ICES Seminars 2009

Tuesday, December 1

Ricardo Nochetto
Professor, Dept. of Mathematics, University of Maryland

ICES Seminar: “Quasi-optimal Convergence Rates for Adaptive cG and dG FEM”

Abstract:

The analysis of cardinality of cG methods on conforming meshes for
symmetric elliptic PDE is based on key properties of the energy error and the residual estimator, as well as geometric properties of simplicial bisection meshes. The latter relate the number of marked elements with those added by bisection. We first review these properties along with the contraction property for cG. This is joint with J.M. Cascon, Ch. Kreuzer, and K.G. Siebert.

We next show how to extend the theory to non-residual estimators, thereby including the most popular estimators, as well as to dG methods. This is joint with A. Bonito and J.M. Cascon.

We finally show that the complexity results valid for conforming bisection grids extend to nonconforming meshes with fixed level of nonconformity and which are made of quadrilaterals or triangles with red refinement as well as their multidimensional counterparts. We prove that the approximation classes for dG and cG methods coincide, and use this to derive quasi-optimal convergence rates for both dG and cG methods on nonconforming meshes. This work is joint with A. Bonito.

host: L. Cafarelli

Friday, November 20 (Time: 3:00 — 4:00 PM)

Harald van Brummelen
Professor, Eindhoven University of Technology Department of Mechanical Engineering / Department of Mathematics and Computer Science

ICES Seminar: “Goal-oriented adaptivity for a 1D prototype of the Boltzmann equation”

Abstract:

With the perpetual trend towards smaller and smaller scales in science and engineering, fluid-flow problems in the transitional molecular/continuum regime have rapidly gained prominence over the past years. Accurate numerical simulation of flow problems in the
transitional regime poses a fundamental challenge, on account of the large difference between the molecular free path and a typical length scale of observation. To bridge the gap between the molecular length scale and the continuum length scale in numerical simulations, many heuristic approaches have recently appeared in the literature to couple molecular-dynamics models to continuum models, such as the Navier-Stokes equations. The appropriateness of such a direct
connection between a molecular model and a continuum model is arguable, however, because the range of validity of the models is highly disparate.

A suitable model for transitional molecular/continuum flows is provided by the Boltzmann equation. In the Boltzmann equation, the flow is characterized by a one-particle probability-density
function, which measures the probability that a molecule resides in a certain subset of the position/momentum space. The Boltzmann equation itself is an integro-differential equation that governs the evolution of the one-particle probability-density. The Boltzmann equation is in principle valid down to the molecular scale, while on the other hand it encapsulates all conventional continuum models, such as the compressible and incompressible Navier-Stokes equations, in the sense that with appropriate scalings of the macroscopic length and time scales, limit solutions of the Boltzmann equation correspond to solutions of these continuum equations. Essentially, the Boltzmann equation is connected to the continuum equations by the fact that solutions of the Boltzmann equation converge to a particular class of
solutions, the so-called Maxwell-Boltzmann equilibrium distributions.

Direct numerical simulation of the Boltzmann equation is prohibited by its high-dimensional setting: for a problem in d spatial dimensions, the corresponding position/momentum domain is 2d dimensional.
However, it is anticipated that in many cases the computational complexity can be significantly reduced by means of adaptive low (d) dimensional approximations based on Boltzmann moment closures. In many
applications, interest is in fact restricted to one particular goal functional. For instance, in micro-scale heat-transfer problems,
it is ultimately only the heat flux across a certain part of the boundary that is of interest. This class of problems provides fertile ground for goal-oriented adaptive-refinement strategies.

An essential impediment in the development of goal-oriented
adaptive-refinement techniques for the Boltzmann equation, is the fact that the convergence-to-equilibrium property which forms the basis of the hierarchical modeling process only occurs for d=2,3. Hence, to test our ideas, we would have to consider problems in 4 or 6 dimensions. To bypass this complication, we have developed a 1D prototype of the Boltzmann equation, which exhibits all the characteristic features of the Boltzmann equation, including the weak-convergence-to-equilibrium property. The underlying molecular model is based on random collisions, which conserve energy but not momentum.

In the presentation, I will give an overview of transitional
molecular/continuum flows, from the perspective of hierarchical modeling and model adaptivity. I will then elaborate the 1D prototype of the Boltzmann equation that we have developed, and derive its characteristic properties, such as an entropy inequality. Finally, I will present numerical result obtained by a discontinuous Galerkin finite-element discretization of the prototype, including recent results for goal-oriented error estimation.

Thursday, November 19 (Time: 10:00 — 11:00 AM)

Daniel M. Zuckerman
University of Pittsburgh

ICES Seminar - Molecular Biology Series: “The Statistical Future of (Computational) Biochemistry”

Abstract:

Proteins don’t “know” biology. They obey the laws of chemistry and physics, most notably statistical physics. However, current experiments and computations are limited in their ability to supply information on the statistical fluctuations of biomolecules. Typical computations are unable to sample the complex configuration spaces of atomistic models of the large biomolecules. This talk will describe general strategies for improving statistical-physics-based computations, based on the simultaneous consideration of algorithms, models, and implementations. Memory-intensive implementations, for example, not only reduce CPU load but also can facilitate the use of potentially powerful algorithms based on models with an adjustable level chemical detail. These methods set the stage for systematic improvements in statistical biochemical computations, ranging from binding-affinity estimation to path-sampling of dynamical processes.

Monday, November 16 (Time: 2:00 — 3:30 PM)

Bernard R. Brooks
Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health

ICES Seminar - Molecular Biology Series: “Examining Protein Structure and Function using Multi-scale Methods”

Abstract:

This presentation focuses on our recent efforts to develop multi-scale macromolecular modeling methods and to apply them to problems of examining protein dynamics and function. One objective in developing multi-scale modeling techniques is to be able to include multiple scale representations within a single study. By combining scales, you can examine properties that would be difficult or too costly to examine with a single model. Examples are presented from the following models:

Grid based map objects (EMAP)

Coarse-graining using elastic network models (ENM) and Langevin network models (LNM)

Coarse-grained models using Hydrophibic/Hydrophibic/Neutral models (BLN)

Atomic models using a classical force field (CHARMM, Amber,…)

Models employing a quantum mechanical subsystem (CHARMM/Q-Chem,…)

Examples of methods employing these models include:

Structural analysis via single particle electron tomography

Protein-protein docking with grid based methods

Vibrational free energy partitioning and subsystem analysis

Examining reaction pathways and free energies

Rapid exploration of local conformational space using self guided Langevin dynamics

http://www.lobos.nih.gov/cbs/publications.shtml

*Refreshments served at 2:15.

Thursday, November 12

Tom Hagstrom
Professor, Department of Mathematics, Southern Methodist University

ICES Seminar: “On the Development of a Hermite-Based Compressible Navier-Stokes Solver”

Abstract:

With the goal of carrying out direct simulations of turbulent mixing noise, we have been working on the development, testing, and (we hope!) eventual application of a compressible Navier-Stokes solver employing Hermite spectral elements. Turbulent mixing noise problems display a daunting range of spatio-temporal scales, and thus pose a stiff challenge to computational methods. In this talk we will review the fundamental theoretical properties of Hermite spatial discretizations which, in our view, make them particularly attractive for exploiting massively-parallel, multicore architectures, and also present results from early code testing. Additionally we will discuss various techniques, ranging from optimal approximate radiation conditions to high-order absorbing layers, for treating the inflow, outflow, and radiating boundaries present in aeroacoustic simulations.

Tuesday, November 10

Andy Terrel
University of Chicago

ICES Seminar: “FEM Automation of Non-Newtonian Fluid Models”

Abstract:

Over the past several years the FEniCS projects have developed many advances in the automation of Finite element codes. These techniques allow the researcher to study numerous models and numerical discretizations quite rapidly. With this technology, we study the numerous viscoelastic models and discretizations. This allows us to systematically address many stability questions with comparisons between a variety of test problems. We present both the abstractions for the FEM automation as well as the comparisons for the different Oldroyd-B type models.

Friday, November 6 (Time: 11:00 — 12:00 PM)

Todd Arbogast
Professor, ICES, UT Austin

ICES Seminar - ICES Forum series: “Aspects of Multiscale Modeling as Applied to Porous Media”

Abstract:

We present an introduction to multiscale analysis, emphasizing aspects applicable to flow in porous media. We describe the flow in a heterogeneous medium from the sub-millimeter scale and upscale it to the 10-100 meter scale, using the continuum hypothesis, simple averaging, mathematical homogenization, and multiscale numerical techniques.

Wednesday, November 4 (Location: ACES 2.302 AVAYA) (Time: 4:00 — 5:00 PM)

Olivier Pinaud
Professor, Université Lyon 1

ICES Seminar - CNA series: “On the moment problem for Quantum Hydrodynamics”

Abstract:

This work is motivated by a recent series of papers by Degond, Méhats and Ringhofer about the formal derivation of Quantum Hydrodynamics models from the entropy principle. Starting from the Quantum Liouville equation, they obtain a non-closed system for the first moments of the density operator. Then, as in the Levermore moment method for kinetic equations, the system is closed by introducing the solution to the quantum moment problem which consists in minimizing the quantum free energy under some constraints of density, current or energy. The first step towards the rigorous derivation of such Quantum Hydrodynamics models is the mathematical analysis of the quantum moment problem. We will present in the talk a result of existence for the quantum moment problem under a density constraint and give some elements of the proof. The solution will also be characterized in a simplified setting. This is joint work with Florian Méhats (Université de Rennes, France).

Tuesday, October 27 (Time: 2:00 — 3:30 PM)

Juan M. Restrepo
Group Leader, Uncertainty Quantification Group Mathematics Department, University of Arizona

ICES Seminar-CNA Series: “Climate: When Data Fail Us, Nonlinear/Non-Gaussian Estimation”

Abstract:

State estimation techniques are used in weather and climate prediction,hydrogeology, seismology, as a way to blend model output and real data in order to improve on predictions from the exclusive use of the model or the data alone.

Techniques that are based upon least-squares ideas, such as the
family of Kalman Filter/Smoothers, or Variational Data Assimilation, are optimal in linear/Gaussian problems. However, they often fail in problems in which nonlinearities are important and/or when Gaussianity in the statistics cannot be assumed. Even linearization may fail, and so do ensemble techniques that make nonlinear predictions but rely on linear analyses. These comprise the practical state of the art, at least in weather forecasting and in hydrogeology. I will describe these as well as how failures arise in these methods.

We have created a number of nonlinear/non-Gaussian data assimilation techniques. Our present efforts are to make them computationally practical as well as to use of these to do problems that are otherwise intractable using conventional means.

One such application is in Lagrangian data assimilation: here we tackle the problem of blending data that has been sampled along paths, which when blended in traditional ways on Eulerian grids will lead to loss of critical features even though the estimates may be variance-minimizing.

Friday, October 23 (Time: 11:00 — 12:00 PM)

Ernesto Prudencio
PECOS

ICES Seminar - Forum series - : “Algorithmic Challenges at the Center for Predictive Engineering and Computational Sciences (PECOS)”

Abstract:

The PECOS Center is composed of an inter-disciplinary team of
researchers dedicated to the development of systematic methodologies and advanced computational methods for the validation of models and the prediction of quantities of interest under uncertainty. In this talk we will go through basic concepts on model validation, uncertainty quantification and Bayesian analysis, followed by a brief explanation of some algorithmic challenges on the research areas of model validation and uncertainty quantification.

Tuesday, October 20

Olof Runborg
KTH

ICES Seminar - CNA Series: “A Multiscale Method for the Wave Equation in Heterogeneous Medium ”

Abstract:

We consider the wave equation in a medium with a rapidly varying speed of propagation. We construct a multiscale scheme based on the heterogeneous multiscale method, which can compute the correct coarse behavior of wave pulses traveling in the medium, at a computational cost essentially independent of the size of the small scale variations. This is verified by theoretical results and numerical examples.

Monday, October 12 (Time: 2:30 — 3:45 PM)

John Crocker
Professor, Chemical and Biomolecular Engineering, Institute for Medicine and Engineering, Pennsylvania Muscle Institute, University of Pennsylvania

ICES Seminar: “What does biophysics teach us about the mechanics of cells?”

Abstract:

It is now widely appreciated that normal tissue morphology and function rely upon cells? Ability to sense and generate forces appropriate to their correct tissue context. Although the effects of forces on cells have been studied for decades, our understanding of how those forces propagate through and act on different cell substructures remains at an early stage. We determine the frequency-dependent shear modulus of cultured mammalian cells by using four different methods, both unique and well established. This approach clarifies the effects of cytoskeletal heterogeneity, ATP-dependent processes, and cell regional variations on the interpretation of such measurements. Subjecting cells to a variety of pharmacological and genetic interventions allows us to dissect the molecular determinants of cell mechanical function, and to hammer out a useful consensus description.

*Refreshments served at 2:15
Seminar: 2:30-3:30

Friday, October 9 (Time: 11:00 — 12:00 PM)

Bill Press
Professor, ICES ICES and the Institute for Cellular and Molecular Biology (ICMB)

ICES Seminar: “ Bandit Problems, Clinical Trials, and Computational Ethics”

Abstract:

As electronic medical records enable increasingly ambitious studies of treatment outcomes, ethical issues previously important only to limited clinical trials become relevant to unlimited whole populations. For randomized clinical trials, adaptive assignment strategies are known that expose substantially fewer patients to avoidable treatment failures than strategies with fixed assignments (e.g., equal sample sizes). An idealized adaptive case, the two-armed Bernoulli bandit problem, can be
exactly optimized for a variety of ethically motivated cost functions that embody principles of duty-to-patient; but the solutions have been thought computationally infeasible when the numbers of patients in the study (the "horizon'') is large. We derive from numerical experiment a heuristic approximation that applies even for very large horizons, and propose a near-optimal strategy that remains valid even when the horizon is unknown or unbounded, thus applicable to comparative effectiveness studies on large populations or to standard-of-care recommendations.

Thursday, October 8

Sergej Rjasanow
Professor, Saarland University, Germany

ICES Seminar: “Mathematical Model of the Nonlocal Electrostatics”

Abstract:

Protein-protein interaction belongs to the most important processes in the body. Today many diseases can be and treated at the protein, i.e. biomolecular level. Prediction and scoring of possible protein-protein interaction is an important prerequisite for efficient drug design on a computer.

In recent years signi?cant interest has been focused on the determination of electrostatic potentials of large biomolecules. However, the standard continuum approach ultimately becomes inaccurate when used to determine electrostatic properties on atomic scales [1]. In the papers [2], [4], we have proposed a novel formulation of nonlocal electrostatics allowing numerical solutions for the nontrivial molecular geometries. Some rather simple examples were solved and demonstrated correct physical behaviour. However, the mathematical model presented in these two papers is not completely equivalent to the physical model formulated in terms of Maxwell equations with nonlocal material relationship in the exterior domain, see [3].

In the recent paper [5], we present new system of four partial differential equations for nonlocal electrostatic which is formally equivalent to the physical model, shows its ellipticity, derive a simple analytical solution in the case of the unit sphere, ?nd the fundamental solution of this system in an explicit analytical form and by the use of this, rewrite the interface problem
in form of boundary integral equations.

References:
[1] T. Simonson. Macromolecular electrostatics: continuum models and their growing pains. Curr. Op. Struct. Biol., 11:243–252, 2001.
[2] A. Hildebrandt, R. Blossey, S. Rjasanow, O. Kohlbacher, and H.-P. Lenhof. A novel formulation of nonlocal electrostatics. Phys. Rev. Let., 93(10):104–108, 2004.
[3] A. A. Kornyshev, A. I. Rubinstein and M. A. Vorotyntsev. Model nonlocal electrostatics.1. J. Phys. C: Solid State Phys. 11:3307–3322, 1978.
[4] A. Hildebrandt, H.-P. Lenhof, R. Blossey, S. Rjasanow, and O. Kohlbacher. Electrostatic potentials of proteins in water: A structured continuum approach. Bioinformatics, 23(2):99–103, 2007.
[5] C. Fasel, S. Rjasanow, and O. Steinbach. A boundary integral formulation for nonlocal electrostatics. In K. Kunisch, G. Of, and O. Steinbach, editors, Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, pages 117–124. Springer, Heidelberg, 2008.

Friday, October 2 (Time: 2:00 — 3:00 PM)

William Rundell
Professor, Dept. of Mathematics, Texas A&M

ICES Seminars-Numerical Analysis Series: “Inverse Obstacle Problems; Uniqueness and Non-Continuous Dependence on the Problem Itself”

Abstract:

Radar and sonar, satellite observations CAT scans, indeed most of medical imaging, are ubiquitous examples of the recovery of a hidden or remote object by making measurements from a distance. They are wonderful case studies of the application of mathematics. In all such problems there is a partial differential equation lurking behind the scenes. If we knew the shape, location
and material properties of the object then mathematics developed in the latter half of the nineteen century and first half of the
twentieth would let us predict, in theory, exactly the kind of
measurements we would obtain. The much harder, but interesting part, is the converse; given the measurements, where, and
what, was the obstacle? This talk will explore this inverse problem, specifically the issues of uniqueness and determination. What is the least amount of measurements one can make in order to obtain a unique recovery? Are there algorithms that would let us reconstruct the object and what are their limitations? But there will be an additional feature. It is well know that such inverse problems are ill-posed -the solution does not depend continuously on the measured data, but we will point out that seemingly minor changes in the partial differential equation or the boundary conditions can result in completely changed answers for the inverse problem.

Friday, September 25 (Time: 11:00 — 12:00 PM)

Antti Niemi
ICES

ICES Seminar - Forum Series: “Do you have the courage to sign the blueprints?”

Abstract:

Part I. Error in the numerical algorithm (September 25th)

The purpose of the computations is to obtain the values of a quantity of interest on which the decision is made. The question is whether there is the courage to take the responsibility for the computed numbers and "sign the blueprints".

In the September 25 presentation the problem of verification will be addressed. Verification is a process leading to the confidence that the numerical approximation of the exact solution of the mathematical problem (which exists and is unique) is sufficiently accurate.

The talk addresses the computational analysis of a simple engineering problem, the shell supported by a ring. Among others we will present the results obtained by various analysts using commercial programs and show that many of these results are significantly or completely wrong. This illustrates various problems with computational engineering. We will address general principles how to get the confidence in the computed numbers and have the courage to “sign the blueprints”. We will illustrate the applications of these principles on the shell problem computation.

We will also show the results obtained with an automatic hp-adaptive finite element solver developed at ICES by Prof. L Demkowicz and collaborators. Our computations are based on the axisymmetric formulation of linear elasticity and energy-based version of the hp-adaptivity. We will discuss what can be concluded from these results and why there is courage to ”sign the blueprints” based on these computations.

Part II. Problem formulation based on literature data (November 6th)

The second, November, presentation will address the computational analysis of a double-pipe heat exchanger, when only the data in the literature , usually insufficient, are available. This is the usual situation. This lack of knowledge leads to what is called epistemic uncertainty. The principles on how to deal with epistemic uncertainties and how to get the confidence that the computational results are sufficiently reliable for the decision will be addressed and illustrated for a double-pipe heat exchanger.

Monday, September 21 (Time: 2:00 — 3:30 PM)

Thomas J. Magliery
Departments of Chemistry and Biochemistry, The Ohio State University

ICES Seminar - Molecular Biophysics Series: “Information in Protein Sequences: Combinatorial and Statistical Protein Design ”

Abstract:

Both the prediction and design of protein structure, using computational and rational approaches, remain significant challenges in protein chemistry. A major limitation to developing a comprehensive physicochemical model of the protein structure-sequence relationship is the vastness of sequence space and the low-throughput nature of biophysical studies. We are pursuing two avenues to understand better the sequence structure-relationship: sorting large libraries of protein variants for structured proteins, and statistical analysis of ubiquitous protein families for protein redesign. In the combinatorial approach, we have developed a high-throughput cell-based screen for activity of the well-studied four-helix bundle protein Rop. To collect quantitative stability data for large numbers of variants, we have developed a method of high-throughput hydrophobic dye binding called High-Throughput Thermal Scanning (HTTS) which can be applied using automation and a real-time PCR machine 96-wells at a time. This system is being used to directly test the “rules” of protein design, taking those rules as hypotheses and sorting the resulting libraries for structure and stability. We are also interested in the role of correlated occurrences of amino acids in natural protein families. To that end, we have generated a consensus version of triosephosphate isomerase (cTIM), which can be thought of as a “correlation-free” variant, as a host to interrogate the roles of correlated positions by mutagenesis and library methods. Two closely-related consensus variants differ dramatically in their physical properties and activity. Methods for the analysis of pair-wise correlations in protein families will be discussed.

*Refreshments served at 2:15 pm.

Tuesday, August 25 (Location: ACES 4.304) (Time: 9:15 — 10:15 AM)

Paolo Podio-Guidugli
Professor, Dipartimento di Ingegneria Civile Facolta di Ingegneria, Universita di Roma TorVergata

ICES Seminar - CVC Biophysics Series: “Atomistic/Continuum Methods”

Abstract:

III. Atomistic/Continuum Methods (2 lectures)

From intermolecular potentials to stored-energy densities: internal stress, material moduli.

http://www.uniroma2.it/ppg/
ppg@uniroma2.it

Monday, August 24 (Location: ACES 4.304) (Time: 9:15 — 10:15 AM)

Paolo Podio-Guidugli
Professor, Dipartimento di Ingegneria Civile Facolta di Ingegneria, Universita di Roma TorVergata

ICES Seminar - CVC Biophysics Series: “ The Molecular Dynamics Approach”

Abstract:

II. The Molecular Dynamics Approach (4 lectures)
a. Statistical Thermodynamics: Gibbs’ notion of ensemble. Liouville Therem. The microcanonical ensemble. Other ensembles.

b. Andersen-Parrinello-Rahman Molecular Dynamics: Kinetic energy. Intermolecular potential. Lagrangian equations of motion. Halmitonian version. Metadynamics)

http://www.uniroma2.it/ppg/
ppg@uniroma2.it

Wednesday, August 19 (Location: ACES 4.304) (Time: 9:30 — 10:15 AM)

Paolo Podio-Guidugli
Professor, Dipartimento di Ingegneria Civile Facolta di Ingegneria, Universita di Roma TorVergata

ICES Seminar - CVC Biophysics Series: “The Molecular Dynamics Approach ”

Abstract:

The Molecular Dynamics Approach (4 lectures)
a. Statistical Thermodynamics: Gibbs’ notion of ensemble. Liouville Theorem. The microcanonical ensemble. Other ensembles.
b. Andersen-Parrinello-Rahman Molecular Dynamics: Kinetic energy. Intermolecular potential. Lagrangian equations of motion. Halmitonian version. Metadynamics)

http://www.uniroma2.it/ppg/
ppg@uniroma2.it

Tuesday, August 18 (Location: ACES 4.304) (Time: 9:30 — 10:15 AM)

Paolo Podio-Guidugli
Professor, Dipartimento di Ingegneria Civile Facolta di Ingegneria, Universita di Roma TorVergata

ICES Seminar - CVC Biophysics Series - CVC Biophysics series: “Phase Transformations by Atomic Rearrangement ”

Abstract:

Phase Transformations by Atomic Rearrangement (4 lectures)
Continuum Thermodynamics: classic heat conduction and classic thermomechanics. Chemical potential and coldness. New mathematical models of Allen-Cahn and Cahn-Hilliard type.

Monday, August 17 (Location: ACES 4.304) (Time: 9:30 — 10:15 AM)

Paolo Podio-Guidugli
Professor, Dipartimento di Ingegneria Civile Facolta di Ingegneria, Universita di Roma TorVergata

ICES Seminar - CVC Biophysics Series: “Phase Transformations by Atomic Rearrangement”

Abstract:

Phase Transformations by Atomic Rearrangement (4 lectures)
Continuum Thermodynamics: classic heat conduction and classic thermomechanics. Chemical potential and coldness. New mathematical models of Allen-Cahn and Cahn-Hilliard type.

Thursday, August 13

Satyendra Tomar
RICAM, Austrian Academy of Sciences

ICES Seminar: “On functional-type a posteriori error estimates for non-conforming approximations of elliptic problems”

Abstract:

In this talk functional-type a posteriori error estimates for non-conforming approximations of scalar second-order elliptic problems will be presented. It is known that the error in the nonconforming approximation, in general, is not in the natural energy space H1(?). Thus, it is useful to decompose the error into conforming and nonconforming parts. For the conforming part we use the functional-type a posteriori estimates, which give guaranteed, robust, fully-computable, and sharp bounds of the error in the energy norm. These estimates are valid for any conforming approximation. Since the nonconforming error, which can be viewed as a penalty for the nonconformity, can be explicitly determined, we obtain estimates that are also valid for any non-conforming approximations (however, for the numerical results we consider the interior-penalty discontinuous Galerkin (IP-DG) method as a particular case). Various numerical examples, which support the theoretical results, and confirm the efficiency and robustness of these estimates, will be presented.

In the second part of the talk, the computational cost of these estimates will be discussed. The discrete problems (for the IP-DG method as well as for the error estimates) are solved by the algebraic multilevel iteration method. By comparing the cost of these estimates with the cost of the IP-DG solution it will be shown that the guaranteed and sharp error bounds can be computed with a reasonable cost.

Tuesday, August 4

Nathan Collier
King Abdullah University of Science and Technology (KAUST)

ICES Seminar: “The Reproducing Kernel Element Method and Applications in Geometry Representation”

Abstract:

In recent years, there has been a focus of work in linking computational geometry to analysis. While a natural solution was to use NURBS which are common in Computer Aided Design (CAD) applications, the tensor product construction of higher dimension functions necesitates that a geometry must be decomposed into sections which are logically square, corresponding to a meshing problem which is not solved. The aim of this research has been to find a method capable of linking geometry to analysis which is free from the topological constraints of NURBS. To this end, the Reproducing Kernel Element Method has been used on triangulations to perform isogeometric analysis.

The Reproducing Kernel Element Method (RKEM) first appeared in a series of papers [2–4, 6] in 2004. The aim of this method was to present a general methodology for constructing finite element shape functions that were smooth between elements while maintaining the interpolating property useful in treating Dirichlet boundary conditions. This was achieved by patching local approximation fields together with meshfree kernels. The RKEM shape functions have been used to represent geometries in two-dimensions [5] as well as in isogeometric analysis in a few simple cases of elasticity.

While the method presents a method for constructing bases which possess higher order smoothness property and the interpolating property, this comes at the cost of added difficulty in meshing. This difficulty was mentioned in the original works, but not realized when the problem domains are simple and the meshes highly structured. Although these constraints were noted in the original works, the expressions developed to assess a mesh were insufficient. In [1] the mesh condition which guarantee RKEM shape function properties was amplified for meshes of arbitrary element type and support shape. An algorithm was also developed for assessing two-dimensional meshes with circular supports. In addition to the checking algorithm, techniques are presented to mend meshes which fail to satisfy these conditions.

This talk will introduce the Reproducing Kernel Element Method and demonstrate how it can be used to perform isogeometric analysis. The meshing difficulties will be discussed as well as a technique for mending offending meshes. Finally the talk will conclude with current challenges in using RKEM for the solution of partial differential equations.

References
[1] Nathan Collier and Dan C. Simkins. The quasi-uniformity condition for reproducing kernel element method meshes. Computational Mechanics, 44:333–342, August 2009.
[2] S. Li, H. Lu, W. Han, W. K. Liu, and D. C. Simkins, Jr. Reproducing kernel element method, Part II. Global conforming Im/Cn hierarchy. Computer Methods in Applied Mechanics and Engineering, 193:953–987, 2004.
[3] W. K. Liu, W. Han, H. Lu, S. Li, and J. Cao. Reproducing kernel element method: Part I. Theoretical formulation. Computer Methods in Applied Mechanics and Engineering, 193:933–951, 2004.
[4] H. Lu, S. Li, D. C. Simkins, Jr., W. K. Liu, and J. Cao. Reproducing kernel element method Part III. Generalized enrichment and applications. Computer Methods in Applied Mechanics and Engineering, 193:989–1011, 2004.
[5] D. C. Simkins, Jr., A. Kumar, N. Collier, and L.B. Whitenack. Geometry representation, modification and iterative design using RKEM. Computer Methods in Applied Mechanics and Engineering, 196:4304–4320, 2007.
[6] Daniel C. Simkins, Shaofan Li, Hongsheng Lu, and Wing Kam Liu. Reproducing kernel element method Part IV. Globally compatible Cn(n 1) triangular hierarchy. Computer Methods in Applied Mechanics and Engineering, 193:1013–1034, 2004.

Thursday, July 23

Youssef Marzouk
Professor, MIT, Department of Aeronautics & Astronautics

ICES Seminar : “Computationally efficient Bayesian inference using polynomial chaos expansions”

Abstract:

Predictive simulation of complex engineering systems increasingly
rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a complete foundation for inference from noisy and limited data. Computationally intensive forward models, however, can render a Bayesian approach prohibitive.

Polynomial chaos expansions, typically used in the forward propagation of uncertainty, are an extremely useful tool in the inverse context as well. We introduce a stochastic spectral formulation that accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior distribution. The posterior is constructed by either stochastic collocation or stochastic Galerkin methods. Theoretical convergence results are verified with several numerical examples---in particular, parameter estimation in transport equations and in chemical kinetic systems. We also extend this approach to the inference of spatially distributed quantities in a hierarchical Bayesian setting, achieving dimensionality reduction via Karhunen-Loeve representations of Gaussian process priors.

Finally, we discuss the utility of polynomial chaos expansions in
density estimation, formulating a hierarchical Bayesian method for
estimating polynomial chaos representations from sparse data. Here, we introduce a reversible-jump Markov chain Monte Carlo scheme that simultaneously traverses polynomial degree and the corresponding spaces of coefficients, thus extending the parameter estimation problem to one of model averaging and model selection.

Host: Omar Ghattas

Note: Dr. Marzouk will be visiting ICES from July 20 - August 4.
Anyone wishing to meet with him should contact Youssef at
ymarz@mit.edu. His office will be ACE 4.234.

Thursday, May 28

Leszek Demkowicz (joint work with Jay Gopalakrishn
Professor, University of Texas at Austin

ICES Seminar: “A New Discontinuous Petrov Galerkin Method for All Seasons'”

Abstract:

The hp-adaptive finite elements combine elements of varying size h
and polynomial order p to deliver approximation properties superior
to any other discretization methods that hold for both regular
and irregular (singular) solutions. The best approximation error
converges exponentially fast to zero as a function of number of
degrees-of-freedom. The hp methods are thus a natural candidate
for singularly perturbed problems experiencing internal
or boundary layers like in compressible gas dynamics.

This is the good news. The bad news is that only a small number
of variational formulations is stable for hp-discretizations.
By the hp-stability we mean a situation where the discretization
error can be bounded by the best approximation error times
a constant that is independent of both h and p. To this class
belong classical elliptic problems (linear and non-linear),
and a large class of wave propagation problems whose discretization
is based on hp spaces reproducing the classical exact grad-curl-div
sequence. Examples include acoustics, Maxwell, elastodynamics,
poroelasticity and various coupled and multiphysics problems.

My presentation will focus on a not-so-simple model problem: advection dominated diffusion. I will present first a new Discontinuous Petrov-Galerkin (DPG) formulation for the pure advection problem. In the
1D case, the idea is not new, the formulation has already been explored in context of parabolic equations. The extension to the
multidimensional case is however non trivial. Whereas the trial space involves just piecewise polynomials (possibly with variable h and p), the test space includes non-polynomial functions. We can prove the hp-stability for the method, and I will show convincing 1D and 2D numerical evidence confirming the theory.

The new DPG method is then extended to about any system of first order
PDE's using concept of numerically determined optimal test functions.
We will use the convection-dominated diffusion to illustrate the general concept and present:
- a general abstract stability and convergence analysis,
- a detailed theory for 1D convection-diffusion,
- 1D numerical results for convection-dominated diffusion,
- 2D numerical results for convection-dominated diffusion.

(joint work with Jay Gopalakrishnan, U. Florida)

This is a preview of the Babuska's Lecture that I will give at Mafelap
2009.

Wednesday, May 20

Jianfeng Lu
Princeton

ICES Seminar - Numerical Analysis Series: “From electrons to elasticity”

Abstract:

Ab initio electronic structure models like density functional theory
have been widely used in a range of applications. The mathematical
understanding of these models are still sparse. In this talk, we will
discuss some recent works about the continuum limit of the electronic structure models, trying to build connection between density functional theory and the elasticity theory. Algorithm developed based on the multiscale strategy enables electronic structure calculations for macroscopic systems. (Joint work with Weinan E)

Monday, May 18 (Location: ACES 4.304) (Time: 3:30 — 4:30 PM)

Lin Lin
Princeton

ICES Seminar- Numerical Analysis Series: “Multipole representation of the Fermi operator”

Abstract:

Ab-initio calculation based on density functional theory has been very popular in quantum chemistry during the past 20 years. Although fast algorithms for insulating systems has been studied extensively, there is no satisfactory algorithms for metallic system so far. This talk introduces briefly the difficulty of metallic system from mathematical point of view, and discuss our recently developed multipole representation for Fermi operator to solve this problem. Theoretical and numerical example shows that multipole representation can reduce the computational cost from O(\beta Delta E) to log(\beta Delta E), where beta is the inverse temperature and Delta E is the spectrum width.

Tuesday, May 12

Valen Johnson
Professor, M.D. Anderson

ICES Seminar - Mathematics series - Statistics: “Better Bayes Factors”

Abstract:

I examine philosophical problems and sampling deficiencies associated with current Bayesian hypothesis testing methodology, paying particular attention to objective Bayes methodology. Because the prior densities used to define alternative hypotheses in many Bayesian tests assign positive probability to regions of the parameter space that are consistent with null hypotheses, resulting tests provide exponential accumulation of evidence in favor of true alternative hypotheses, but only sub-linear accumulation of evidence in favor of true null hypotheses.
Thus, it is often impossible for such tests to provide strong evidence in favor of a true null hypothesis, even when moderately large sample sizes have been obtained. Because Bayesian hypothesis tests yield probability statements regarding the truth of the null hypothesis (rather than a frequentist decision to simply not reject the null), this imbalance in the rates of accumulation of evidence is problematic. In this talk, I review asymptotic convergence rates of Bayes factors and propose two new classes of prior densities that ameliorate the imbalance in convergence rates inherited by most Bayesian tests. Using members of these classes, I obtain analytic expressions for Bayes factors in linear models and derive approximations to Bayes factors in large-sample settings.

Friday, May 8 (Location: ACES 2.402) (Time: 10:00 — 11:00 AM)

Shuyu Sun
Assistant Professor, Clemson University

Special ICES Seminar: “Adaptive Discontinuous Galerkin Methods for Single- and Two-Phase Flow and Reactive Transport in Porous Media”

Abstract:

Flow and transport in porous media have important applications in petroleum reservoir engineering and environmental science. Both types of applications are computationally challenging as they may involve multiple time and spatial scales, long simulation time periods, and many coupled nonlinear components. In particular, spatially varying adsorption parameters, reaction coefficients, heterogeneous permeability of media and the nonlinear coupling of transport with flow frequently lead to the formation of complex concentration profiles. For multiphase flow, the advection-dominated saturation equation and the nonlinearity from the capillary pressure and relative permeability often result in sharp and moving saturation fronts. Accurate simulation of these phenomena demands steep gradients to be preserved with minimal oscillation and numerical diffusion. In addition, it is desirable to preserve important physics. For example, it is important to retain the local conservation of mass and the continuity of normal flux components in numerical approximations, as violation of either one could cause serious nonphysical source or sink for coupled flow and transport. To address these issues, we propose to solve the system by discontinuous Galerkin (DG) method, a specialized finite element method that utilizes discontinuous spaces to approximate solutions. Among other advantages, DG possesses local mass conservation, small numerical diffusion and little oscillation as well as its abilities to capture the discontinuities and sharp fronts in the solution. In this talk, we will present DG with dynamic mesh adaptation as applied to flow and transport in porous media. Coupling of DG with mixed finite elements for simulating two-phase flow will also be discussed, with emphasis on its ability to treat counter-current flow driven by capillary pressure and gravity.

Host: Omar Ghattas

Monday, May 4 (Location: ACES 4.304) (Time: 3:15 — 4:15 PM)

Michael Gilson
Professor, Biochemistry and Molecular Biophysics, University of Maryland Biotechnology Institute

ICES Seminar - Molecular Biophysics Series: “ Molecular Recognition, Computer-Aided Drug-Design and the Role of Entropy”

Abstract:

We have developed an approach to modeling receptor-ligand interactions which yields free energies based on analysis of multiple energy wells of the receptor, the ligand, and their complex. This method has provided encouraging agreement with experiment for a range of miniature receptors -- i.e., host-guest systems -- and has recently been adapted for protein-ligand modeling. It has also provided unexpected insight regarding changes in configurational entropy on binding and the role of entropy as a key determinant of affinity. We are now exploring a new method of extracting information about entropy from molecular dynamics simulations. Application to this mutual information expansion approach to protein-peptide binding indicates that changes in motional correlation on binding make a large contribution to the overall entropy change. This has implications for the entropic interpretation of NMR order parameters.

Thursday, April 30 (Time: 2:00 — 3:00 PM)

Hannes Jónsson
Director of Chemistry Division, Science Institute, University of Iceland

ICES Seminar - CCMS series: “Calculations of hydrogen atom tunneling in surface adsorption/ desorption, diffusion and reaction”

Abstract:

An implementation of harmonic quantum transition state theory has been developed to make it possible to calculate thermal rate constants for transitions such as diffusion and chemical reactions where tunneling is the dominant mechanism. The calculations can be carried out for large systems where all degrees of freedom are treated in the same way and by using directly atomic forces obtained from electronic structure methods, such as plane wave based density functional theory. The method, therefore, does not require parametrization of a potential energy surface. Also,
calculations of quantum dynamics is not required if the goal is to
estimate the thermal rate. We have applied the method to study various processes, such as hydrogen atom diffusion, formation of ammonia on the Ru(0001) surface, associative desorption of hydrogen from Cu surfaces and ammonia borane. The method is based on a quantum mechanical extension of the minimum mode following method for finding first order saddle points and a harmonic approximation to a more general, Feynman path integral
based quantum rate theory.

Tuesday, April 28 (Location: 2.302 Avaya Auditorium)

Gregor Hillers
Caltech University

ICES Seminar - Special Seminar: “Earthquake Pattern, Source Physics, and Slip Transients: Results from Numerical Experiments and Large Scale Data Analysis”

Abstract:

We conduct numerical experiments of an earthquake fault governed by a laboratory derived friction law to study multiple aspects of seismicity pattern, earthquake source physics, and scaling relations. The simulations are targeted at the investigation of the relative effects of structural heterogeneity and hydro-mechanical frictional properties on seismicity evolution. The physically consistent results from the numerical experiments will be linked with Strong Ground Motion calculations. The model is used for systematic tests of earthquake scaling relations, to explore coseismic behavior at depth, and to study relations between earthquake nucleation properties and the final event size.

Earthquake scaling relations are also the subject of a pilot study to estimate corner frequencies using an innovative Green's-function approach. High-resolution borehole data will be analyzed to infer the method's applicability. Motivated by the detection of ambient non-volcanic tremor (NVT) related to the central section of the San Andreas fault, and triggered NVT at two sites in southern California, we conduct a systematic search for tremor analyzing eight years of continuous data from the California Integrated Seismic Network. We are developing a multi-scale analysis technique to detect transients in the frequency band associated with NVT. Pattern recognition tools are applied to isolate spatial (and later temporal) clusters, that are analyzed using high-resolution tremor detection techniques. The method has the potential to be applied to a variety of data sets.

Bio:
Dr. Gregor Hillers received his Diploma in Geophysics from Univ. Bochum, Germany in 2001. His Diploma Thesis was carried out at GeoForschungsZentrum, Potsdam, Germany on static Coulomb stress modeling. He received his PhD in Geophysics from ETH Zurich, Switzerland in 2005, on seismicity patterns, scaling relations, and friction. He spent the period 2006-2008 as a Fellow of the Swiss National Science Foundation Postdoc at UC Santa Barbara studying evolution of fault zone properties and earthquake scaling. Since August 2008, he has been a postdoc at Caltech's Seismolab working on tremor detection and source modeling.

Host:
Omar Ghattas

Wednesday, April 22

Yalchin Efendievby
Professor, Texas A&M

ICES Seminar - Numerical Analysis Series: “Uncertainty quantification in inverse problems for flows in heterogeneous porous media using coarse-scale models”

Abstract:

In this talk, I will consider uncertainty quantification in inverse problems that arise in flow through heterogeneous porous media applications. The inverse problem is written in a Bayesian framework and reduces to the sampling from the complicated posterior probability distribution. Bayesian framework provides a flexibility for handling the uncertainties in the problem. Our objective is to sample the subsurface properties, permeability field, given an integrated measurement response, e.g., production data. I will discuss various modeling for the prior probability distributions and efficient algorithms for sampling from the posterior. Numerical examples with petroleum applications will be presented.

Monday, April 20 (Time: 3:15 — 4:15 PM)

Joachim Frank
Professor, Biological Sciences, Columbia University

ICES Seminar - Molecular Biophysics Series: “The Dynamics of the Ribosome as Seen by Cryo-EM”

Abstract:

Cryo-EM and Single-Particle Reconstruction has been employed to capture the ribosome in various functional states. We have looked at several states during the elongation cycle of translation, specifically the decoding and translocation processes, each state trapped by using antibiotics and non-hydrolyzable GTP analogs. By correlating these findings from cryo-EM with those from single-molecule FRET studies, a fascinating picture emerges of a complex molecular machine in motion.

*Refreshments served at 3:00.

Thursday, April 16

Alexander Movchan
Professor, University of Liverpool

ICES Seminar: “Green’s Functions and Boundary Value Problems in Perforated Domains: Asymptotic Treatment Without Homogenization”

Abstract:

The lecture is based on the results of the joint work with V. Maz’ya. We consider a domain with many small inclusions. Periodicity is not required. A method of meso-scale asymptotic approximations is developed to construct and justify a uniform asymptotic approximation of Green’s function of the Dirichlet problem for the Laplacian in multiply perforated domains. First, the ideas of the method are illustrated on analysis of the Dirichlet boundary value problem for the Laplacian in a domain with many inclusions. The uniform asymptotic approximation of the solution incorporates a linear combination of model fields (like capacitary potentials and Green’s function in the unperturbed domain), and the coefficients satisfy a linear algebraic system, whose solvability is proved under weak geometrical assumptions. The estimates of the remainder are given. Then the method is applied to derive the uniform asymptotic approximation of Green’s function in the perforated domain of the same type. Connections with the homogenization approximations are also discussed.

Thursday, April 9 (Time: 11:00 — 1:00 PM)

Pierre-Louis Lions
Professor, Collège de France and Ecole Polytechnique.

ICES Seminar: “Mean Field Games and Applications to Nonlinear PDE”

Abstract:

Series of Lectures. See posting for March 24, 2009.

Tuesday, April 7 (Time: 11:00 — 1:00 PM)

Pierre-Louis Lions
Professor, Collège de France and Ecole Polytechnique.

ICES Seminar: “Mean Field Games and Applications to Nonlinear PDE”

Abstract:

Series of Lectures. See posting for March 24, 2009.

Tuesday, March 31 (Time: 11:30 — 1:00 PM)

Pierre-Louis Lions
Professor, Collège de France and Ecole Polytechnique.

ICES Seminar: “Mean Field Games and Applications to Nonlinear PDE”

Abstract:

Series of Lectures. See posting for March 24, 2009.

Friday, March 27 (Location: ACES 4.304) (Time: 11:00 — 12:00 PM)

Tom Hughes
Professor, ICES

ICES Seminar: ICES Forum series: “ Isogeometric Analysis”

Abstract:

Geometry is the foundation of analysis yet modern methods of computational geometry have until recently had very little impact on computational mechanics. The reason may be that the Finite Element Method (FEM), as we know it today, was developed in the 1950’s and 1960’s, before the advent and widespread use of Computer Aided Design (CAD) programs, which occurred in the 1970’s and 1980’s. Many difficulties encountered with FEM emanate from its approximate, polynomial based geometry, such as, for example, mesh generation, mesh refinement, sliding contact, flows about aerodynamic shapes, buckling of thin shells, etc. It would seem that it is time to look at more powerful descriptions of geometry to provide a new basis for computational mechanics.

The purpose of this talk is to explore the new generation of computational mechanics procedures based on modern developments in computational geometry. The emphasis will be on Isogeometric Analysis in which basis functions generated from NURBS (Non-Uniform Rational B-Splines) and T-Splines are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element h- and p-refinement schemes are presented and a new, more efficient, higher-order concept, k-refinement, is described. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description.

In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions. Extraordinary accuracy is noted for k-refinement in structural vibrations and wave propagation calculations. Surprising robustness is also noted in fluid mechanics problems. It is argued that Isogeometric Analysis is a viable alternative to standard, polynomial-based, finite element analysis and possesses many advantages. In particular, k-refinement seems to offer a unique combination of attributes, that is, robustness and accuracy, not possessed by classical p-methods, and is applicable to models requiring smoother basis functions, such as, thin bending elements, and strain-gradient and phase-field theories. A new modeling paradigm for patient-specific simulation of cardiovascular fluid-structure interaction is described, and a précis of the status of current mathematical understanding is presented.

Wednesday, March 25

Mark Embree
Professor, Rice University

ICES Seminar - Center for Numerical Analysis - Math series: “Convergence and Shift Behavior for Arnoldi Eigenvalue Computations”

Abstract:

The restarted Arnoldi algorithm is among the most widespread methods for computing a subset of the eigenvalues of large, nonsymmetric matrices, thanks to its robust implementation in ARPACK and MATLAB's "eigs" command. While the method is highly effective in practice, its convergence behavior is not well understood. In this talk we shall explain the factors that control convergence (number and location of the sought-after eigenvalues, nonnormality, starting vector), indicate why a complete convergence theory has proved so elusive through examples that cause the method to fail in exact arithmetic, and describe some restrictive sufficient conditions that ensure convergence (a collaboration with Russell Carden).

Monday, March 23

Eugenio Oñate
Professor, International Center for Numerical Methods,in Engineering (CIMNE)

ICES Seminar: “Advances in the Particle Finite Element Method (PFEM) for Problems in Sea, Earth and Fire”

Abstract:

The Particle Finite Element Method (PFEM) is a general numerical
procedure for the analysis of problems in fluid and solid mechanics combining techniques from finite element and particle methods. The key feature of the PFEM is the use of a Lagrangian description to model the motion of the nodes in both the fluid and the solid domains. Surface nodes are viewed as particles which can freely move and separate from the main analysis domain representing, for instance, the effect of water drops or disgregated solid particles. The boundary of the analysis domain is defined at each step using the Alpha Shape method. A mesh connects the node defining the discretized analysis domain where the governing equations are solved using state of the art FEM. The PFEM is particularly suited for multidisciplinary problems in mechanics such as fluid-structure interaction situations accounting for large motions of the free surface and splashing of waves, heterogeneous fluid mixtures and non linear problems in solids accounting for large deformations with multiple frictional contacts, material fragmentation and thermal coupled effects.

In the presentation a wide range of examples of application of the PFEM are shown including the study of water streams on structures accounting for erosion of the foundation, the analysis of the failure of earth dams in overtopping scenarios, the stability of harbour structures under large waves, the analysis of mixing processes in fluids, the study of the melting and burning of objects in fire and the simulation of industrial forming processes.

References
[1] Oñate E., Idelsohn S.R., del Pin F., Calvo N. and Aubry R. The particle finite element method. An overview. Int. J. Computational
Methods, Vol. 1, No. 2, pp. 267-307, 2004.
[2] Oñate E., Idelsohn S.R., Celigueta, M.A. and Rossi R., Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows. Comput. Methods Appl. Mech. Engrg., 197, (19-20), pp. 1777-1800, 2008.

Wednesday, March 11

Nicholas Zabaras
Professor, Cornell University

ICES Seminar - Center of Numerical Analysis Series: “A Bayesian inference approach to inverse problems using an adaptive sparse grid collocation method”

Abstract:

A new approach to modeling inverse problems using Bayesian inference is presented. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media.

Monday, March 9 (Time: 3:15 — 4:15 PM)

Benoit Roux
Professor, Department of Biochemistry & Molecular Biology, University of Chicago

ICES Seminar-Molecular Biophysics Series: “Multiscale approach to the activation/inactivation of Src kinases”

Abstract:

Src kinases are highly conserved signaling proteins involved in the regulation of many key processes in the cell and whose catalytic activity can be modulated in response to specific cellular signals. Members of this family share a common multi-domain architecture, which comprises a catalytic tyrosine kinase domain, preceded by two peptide-binding modules, the Src-homology domains SH2 and SH3. Available X-ray structures reveal that, in its down-regulated form, the catalytic domain and the SH2 and SH3 modules interact to adopt an auto-inhibitory assembled conformation. A multitude of factors, modulated by various intra-molecular conformational switches and inter-molecular binding processes, can lead to an increase in catalytic activity. The two most well known factors are the dephosphorylation of the C-terminal Tyr527 and the phosphorylation of Tyr416 near the catalytic site. Comparison with X-ray structures of the catalytic domain in its active state indicates the conformational changes required for enzyme activation. Yet, the available X-ray structures do not explain how this occurs or how it is controlled at the atomic level. The critical role that the Src-family kinases play in the onset of cancer makes them important targets for therapeutic intervention. Knowing the microscopic factors regulating Src will help understand the action of kinase inhibitors. Understanding the regulation of Src kinases is about (1) intramolecular conformational changes, (2) multi-domain reorganization, and (3) association of signal peptides to binding modules. I will describe the results of recent computational studies and experiment designed to probe the conformational flexibility of Src.

M.A. Young, S. Gonfloni, G. Superti-Furga, B. Roux and J. Kuriyan, Dynamic Coupling Between the SH2 and SH3 Domains of c-Rc and Hck Underlies Their Inactivation by C-terminal Tyrosine Phosphorylation, Cell 105, 115-126 (2001).
H.J. Woo and B. Roux, Calculation of absolute protein-ligand binding free energy from computer simulations, Proc. Nat. Acad. Sci. USA 102, 6825-6830 (2005).
N.K. Banavali and B. Roux, The N-terminal end of the catalytic domain of SRC kinase Hck is a conformational switch implicated in long-range allosteric regulation, Structure 11, 1715-1723 (2005).
N.K. Banavali and B. Roux, Anatomy of a structural pathway for activation of the catalytic domain of Src kinase Hck. Proteins 67:1096-112 (2007).
J. Faraldo-Gomez and B. Roux, On the importance of a funneled energy landscape for the assembly and regulation of multidomain Src tyrosine kinases. Proc. Natl. Acad. Sci. USA. 104:13643-8 (2007).
A. C. Pan, D. Sezer and B. Roux, Finding Transition Pathways Using the String Method with Swarms of Trajectories, J. Phys. Chem. B 112, 3432-3440 (2007).
N.K. Banavali and B. Roux, Flexibility and charge asymmetry in the activation loop of Src tyrosine kinases, Proteins 74, 378-89 (2009).
S. Yang and B. Roux Kinase Conformational Activation: Thermodynamics, Pathways, and Mechanisms, Plos Comp. 4, e1000047 (2008).
A. C. Pan and B. Roux, Building Markov state models along pathways to determine free energies and rates of transitions, J. Chem. Phys. 129, 064107 (2008).
W. Gan and B. Roux, Binding Specificity of SH2 Domains: Insight from Free Energy Simulations, Proteins (2008, Epub ahead of print).
S. Yang, N.K. Banavali and B. Roux, "Mapping the conformational transition in Src activation by cumulating the information from multiple molecular dynamics trajectories", PNAS (2008, in press).

*Refreshments served at 3:00.

Monday, March 2 (Time: 3:15 — 4:15 PM)

Monte Pettit
Professor,Director of the Institute for Molecular Design, Chair of the Keck Center for Interdisciplinary Biology, University of Houston

ICES Seminar - Molecular Biophysics Series: “Knots loops and writhes: How does topo undo them?”

Abstract:

Type II topoisomerases resolve problematic DNA topologies such as knots, catenanes, and supercoils that arise as a consequence of DNA replication and recombination. Failure to restore nominal DNA topology prohibits cell division and can result in cell death or genetic mutation. Such catastrophic consequences make topoisomerases an effective target for antibiotics and anticancer agents. Despite their biological and clinical importance, little is understood about how a topoisomerase differentiates DNA topologies in a molecule that is significantly larger than the topoisomerase itself. It has been proposed that type II topoisomerases recognize angle and curvature between two DNA helices characteristic of knotted and/or catenated DNA to account for the enzymes preference to unlink instead of link DNA. Here we consider mechanism of recognition of DNA juxtapositions. We found that despite the large negative electrostatic potential formed between two juxtaposed DNA helices, a bulk counterion concentration as small as 50mM provides sufficient electrostatic screening to prohibit significant interaction beyond an interhelical separation of 3nm in both hooked and free juxtapositions. This suggests that instead of electrostatics, other mechanical forces such as those occurring in anaphase, knots, catenanes, or the writhe of supercoiled DNA may be responsible for the formation of DNA juxtapositions and their and recognition by topoisomerase.

*Refreshments served at 3:00.

Thursday, February 26

Susanne Brenner
Professor, Department of Mathematics, Center for Computation & Technology, Louisiana State University

ICES Seminar: “Nonconforming Methods for Electromagnetics”

Abstract:

We will discuss several new nonconforming methods for the time-harmonic Maxwell equations and the Maxwell eigenproblem. These methods are based on elliptic formulations of electromagnetic problems, and they use techniques from classical nonconforming finite element methods and discontinuous Galerkin methods. Both theoretical and numerical results will be presented.

Monday, February 23 (Location: ACES 2.402) (Time: 1:30 — 2:30 PM)

Pinaki Chakraborty
Post-Docoral Research Assistant, University of Illinois

ICES Seminar: “Dynamics of Volcanic Mesocylones”

Abstract:

A strong volcanic plume consists of a vertical column of hot gases and dust topped with a horizontal umbrella. The column rises buoyed by entrained and heated ambient air, reaches the neutral-buoyancy level, then spreads radially to form the umbrella. In standard models of strong volcanic plumes, the plume is assumed to remain always axisymmetric and non-rotating. In this talk I show that the updraft of the rising column induces a hydrodynamic effect not addressed to date: a "volcanic mesocyclone." This volcanic mesocyclone sets the entire plume rotating about its axis, as confirmed by an unprecedented analysis of satellite images from the 1991 eruption of Mount Pinatubo. The rotation triggers a turbulent Rayleigh-Taylor instability which makes the umbrella lose axial symmetry and become lobate in plan view, in accord with satellite records of recent eruptions on Mounts Pinatubo, Manam, Reventador, Okmok, Chaiten, and Ruang. The volcanic mesocyclone spawns waterspouts or dustdevils, as seen in numerous eruptions, and groups the electric charges about the plume to form the "lightning sheath" that was so prominent in the recent eruption of Mount Chaiten. The concept of volcanic mesocyclone provides a unified explanation for a disparate set of poorly understood phenomena in strong volcanic plumes. My collaborators for this research are Gustavo Gioia and Susan Kieffer.

Bio:
Pinaki Chakraborty is a postdoctoral research associate in Prof. Susan Kieffer's Geological Fluid Dynamics group at the University of Illinois. He obtained a Ph.D. in Theoretical and Applied Mechanics from the University of Illinois in 2006.

Host: Omar Ghattas

Monday, February 23 (Location: ACES 2.302/Avaya Auditorium) (Time: 4:00 — 5:00 PM)

Bin Yu
Chancellor's Professor in Statistics, Electrical Engineering and Computer Science, UC Berkeley

ICES Seminar - Distinguished Statistics Lecture: “Seeking Interpretable Models for High Dimensional Data”

Abstract:

Extracting useful information from high-dimensional data is the focus of today's statistical research and practice. After road success of statistical machine learning on prediction through regularization, interpretability is gaining attention and sparsity has been used now as its proxy. With the virtues of both regularization and sparsity, Lasso (L1 penalized L2 minimization) has been very popular recently.

In this talk, I would like to discuss the theory and practice of sparse modeling.

First, I will give an overview of recent research on model selection consistency property of l1 penalized minimization including Lasso and explain what useful insights have been learned.

Second I will present collaborative research on building nonparametric sparse hierarchical models that describe fMRI responses in primary visual cortex area V1 to natural images.

Speaker Bio

Bin Yu is Chancellor's Professor in the departments of Statistics and of Electrical Engineering and Computer Science at UC Berkeley. She is also a founding co-director of the Microsoft Lab on Statistics and Information Technology at Peking University where she co-advises students and organizes conferences and short courses. She has also been a ChangJiang (visiting) Chair Professor at Peking University (2005-2008).

She got her B.S. in mathematics from Peking University in 1984 and her M.A. and Ph.D. in statistics from UC Berkeley in 1987 and 1990, respectively. She was an Assistant Professor in Statistics at University of Wisconsin at Madison from 1990 to 1992, an visiting Assistant Professor at Yale University in Spring 1993, and an Assistant Professor (1993-1997) and an Associate Professor (1997-2001) at UC Berkeley. She was a Memeber of Technical Staff in the math center at Lucent-Bell Labs from 1998 to 2000, while on leave from Berkeley. She has held visiting positions at ETH, the Poincare Institute in Paris, Columbia Univeristy, and Peking University. Jointly with others, she holds two U.S. patents on information technology.

Her current research interests include statistical machine learning for high dimensional data, information theory, and data problems from remote sensing, neuroscience, sensor networks, and finance. She is currently on the editorial boards of Journal of Machine Learning Research, Journal of American Statistical Society, Statistica Sinica, and Tecnometrics, among others. She has chaired many international conferences on statistics and machine learning and has been on numerous program committees. She is a co-chair of the National Advisory Board of SAMSI.

She is a Fellow of AAAS, IEEE, IMS (Inst of Math. Stats) and ASA (Amer. Stat. Assoc.). In 2004, she was named a Miller Research Professor for Basic Research by Miller Institute at Berkeley. In 2006, she was a Guggenheim Fellow. In 2007, she was named Outstanding Overseas Chinese Young Schalor by NSF-China.

Tuesday, February 17

Eric Darve
Professor, Stanford University

ICES Seminar: “Generalized Langevin Equations and Fokker-Planck Equations for Molecular Systems”

Abstract:

Modeling molecular systems is often very expensive because of the large number of degrees of freedom, such as all the coordinates of the atoms, which are required to describe the system and because of the presence of multiple time scales (femto second to millisecond). This often results in
significant computational costs. One approach to address this issue is to formulate stochastic differential equations or Fokker-Planck equations in terms of a small number of resolved variables(sometimes called observables). In particular, such methods can predict slow reaction rates which are beyond the time scales which can be resolved using direct molecular dynamics. We will present new
techniques to calculate such equations based on the Mori-Zwanzig projection formalism. Numerical examples from benchmark problems to small solvated proteins will be presented.

Friday, February 13 (Time: 3:15 — 4:15 PM)

Liviu Movileanu
Assistant Professor, Department of Physics, Syracuse University

ICES Seminar - Molecular Biophysics Seminar Series: “Interrogating single proteins with a nanopore: challenges and opportunities”

Abstract:

A single nanopore represents an amazingly versatile single-molecule probe that can be employed to reveal several important features of polypeptides, such as their folding state, backbone flexibility, mechanical stability, binding affinity to other interacting ligands, and enzymatic activity. Moreover, groundwork in this area using engineered protein nanopores demonstrated new opportunities for discovering the biophysical rules that govern the transport of proteins through transmembrane protein pores. With their adaptation to a microfabricated chip platform, these approaches not only will provide a new generation of research tools in nanomedicine for examining the details of complex recognition events in a quantitative manner, but also will represent a crucial step in designing other pore-based nanostructures and high-throughput devices for molecular biomedical diagnosis.

*Refreshments served at 3:00.

Tuesday, February 10

Yarden Livnat
Scientific Computing and Imaging Institute

ICES Seminar: “Visual Correlation”

Abstract:

Visual correlation aims to facilitate comprehension of relationships within complex data, in particular when the underlying domain is not well understood or is hard to quantified. In these areas one typically only knows how to measure simple aspects of the problem, which in turn do not provide global insights. it is vital in these cases to incorporate human judgment and support dynamic discourse with the user. One class of such domains is situational awareness, where multiple complex and dynamic information channels must to integrated, analyzed and acted upon in relatively short time, yet the nature of the problem (or the emergency) is not know in advance. In science research, visual correlation can help gain insight to form initial hypotheses. The question then is how to convey multitude of heterogeneous data and processed information in a concise and clear manager without causing information overload.

We have developed two approaches to visual correlation of heterogeneous data from disparate sources. The first is based on a radial interfaces and was initially developed to support network intrusion detection. We have since worked on generalization on this approach to other areas from emergency centers to data annotation, to investigation of gene expressions, to interrogation of the demographics aspects of political votes. The second approach is based on the notion of tag clouds and has been directed at identifying infectious disease outbreaks.

Speaker Bio:
Yarden Livnat is a research computer scientist at the Scientific Computing and Imaging Institute in the University of Utah. Dr. Livnat holds a B.Sc in Computer Science from Ben-Gurion University in Israel, an M.Sc. in Computer Science from the Hebrews University in Israel and a Ph.D. in Computer Science from the University of Utah. His research areas include information visualization, scientific visualization, computer graphics and software architecture.

Friday, February 6 (Time: 2:00 — 3:00 PM)

Eran Rabani
Professor and Director, Raymond and Beverly Sackler Institute of Chemical Physics, Tel Aviv University

ICES Seminar - Computational Molecular Sciences Series: “Distribution of carrier multiplication rates in nanocrystals ”

Abstract:

Multiexciton generation (MEG) is a process where several excitons are generated upon the absorption of a single photon in semiconductors. This process enjoys great technological ramifications for solar cells and other light harvesting technologies. For example, it is expected that the more charge carriers created shortly after the photon is absorbed, the larger fraction of the photon energy can successfully be converted into
electricity, thus increasing the device efficiency.

Strict selection rules and competing processes in the bulk allows MEG at energies of five times the band gap. It was suggested
that nanocrystals, where quantum confinement effects are important, may exhibit MEG at lower values of (typically 2 to 3 times the band gap).
Indeed, MEG in NCs has been reported recently for several systems, showing that the threshold was size and band-gap independent. However, more recent studies have questioned the efficiency of MEG in nanocrystals, in particular for CdSe and InAs. The goal of the present talk is to address this controversy.

We present a theoretical study of the problem, where the rates of MEG following photon absorption is calculated for semiconductor nanocrystals using Fermi's golden rule with all relevant Coulomb matrix elements, taking into account proper selection rules within a screened
semiempirical pseudopotential approach. In CdSe and InAs nanocrystals we find a broad distribution of biexciton generation rates depending strongly on the exciton energy and size of the nanocrystal. We find that the process becomes inefficient for nanocrystals exceeding 3 nm in diameter in the photon energy range of 2-3 times the band gap.

Tuesday, February 3

L. Demkowicz, J. Kurtz, P. Gatto, M. Paszynski
ICES-UT Austin and AGH University of Science and Technology, Cracow, Poland

ICES Seminar: “A New 3D hp FE Code for Coupled Multiphysics Problems ”

Abstract:

We shall report on an ongoing effort of building a new, significantly
expanded version of our three-dimensional FE code - hp3d supporting
h-, p- and hp-adaptivity. The main functionalities of the new
infrastructure are as follows:
1. Elements of all shapes: tets, prisms, pyramids and hexas.
2. Support of the whole exact sequence: H^1-, H(curl)-, H(div)
and L^2-conforming elements. This is crucial for multiphysics
problems.
3. Support of coupled multiphysics problems. The number of variables
and their discretization type may vary for different
subdomains.
4. Full support of curvilinear geometries using the concept
of Mesh Based Geometry (MBG) description, transfinite interpolation
and implicit parametrizations.
5. An interface with NETGEN for an automatic geometry model
generation.
6. Support of p-, h-, and hp-adaptivity.
7. A parallel multifrontal solver based on MUMPS (the code interfaces
also with other linear solvers).
8. An interface with VTK.

The development of the code has been driven by a project on modeling
the propagation of acoustic waves in the human head, and we shall use
the problem to illustrate the main concepts and functionalities
of the code. The main reason for giving the presentation is to inform
the ICES community about the development and solicit a possible
collaboration.
The code is maintained in an ICES depository under SVN.

The plan of the presentation is as follows:
LD (20 minutes):
1. Multiphysics and coupled problems: a few motivating examples
2. Overall code structure and design assumptions.
3. An overview of Geometrical Modeling Package and mesh generation.
PG (20 minutes):
4. Construction of shape functions accounting for orientations.
5. Relation wth Transfinite Interpolation
MP (15 minutes):
6. Parallel multifrontal solver
JK (15 minutes):
7. Interface with VTK.

Friday, January 30 (Time: 11:00 — 5:15 PM)

Leszek Demkowicz
Professor, ICES

ICES Seminar - ICES Forum Series: “Galerkin Method and Babuska's Theorem”

Abstract:

The Galerkin method lays down a foundation for discretization of various boundary-value problems. I will attempt to present fundamentals of the Galerkin method. I will try to make two points. In the first part of the presentation, I will show how the same physical problem can be formulated in different ways that give rise to different numerical methods. In the second part, I will recall the fundamental inf-sup condition of Babuska and use a couple of examples to
demonstrate how the Theorem can guide you to construct stablediscretizations.

Wednesday, January 21 (Time: 4:00 — 5:00 PM)

James Berger
Professor, Duke University and SAMSI

ICES Seminars - Distinguished Statistics Lectures: “Risk Assessment for Pyroclastic Flows”

Abstract:

Risk assessment of rare natural hazards -- such as large volcanic block and ash or pyroclastic flows -- is addressed. Assessment is approached through a combination of computer modeling, statistical modeling, and extreme-event probability computation. A computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive. Solution instead requires a combination of adaptive design of computer model approximations (emulators) and rare event simulation. The techniques that are developed for risk assessment are illustrated on a test-bed example involving pyroclastic flow.

Tuesday, January 13

Prof. Leonid Berlyand
Penn State University

ICES Seminar: “Homogenization of Elasticity Equations without Scale Separation”

Abstract:

In this joint work with H. Owhadi, we investigate the homogenization of divergence form elliptic (scalar and vectorial equations with arbitrary bounded coefficients (in particular, in situations where assumptions of scale separation and/or ergodicity are not satisfied). We prove the existence of an h-basis that is superior to standard piecewise polynomial bases with the same number of degrees of freedom. We also obtain an explicit error constant for h-basis approximations, which is independent of the contrast of the material and geometry of its microstructure. We also discuss minimization of the number of 'cell' (precomputed problems for homogenization with arbitrary bounded coefficients and show that this issue is related to a new class of analytical inequalities (work in progress). Finally, we will discuss potential applications of this work ranging from brain damage and virtual liver surgery to reservoir modeling and
upscaling of atomistic models.