MEAM Seminar Series Archive: Spring 2008

January 17
Per-Gunnar J Martinsson
"Fast methods for solving partial differential equations"

Speaker: Per-Gunnar J Martinsson
Assistant Professor of Applied Mathematics
University of Colorado at Boulder

The development over the last several decades of powerful computers and fast algorithms has dramatically increased our capability to computationally model a broad range of phenomena in science and engineering. Our newfound ability to design complex systems (cars, new materials, city infrastructures, etc) via computer simulations rather than physical experiments has in many fields led to both cost savings and dramatically improved performance. Intense efforts are currently being made to extend these advances to biochemistry, physiology, and several other areas in the biological and medical sciences.

In many computational simulations, the most time consuming step is the construction of approximate solutions to partial differential equations. In this talk, we will focus on linear PDEs; we will give an overview of well-established fast solvers for such equations, and describe some recent advances that have the potential to profoundly increase our computational capabilities. Specifically, we will discuss new techniques for (1) representing functions and operators, (2) directly inverting the large matrices that arise upon the discretization of many integral and differential equations, and (3) constructing low-rank approximations to operators using randomized sampling techniques.

January 31
Krishna Garikipati
"A theoretical study of the thermodynamic driving forces and kinetics of focal adhesion dynamics"

Speaker: Krishna Garikipati
Mechanical Engineering and Michigan Center for Theoretical Physics
University of Michigan

Focal adhesions constitute a type of structure by which cells attach to substrates. They mediate cell traction and migration, and form central components of the pathway by which cells mechanically sense their environment. It is now increasingly believed that at least some of a cell's biochemical response is regulated by mechanical signaling, and even much of the biochemical life of a cell has an eventual mechanical purpose. Focal adhesions orchestrate much of this action, so an understanding of their response has become an important quest to cell biologists and biophysicists. In this talk I will focus on the dynamics that is displayed by focal adhesions under mechanical and chemical influences. Consider this: A piece of tape adhering to a surface can be peeled off by a force. Focal adhesions, the "bits of tape" by which cells adhere to substrates, also appear to peel under the application of force. However, in certain force regimes they also grow, and in others, slide along the force. I will draw upon what has been learnt, from other branches of Physics, about thermodynamic driving forces and kinetics in an attempt to identify the physical mechanisms that control focal adhesion dynamics.

February 7
Baskar Ganapathysubramanian, PhD Candidate
"Flow through heterogeneous porous media: A stochastic variational multiscale framework"

Speaker: Baskar Ganapathysubramanian
PhD candidate, Materials Process Design and Control Laboratory
Sibley School of Mechanical and Aerospace Engineering
Cornell University


Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these inherently multiscale phenomena. Such analysis is complicated by the limited information available to characterize the system. In this talk, I will discuss a recently developed strategy that comprehensively accounts for the twin issues of stochasticity and multiscale nature exhibited by such systems. The topics covered in this talk are:

  1. A stochastic variational multiscale formulation to incorporate uncertain multiscale features,
  2. Effective computational strategies to solve the resulting stochastic partial differential equations (SPDEs), and
  3. A data driven strategy to incorporate limited experimental data into the stochastic analysis

A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Adaptive sparse grid collocation techniques are used to efficiently solve the resulting SPDEs. Strategies to incorporate the available (incomplete) information about the system properties are discussed. These strategies are based on ideas in manifold learning used in cognitive sciences and signal processing. Examples that illustrate the complete framework are presented. Extensions to the analysis, design and control of other physical processes that exhibit inherent stochasticity and multiscale character are discussed.

February 25
Per-Olof Persson
"High-order discontinuous galerkin methods for fluid and solid mechanics"

Speaker: Per-Olof Persson
Instructor of Applied Mathematics
Massachusetts Institute of Technology

Discontinuous Galerkin (DG) methods have gained popularity because of their ability to discretize conservation laws with high-order accuracy on complex geometries. They have the potential to produce highly accurate solutions with minimum numerical dissipation, which makes them attractive for aerodynamic applications such as aeroacoustics and turbulence simulations, and other problems involving wave propagation, multiple scale phenomena, and non-linear interactions. Moreover, DG methods can be used with unstructured meshes of tetrahedra, which appears to be a requirement for real-world geometries.

However, as of today DG methods have only been demonstrated in the research community for academic applications with relatively simple physics and geometries. One of the main challenges is to extend these methods to relevant scientific and engineering applications. This requires the ability to generate appropriately stretched high-order meshes and robust discretizations, maintain stability in the presence of shocks, and solve the resulting systems of equations in a competitive manner. We present a number of new developments in our work on DG methods: (i) The Compact Discontinuous Galerkin (CDG) method, an accurate and low cost discretization for viscous terms. (ii) A Newton-GMRES preconditioner based on p-multigrid and block-ILU smoothing, with optimized element numbering using a Minimum Discarded Fill method. (iii) A stabilization technique based on artificial viscosity which gives subgrid accuracy for shock capturing and the ability to handle RANS problems. (iv) A high-order ALE formulation for deforming geometries based on mappings. We show examples of aeroacoustic simulations, high-Reynolds number transonic flows, non-linear solid dynamics, and applications involving fluid-structure interaction with particular emphasis on flapping flight.

February 28
Amy Shen
"Complex fluids under confinement and flow"

Speaker: Amy Shen
Assistant Professor of Mechanical and Aerospace Engineering
Washington University, St. Louis

The flow of complex fluids in confined geometries produces rich and new phenomena due to the interaction between the intrinsic length-scales of the fluid and the geometric length-scales of the device. In this talk, I will focus on a micellar solution system that yields a novel route to synthesizing nanoporous sol-gels.

March 4
Katia Bertoldi
"Microstructures in solids: Their critical role in governing material mechanical behavior"

Speaker: Katia Bertoldi
Postdoctoral Associate, Department of Mechanical Engineering
Massachusetts Institute of Technology

One of the most exciting technological advancements of recent decades is the ability to probe, understand, and design novel materials at the small scale, such as nano-composites and biological composites. These novel materials are particularly interesting, since their morphology is tailored at the nanometer and the micrometer length scales to enable a wide range of macroscopic level functions and they often exhibit superior mechanical properties.

The microstructure of small-scale materials can now be accurately measured using a variety of scale appropriate microscopy tools (from optical to electronic to atomic force microscopy) as well as x-ray and spectroscopic techniques. This knowledge of structural details enables rigorous micromechanics-based development of constitutive equations for the macroscopic behavior of such materials. The constitutive equations are of crucial importance, since they help us to better understand, explain and predict experimental results as well as provide a framework to probe the underlying physics of the mechanical behavior of the materials.

The development of microstructurally-informed macroscopic constitutive equations for the deformation of a selection of novel materials will be presented, including lattice structures, structural interfaces, fiber-bridged elliptical voids. The critical role of microstructure in governing specific features of mechanical behavior will be discussed.

Specifically, in the field of lattice structures, periodic elastomeric solids are subjected to uniaxial compression and novel transformations of the patterned structures are found upon reaching a critical value of applied load. Numerical analyses clearly show the mechanism of the pattern switch to be a form of microstructural elastic instability, giving reversible and repeatable transformation events as confirmed by experiments. This behaviour provides opportunities for transformative phononic/photonic crystals which can switch in a sudden, but controlled manner.

In the field of structural interfaces, a new model of structure embedded in a continuum has been introduced and systematically investigated. The interest in the proposal is that the incorporation of a specific structure in general introduces non-local effects and that these follow from the description in a natural and rational way.

An unexpected outcome from the structural interface model has been the possibility of analyzing elliptical voids bridged by fibers, demonstrating the effects of fibers geometry and stiffness.

March 6
Patrick Le Tallec
"From homogeneisation to domain decomposition in the numerical modeling of materials"

Speaker: Patrick Le Tallec
Professor of Computational Mechanics and
Vice President for Academic Research
École Polytechnique

Homogeneisation techniques aim to solve problems where there is a significant separation of scales between the global macroscopic problem and the local heterogeneities governing the response of the constitutive materials.

They are based on the notion of representative volume elements (RVE), which are microscopic samples of the system under study. Each sample is solved at a microscopic scale taking as boundary conditions uniform or periodic displacement data deduced from the solution observed at macroscopic scale.

The talk will review some of these techniques and explain how to adapt mortar elements techniques as introduced in domain decomposition techniques to the construction of aposteriori error estimates in numerical homogeneization. The domain decomposition strategies turn out also to be useful for developing several approximate strategies for the numerical solution or the iterative coupling of the microscopic problems.

March 7
Kostas Danas, PhD Candidate
"Homogenization-based constitutive models for viscoplastic porous media with evolving microstructure"

Speaker: Kostas Danas
PhD Candidate
Advisor: Pedro Ponte Castañeda
Mechanical Engineering and Applied Mechanics, University of Pennsylvania

This work is concerned with the application of the "second-order" nonlinear homogenization procedure of Ponte Castañeda (2002) to generate estimates of the Willis (1977) type for the effective behavior of viscoplastic porous materials. The main concept behind this procedure is the construction of suitable variational principles utilizing the idea of a "linear comparison composite" to generate corresponding estimates for the nonlinear porous media. Thus, the main objective of this work is to propose a general constitutive model that accounts for the evolution of the microstructure and hence the induced anisotropy resulting when the porous material is subjected to finite deformations.

The model is constructed in such a way that it reproduces exactly the behavior of a "composite-sphere" assemblage in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson's (1977) criterion in the special case of ideal plasticity and isotropic microstructures. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly stiff for sufficiently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a significant effect on the effective response of the material at moderate and high stress triaxialities.

Finally, the above-mentioned results are generalized to more complex anisotropic microstructures (arbitrary pore shapes and orientation) and general, three-dimensional loadings, leading to overall anisotropic response for the porous material. The model is then extended to account for the evolution of microstructure when the material is subjected to finite deformations. To validate the proposed model, finite element axisymmetric unit-cell calculations are performed and the agreement is found to be very good in all the range of stress triaxialities and nonlinearities considered.

March 20
Martin H. Müser
"Simulations of extreme conditions: From tribology to optoelectronic materials"

Speaker: Martin H. Müser
Associate Professor, Department of Applied Mathematics
University of Western Ontario, Canada

In my talk, I will discuss two examples, which demonstrate how computer simulations guide the understanding of materials and thereby assist the optimization of technical applications. The first example is concerned with mechanical contacts between two solids that have surfaces with self-affine topographies. Multi-scale simulations techniques were developed which made possible the calculation of the pressure distributions in these systems. These in turn were required to model chemical processes at the molecular scale. One result of practical importance is that molecules, which crosslink under pressure, form protective films on surfaces.

The second example demonstrates the relevance of pressure-induced transitions in opto-electronic materials. Their functionality is based on the strong contrast of their properties between their crystalline and amorphous state. A recently proposed reason for this contrast is the difference in the local order in the two phases. Simulations of the commercially used alloys confirm this hypothesis and demonstrate in addition that the materials cannot only be switched thermally but also with pressures and tensile loads opening a pathway to "cool" memory.

March 27
James R. Rice
Tedori-Callinan Lecture: "Thermo-hydro-mechanics of earthquake rupture"

Learn more about the lecture here!

March 28
Andy Perrin, PhD Candidate
"Explicit finite difference schemes for particulate flows"

Speaker: Andy Perrin
PhD Candidate
Advisor: Howard H. Hu
Mechanical Engineering and Applied Mechanics, University of Pennsylvania

Many schemes have been proposed for direct numerical simulation of particles in fluids, but they can be quite complicated and require a lot of memory when the fraction of particles is high. Explicit finite difference schemes on a Cartesian grid are one way around these issues. The fluid velocity and density can be marched in time without inverting any matrices, and the particles can be moved according to Newton's laws. Enforcing the no-slip condition on the spherical particle's surfaces as they move on a Cartesian grid is not so easy, however, so we have proposed a spectral expansion method that exactly satisfies no-slip to deal with the problem. This method allows a grid as coarse as ten grid spacings per particle diameter to give smooth forces and accurately resolved pressure distributions on the particle surface. Up to 1035 particles have been simulated on a (fast) PC.

April 3
Gareth H. McKinley
"Elasto-capillary thinning and the breakup of complex fluids" (or why some things are stickier than others!)

Speaker: Gareth H. McKinley
Director, Hatsopoulos Microfluids Laboratory
Department of Mechanical Engineering, M.I.T.

The uniaxial extensional viscosity is a fundamental material property of a fluid which characterizes the resistance of a material to stretching deformations. For microstructured fluids, this extensional viscosity is a function of both the rate of deformation and the total strain accumulated. Some of the most common manifestations of extensional viscosity effects in complex fluids are the dramatic changes they have on the lifetime of a fluid thread undergoing capillary breakup. In a pinching thread, viscous, inertial and elastic forces can all resist the effects of surface tension and control the ‘necking’ that develops during the pinch-off process. The dominant balance of forces depends on the relative magnitudes of each physical effect and can be rationalized by dimensional analysis. The high strains and very large molecular deformations that are obtained near breakup can result in a sharp transition from a visco-capillary or inertio-capillary balance to an elasto-capillary balance. As a result of the absence of external forcing the dynamics of the necking process are often self-similar and observations of this ‘self-thinning’ can be used to extract the transient extensional viscosity of the material. It can also lead to iterated dynamical processes that result in self-similar spatial structures such as a ‘beads on a string’ morphology. The intimate connection between the degree of strain-hardening that develops during free extensional flow and the dynamical evolution in the profile of a thin fluid thread is important in many industrial processing operations and is also manifested in heuristic concepts such as ‘spinnability’, ‘tackiness’ and ‘stringiness’. Common examples encountered in every-day life include the spinning of ultra-thin filaments of silk by orb-weaving spiders, the stringiness of cheese, the drying of liquid adhesives, splatter-resistance of paints and the unexpectedly long life-time of strands of saliva.

April 9
Tully Foote, MSE Student
"3D ladar-based sensing for autonomous ground vehicles"

Speaker: Tully Foote
MSE Student
Advisor: Vijay Kumar
Mechanical Engineering and Applied Mechanics, University of Pennsylvania

To successfully navigate through the DARPA Urban Grand Challenge the Ben Franklin Racing Team, lead by the University of Pennsylvania, developed an autonomous vehicle named Little Ben. The primary sensors on Little Ben were laser range finders. The data from these sensors had to be processed to be useful for navigation. We developed efficient methods to classify measurements from the 3D Ladar to differentiate obstacles from ground in real time. Modern autonomous vehicles employ many laser sensors in unstructured environments. But currently no method exists to calibrate these sensors against each other to allow easy fusion of sensor data. To this end a method is developed to calibrate one laser sensor against a second laser sensor in an unstructured environment. This method demonstrated that automatic sensor calibration in unstructured environments is possible.

April 10
William M. Gelbart
"Making viruses and virus-like particles"

Speaker: William M. Gelbart
Professor of Chemistry and Biochemistry
University of California, Los Angeles

Viruses are the simplest examples of evolving systems; at the same time, they are arguably the deadliest disease agents. Unlike any living system, they have, for example, been reconstituted in vitro from purified components and, in most cases, their structures have high symmetry, most often icosahedral. Also, whereas the genomes of living organisms are exclusively double-stranded (ds) DNA molecules, the genomes of viruses are predominantly single-stranded (ss) RNA, a molecule with very different physical (as well as chemical) properties.

All viruses involve a genome packaged inside a protein shell, some with an extra layer of protection in the form of a lipid bilayer envelope. In this talk I discuss the physical considerations involved in making viruses "from scratch" and what these experiments can tell us about in vivo viral "life cycles". I also describe our ongoing efforts to synthesize "artificial viruses" and "virus-like particles", featuring the physical differences between dsDNA (a stiff, linear, polyelectrolyte), ssRNA (flexible, branched), and charged homopolymers (flexible, linear).

April 17
Mandayam A. Srinivasan
"Haptics: Science, technology and applications"

Speaker: Mandayam A. Srinivasan
Director, The Touch Lab
Massachusetts Institute of Technology

The human haptic system with its tactile, kinesthetic, and motor capabilities together with the associated cognitive processes, presents a uniquely bi-directional information channel between our hands and brains, but is underutilized. Recent development of haptic technologies that enable a user to touch, feel, and manipulate virtual or remote objects, show promise in myriad applications such as education, entertainment, training, communication, healthcare, hazardous operations, design, manufacturing and marketing.

In this talk, I will describe the scientific and technological underpinnings of the emerging field of Haptics. I will give a brief overview of our recent advances in skin biomechanics, tactile neuroscience, human haptic perception, robotic hardware and real-time simulation software, all of which have helped establish Haptics as an exciting area of research. I will also cover our contributions to its applications such as virtual reality based simulators for training surgeons, real-time touch interactions between people across the internet and direct control of machines from brain neural signals.

April 21
Alberto Peisach
"Engineers as entrepreneurs"

Speaker: Alberto Peisach
President, Phoenix Capital, Ltd.

Alberto Peisach is an entrepreneurial executive with more than twenty years of experience in building teams to execute mergers and acquisitions, corporate roll-ups, management, operations, financings and restructurings. Currently, he is the President of Phoenix Capital, Ltd. He Established Phoenix as a packaging manufacturer based in Colombia and expanded it into one of the largest rigid packaging manufacturers in Latin America. Previously, he managed investments in Latin American in fast food, entertainment, media, and communications, among others. He graduated from the School of Engineering at the University of Pennsylvania in 1986.

April 24
Pradeep R. Guduru
"Mechanics of biologically inspired adhesion, friction and engineered surfaces"

Speaker: Pradeep R. Guduru
Division of Engineering
Brown University

Recent discoveries in biological adhesion in animals such as geckos, flies, etc. have inspired attempts to develop practically useful surface engineering technologies to maximize reversible adhesion and frictional properties of a surface. These attempts have opened up a set of contact mechanics related problems, the solutions to which can potentially lead to practical benefits. As part of this effort, a theory of wavy surface adhesion and friction has been developed. It is shown that surface waviness causes the detachment process to proceed in alternating stable and unstable segments. Unstable segments dissipate mechanical energy and lead to apparent toughening and apparent strengthening. The instability induced toughening and strengthening have the potential to be exploited in designing surface topographies to enhance reversible adhesion of soft materials. The predictions of the theory have been verified experimentally. The work also presents an analysis of the effect of shape of a fiber tip in enhancing adhesion. The second aspect of this work is to create biologically inspired surface micro-scale architectures and investigate their adhesive and frictional properties. A film terminated tilted fiber architecture has been fabricated and its directional adhesion and sliding resistance behaviors have been investigated experimentally. The experiments show that such a surface displays a highly anisotropic sliding resistance. Also, sliding resistance in the fiber tilt direction shows a phase transformation-like behavior, with a sudden increase in magnitude with a small drop in the normal tensile force. Possible mechanisms responsible for such a response are discussed.

May 1
Charbel Farhat
"Recent advances in high-fidelity and reduced order modeling of a class of multidisciplinary flow problems: Towards near real-time computational mechanics"

Speaker: Charbel Farhat
Professor of Mechanical Engineering
Stanford University

Recent advances in high-fidelity nonlinear transient computational aeroelasticity, aerothermoelasticity, and aeroservoelasticity are first discussed. These include theoretical as well as algorithmic updates and extensions to previously developed methodologies for the design of provably stable and time-accurate high-order viscous CFD schemes on moving grids, energy-conserving and quadrature-free load transfer algorithms, and robust loosely-coupled solution procedures. Next, a reliable methodology for constructing parameterized reduced-order models (ROMs) for these multidisciplinary problems and updating them in near real-time for new parameter values is presented. This new methodology is based on concepts from differential geometry and interpolation on a tangent space to a Grassman manifold. Finally, the application of all aforementioned technical advances to the design of near real-time predictive aeroelastic and aeroservoelastic capabilities based on the concept of computational databases is described. These capabilities are demonstrated with the parametric aeroelastic identification of an F-16 configuration in subsonic, transonic, and supersonic air streams, the prediction of the aeroservoelastic response of an F-18/A configuration to a given input, and the aeroelastic tailoring of a Formula One car for performance improvement. In all cases where test data is available, good correlations with this data are reported. Concluding remarks about the potential of the discussed near real-time capabilities for assisting design optimization are also offered.

May 9
William Paul King
"Thermomechanical probes at the nanometer scale"

Speaker: William Paul King
Kritzer Faculty Scholar and Associate Professor
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign

This talk describes fundamental measurements on and applications of heated atomic force microscope (AFM) cantilevers. The cantilevers can reach temperature above 1000 C and can be heated as fast as 1 usec. When the heated tip is in contact with a surface, the ultra small hot spot is an excellent tool for nanometer-scale manufacturing, metrology, and surface science measurements. In one application, the heated probe tip can be used like a miniature soldering iron. In another application, the cantilever heaters can also be used as sensors, where the heating can be used to modulate cantilever resonant frequency or to clean and refresh the cantilever surface. Nanometer-scale heated probes can be used to measure spatially resolved glass transition temperature, decomposition temperature, and mechanical properties with later resolution 50 nm and in films as thin as 10 nm.

May 27
Shravan Veerapaneni, PhD Candidate
"High-order fast integral equation methods for PDEs with moving interfaces"

Speaker: Shravan Veerapaneni
PhD Candidate
Advisor: George Biros
Mechanical Engineering and Applied Mechanics, University of Pennsylvania

Many problems in Science and Engineering require the solution of partial differential equations (PDEs) on moving domains. Stencil-based numerical techniques like the Finite Element Method (FEM) tend to be computationally expensive for such problems. For certain classes of PDEs, there are promising alternatives that are based on integral equations. Unlike FEM-based schemes, they do not require unstructured mesh-generation and remeshing. In this work, we construct fast, high-order solvers based on integral equations for two problems: Solving the heat equation on moving domains; Simulating the dynamics of deformable vesicles suspended in viscous fluid flows.

For the heat equation, we describe a fast high-order accurate method for its solution on domains with moving Dirichlet or Neumann boundaries and distributed forces. We assume that the motion of the boundary is prescribed. Our method extends the work of L. Greengard and J. Strain, “A fast algorithm for the evaluation of heat potentials”, Comm. Pure & Applied Math. 1990. Our scheme is based on a time-space Chebyshev pseudo-spectral collocation discretization, which is combined with a recursive product quadrature rule to accurately and efficiently approximate convolutions with the Green's function for the heat equation. We present numerical results that exhibit up to sixteenth-order convergence rates. Assuming N time steps and M spatial discretization points, the evaluation of the solution of the heat equation at the same number of points in space-time requires O(NM logM) work.

Vesicle flows model numerous biophysical phenomena that involve deforming particles interacting with a Stokesian fluid. While conventional techniques can be used to simulate isolated vesicles, new approaches are needed for large number of interacting vesicles. An integral equation formulation leads to a system of nonlinear integro-differential equations whose unknowns reside on the fluid-vesicle interfaces. We have developed a novel numerical scheme for such equations. It incorporates a new time-stepping scheme that allows much larger time-steps than the existing explicit schemes. The associated linear systems are solved in optimal time using spectral preconditioners, FFTs and the Fast Multipole Method.