative motions are well described by plate tectonics, their dynamics and properties remain poorly understood. A key feature of plate boundaries, however, is that many of them are magmatic with active volcanism and it may be that the interaction of molten rock (magma) with its solid host can lead to the necessary structures and weakness preserving plate boundaries. Laboratory experiments by the PI and others, demonstrate that deformation of partially molten rocks can lead to spontaneous localization into melt-rich networks that weaken the rock and provide efficient paths for heat and melt transport. Thus understanding the dynamics of partially molten systems is critical for understanding the behavior and evolution of plate boundaries. The aim of this project is to advance our theoretical understanding of the process, in order to extrapolate results from experiments to a wide range of conditions in the Earth.

There exists a wealth of data from high-pressure and temperature experiments on partially molten rocks deformed in torsion, from which a great deal of information about the mechanisms active in stress-driven segregation may be inferred. The emphasis of this project is to develop better theoretical and computational models of these experiments. We are using two methods in parallel to model the process and compare model to experiment. The first is to develop numerical models of the partial differential equations derived from two-phase flow or magma dynamics theory, solved in torsional deformation geometry. A spinoff of this work will be the development and release of an advanced computational system for general multi-physics problems. The effects to be tested will include various constitutive models for matrix deformation as well as various effects of surface energy and damage. The second methodology is to develop effective macroscopic constitutive models within a non-equilibrium thermodynamic framework, using a formalism that is well-established in metallurgy but is just beginning to be applied to earth science. This method describes the structural characteristics of the material with "internal state variables", and tracks the stored and dissipated energy associated with those. The result will be thermodynamically consistent constitutive equations that can be solved in geodynamic models that explore the large-scale effects of stress-driven segregation occurring at length scales much smaller than can ever be resolved in a geodynamic model. This effective constitutive model will also include melt transport properties so that the potential consequences of coupling between deformation and fluid flow can be explored in subduction zones, ridges, rifts and other planetary settings.

The interactions of fluids and solids control some of the most critical geochemical and geodynamic processes in subduction zones. These include flux melting of the mantle and geochemical transport by fluids and magma, possible rheological weakening of the mantle wedge, and control of seismicity and fault mechanics. Quantitative models for the solid mantle flow have been developed but there has been relatively little work to numerically simulate the production, transport, and coupled interactions of fluids and melts with the solid. This requires a more general computational framework that can deal with a wide range of uncertainty both in the physical model and input parameter space. This project continues the development of TerraFERMA (the Transparent Finite Element Rapid Model Assembler), which will be used to: quantify potential fluid and solid flow paths at subduction zones; develop a better understanding of reactive, open system flux melting; and investigate the effects of fluids on solid-state rheology. Model predictions will be tested against a suite of observations from the relatively robust location of arc volcanism to the compositions of lava samples produced at these sites.

Broader impacts of this project include support of an early career scientist working at the interface between computational and Earth science and the development of a new computer code for integrating geochemical and geochemical dynamics in subduction zones. The resulting computer code will be incorporated into holdings of Computational Infrastructure for Geosciences, which provides open access to software for scientific purposes. Increased understanding of mantle deformation, magmatism, and thermal structure of the Earth at subduction zones could lead to improved knowledge of where brittle behavior (earthquakes) is more or less likely along the megathrust fault that marks the boundary between the downgoing plate and the surrounding mantle.

This project involves an interdisciplinary study of hydration, carbonation and oxidation of mantle peridotite interacting with aqueous fluids at temperatures below ~ 300C. The PIs will combine observations of outcrops and boreholes, geochemical analyses, structural measurements, geomechanical experiments and numerical modeling to investigate feedback between alteration and fluid transport, and to quantify the resulting geochemical fluxes. Field observations and sampling will take place mainly in the Samail ophiolite of Oman, where peridotite has undergone spreading-ridge-related hydrothermal alteration, hydration and carbonation in the hanging-wall of the subduction zone that emplaced the ophiolite over metasediments, and subaerial weathering. The PIs project will provide matching funds and results that dovetail with the 2015-2018 International Continental Scientific Drilling Program (ICDP) Oman Drilling Project, and the many other related efforts just getting underway. The PIs will continue their independently supported research on subduction zone alteration of mantle wedge peridotites at a range of pressures and temperatures, and work closely with other groups investigating seafloor and subduction-related peridotite alteration, in order to quantify the similarities and differences in alteration processes in these different tectonic environments. They will generalize their results to global alteration processes and geochemical cycles.

Alteration of peridotite is an essential process in Earth dynamics. Hydration of oceanic crust and mantle, followed by subduction, supplies water to drive arc volcanism, and modulates the hydrogen content of the mantle over time. Carbonate formation during alteration of peridotite, near the surface and in the hanging wall in subduction zones, is an important but poorly characterized link in the carbon cycle. Oxidation of minerals and concomitant reduction of fluids produces H2 and hydrocarbons, and a niche for chemosynthetic microbes. Chemical weathering is as important as magmatism and plate tectonics in shaping the Earths surface. The interplay of chemical and physical mechanisms of peridotite alteration is not well understood, but will be transformed as a result of emerging understanding of equilibria and kinetics in peridotite alteration, and reaction-driven cracking that has left us poised on the brink of a breakthrough at this little-studied frontier. The PIs will take advantage of low temperature, near surface, active peridotite alteration in Oman to study inputs, outputs, and the reaction zone in situ. Such a study is more difficult in smaller peridotite exposures with limited outcrop and more rainfall, nearly impossible in submarine hydrothermal systems, and completely impossible in studies of ancient systems. Such a comprehensive approach via 250 to 600 meter boreholes is very rare, if not unprecedented.

Many important processes in the natural and engineered world involve the infiltration of fluids into materials that then react to form new materials with significantly larger volume. These large volume changes, in turn are thought to induce fracturing which opens up new avenues for fluid infiltration, potentially leading to a cascade of pervasively cracked materials in a process dubbed ?reaction induced cracking?. While many natural systems give indirect evidence of these processes, very little is understood about the physics and efficiency of these mechanisms (or if they even work). The purpose of this proposal is to develop a fundamental understanding of the reactive cracking process by combining laboratory experiments, theory and advanced computational models of reactive brittle materials. A better understanding of these processes could lead to new engineering methods for efficient carbon sequestration or hydrocarbon extraction, could give insight into induced seismicity as well important Earth science processes in the natural world.

During this award, we will combine laboratory rock mechanics experiments on simplified systems with computational models that can be used to test and validate a range of hydro-mechanical failure theories directly against the experiments. Lab experiments will be conducted in Lamont?s tri-axial deformation apparatus, with control of fluid flow and monitoring of stresses, pore pressures, acoustic emissions and permeability changes. Experiments will investigate both hydration and dehydration reactions on analog materials chosen to provide large volume changes in a simplified geometry. We will explore the behavior of nested cylinders of materials with an interior reactive cylinder that can either produce or ingest hydrous fluids, surrounded by an outer cylinder of brittle rock under various level of confining pressure. The modeling will be a collaborative effort across multiple departments and schools at Columbia and use an open-source computational framework developed by the PIs. Direct modeling of the experiments will provide the needed control for testing hypotheses, validating theories, and calibrating constitutive relations and failure models. Improved theoretical models of fluid-brittle solid interaction can then be extended to explore their consequences for large-scale geodynamics such as volatile cycling through subduction zones.

Earth scientists seek to understand the mechanisms of planetary evolution from a process perspective in order to promote the progress of science. They model the chemistry of melting of the interiors of planets as a result of heat flow within the body. They calculate the flows of energy and mass from the interior to the surface. They model the interaction of fluids and rocks, which drives chemical weathering and the formation of ore deposits. They seek to understand the synthesis and stabilities of organic compounds and their economic and biological roles. They study the interactions of atmosphere, oceans, biosphere and land as a dynamically coupled evolving chemical system. To achieve this level of understanding of planetary evolution, Earth scientists use software tools that encode two fundamentally different types of models: (1) thermodynamic models of naturally occurring materials, and (2) models of transport that track physical flows of both fluids and solids. Much of the fundamental science of planetary evolution lies in understanding coupled thermodynamic and transport models. This grant funds development of a software infrastructure that supports this coupled modeling of the chemical evolution of planetary bodies. It is their aim to establish an essential and active community resource that will engage a large number of researchers, especially early career scientists, in the exercise of model building and customization.

This is a project to create ENKI, a collaborative model configuration and testing portal that will transform research and education in the fields of geochemistry, petrology and geophysics. ENKI will provide software tools in computational thermodynamics and fluid dynamics. It will support development and access to thermochemical models of Earth materials, and establish a standard infrastructure of web services and libraries that permit these models to be integrated into fluid dynamical transport codes. This infrastructure will allow scientific questions to be answered by quantitative simulations that are presently difficult to impossible because of the lack of interoperable software frameworks. ENKI, via the adoption of state-of-the-art model interfacing (OpenMI) and deployment environments (HubZero), will modernize how thermodynamic and fluid dynamic models are used by the Earth science community in five fundamental ways: (1) provenance tracking will enable automatic documentation of model development and execution workflows, (2) new tools will assist users in updating thermochemical models as new data become available, with the ability to merge these data and models into existing repositories and frameworks, (3) automated code generation will eliminate the need for users to manually code web services and library modules, (4) visualization tools and standard test suites will facilitate validation of model outcomes against observational data, (5) collaborative groups will be able to share and archive models and modeling workflows with associated provenance for publication. With these tools we seek to transform the large community of model users, who currently depend on a small group of dedicated and experienced researchers for model development and maintenance, into an empowered ensemble of model developers who take ownership of the process and bring their own expertise, intuition and perspective to shaping the software tools they use in daily research. ENKI development will be community driven. Participation of a dedicated and diverse group of early career professionals will guide us in user interface development - insuring portal capabilities are responsive to user needs, and in development of a rich set of documentation, tutorials and examples. All software associated with this project will be released as open source.