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Mathematics Group



T Perciano, DM Ushizima, EW Bethel, YD Mizrahi, D Parkinson, JA Sethian, "Reduced-complexity image segmentation under parallel Markov Random Field formulation using graph partitioning", Proceedings - International Conference on Image Processing, ICIP, 2016, 2016-Aug:1259--1263, doi: 10.1109/ICIP.2016.7532560


J. Hesthaven, B. Stamm, S. Zhang, "New greedy algorithms for the empirical interpolation and reduced basis methods: with applications to high dimensional parameter spaces", ESAIM-Math. Model. Num. Submitted, 2013,

G. I. Barenblatt, Flow, Deformation and Fracture: Lectures on Fluid Mechanics and Mechanics of Deformable Solids for Mathematicians and Physicists, Cambridge Texts in Applied Mathematics, (Cambridge University Press: 2013) Pages: 49

A. J. Chorin, M. Morzfeld, X. Tu, "A survey of implicit particle filters for data assimilation", Statistics for Financial Engineering and Econometrics: State-Space Models and Applications in Economics and Finance, edited by S. Wu, (Springer. In print: 2013)


Richard L. Martin, Prabhat, David D. Donofrio, James A. Sethian & Maciej Haranczyk, "Accelerating Analysis of void spaces in porous materials on multicore and GPU platforms", International Journal of High Performance Computing Applications, February 5, 2012, 26:347-357,

Developing computational tools that enable discovery of new materials for energy-related applications is a challenge. Crystalline porous materials are a promising class of materials that can be used for oil refinement, hydrogen or methane storage as well as carbon dioxide capture. Selecting optimal materials for these important applications requires analysis and screening of millions of potential candidates. Recently, we proposed an automatic approach based on the Fast Marching Method (FMM) for performing analysis of void space inside materials, a critical step preceding expensive molecular dynamics simulations. This breakthrough enables unsupervised, high-throughput characterization of large material databases. The algorithm has three steps: (1) calculation of the cost-grid which represents the structure and encodes the occupiable positions within the void space; (2) using FMM to segment out patches of the void space in the grid of (1), and find how they are connected to form either periodic channels or inaccessible pockets; and (3) generating blocking spheres that encapsulate the discovered inaccessible pockets and are used in proceeding molecular simulations. In this work, we expand upon our original approach through (A) replacement of the FMM-based approach with a more computationally efficient flood fill algorithm; and (B) parallelization of all steps in the algorithm, including a GPU implementation of the most computationally expensive step, the cost-grid generation. We report the acceleration achievable in each step and in the complete application, and discuss the implications for high-throughput material screening.

D. Ambrose, J. Wilkening, "Computing Time-Periodic Solutions of Nonlinear Systems of Partial Differential Equations", Proceedings of Hyperbolic Problems: Theory, Numerics, Applications (HYP2010), Beijing, Higher Education Press, 2012, 273--280,

Alexandre J. Chorin, Xuemin Tu, "An iterative implementation of the implicit nonlinear filter", ESAIM: Mathematical Modelling and Numerical Analysis, 2012, 46:535--543,

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

Jens L. Eftang, Benjamin Stamm, "Parameter multi-domain ‘hp’ empirical interpolation", International Journal for Numerical Methods in Engineering, 2012, 90:412--428, doi: 10.1002/nme.3327

Matthias Morzfeld, Xuemin Tu, Ethan Atkins, Alexandre J. Chorin, "A random map implementation of implicit filters", Journal of Computational Physics, 2012, 231:2049--2066, doi: 10.1016/

Maxime Theillard, Chris H. Rycroft, Frédéric Gibou, "A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids", Journal of Scientific Computing, 2012, 1--15, doi: 10.1007/s10915-012-9619-2

Jon Wilkening, Jia Yu, Overdetermined shooting methods for computing standing water waves with spectral accuracy, Computational Science & Discovery, Pages: 014017 2012,

A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge–Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly discussed, and the performance of the algorithm is tested for a number of hardware configurations.

Thomas F. Willems, Chris H. Rycroft, Michaeel Kazi, Juan C. Meza, Maciej Haranczyk, "Algorithms and tools for high-throughput geometry-based analysis of crystalline porous materials", Microporous and Mesoporous Materials, 2012, 149:134--141, doi: 10.1016/j.micromeso.2011.08.020

M. Williams, E. Shlizerman, J. Wilkening, J. Kutz, "The Low Dimensionality of Time-Periodic Standing Waves in Water of Finite and Infinite Depth", SIAM Journal on Applied Dynamical Systems, 2012, 11:1033--1061, doi: 10.1137/11084621X

M. J. Cantero, F. A. Grünbaum, L. Moral, L. Veláquez, "One-Dimensional Quantum Walks with One Defect", Reviews in Mathematical Physics, 2012, 24:1250002, doi: 10.1142/S0129055X1250002X

M. Ganesh, J. S. Hesthaven, B. Stamm, "A reduced basis method for electromagnetic scattering by multiple particles in three dimensions", Journal of Computational Physics, 2012, 231:7756--7779, doi: 10.1016/

M. Garzon, L. J. Gray, J. A. Sethian, "Axisymmetric boundary integral formulation for a two-fluid system", International Journal for Numerical Methods in Fluids, 2012, 69:1124--1134, doi: 10.1002/fld.2633

Maria Garzon, L. J. Gray, James A. Sethian, "Droplet and bubble pinch-off computations using level sets", Journal of Computational and Applied Mathematics, 2012, 236:3034--3041, doi: 10.1016/

Sanjay Govindjee, Per-Olof Persson, "A time-domain Discontinuous Galerkin method for mechanical resonator quality factor computations", Journal of Computational Physics, 2012, 231:6380--6392, doi: 10.1016/

J. Hesthaven, B. Stamm, S. Zhang, "Certified Reduced Basis Method for the Electric Field Integral Equation", SIAM Journal on Scientific Computing, 2012, 34:A1777--A17, doi: 10.1137/110848268

R. H. Nochetto, B. Stamm, "A posteriori error estimates for the Electric Field Integral Equation on polyhedra", Mathematics of Computation. Submitted, 2012,

Per-Olof Persson, "High-order Navier-Stokes simulations using a sparse line-based discontinuous Galerkin method", 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, American Institute of Aeronautics and Astronautics, 2012, 436:1--10, doi: 10.2514/6.2012-456

P.-O. Persson, D.J. Willis, J. Peraire, "Numerical simulation of flapping wings using a panel method and a high-order Navier–Stokes solver", International Journal for Numerical Methods in Engineering, 2012, 89:1296--1316, doi: 10.1002/nme.3288

Chris H. Rycroft, Frédéric Gibou, "Simulations of a stretching bar using a plasticity model from the shear transformation zone theory", Journal of Computational Physics, 2012, 231:2155--2179, doi: 10.1016/

Chris H. Rycroft, Terttaliisa Lind, Salih Güntay, Abdel Dehbi, "Granular Flow in Pebble Bed Reactors: Dust Generation and Scaling", International Congress on Advances in Nuclear Power Plants 2012 (ICAPP 2012), Chicago, IL, Curran Associates, Inc., 2012, 1:447,

R. I. Saye, J. A. Sethian, "Analysis and applications of the Voronoi Implicit Interface Method", Journal of Computational Physics, 2012, 231:6051 - 608, doi: 10.1016/

Robert I. Saye, James A. Sethian, "The Voronoi Implicit Interface Method and Computational Challenges in Multiphase Physics", Milan Journal of Mathematics, 2012, 80:369--379, doi: 10.1007/s00032-012-0187-6

B. Stamm, T. P. Wihler, "A Total Variation Discontinuous Galerkin Approach for Image Restoration", SIAM Journal of Imaging Science. Submitted, 2012,


Avin Babataheri, Marcus Roper, Marc Fermigier, Olivia Du Roure, "Tethered fleximags as artificial cilia", Journal of Fluid Mechanics, 2011, 678:5--13, doi: 10.1017/S002211201100005X

M. Garzon, L. J. Gray, J. A. Sethian, "Simulation of the droplet-to-bubble transition in a two-fluid system", Phys. Rev. E, 2011, 83:046318, doi: 10.1103/PhysRevE.83.046318

F. Alberto Grünbaum, "The Darboux process and a noncommutative bispectral problem: some explorations and challenges", Progress in Mathematics: Geometric Aspects of Analysis and Mechanics, edited by Johan A.C. Kolk, Erik P. van den Ban, (Birkhäuser Boston: 2011) Pages: 161--177 doi: 10.1007/978-0-8176-8244-6_6

F. Alberto Grünbaum, Mizan Rahman, "A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application", Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2011, 7, doi: 10.3842/SIGMA.2011.119

F.A. Grünbaum, I. Pacharoni, J. Tirao, "Two stochastic models of a random walk in the U(n)-spherical duals of U(n + 1)", Annali di Matematica Pura ed Applicata, 2011, 1-27, doi: 10.1007/s10231-011-0232-z

F. Alberto Grünbaum, Manuel D. de la Iglesia, Andrei Martínez-Finkelshtein, "Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization", Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2011, 7, doi: 10.3842/SIGMA.2011.098

M. Fares, J.S. Hesthaven, Y. Maday, B. Stamm, "The reduced basis method for the electric field integral equation", Journal of Computational Physics, 2011, 230:5532--5555, doi: 10.1016/

Daniel T. Kawano, Matthias Morzfeld, Fai Ma, "The decoupling of defective linear dynamical systems in free motion", Journal of Sound and Vibration, 2011, 330:5165--5183, doi: 10.1016/j.jsv.2011.05.013

F. Ma, M. Morzfeld, "A general methodology for decoupling linear dynamical systems", 12th East Asia‐Pacific Conference on Structural and Construction (EASEC‐12), 2011,

F. Ma, M. Morzfeld, "A Method and Algorithm for Transforming Damped Linear into Independent Equations", ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011), 2011, DETC2011-4,

Matthias Morzfeld, Fai Ma, "The decoupling of damped linear systems in configuration and state spaces", Journal of Sound and Vibration, 2011, 330:155--161, doi: 10.1016/j.jsv.2010.09.005

F. Ma, M. Morzfeld, "The Decoupling of Linear Dynamical Systems", COMPDYN 2011: III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Corfu, Greece, Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Techn, 2011, 791--802,

M. Morzfeld, F. Ma, B. Parlett, "The Transformation of Second-Order Linear Systems into Independent Equations", SIAM Journal on Applied Mathematics, 2011, 71:1026-1043, doi: 10.1137/100818637

J. Peraire, P.-O. Persson, "High-Order Discontinuous Galerkin Methods for CFD", Advances in Computational Fluid Dynamics: Adaptive High-Order Methods in Computational Fluid Dynamics, edited by Z. J. Wang, (World Scientific: 2011)

Per-Olof Persson, David Willis, "High Fidelity Simulations of Flapping Wings Designed for Energetically Optimal Flight", 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, American Institute of Aeronautics and Astronautics, Inc., 2011, 568:1--10, doi: 10.2514/6.2011-568

Robert I. Saye, James A. Sethian, "The Voronoi Implicit Interface Method for computing multiphase physics", Proceedings of the National Academy of Sciences, 2011, 108:19498--195, doi: 10.1073/pnas.1111557108

We introduce a numerical framework, the Voronoi Implicit Interface Method for tracking multiple interacting and evolving regions (phases) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.), intricate jump conditions, internal constraints, and boundary conditions. The method works in two and three dimensions, handles tens of thousands of interfaces and separate phases, and easily and automatically handles multiple junctions, triple points, and quadruple points in two dimensions, as well as triple lines, etc., in higher dimensions. Topological changes occur naturally, with no surgery required. The method is first-order accurate at junction points/lines, and of arbitrarily high-order accuracy away from such degeneracies. The method uses a single function to describe all phases simultaneously, represented on a fixed Eulerian mesh. We test the method’s accuracy through convergence tests, and demonstrate its applications to geometric flows, accurate prediction of von Neumann’s law for multiphase curvature flow, and robustness under complex fluid flow with surface tension and large shearing forces.

Benjamin Stamm, "A posteriori estimates for the Bubble Stabilized Discontinuous Galerkin Method", J. Comput. Appl. Math., 2011, 235:4309--4324, doi: 10.1016/

A. Uranga, P.-O. Persson, M. Drela, J. Peraire, "Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method", International Journal for Numerical Methods in Engineering, 2011, 87:232--261, doi: 10.1002/nme.3036

Alejandra Uranga, Per-Olof Persson, Mark Drela, Jaime Peraire, "Preliminary Investigation Into the Effects of Cross-Flow on Low Reynolds Number Transition", 20th AIAA Computational Fluid Dynamics Conference: Fluid Dynamics and Co-located Conferences, American Institute of Aeronautics and Astronautics, 2011, doi: 10.2514/6.2011-3558

Jon Wilkening, Jia Yu, "A local construction of the Smith normal form of a matrix polynomial", J. Symb. Comput., 2011, 46:1--22, doi: 10.1016/j.jsc.2010.06.025

M.O. Williams, J. Wilkening, E. Shlizerman, J. N. Kutz, "Continuation of periodic solutions in the waveguide array mode-locked laser", Physica D: Nonlinear Phenomena, 2011, 240:1791--1804, doi: 10.1016/j.physd.2011.06.018

We apply the adjoint continuation method to construct highly accurate, periodic solutions that are observed to play a critical role in the multi-pulsing transition of mode-locked laser cavities. The method allows for the construction of solution branches and the identification of their bifurcation structure. Supplementing the adjoint continuation method with a computation of the Floquet multipliers allows for explicit determination of the stability of each branch. This method reveals that, when gain is increased, the multi-pulsing transition starts with a Hopf bifurcation, followed by a period-doubling bifurcation, and a saddle-node bifurcation for limit cycles. Finally, the system exhibits chaotic dynamics and transitions to the double-pulse solutions. Although this method is applied specifically to the waveguide array mode-locking model, the multi-pulsing transition is conjectured to be ubiquitous and these results agree with experimental and computational results from other models.

Per-Olof Persson, "High-order LES simulations using implicit-explicit Runge--Kutta schemes", 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, American Institute of Aeronautics and Astronautics, Inc., 2011, 684:1--10, doi: 10.2514/6.2011-684


D. M. Ushizima, F. Medeiros, "Retinopathy diagnosis from ocular fundus image analysis, Modeling and Analysis of Biomedical Image", SIAM Conference on Imaging Science (IS10), Chicago, Il, April 2010,

Daniela Ushizima, Cameron Geddes, Estelle Cormier-Michel, E. Wes Bethel, Janet Jacobsen, Prabhat, Oliver Rubel, Gunther Weber, Bernard Hamann, Peter Messmer, Hans Hagen, "Automated detection and analysis of particle beams in laser-plasma accelerator simulations", Machine Learning, edited by Yagang Zhang, (In-Teh: February 2010) Pages: 367-389, LBNL 3845E,

E. A. Carvalho, D. M. Ushizima, F. N. S. Medeiros, C. I. O. Martins, R. C. P. Marques, I. N. S. Oliveira, "SAR imagery segmentation by statistical region growing and hierarchical merging", Digital Signal Processing, 2010, 20:1365-1378, doi: 10.1016/j.dsp.2009.10.014

Oliver R\ ubel, Sean Ahern, E Wes Bethel, Mark D Biggin, Hank Childs, Estelle Cormier-Michel, Angela DePace, Michael B Eisen, Charless C Fowlkes, Cameron GR Geddes, others, "Coupling visualization and data analysis for knowledge discovery from multi-dimensional scientific data", Procedia computer science, Elsevier, January 2010, 1:1757--1764, LBNL 3669E,

Àlex Arenas, Antonio Cabrales, Leon Danon, Albert Díaz-Guilera, Roger Guimerà, Fernando Vega-Redondo, "Optimal information transmission in organizations: search and congestion", Review of Economic Design, 2010, 14:75-93, doi: 10.1007/s10058-008-0067-2

David M. Ambrose, Jon Wilkening, "Computation of symmetric, time-periodic solutions of the vortex sheet with surface tension", Proceedings of the National Academy of Sciences, 2010, doi: 10.1073/pnas.0910830107

A numerical method is introduced for the computation of time-periodic vortex sheets with surface tension separating two immiscible, irrotational, two-dimensional ideal fluids of equal density. The approach is based on minimizing a nonlinear functional of the initial conditions and supposed period that is positive unless the solution is periodic, in which case it is zero. An adjoint-based optimal control technique is used to efficiently compute the gradient of this functional. Special care is required to handle singular integrals in the adjoint formulation. Starting with a solution of the linearized problem about the flat rest state, a family of smooth, symmetric breathers is found that, at quarter-period time intervals, alternately pass through a flat state of maximal kinetic energy, and a rest state in which all the energy is stored as potential energy in the interface. In some cases, the interface overturns before returning to the initial, flat configuration. It is found that the bifurcation diagram describing these solutions contains several disjoint curves separated by near-bifurcation events.

David M. Ambrose, Jon Wilkening, "Computation of Time-Periodic Solutions of the Benjamin–Ono Equation", Journal of Nonlinear Science, 2010, 20:277--308, doi: 10.1007/s00332-009-9058-x

G. I. Barenblatt, P. J. M. Monteiro, "Scaling laws in nanomechanics", Physical Mesomechanics, 2010, 13:245--248, doi: 10.1016/j.physme.2010.11.004

G. I. Barenblatt, M. Betsch, L. Giacomelli, "Steady and quasi-steady thin viscous flows near the edge of a solid surface", European Journal of Applied Mathematics, 2010, 21:253--270, doi: 10.1017/S0956792510000124

V. Carey, D. Estep, A. Johansson, M. Larson, S. Tavener, "Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions", SIAM Journal on Scientific Computing, 2010, 32:2121-2145, doi: 10.1137/090753826

Alexandre J. Chorin, Xuemin Tu, "Interpolation and iteration for nonlinear filters", ESAIM: Mathematical Modelling and Numerical Analysis. Submitted, 2010, arXiv:0910,

We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior densities, and are designed to focus the particle paths so as to reduce the number of particles needed in nonlinear data assimilation. Examples are given.

Alexandre J. Chorin, Xuemin Tu, Matthias Morzfeld, "Implicit Particle Filters for Data Assimilation", Comm. Appl. Math. Comp. Sc., 2010, 5:221--240,

Maciej Haranczyk, James A. Sethian, "Automatic Structure Analysis in High-Throughput Characterization of Porous Materials", Journal of Chemical Theory and Computation, 2010, 6:3472-3480, doi: 10.1021/ct100433z

L. C. Lee, S. J. S. Morris, J. Wilkening, T. I. Zohdi, "Effects of stress concentrations on the attenuation by diffusionally assisted grain boundary sliding", 16th US National Congress on Theoretical and Applied Mechanics (USNCTAM), 2010,

Gladeston C. Leite, Daniela M. Ushizima, Fátima N. S. Medeiros, Gilson G. De Lima, "Wavelet Analysis for Wind Fields Estimation", Sensors, 2010, 10:5994--6016, doi: 10.3390/s100605994

T. Lind, S. Güntay, A. Dehbi, Y. Liao, C. H. Rycroft, "PSI Project on HTR Dust Generation and Transport", 5th International Conference on High Temperature Reactor Technology (HTR), 2010,

Fai Ma, Matthias Morzfeld, Ali Imam, "The decoupling of damped linear systems in free or forced vibration", Journal of Sound and Vibration, 2010, 329:3182--3202, doi: 10.1016/j.jsv.2010.02.017

Vinh-Tan Nguyen, Jaime Peraire, Boo Cheong Khoo, Per-Olof Persson, "A discontinuous Galerkin front tracking method for two-phase flows with surface tension", Computers & Fluids, 2010, 39:1--14, doi: 10.1016/j.compfluid.2009.06.007

Per-Olof Persson, D. J. Willis, J. Peraire, "The numerical simulation of flapping wings at low Reynolds numbers", 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, American Institute of Aeronautics and Astronautics, Inc., 2010, 724:1--10, doi: 10.2514/6.2010-724

C.H. Rycroft, M. Koeppe, F. Lam, Recombination lower bounds for missing and circular data: a branch and bound approach, preprint, 2010,

Chris H. Rycroft, Yee Lok Wong, Martin Z. Bazant, "Fast spot-based multiscale simulations of granular drainage", Powder Technology, 2010, 200:1-11, doi: 10.1016/j.powtec.2010.01.009

Michael Westdickenberg, Jon Wilkening, "Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations", ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44:133--166, doi: 10.1051/m2an/2009043

Jon Wilkening, "Non-existence of a limiting standing wave of extreme form deep water", arXiv:1011.2476, 2010,

This dissertation consists of two separate chapters. In the first chapter, we present an algorithm for computing a Smith normal form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular operations to the original matrix row by row (or column by column) to obtain the Smith normal form. The performance of the algorithm in exact arithmetic is reported for several test cases. The second chapter is devoted to a numerical method for computing nontrivial time-periodic, gravity-driven water waves with or without surface tension. This method is essentially a shooting method formulated as a minimization problem. The objective function depends on the initial conditions and the proposed period, and measures deviation from time-periodicity. We adapt an adjoint-based optimal control method to rapidly compute the gradient of the functional. The main technical challenge involves handling the nonlocal Dirichlet to Neumann operator of the water wave equations in the adjoint formulation. Several families of traveling waves and symmetric breathers are simulated. In the latter case, we observe disconnections in the bifurcation curves due to nonlinear resonances at critical bifurcation parameters.

F. Alberto Grünbaum, Mizan Rahman, "On a Family of 2-Variable Orthogonal Krawtchouk Polynomials", Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2010, 6, doi: 10.3842/SIGMA.2010.090

L. C. Lee, S. J. S. Morris, J. Wilkening, "Stress concentrations, diffusionally accommodated grain boundary sliding and the viscoelasticity of polycrystals", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2010, doi: 10.1098/rspa.2010.0447

Using analytical and numerical methods, we analyse the Raj–Ashby bicrystal model of diffusionally accommodated grain-boundary sliding for finite interface slopes. Two perfectly elastic layers of finite thickness are separated by a given fixed spatially periodic interface. Dissipation occurs by time-periodic shearing of the viscous interfacial region, and by time-periodic grain-boundary diffusion. Although two time scales govern these processes, of particular interest is the characteristic time tD for grain-boundary diffusion to occur over distances of order of the grain size. For seismic frequencies ωtD≫1, we find that the spectrum of mechanical loss Q−1 is controlled by the local stress field near corners. For a simple piecewise linear interface having identical corners, this localization leads to a simple asymptotic form for the loss spectrum: for ωtD≫1, Q−1∼const.ω−α. The positive exponent α is determined by the structure of the stress field near the corners, but depends both on the angle subtended by the corner and on the orientation of the interface; the value of α for a sawtooth interface having 120° angles differs from that for a truncated sawtooth interface whose corners subtend the same 120° angle. When corners on an interface are not all identical, the behaviour is even more complex. Our analysis suggests that the loss spectrum of a finely grained solid results from volume averaging of the dissipation occurring in the neighbourhood of a randomly oriented three-dimensional network of grain boundaries and edges.

J. Suckale, J.-C. Nave, B. H. Hager, "It takes three to tango: 1. Simulating buoyancy-driven flow in the presence of large viscosity contrasts", Journal of Geophysical Research, 2010, 115:B07409,

J. Suckale, B. H. Hager, L. T. Elkins-Tanton, J.-C. Nave, "It takes three to tango: 2. Bubble dynamics in basaltic volcanoes and rami cations for modeling normal Strombolian activity", Journal of Geophysical Research, 2010, 115:B07410,


E. W. Bethel, C. Johnson, S. Ahern, J. Bell, P.-T. Bremer, H. Childs, E. Cormier-Michel, M. Day, E. Deines, T. Fogal, C. Garth, C. G. R. Geddes, H. Hagen, B. Hamann, C. Hansen, J. Jacobsen, K. Joy, J. Kruger, J. Meredith, P. Messmer, G. Ostrouchov, V. Pascucci, K. Potter, Prabhat, D. Pugmire, O. Rubel, A. Sanderson, C. Silva, D. Ushizima, G. Weber, B. Whitlock, K. Wu, "Occam's Razor and Petascale Visual Data Analysis", SciDAC 2009, J. of Physics: Conference Series, San Diego, California, July 2009, LBNL 2210E,

C. G. R. Geddes, E Cormier-Michel, E. H. Esarey, C. B. Schroeder, J.-L. Vay, W. P. Leemans, D. L.. Bruhwiler, J. R. Cary, B. Cowan, M. Durant, P. Hamill, P. Messmer, P. Mullowney, C. Nieter, K. Paul, S. Shasharina, S. Veitzer, G. Weber, O. Rübel, D. Ushizima, Prabhat, E. W.Bethel, K. Wu, Large Fields for Smaller Facility Sources, SciDAC Review, Pages: 13-21, 2009,

C. I. O. Martins, D. M. Ushizima, F. N. S. Medeiros, F. N. Bezerra, R. C. P. Marques, N. D. A. Mascarenhas, "Iterative Self-dual Reconstruction on Radar Image Recovery", Proc. of IEEE Workshop on Applications of Computer Vision, Snowbird, Utah, 2009, 37-42, LBNL 3846E,

Oliver R\ ubel, Cameron GR Geddes, Estelle Cormier-Michel, Kesheng Wu, Gunther H Weber, Daniela M Ushizima, Peter Messmer, Hans Hagen, Bernd Hamann, Wes Bethel, others, "Automatic beam path analysis of laser wakefield particle acceleration data", Computational Science \& Discovery, January 2009, 2:015005, LBNL 2734E,

Juan A. Acebréon, Sergi Lozano, Alex Arenas, "Enhancement of Signal Response in Complex Networks Induced by Topology and Noise", Understanding Complex Systems, (Springer Berlin Heidelberg: 2009) Pages: 201--209 doi: 10.1007/978-3-540-85632-0_16

David M. Ambrose, Jon Wilkening, "Global paths of time-periodic solutions of the Benjamin-Ono equation connecting pairs of traveling waves", Communications in Applied Mathematics and Computational Science, 2009, 4:177-215, doi: 10.2140/camcos.2009.4.177

Alex Arenas, Sergio Gómez, Alberto Fernández, "An Optimization Approach to the Structure of the Neuronal Layout of C. elegans", Handbook on Biological Networks, edited by Stefano Boccaletti, Vito Latora, Yamir Moreno, (World Scientific: 2009) Pages: 243-256 doi: 10.1142/9789812838803_0011

Alexandre J. Chorin, Xuemin Tu, "Implicit sampling for particle filters", Proceedings of the National Academy of Sciences, 2009, 106:17249-1725, doi: 10.1073/pnas.0909196106

We present a particle-based nonlinear filtering scheme, related to recent work on chainless Monte Carlo, designed to focus particle paths sharply so that fewer particles are required. The main features of the scheme are a representation of each new probability density function by means of a set of functions of Gaussian variables (a distinct function for each particle and step) and a resampling based on normalization factors and Jacobians. The construction is demonstrated on a standard, ill-conditioned test problem.

A. Chorin, O. H. Hald, Stochastic Tools in Mathematics and Science, Surveys and Tutorials in the Applied Mathematical Sciences, (Springer: 2009)

M. Garzon, L. Gray, J. A. Sethian, "Potential fluid flow computations involving free boundaries with topological changes", Proc. International Conference on Computational and Mathematical Methods on Science and Engineering, Gijón, Spain, CMMSE, 2009, 2:521--531,

M. Garzon, L. J. Gray, J. A. Sethian, "Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method", Journal of Computational Physics, 2009, 228:6079--6106, doi: 10.1016/

Dror Givan, Panagiotis Stinis, Jonathan Weare, "Variance reduction for particle filters of systems with time scale separation", Trans. Sig. Proc., 2009, 57:424--435, doi: 10.1109/TSP.2008.2008252

M. Haranczyk, J. A. Sethian, "Navigating molecular worms inside chemical labyrinths", Proceedings of the National Academy of Sciences, 2009, 106:21472-2147, doi: 10.1073/pnas.0910016106

Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, “triaging” the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving “molecular worm,” which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.

H. Kim, X. Tu, "A Three-Level BDDC Algorithm for Mortar Discretizations", SIAM Journal on Numerical Analysis, 2009, 47:1576-1600, doi: 10.1137/07069081X

Regis C. P. Marques, Fatima N. S. Medeiros, Daniela M. Ushizima, "Target Dectection on SAR Images Using Level Set Methods", IEEE Transactions on Systems, Man and Cybernetics, 2009, 39:214-222, LBNL 958E, doi: 10.1109/TSMCC.2008.2006685

P.-O. Persson, "Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations", Proceeding of the 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, American Institute of Aeronautics and Astronautics, 2009, 606:1--12,

P.-O. Persson, J. Peraire, "Curved mesh generation and mesh refinement using Lagrangian solid mechanics", Proceeding of the 47th AIAA Aerospace Sciences Meeting, Orlando, Florida, American Institute of Aeronautics and Astronautics, Inc., 2009, 949:1--11,

P.O. Persson, J. Bonet, J. Peraire, "Discontinuous Galerkin solution of the Navier--Stokes equations on deformable domains", Computer Methods in Applied Mechanics and Engineering, 2009, 198:1585--1595,

Marcus Roper, Michael P. Brenner, "A nonperturbative approximation for the moderate Reynolds number Navier–Stokes equations", Proceedings of the National Academy of Sciences, 2009, 106:2977-2982, doi: 10.1073/pnas.0810578106

The nonlinearity of the Navier–Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier–Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

A. L. Roytburd, V. Roytburd, J. Slutsker, "Domain structures in continuously graded ferroelectric films", Applied Physics Letters, 2009, 94:152904--15, LBNL 1429E,

Chris H. Rycroft, "VORO++: A three-dimensional Voronoi cell library in C++", Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009, 19:041111, LBNL 1432E, doi: 10.1063/1.3215722

Voro++ is a free software library for the computation of three dimensional Voronoi cells. It is primarily designed for applications in physics and materials science, where the Voronoi tessellation can be a useful tool in the analysis of densely-packed particle systems, such as granular materials or glasses. The software comprises of several C++ classes that can be modified and incorporated into other programs. A command-line utility is also provided that can use most features of the code. Voro++ makes use of a direct cell-by-cell construction, which is particularly suited to handling special boundary conditions and walls. It employs algorithms which are tolerant for numerical precision errors, and it has been successfully employed on very large particle systems.

Chris H. Rycroft, Ken Kamrin, Martin Z. Bazant, "Assessing continuum postulates in simulations of granular flow", Journal of the Mechanics and Physics of Solids, 2009, 57:828--839, doi: 10.1016/j.jmps.2009.01.009

Chris H. Rycroft, Ashish V. Orpe, Arshad Kudrolli, "Physical test of a particle simulation model in a sheared granular system", Phys. Rev. E, 2009, 80:031305, LBNL 1430E, doi: 10.1103/PhysRevE.80.031305

J. Wilkening, "Practical error estimates for Reynolds' lubrication approximation and its higher order corrections", SIAM Journal on Mathematical Analysis, 2009, 41:588--630,

J. Kinser, Python for Bioinformatics, The Jones and Bartlett Series in Biology, (Jones & Bartlett Learning: 2009)

A. Uranga, P.-O. Persson, M. Drela, J. Peraire, "Implicit large eddy simulation of transitional flows over airfoils and wings", AIAA Paper, San Antonio, Texas, American Institute of Aeronautics and Astronautics, 2009, 4131,