IAM Event Schedule

Event Schedule 2011/12

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The 2011/12 IAM seminar talks take place from 3:00 pm to 4:00 pm on Mondays in Room 301, Leonard S. Klinck Building, 6356 Agricultural Road, UBC, unless noted otherwise. Refreshments start 15 minutes before each talk in the IAM Lounge, Room 306.

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Upcoming Events

Monday, 13 Feb 2012, 3:00-4:00 pm, LSK 301: IAM Seminar Series and Fluids Seminar
Prof. Eckart Meiburg, Department of Mechanical Engineering, University of California at Santa Barbara, California
Gravity and Turbidity Currents Interacting with Submarine Topography

We will present an overview of high-resolution, Navier-Stokes based simulations of gravity and turbidity currents. The turbidity currents are driven by particles that have negligible inertia and are much smaller than the smallest length scales of the buoyancy-induced fluid motion. For the mathematical description of the particulate phase an Eulerian approach is employed, with a transport equation for the particle-number density.
We will discuss differences between two- and three-dimensional turbidity current dynamics, and we will introduce some effects due to complex topography. Results will be shown regarding the unsteady interaction of a gravity current with a submarine structure, such as a pipeline. Furthermore, we will discuss the linear stability problem of channel and sediment wave formation by turbidity currents.

Tuesday, 14 Feb 2012, 12:30-13:30, WMAX 110: SCAIM Seminar
Tristan van Leeuwen, Department of Earth and Ocean Sciences, UBC
Recent Advances in Seismic Waveform Inversion

Images obtained from (active) seismic data are used by the oil and gas industry for geophysical exploration. Waveform inversion tries to obtain a detailed image of the subsurface by solving a PDE-constrained optimization problem. The scale of the problem – typically 109 unknowns – and the size of the data – typically 1015 data points – severely limits us in the approaches that we can use to solve the problem. On top of that, the problem is highly nonlinear and the least-squares objective exhibits local minima. In this talk, I will give an overview of typical issues in waveform inversion and present recent research that addresses some of these issues. This includes optimization techniques that work with only small portions of the data at a time, robust data-fitting schemes and formulations that incorporate other unknown parameters, such as the source signature. Finally, I will discuss the object-oriented framework that we have developed in Matlab to test these algorithms.

Monday, 27 Feb 2012, 3:00-4:00 pm, LSK 301: Fourth IAM Distinguished Alumni Lecture
Prof. Marc Mangel, Department of Applied Mathematics and Statistics, University of California at Santa Cruz, California
Of Flour Beetles and Wikipedians

I will begin with a summary of the principles that have guided my work over the last 30+ years. Then I will explain a classic problem in population biology: the competition between species of flour beetles that had both determinate (always the same) and indeterminate (probabilistic) outcomes, according to the initial sizes of the competing species. I will describe a number of methods that were used to solve the problem, including one that Don Ludwig and I developed during my PhD studies, and extension of those methods to other problems in biology. I will then turn to the Wikipedia, describe the dynamics of the editors of the Wikipedia, and show that the methods used to characterize the outcome of competition between flour beetles can also be used to characterize the success or failure of a Wikipedia based on its early patterns. The latter work suggests various kinds of levels that can make Wikipedias more or less likely to succeed.

Marc Mangel holds BS (Physics) and MS (Biophysics) degrees from the University of Illinois and a PhD (Applied Mathematics and Statistics) degree from the University of British Columbia. After three years at the Center for Naval Analyses, he joined the University of California at Davis. From 1980 to 1996, he served as Assistant, Associate and Full Professor � for eight years in the Department of Mathematics and eight years in the Department of Zoology (Section of Evolution and Ecology). He chaired the Department of Mathematics (1984-1989) and was founding Director of the Center for Population Biology (1989-1993). Currently Marc is Distinguished Professor of Applied Mathematics and Statistics and Director of the Center for Stock Assessment Research at the University of California Santa Cruz, where he has served since 1996. At Santa Cruz, he directed the Geographic Information Systems Laboratory (1996-1999), served as Associate Vice Chancellor, Planning and Programs (1997-1999), and chaired the Department of Applied Mathematics and Statistics (2007-09). Since July 2010, he has also chaired the Program in Technology and Information Management.

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Tuesday, 28 Feb 2012, 12:30-13:30, WMAX 110: SCAIM Seminar
Christoph Schwarzbach, Department of Earth and Ocean Sciences, UBC
Finite Element Based Inversion for Geo-Electromagnetics

High contrast in electrical conductivity motivates the investigation of electromagnetic methods in geophysics, for instance, for hydrocarbon and mineral exploration. A straightforward approach to modelling the spatial distribution of this parameter within the earth is the assumption of piecewise constant values, defined on a moderately fine tessellation of the volume under investigation by hexahedra or tetrahedra. We study here the solution of the 3-D forward problem for time-harmonic electromagnetic fields using finite elements, based on the above mentioned tessellation. Furthermore, we seek to reconstruct the spatial distribution of conductivity of an overparameterized model by a regularised output least squares approach. Our model assumption, a piecewise constant coefficient, allows for simplifications of the forward solver which eventually lead to an overall faster imaging algorithm. The model assumption also requires special care when the regularisation operator is derived for unstructured meshes within the finite element framework.

Monday, 05 Mar 2012, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Prof. Andy Woods, Department of Earth Sciences, University of Cambridge, United Kingdom
Modelling Carbon Sequestration Processes

In this talk we will present a series of models of the motion of CO₂ following injection into the subsurface, including models of the migration of a buoyant plume as it experiences capillary trapping, drainage and dissolution in a heterogeneous rock. The models will focus on identifying leakage pathways and the fraction of the CO₂ which may leak from the system. We will also present models of the dynamics of near surface leakage including possible lake eruptions driven by CO₂ seeps.

Professor Andy Woods has research interests in a wide range of fluid mechanical problems, ranging from the dynamics of explosive volcanic systems and natural ventilation to oil recovery, geothermal energy and carbon sequestration. He has been a Green Scholar at Scripps Institution of Oceanography and won several prestigious awards including the Marcello Carapezza Prize and the Wagner Medal. He is currently the B.P. Professor of Applied Mathematics and Geophysics at the University of Cambridge, as well as the Director of the B.P. Institute for Multiphase Flow.

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Monday, 12 Mar 2012, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Prof. Andrew Bernoff, Department of Mathematics, Harvey Mudd College, Claremont, California
Langmuir Layers: Exploring A (Nearly) Two-Dimensional Fluid Experiment

A Langmuir Layer is a molecularly thin layer of a polymer, lipid or liquid crystal on the surface of another fluid. In this (nearly) two-dimensional layer, we can observe bubbles of a fluid phase that even when stretched or highly contorted always appear to return to a circular shape. The force driving these evolutions is line tension, a two-dimensional analog of surface tension. We report on a combined experimental, theoretical, and numerical study of Langmuir layers and show how we can deduce the strength of the line tension in the system by comparing theory and experiment. As time permits we will also describe other phenomena observed in Langmuir systems, including collapse of gas phase bubbles, co-existence of three or more fluid phases, and formation of dogbone and labyrinth patterns due to dipolar repulsion in the layer. This work is the result of collaboration with Prof. Elizabeth Mann, an experimental physicist at Kent State University, Prof. J. Adin Mann, Jr., a chemical engineer at Case Western Reserve University, and Prof. James Alexander, a mathematician also at Case Western Reserve University and is supported by the National Science Foundation.

Andrew Bernoff is a Professor of Mathematics at Harvey Mudd College. His research specializes in bridging the gaps between mathematics, physics, biology and engineering with a particular emphasis on using dynamical systems methods to understand experiments and natural phenomena. Prof. Bernoff was an undergraduate at MIT where he received BS degrees in mathematics and physics. While an undergraduate, he founded the MIT Integration Bee. In 1978 he was awarded a Marshall Scholarship to pursue a PhD at the University of Cambridge in England. His PhD studies were on the application of dynamical systems methods in fluid mechanics in the Department of Applied Mathematics and Theoretical Physics (DAMTP). Prof. Bernoff has spent time on the faculty at Northwestern, Duke and the University of California at Berkeley before settling in at Harvey Mudd College, where he is the Diana and Kenneth Jonsson Professor of Mathematics and Chair of the Mathematics Department. He is passionate about mentoring undergraduate research, coaching the Harvey Mudd College Putnam Team, and supporting Harvey Mudd College�s Clinic Program, a year-long practicum in which teams of undergraduates work for industrial sponsors on real-world problems and applications. His NSF-supported research program centers on understanding the behavior of fluids at small scales and modeling the swarming of organisms, in particular locusts, and is built on collaborations at multiple colleges and universities.

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Monday, 19 Mar 2012, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Prof. John M. Guckenheimer, Mathematics Department, Cornell University, Ithaca, New York
Complex Oscillations

Biological and chemical systems display bursting and mixed mode oscillations. This lecture will survey recent advances in the theory of dynamical systems with multiple time scales that has dramatically improved our understanding of these complex temporal behaviors. A natural classification of different types of bursting and mixed modes is developed and used as a foundation for numerical methods that analyze multiple time scale models. These methods are applied to mixed mode oscillations of chemical reactions that were intensively studied thirty years ago without producing models that faithfully reproduced experimental observations. Additional examples are drawn from neuroscience.

John Guckenheimer obtained his Ph.D. from University of California at Berkeley in 1970 and is currently the Abram R. Bullis Professor in Mathematics at Cornell University. His research is a blend of theoretical investigation, development of computer methods and studies of nonlinear systems that arise in diverse fields of science and engineering. Two of the primary themes have been bifurcation theory and the effects of multiple time scales in shaping dynamical behavior. Application areas in which he has worked include population biology, fluid dynamics, neurosciences, animal locomotion and control of nonlinear systems. His work on algorithm development includes contributions to methods for computing bifurcations, periodic orbits and invariant manifolds of vector fields and for the analysis of fractal dimensions of attractors.

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Monday, 26 Mar 2012, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Prof. Richard Montgomery, Department of Mathematics, University of California at Santa Cruz, California
From Brake to Syzygy in the Three-Body Problem

A brake orbit for the Newtonian three-body problem is a solution for which all three velocities are zero at some instant: the brake instant. If we follow such an orbit there will be a later instant at which the three bodies become colinear: the instant of syzygy. In this manner we can define a flow-induced "Poincare map" from brake initial conditions to syzygy configurations. Appropriately viewed, this brake-to-syzygy map is a map between planar domains. Understanding its image destroyed certain myths that the speaker had regarding action-minimizing orbits. The map fits in towards a possible global understanding of the planar three-body problem which we will explain. Key is a viewpoint on the planar three-body problem in which the configuration of all three bodies is represented as a single point in 3-space (its "shape") and in which Newton's equations become a mechanical system on this 3-space. Some movies of Paul Klee-like periodic brake orbits inspired by this work will be shown.

Richard Montgomery got undergraduate degrees in mathematics and physics from Sonoma State in Northern California in 1980. He got his PhD under Jerry Marsden at Berkeley in 1986 and after that had a Moore Instructorship at MIT for two years, then two years of postdoc in Berkeley. His research fields are geometric mechanics, celestial mechanics, control theory, and differential geometry. He is perhaps best known for his rediscovery, with Alain Chenciner, of Cris Moore's figure eight solution to the three-body problem, which led to a slew of new 'choreography' solutions. He also established the existence of the first-known abnormal minimizer in subRiemannian geometry (in control lingo this is an abnormal extremal for a problem linear in controls, with control quadratic cost function), and is known for investigations using gauge-theoretic ideas of how a falling cat lands on its feet. He has written one book on subRiemannian geometry. In addition to mathematics and mechanics, he is a minor slowly fading legend in the kayaking world of California for first descents done in the early 1980s. He has two daughters, is married, and lives and works in Santa Cruz, CA.

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Past Events

Tuesday, 13 Sep 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Luis Zarrabeitia, University of Ontario, Institute of Technology
Extracting 3D Blood Flight Trajectories from Videos for Forensic Analysis

At present, blood stain pattern analysis (BPA) is a largely qualitative sub-discipline of forensic science. Our ultimate aim is to develop software for quantitative analysis to aid BPA forensic analysts. Towards this end, we are developing a sound physics-based model (i.e, incorporating gravity and air resistance) for bloodstain pattern formation using pre-recorded videos of simulated blood-letting events. The simulations consist of fake blood encased in ballistic gel being splattered by projectiles. The resulting blood flight trajectories are recorded by a high speed camera.
We present a method for extracting the three-dimensional flight trajectories of liquid droplets from video data. A high-speed stereo camera pair records videos of experimental reconstructions of projectile impacts and ensuing droplet scattering. After background removal and segmentation of individual droplets in each video frame, we introduce a model-based matching technique to accumulate image paths for individual droplets. Our motion detection algorithm is designed to deal gracefully with the lack of feature points, with the similarity of droplets in shape, size, and color, and with incomplete droplet paths due to noise, occlusions, etc. The final reconstruction algorithm pairs two-dimensional paths accumulated from each of the two cameras' videos to reconstruct trajectories in three dimensions.
Traditional forensic methods for reconstructing crime scenes, such as "stringing", ignore the effects of gravity and drag. Our preliminary results show that gravity and drag play an important role in the trajectories of the droplets. The reconstructed droplet trajectories constitute a starting point for a physically accurate model of blood droplet flight for forensic bloodstain pattern analysis.
This is joint work with Dhavide Aruliah and Faisal Qureshi, based on experiments by Raquel Murray, Paul Prior and Franco Gaspari.

Monday, 19 Sep 2011, 3:00-4:00 pm, LSK 301: IAM Seminar Series
Prof. David Muraki, Department of Mathematics, Simon Fraser University
Rossby Waves on the Sphere for Rotating Shallow Water

There is a marked difference in the weather patterns and climate between the Earth's equatorial and midlatitude regions. Much of this difference is due to the active role of moisture and convection in the tropics. However, the even the dry fluid dynamiics of both regions are sufficiently different that their wave theories are typically found in disjoint chapters in the textbooks on atmospheric science. In this talk, two aspects of planetary waves are given a unified presentation for the entire sphere. The first is an extension of the midlatitude concept of potential vorticity which now gives a description for waves crossing the equator. The second is an embedding of equatorial wave theory into a global context that includes the tradewinds which are known to block midlatitude waves from the tropics.

Wednesday, 21 Sep 2011, 2:00 pm, Math 125: Fluids Seminar
Mona Rahmani, Department of Civil Engineering, UBC
Kelvin-Helmholtz Instabilities in Sheared Density Stratified Flows

Kelvin-Helmholtz instabilities are the most commonly studied type of instability in sheared density stratified flows. Turbulence caused by these instabilities is an important mechanism for mixing in geophysical flows. The primary objectives of this study are the evolution of these instabilities and quantifying the mixing they generate using direct numerical simulations. The evolution of primary Kelvin-Helmhlotz instabilities in two dimensions is studied for a wide range of Reynolds and Prandtl numbers, representing real oceanic and atmospheric flows. The results suggest that some properties of KH billows are predictable by a semi-analytical model. It is shown that a new Corcos-Sherman scale is a useful guide when simulating turbulent KH flow fields. The details of the mixing process generated by the evolution of Kelvin-Helmholtz instabilities as it goes through different stages, is analyzed. As the Reynolds number increases a transition in the overall amount of mixing is found, which is in agreement with previous experimental studies. This transition is explained quantitatively by the entrainment and mixing caused by three-dimensional motions, in addition to those resulted from the two-dimensional growth of the instability. The effect of Prandtl number on mixing is studied to understand the characteristics of high Prandtl number mixing events in the ocean; these cases have usually been approximated by low Prandtl number simulations. The increase in the Prandtl number has some significant implications for the evolution of the billow, the time variation of mixing properties, and the overall mixing.

Monday, 26 Sep 2011, 3:00-4:00 pm, LSK 460: IAM Seminar Series
Prof. Bhushan Gopaluni, Department of Chemical and Biological Engineering, UBC
Time Series Modeling in Process Control: State-of-the Art and Challenges

Process control engineers have been using time series models in a variety of applications for many decades. In this presentation, a number of approaches to linear and nonlinear dynamic models including recent advances in application of Markov Chain Monte Carlo simulations will be discussed. A variety of applications from oil & gas, pulp & paper, and biotech/biomedical industries will be outlined. While the theory and applications of these models have evolved over the years, a number of challenges remain, especially in modeling processes with sparse measured data. These challenges and potential avenues for solutions will be addressed.

Monday, 03 Oct 2011, 3:00-4:00 pm, LSK 301: IAM Seminar Series
Prof. Robert Bridson, Department of Computer Science, UBC
Computational Geometry and Physics in Feature Film Animation

I'll discuss the joys and sorrows of simulating liquids for visual effects in films, with a focus on surface tracking which lies in the intersection of fluid dynamics, computational geometry, and scientific computing. Specific problems include controling water to stay close to a director's vision, and low-level algorithms for tracking water surfaces with meshes. I'll reveal a brand new approach from our research group that robustly deals with the related problem of continuous collision detection, which extends into several interesting mathematical topics in its own right. Gratuitous scenes of computer-generated sharks eating jet-skiers will be shown.

Wednesday, 05 Oct 2011, 2:00 pm, Math Annex 1118: Fluids Seminar
Giovanni Ghigliotti, Department of Chemical and Biological Engineering, UBC
Vesicles and Red Blood Cell Clusters in Poiseuille Flow

We present 2D numerical simulations of sets of vesicles (closed bags of a lipid bilayer membrane) in a parabolic flow, a setup that mimics red blood cells in the microvasculature. Vesicles, submitted to sole hydrodynamical interactions, are found to form aggregates (clusters) of finite size. The existence of a maximal cluster size is pointed out and characterized as a function of the flow intensity and the swelling ratio of the vesicles. Moreover bigger clusters move at lower velocity, a fact that may prove of physiological interest. These results quantify previous observations of the inhomogeneous distribution of red blood cells in vivo. An interpretation of the phenomenon is put forward based on the presence of boli (vortices) between vesicles. Both the results and the explanation can be transposed to the three-dimensional case.

Monday, 17 Oct 2011, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Prof. Joel A. Tropp, Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Low-Rank Matrix Decompositions

Computer scientists have long known that randomness can be used to improve the performance of algorithms. A familiar application is the process of dimension reduction, in which a random map transports data from a high-dimensional space to a lower-dimensional space while approximately preserving some geometric properties. By operating with the compact representation of the data, it is theoretically possible to produce approximate solutions to certain large problems very efficiently. Recently, it has been observed that dimension reduction has powerful applications in numerical linear algebra and numerical analysis. This talk provides a high-level introduction to randomized methods for computing standard matrix approximations, and it summarizes a new analysis that offers (nearly) optimal bounds on the performance of these methods. In practice, the techniques are so effective that they compete with – or even outperform – classical algorithms. Since matrix approximations play a ubiquitous role in areas ranging from information processing to scientific computing, it seems certain that randomized algorithms will eventually supplant the standard methods in some application domains. This is joint work with Gunnar Martinsson and Nathan Halko (the paper is available here).

Joel A. Tropp is Assistant Professor of Applied & Computational Mathematics at the California Institute of Technology. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. Dr. Tropp�s work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. The bulk of this research concerns the theoretical and computational aspects of sparse approximation, compressive sampling, and randomized linear algebra. He has also worked extensively on the properties of structured random matrices. Dr. Tropp has received several major awards for young researchers, including the 2007 ONR Young Investigator Award and the 2008 Presidential Early Career Award for Scientists and Engineers. He is also winner of the 6th Vasil A. Popov prize and the 2011 Monroe H. Martin prize.

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Tuesday, 18 Oct 2011, 12:30-1:30 pm, WMAX 110: SCAIM Seminar
Markus Bürg, Karlsruhe Institute of Technology, Germany
A Fully Automatic hp-Adaptive Refinement Strategy

The finite element method is a widely accepted tool for the numerical solution of partial differential equations. Nowadays a posteriori error estimation is an expected and assessed feature in scientific computing. It is used for adaptively creating approximation spaces and to assess the accuracy of numerical solutions. The performance of the method can be improved by mesh refinement (h-refinement) or the use of higher oder ansatz spaces (p-refinement). Taking a combination of both (hp-refinement) can lead to exponentially fast convergence with respect to the number of degrees of freedom. Especially for hp-FEM there have been proposed several strategies for adaptively creating problem-dependent meshes, e.g. estimating the analyticity of the solution, solving local boundary value problems and minimize the global interpolation error can be minimized. In this talk we present a fully automatic hp-adaptive refinement strategy, which is based on the solution of local boundary value problems. We present the strategy for the Poisson and the Maxwell boundary value problem and show convergence of the algorithm. The talk is concluded by some numerical examples.

Wednesday, 19 Oct 2011, 2:00-3:00 pm, Math Annex 1118: Fluids Seminar
Mohammad Taghavi
From Displacement to Mixing in a Slightly Inclined Duct

This work studies buoyant displacement flows with two miscible fluids in pipes and 2D channels that are inclined at angles close to horizontal. Detailed experimental, analytical and computational approaches are employed in an integrated fashion. The displacements are at low Atwood numbers and high Peclet numbers, so that miscibility effects are mostly observable after instability and via dispersive mixing. For iso-viscous Newtonian displacements, studying the front velocity variation as a function of the imposed flow velocity allows us to identify 3 distinct flow regimes: an exchange flow dominated regime characterized by Kelvin-Helmholtz-like instabilities, a laminarised viscous displacement regime with the front velocity linearly increasing with the mean imposed flow rate, and a fully mixed displacement regime. The transition between the first and the second regimes is found to be marked by a stationary layer of displaced fluid. In the stationary layer the displaced fluid moves in counter-current motion with zero net volumetric flux. Different lubrication/thin-film models have been used to predict the flow behaviour. We also succeed in characterising displacements as viscous or inertial, according to the absence/presence of interfacial instability and mixing. This dual characterisation allows us to define 5-6 distinct flow regimes, which we show collapse onto regions in a two-dimensional parameter plane. In each regime we have been able to offer a leading order approximation to the leading front velocity. A weighted residual method has also been used to include the effect of inertia within the lubrication modelling approach, which allows us to predict long-wave instabilities.

Friday, 21 Oct 2011, 3:00 pm, Math Annex 1100: Math Department Colloquium
Dominik Schötzau, Department of Mathematics, UBC
hp-Adaptive Finite Element Methods

We develop hp-adaptive finite element schemes for the numerical approximation of linear second-order elliptic boundary-value problems. We begin by reviewing some classical results from the late eighties. Then we show that on geometrically and anisotropically refined meshes in three dimensional polyhedral domains, hp-methods achieve exponential rates of convergence in the number of degrees of freedom, thereby proving a longstanding conjecture in the theory of hp-finite element methods. In the last part of the talk, we discuss some recent results related to fully automated hp-adaptivity and illustrate numerically that our proposed adaptive refinement strategies lead to exponential rates of convergence. The talk includes work done with my former Ph.D. student Liang Zhu.

Monday, 24 Oct 2011, 3:00-4:00 pm, LSK 301: Special IAM Workshop
Prof. Ian Mitchell, Department of Computer Science, UBC; and Prof. Dhavide Aruliah, University of Ontario institute of Technology
A Course on Reproducible Research in Computational and Data Science: What Should it Be?

Computers have become a vital tool in all areas of research. Unfortunately the software and data that enables this research is too often developed and managed in a haphazard fashion. Reproducible research is the idea that research contributions in the computational and data sciences involve not only publication of an article in an academic venue, but also release of sufficient components of the software and data such that the results claimed in the publication can be reproduced and extended by other scientists. Reproducible research therefore is a cornerstone of open access to scientific scholarship. Starting in January 2012, the presenters will be offering a pilot course on tools, techniques & strategies to improve the reproducibility of scientific research of a computational or data-intensive nature. The goals of this panel discussion are to inform the UBC community of our intentions with this course and to solicit feedback from the community on what the course should contain. Topics may include: tools and best-practices for software management; data provenance, anonymization and maintenance; intellectual property issues; avenues for effective dissemination; case studies (both good and bad).

Dr. Ian M. Mitchell completed his doctoral work in engineering at Stanford University in 2002, spent a year as a postdoctoral researcher at the University of California at Berkeley and is now an Associate Professor of Computer Science at the University of British Columbia. His research interests include scientific computing, cyber-physical systems, formal methods for verification robotics and reproducible research.

Dr. Dhavide Aruliah obtained his doctorate from the Department of Computer Science at UBC in 2001. He was subsequently a postdoctoral fellow at the Fields Institute for Research in the Mathematical Sciences and then at the University of Western Ontario. Since 2004, he has been at the University of Ontario Institute of Technology (Oshawa, ON) where he is an associate professor in the Faculty of Science. At present, he is a Visiting Professor in Department of Computer Science at UBC. His research interests are in scientific computing, specifically in computational inverse problems and the numerical solution of PDEs. He is also interested in software design for scientific computing, specifically in how scientists actually use scientific software.

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Tuesday, 25 Oct 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Lisa Gordeliy, Department of Mathematics, UBC
Modelling Hydraulic Fractures using a Boundary Element Method (BEM) and the Extended Finite Element Method (XFEM)

This talk presents the development of BEM and XFEM frameworks for modelling hydraulic fractures, which arise in a wide range of geoengineering applications. The mathematical formulation of the problem involves a system of coupled nonlinear partial differential equations with a moving boundary, arising from the coupling between the fluid flow in the evolving fracture and the deformation of the parent material. Each of the discussed approaches has its own advantages: the BEM can efficiently simulate a propagating crack in linear homogeneous domains, while the XFEM is able to model complex settings such as multiple fractures in porous and layered rocks or plastic material deformation. The first part of the talk presents a BEM algorithm coupled with the finite-volume fluid flow model. An example of a near-surface radial crack is investigated, for which the required Green's functions, that represent the crack as a distribution of material discontinuities, are derived. A comparison of the numerical results generated by this numerical model with data from laboratory experiments identifies particular physical phenomena that have to be accounted for in the mathematical formulation for accurately capturing the complex fracture propagation process. In the second part of the talk, an XFEM approach to this problem is discussed. The development includes derivation of shape functions that enrich the underlying finite element formulation by representing discontinuities and singularities associated with the hydraulically driven crack. An example is presented in which a coupled XFEM model simulates a crack driven by a viscous fluid through a layered material.

Monday, 31 Oct 2011, 3:00-4:00 pm, LSK 301: IAM Seminar Series and MathBio Seminar
Yanghong Huang, Department of Mathematics, Simon Fraser University
A Nonlocal Aggregation Model with Repulsive-Attractive Kernels

We consider the aggregation equation ρ_t = ∇ · (ρ∇K ∗ ρ) in ℜⁿ, where the interaction potential K models short-range singular repulsion and long-range power-law attraction. Here, ρ represents the density of the aggregation and K is a social interaction kernel that models attraction and repulsion between individuals. We show that there exist unique radially symmetric equilibria supported on a ball. We perform asymptotic studies for the limiting cases when the exponent of the power-law attraction approaches infinity and a Newtonian singularity, respectively. Numerical simulations suggest that equilibria studied here are global attractors for the dynamics of the aggregation model. This work is in collaboration with Razvan Fetecau (SFU) and Theodore Kolokolnikov (Dalhousie).

Tuesday, 01 Nov 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Ye Yang, University of Cincinnati
An Enriched Space-Time Finite Element Method for Nonlinear Continuum Systems

There is a continuing interest in developing numerical methods for treating problems that are characterized by multiple time scale features. Traditional finite element method (FEM) based on semi-discrete schemes, however, is not well suited for these classes of problems due to their lack of flexibility in establishing multiscale approximations in the temporal domain. In this presentation, we show that a multiscale method that is capable of incorporating both multiple spatial and temporal features can be established based on the space-time discontinuous Galerkin method which was originally developed in the context of linear elastodynamics. After an initial assessment of the convergence and its connection to the various time stepping algorithms, we show that space-time FEM is a stable, high-order convergent numerical method. We further explore the incorporation of fine scale features based on the extended finite element method. The nonlinear formulation incorporating enriched space-time FEM with stabilization least-square term is further developed and numerical solution based on GMRES is proposed. Through numerical examples, it is shown that multiscale space-time FEM enjoys superior convergence properties over the traditional space-time FEM and the proposed method represent a new paradigm towards resolving structural and solid mechanics problems with strong temporal nonlinearity.

Wednesday, 02 Nov 2011, 2:00-3:00 pm, Math Annex 1118: Fluids Seminar
Sarah Hormozi, Department of Mathematics, UBC
Visco-Plastic Lubrication: From Theory to Application

Interfacial instabilities of multi-layer shear flows may be eliminated by astute positioning of yield stress fluid layers that remain unyielded at the interface(s). This lecture consists of three parts. Firstly, I present a computational study of these flows in the setting of a Newtonian core fluid surrounded by a Bingham lubricating fluid, within pipe and channel configurations. The simulations include an inlet geometry in the computational model and study the multi-layer flows, both as the fluids are initially injected (start up) and later the established steady flows (development lengths). Nonlinear perturbations are also studied, showing in particular that during energy decay of stable perturbations the initial rapid decay of the perturbation kinetic energy relates to reforming/breaking of the unyielded plug and is followed by slower viscous decay. For axisymmetric perturbations these flows can be stable to order unity initial perturbation amplitudes and for Re<100. The channel geometry allows for symmetry breaking and appears to be less stable. A number of interesting effects are explored using the channel geometry. Secondly, I focus on demonstrating whether the stable core annular flow can be achieved when lubricating a visco-elastic core fluid with a yield stress fluid. Over 100 experiments have been performed using Carbopol solutions as the lubricating yield stress fluid and Polyethylene Oxide solutions as the visco-elastic fluid. Thirdly, I will briefly explain application of energy stability method to study nonlinear stability of a core-annular flow of an Oldroyd-B fluid surrounded by a Bingham fluid. Together with the experimental study, this shows that visco-elasticity is not a barrier to use of this methodology.

Monday, 07 Nov 2011, 3:00-4:00 pm, Math Annex 1100: PIMS Hugh C. Morris Lecture
Pre-lecture reception at 2 pm in MATH 126
Prof. George C. Papanicolaou, Mathematics Department, Stanford University
Uncertainty Quantification and Systemic Risk

The quantification of uncertainty in large-scale scientific and engineering computations is rapidly emerging as a research area that poses some very challenging fundamental problems which go well beyond sensitivity analysis and associated small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. How are these regimes characterized? Can the small probabilities of large (possibly catastrophic) changes be calculated? These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex, interconnected system will fail simultaneously. I will give a brief overview of these problems and then discuss in some detail two model problems. One is a mean field model of interacting diffusion and the other a large deviation problem for conservation laws. The first is motivated by financial systems and the second by problems in combustion, but they are considerably simplified so as to carry out a mathematical analysis. The results do, however, give us insight into how to design numerical methods where detailed analysis is impossible.

George C. Papanicolaou is the Robert Grimmett Professor in Mathematics at Stanford University, a member of the U.S. National Academy of Sciences, winner of the SIAM von Neumann Prize (2006) and the William Benter Prize in Applied Mathematics (2010).

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Tuesday, 08 Nov 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Robert Kircheis, Universität Heildelberg, Germany
Numerical Methods for Parameter Estimation and Optimum Experimental Design for Nonlinear PDE Models

To fit a model of a process described by a system of partial differential algebraic equations to a given set of experimental data we have to solve constrained, nonlinear parameter estimation problems. Since the data usually contain statistical errors, the parameters are random variables too. The uncertainty of a parameter estimation can be quantified by the variance-covariance matrix of the estimator. For minimizing the confidence region of the parameter estimation an optimized experimental setup is needed. We present our approach for the minimization of quality criterions on the variance-covariance matrix of the parameters. Thereby process controls and the layout of measurements are the optimization variables. Our approach are derivative based optimization strategies. We introduce the general optimum experimental design optimization problem and the methods implemented in the software package VPLAN, such as quasi-Newton methods, tailored derivative evaluation by internal numerical differentiation and automatic differentiation and exploitation of multiple experiment structures. To use experimental design for practical problems, we have developed strategies including robustification, multiple experiment formulations, a sequential strategy and an online-approach. In the second part of the talk we give an overview of parameter estimation methods to fit the parameters to the data. We treat this kind of problems by (reduced) Gauss-Newton-type methods and multiple-shooting. Furthermore, we will give a short outlook on what is next to come (multiple shooting for OED, proper orthogonal decomposition [POD] and reduced approach).

Monday, 14 Nov 2011, 3:00-4:00 pm, LSK 301: Fifteenth IAM-PIMS-MITACS Distinguished Colloquium Series
Dr. William L. Oberkampf, Consulting Engineer, Austin, Texas
Perspectives on Verification, Validation, and Uncertainty Quantification FULL TALK

Verification and validation (V&V) are the primary means to assess mathematical model and numerical accuracy in computational simulations. Code verification deals with the assessment of the reliability of the software coding and the numerical algorithms used, while solution verification deals with numerical error estimation of the computational solution to the mathematical model. Validation assesses the accuracy of the mathematical model as compared to an appropriate fiducial reference. In the natural sciences, this reference is commonly experimental measurements of the system of interest. Uncertainty quantification attempts to characterize the uncertainties represented by, and due to, the mathematical model, the numerical solution error, and the experimental data. Important research questions in uncertainty quantification deal with (a) model updating and calibration, as opposed to predictive uncertainty estimation, (b) estimation of model form uncertainty for cases where experimental data are available, and (c) extrapolation of estimated model form uncertainty to conditions for which no experimental data are available. This talk will briefly discuss all of these issues within the framework of how computational simulations are used in a decision-making environment.

William L. Oberkampf received his PhD in 1970 from the University of Notre Dame in Aerospace Engineering. He has 41 years of experience in research and development in fluid dynamics, heat transfer, flight dynamics, and solid mechanics. He served on the faculty of the Mechanical Engineering Department at the University of Texas at Austin from 1970 to 1979. From 1979 until 2007 he worked in both staff and management positions at Sandia National Laboratories in Albuquerque, New Mexico. During his career he has been deeply involved in both computational simulation and experimental activities. During the last 20 years he has been focused on verification, validation, uncertainty quantification, and risk analyses in modeling and simulation. He retired from Sandia as Distinguished Member of the Technical Staff and is a Fellow of the American Institute of Aeronautics and Astronautics. He has over 160 journal articles, book chapters, conference papers, and technical reports, and has taught 35 short courses in the field of verification and validation. He recently co-authored, with Christopher Roy, the book "Verification and Validation in Scientific Computing" published by Cambridge University Press.

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Tuesday, 15 Nov 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Ben Adcock, Simon Fraser University
Generalized Sampling and Infinite-Dimensional Compressed Sensing

Compressed sensing has been one of the great successes of applied mathematics in the last decade. It allows one to reconstruct sparse signals from seemingly incomplete collections of measurements, and thereby circumvent the classical Nyquist barrier. However, compressed sensing is currently a finite-dimensional theory: it concerns the recovery of vectors in finite-dimensional vector spaces. With this in mind, the purpose of this talk is to introduce a new framework that extends the current theory and techniques to infinite-dimensional problems. This new framework originates from recent developments in classical (i.e. Nyquist rate) signal recovery, known as generalized sampling. Generalized sampling, which I will introduce in the first part of the talk, allows for signal reconstruction in arbitrary bases in a manner which is both numerically stable and, in a certain sense, optimal. The infinite-dimensional compressed sensing framework builds on this approach by allowing one to take advantage of sparsity to obtain significant subsampling. This is joint work with Anders Hansen (Cambridge).

Wednesday, 16 Nov 2011, 2:00-3:00 pm, Math Annex 1118: Fluids Seminar
Ian Hewitt, Department of Mathematics, UBC
Instabilities of a Plough Towed over a Fluid Layer

I will describe recent experiments in which an angled plate is dragged horizontally over a fluid surface; the plate is attached by a pivot in such a way as to be able to move freely up and down in response to the lift force from the fluid. We find that the steady planing state, in which the plate's vertical position remains constant, becomes unstable if it is towed above a threshold speed. Instead, the plate oscillates up and down, leaving a rippled imprint on the fluid layer. The same instability occurs on a granular layer, and is responsible for the troublesome phenomenon of 'washboard' or 'corrugated' roads. After describing the experiments I will discuss attempts to rationalize these observations using simple theoretical models for the dynamics of the plate and the lift force provided by the deforming fluid. Special attention will be given to yield stress fluids, for which the imprinted pattern remains 'frozen' into the surface.

Monday, 21 Nov 2011, 3:00-4:00 pm, LSK 301: IAM Seminar Series
Prof. Neil Balmforth, Department of Mathematics and Department of Earth and Ocean Sciences, UBC
Gravity Waves and Tidal Friction

About a hundred years ago it was popularly accepted that the problem of the recession of the moon had been solved by estimating tidal friction in shallow areas of the ocean such as the Irish Sea. Only recently have observations also revealed that the tide is dissipated significantly in the deep ocean. The explanation is that the tide is converted into internal gravity waves as it is forced to flow over topographic features (such as the Hawaiian island chain) on the sea floor. These gravity waves, the "internal tide", provide dissipation and mixing if they overturn or break down into turbulence, and there is speculation that they may thereby contribute significantly to the dynamics of the large-scale ocean circulation. In this seminar I will describe recent modelling efforts to determine the amount of energy converted into gravity waves from the tide, along with some ideas regarding the subsequent fate of those waves.

Tuesday, 22 Nov 2011, 12:30-13:30, WMAX 110: SCAIM Seminar
Prof. Nick Harvey, Department of Computer Science, UBC
Solving Laplacian Systems: Some Contributions from Theoretical Computer Science

This talk discusses algorithms to solve systems of linear equations where the matrix is the Laplacian matrix of a graph. These systems arise in many applications: in scientific computing, when using the finite difference method to approximately solve Poisson's equation; in machine learning, in some methods for semi-supervised learning on graphs; and in theoretical computer science, in fast algorithms for network flow problems. For two decades, theoretical computer scientists have been developing algorithms with provable running-time bounds for solving such systems of equations. The current state-of-the-art algorithm computes a solution with relative error ε in the energy norm in running time O (m log n (log log n)² log (1/ε)) for any Laplacian matrix of size n × n with m non-zero entries. These algorithms use several sophisticated tools, including low-stretch trees and concentration of random matrices. In this talk we give a survey of these results.

Monday, 28 Nov 2011, 3:00-4:00 pm, LSK 301: IAM Seminar Series
Prof. Mary-Catherine Kropinski, Department of Mathematics, Simon Fraser University
Fast Integral Equation Methods for the Navier Stokes Equations

Integral equation methods have become increasingly popular in computational simulations involving the solution to PDEs. These methods offer significant advantages over conventional finite difference or finite element methods: for example, their superior stability allows highly accurate solutions to be computed, and complex physical boundaries are easily incorporated. While the Navier Stokes equations are not directly amenable to solution via integral equations, a suitable temporal discretization yields a collection of linear, high-order elliptic equations that must be solved at each time step; this approach is known as Rothe's method. Rothe's method applied to the stream-function/vorticity formulation of the 2D Navier Stokes equations, for example, yields the Poisson and modified Helmholtz equations at each time step. In the case of a pure stream-function formulation, a modified biharmonic equation results. In each case, the general solution procedure is the same: solutions to these PDEs are expressed as the sum of layer and volume potentials, which are carefully coupled together and evaluated using fast multipole-accelerated algorithms. In order to demonstrate these ideas, we present a fast integral equation method for solving the nonlinear heat equation, with examples including solutions to the Allen-Cahn equation. In addition, we present preliminary work on a second-kind integral equation formulation for the homogeneous modified biharmonic equation.

Wednesday, 30 Nov 2011, 2:00-3:00 pm, Math Annex 1118: Fluids Seminar
Harish Dixit, Department of Mathematics, UBC
Linear Stability of Vortices: Transient Growth and Continuous Spectrum

A vortex column supports oscillations known as Kelvin modes. These modes only exist for vortices with a compact core. For smooth vortices, the Kelvin modes are replaced by exponentially damped quasi-modes, a collective response of the continuous spectrum eigenfunctions. In the first part of this talk, we discuss the inviscid response of a 2D vortex to external disturbances. We show that for certain initial conditions, vorticity gradient can arrest the Landau damping process by a screening mechanism. In the second part of the talk, we discuss a novel way to understand the continuous spectrum of smooth 3D vortices. This is facilitated by a well known analogy between 3D disturbances to a vortex column and disturbances in a stratified shear flow. This work is in collaboration with Anubhab Roy, Ganesh Subramanian (both at Jawaharlal Nehru Centre for Advanced Scientific Research) and S. Abhishek (Stanford University).

Wednesday, 30 Nov 2011, 3:00 pm, Math Annex 1100: Math Department Colloquium
Andrea Bertozzi, Department of Mathematics, University of California at Los Angeles
Mathematics of Crime

There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems, especially for young researchers. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, methods in linear and nonlinear partial differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes. Examples will consider both "bottom up" and "top down" approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.

Monday, 09 Jan 2012, 3:00-4:00 pm, LSK 301: IAM Seminar
Prof. Dhavide Aruliah, University of Ontario institute of Technology
A Parallel Adaptive Method for Pseudo-Arclength Continuation

Pseudo-arclength continuation is a well-established framework for generating a curve of numerical solutions of nonlinear equations. The usual predictor-corrector scheme uses a prediction of a prescribed step-length along a tangent direction followed by correction steps (typically using Newton's method) in a hyperplane containing the prediction point. In many complicated high-dimensional systems, the correction steps can be extremely costly to compute; as a result, the step-length of the original prediction step must be chosen carefully to avoid prohibitively many failed steps and corresponding wasted CPU cycles. In this talk, I present a parallel method for adapting the step-length of pseudo-arclength continuation (jointly developed at UOIT with Alexander Dubitski and Lennaert van Veen). Our method employs several predictor-corrector sequences run concurrently on distinct processors with differing step-lengths. Our parallel framework permits intermediate results of unconverged correction sequences to seed new predictor-corrector sequences with longer step-lengths; the goal is to amortise the cost of corrector steps to make further progress along the underlying numerical curve. I shall describe the essence of the parallel algorithm and provide evidence from numerical experiments to support its efficacy. Results from numerical experiments suggest that a three-fold speed-up is attainable when the continuation curve sought has great topological complexity and the corrector steps require significant processor time. Our implementation can be used without extensive experience with High-Performance Computing (HPC); users need only supply a routine for computing the corrector steps.

Dr. Dhavide Aruliah obtained his doctorate from the Department of Computer Science at UBC in 2001. He was subsequently a postdoctoral fellow at the Fields Institute for Research in the Mathematical Sciences and then at the University of Western Ontario. Since 2004, he has been at the University of Ontario Institute of Technology (Oshawa, ON) where he is an associate professor in the Faculty of Science. At present, he is a Visiting Professor in Department of Computer Science at UBC. His research interests are in scientific computing, specifically in computational inverse problems and the numerical solution of PDEs. He is also interested in software design for scientific computing, specifically in how scientists actually use scientific software.

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Monday, 16 Jan 2012, 3:00-4:00 pm, LSK 301: IAM Seminar Series and Fluids Seminar
Prof. Lucien Brush, Department of Materials Science and Engineering, University of Washington, Seattle, Washington
Dynamics of Metal Foam Films

Metallic gas-liquid foams are precursors to porous solid materials that are lightweight and useful in transportation, energy, medical and other applications. The crowded gas bubbles in a gas-liquid metal foam are highly unstable, because there is capillary-suction flow of liquid from the thin lamellar regions into the Plateau borders. The liquid drainage leads to lamellar rupture, gas bubble coalescence and rapid foam coarsening, so that successful solidification of a metal foam is not possible without liquid additives such as particles. Our research focuses on the microscale flow and interface evolution of pure liquid foam films, in order to glean knowledge that can be used to improve the processing of bulk metal foam. In this talk, our calculations of the thinning and the onset of instability of foam lamella and of the evolving unstable foam films with Plateau borders in a pure gas-liquid metallic foam will be presented. The linear stability results show that a draining lamella with Plateau borders is more stable than a lamellar film without flow and without Plateau borders. Numerical calculations track film evolution to a time just prior to rupture. The effects of variations in the Plateau border radii of curvature and of different initial conditions on rupture phenomena will be shown.
In practice, gas-liquid metal foams are stabilized against coarsening by the addition of particles. One effect of the addition of particles to thin draining films is the development of an oscillatory structural component of the disjoining pressure. Our research involving the analysis of a model of a particle-laden free film that includes the oscillatory structural component of the disjoining pressure will also be presented. By studying the effect of this component of the disjoining pressure on film dynamics we hope to gain insight into its role as a possible mechanism for foam stabilization by particles, to explain unique behaviors observed in particle-laden films such as stepwise thinning, and to identify potential novel film or foam structures. To date, the results of our analysis show that for certain ranges of film thickness to particle diameter ratios, a uniform film can spontaneously evolve into a multilayered film as a result of the structural oscillatory effect. The results reveal an analogy between the layering behavior of a particle-laden free film and classical first-order phase transformation kinetics observed in multicomponent solutions. A "phase" diagram delineating regions of stable layered and uniform films, constructed on a plot of the ratio of structural oscillatory to van der Waals components of the disjoining pressure versus the ratio of film thickness to particle diameter, will also be discussed.

Tuesday, 17 Jan 2012, 12:30-13:30, WMAX 110: SCAIM Seminar
Ricardo Oyarzúa, Department of Mathematics, UBC
Mixed Finite Element Methods for the Coupling of Fluid Flow with Porous Media Flow

In this talk we a introduce mixed finite element method for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We consider mixed formulations in both the Stokes domain and the Darcy region, which yields the introduction of the traces of the porous media pressure and the fluid velocity as suitable Lagrange multipliers. Then, considering generic finite element spaces with some technical conditions, we apply the Babuska-Brezzi theory together with a classical result on projection methods for Fredholm operators of index zero to show stability, convergence, and a priori error estimates for the associated Galerkin scheme. Finally, we generalize the previous results and introduce a mixed finite element method for the coupling of fluid flow with nonlinear porous media flow. This is joint work with G.N. Gatica (University of Concepción) and F.-J. Sayas (University of Delaware).

Monday, 30 Jan 2012, 3:00-4:00 pm, LSK 301: IAM Seminar Series and Fluids Seminar
Prof. James Riley, Department of Mechanical Engineering, University of Washington, Seattle, Washington
On the Kinematics of Flame Surfaces in a Turbulent Flow

An important aspect of the dispersive influence of turbulent flows is their ability to rapidly increase the area of fluid surfaces. An example of such a surface is the stoichiometric surface in a non-premixed, chemical reaction, which approximates the flame surface. The stoichimetric surface can itself be approximated by a surface of constant value of a passive scalar, the mixture fraction. In this presentation, results will be presented for the growth and decay of iso-surfaces in turbulent flow. Direct measurements of iso-surfaces from numerical simulation will be presented, along with their indirect measurement using Rice's theorem (1944). This theorem leads to two separate modeling approaches to predict the evolution of the iso-surfaces. Comparisons of the predictions of these models with simulation results will be presented.

Monday, 06 Feb 2012, 3:00 pm, LSK 301: IAM Seminar Series and Math Department Colloquium
Alison Malcolm, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
Seismic Imaging with Multiply Scattered Waves

The acoustic wave equation is a mathematical model commonly used for the propagation of seismic waves through the Earth's subsurface, where the wavespeed is determined by the geological composition of the Earth. The seismic imaging problem is to recover this geological composition based on surface data, and is typically formulated as an inverse problem to recover the wavespeed in the acoustic wave-equation model. To linearize this inverse problem, it is typically assumed that waves reflect only once in the subsurface. This assumption, combined with the data acquisition geometry which restricts sources and receivers to lie on the Earth's surface, makes these algorithms most effective at imaging structures that are nearly flat. The inclusion of multiply scattered waves mitigates this to some extent, but at the cost that the inverse problem becomes nonlinear. I will describe a series framework for including multiply scattered waves in the seismic inverse problem allowing us to approach this nonlinear problem as a series of linear problems. Within this approach, we use techniques of seismic interferometry, a method based on Green's theorem. I will briefly describe how we use these techniques in other applications, in particular for locating micro earthquakes relative to one another.

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