## 2005 Seminar Archive

Back to Current Seminars

## Spring, 2005

#### Interfacial Dynamics in Fluid Dynamics and Materials Science

##### Stephen Davis

Walter P Murphy Professor of Engineering and Applied Mathematics

Northwestern University

Evanston, Illinois

Interfacial forces are a key element in the behavior of small-scale phenomena in fluids and in materials. In the former surface tension and its gradients drive viscous flows that affect film rupture and droplet coalescence. In the latter anisotropic surface energies interact with elastic forces and surface diffusion to produce nano- islands. In both cases van der Waals interactions are key to the production of small-scale morphologies that determine the physical behavior of the systems.

In this talk three topics, particle encapsulation by a freezing front, the dynamics and solidification of metallic fronts, and VLS growth of nanowires will be discussed briefly. A detailed discussion will be made of the dynamics and evolution of quantum dots.

##### Wednesday, January 19, 2005

11:00 AM

Taper Hall of Humanities, Rm. 114 (THH 114)

#### Numerical Integration of the Nonlinear Dynamics of Solids and Structures

##### F. Armero

Structural Engineering, Mechanics and Materials

Department of Civil and Environmental Engineering

University of California

Berkeley, CA

Standard time-stepping algorithms show a number of limitations when integrating problems in nonlinear dynamics. For example, algorithms that are known to be unconditionally stable in the linear range show numerical instabilities when applied to nonlinear problems, exhibiting an uncontrolled growth of the energy of the system. This observation has motivated the formulation of algorithms that strictly conserve the energy when considering Hamiltonian systems, as it is typical in nonlinear continuum and structural elastodynamics, and that exactly capture the non-negative energy dissipation associated with inelastic models. The need of algorithms that exhibit a controlled numerical dissipation in the high-frequency range also appears as a basic requirement to handle the high numerical stiffness of the problems of interest. The algorithms must also preserve the conservation laws of linear and angular momenta and the associated relative equilibria of the mechanical system, in contrast again with existing schemes.

We present in this talk a general framework for the formulation of energy-consistent momentum-conserving algorithms for solid dynamics in the fully nonlinear finite deformation range, including applications in nonlinear elastodynamics, finite strain multiplicative plasticity, frictionless and frictional contact/impact of solids, and directed Cosserat theories of rods and shells. The correct treatment of the finite rotations involved in the latter theories of structural dynamics requires a special attention to arrive at frame indifferent integration schemes. The aforementioned dissipation/conservation properties have been proven rigorously for the newly developed schemes in the general nonlinear range, accounting also for the finite element interpolations employed in their spatial discretization. We present a number of representative numerical simulations illustrating the properties of the new algorithms and their applications.

##### Thursday, January 20, 2005

11:00 AM

Von KleinSmid Center, Rm. 150 (VKC 150)

#### Helios Mishap Review Board Findings From The Pilot’s Perspective

##### Wyatt Sadler

AeroVironment, Inc.

Simi Valley, CA

The flying wing Helios aircraft was developed over more than a decade by AeroVironment. Its wing had a span of 247 feet and its upper surface was covered with solar cells. With batteries and/or fuel cells, it was designed to remain at 100,000 feet for six months or more. On August 13, 2001, an earlier configuration of the plane set an altitude record for propeller driven aircraft of 96,983 feet. Unfortunately on June 26, 2003 the Helios encountered some low level turbulence while flying over Kauai which increased the wing’s dihedral significantly which caused the plane to become unstable and crash. The seminar will discuss the flights of the Helios and the investigative report on the crash.

##### Monday, January 24, 2005

5:00 PM

Grace Ford Salvatori Hall, Rm. 118 (GFS 118)

#### Disc Drive Design and Nonlinear Control Solutions for Robust Non-operational Shock Performance

##### Prabhakar R. Pagilla

Associate Professor

Department of Mechanical and Aerospace Engineering

Oklahoma State University

Stillwater, OK

As disc drives become more of a commodity based product, quality and cost control have become top industry priorities. Disc drive manufacturers are now heavily focused on efforts to reduce costs while maintaining quality and improving performance. Shock damage of the head/disc interface is one area that causes many quality issues and cost constraints. The most damaging shocks, which can be both linear and rotational, occur during the non-operational state and can potentially cause data loss, read/write head and disc damage. Currently, several methods are used to combat shocks, many of which preserve servo control performance at the expense of cost increases, reliability issues, and reduced performance. A combination of improved mechanical designs and advanced nonlinear control methods were investigated to improve servo controller performance while maintaining shock resistance, improving product quality, and providing cost reduction. A unique disc drive was manufactured with the design changes and experiments were conducted to evaluate the performance of the controller. In this talk, disc drive design changes, developed control algorithms, and experimental results will be presented and discussed.

##### Wednesday, January 26, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

#### Swimming in a Perfect Fluid

##### Eva Kanso

CDS-Caltech

We study the self-propulsion of articulated bodies in a perfect fluid. The goal of this work is to provide a deeper understanding of the locomotion of aquatic animals due to the coupling between their shape changes and the surrounding fluid dynamics. This investigation will have important implications on the development of biologically-inspired underwater vehicles that use shape changes for locomotion and control of their dynamics. Our model of the motion of articulated bodies in potential flow relies on geometric mechanics for systems with symmetry combined with numerical simulation. The articulated body model achieves forward locomotion and turning maneuvers by merely changing its shape. We address the problem of motion planning or trajectory design as one in optimal control; that is, we investigate the question “what are the most efficient shape changes that achieve a desired net locomotion?”

##### Wednesday, February 2, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Dynamics of propagating fronts: flames, aqueous reactions, free-radical polymerization and bacteria

##### Paul D. Ronney

Professor

Aerospace & Mechanical Engineering Department

USC

Self-propagating reaction fronts occur in many chemical and physical systems possessing two key ingredients: a reactive medium (for example a fuel-air mixture in the case of flames) and an autocatalyst that is a product of the reaction which also accelerates the reaction (for example thermal energy in the case of flames). Self-propagation occurs when the autocatalyst diffuses into the reactive medium, initiating reaction and creating more autocatalyst. This enables reaction-diffusion fronts to propagate at steady rates far from any initiation site. In addition to flames, propagating fronts have been observed in aqueous reactions, free-radical initiated polymerization processes and even propagating fronts of motile bacteria such as E. coli.

This talk will focus on a comparison of the dynamics of these four different types of fronts including propagation rates, extinction conditions and instability mechanisms. Our research has shown that despite the disparate nature of the reactants and autocatalysts in these four systems, remarkably similar dynamical behavior is observed since the underlying driving mechanisms for propagation are similar. The key role of loss mechanisms (heat, chemical species or cell death) and differential diffusion of reactant and autocatalyst (“Lewis number”) is demonstrated.

##### Wednesday, February 9, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Shaped Sonic Boom Demonstration

##### Edward A. Haering, Jr.

Professor

Research Aerodynamics

NASA Dryden Flight Research Center

The goal of the DARPA Shaped Sonic Boom Demonstration (SSBD) Program was to demonstrate for the first time in flight that the sonic boom overpressure created when an aircraft breaks the sound barrier can be substantially reduced by incorporating specialized vehicle shaping techniques. Although mitigation of the sonic boom via specialized shaping techniques was theorized decades ago, until now, this theory had never been tested with a flight vehicle subjected to actual flight conditions in a real atmosphere. The demonstrative success, which occurred on 27 August 2003 with repeat flights in the supersonic corridor at Edwards Air Force Base, is a critical milestone in the development of next generation supersonic aircraft that could one day fly unrestricted over land and help usher in a new era of time-critical air transport. Pressure measurements obtained on the ground and in the air confirmed that the specific modifications made to a Northrop Grumman F-5E aircraft not only changed the shape of the shock wave signature emanating from the aircraft, but also produced a “flat-top” signature whose shape persisted, as predicted, as the pressure waves propagated through the atmosphere to the ground. This accomplishment represents a major advance towards reducing the startling and potentially damaging noise of a sonic boom. The Shaped Sonic Boom Demonstration program will be discussed, with an emphasis on flight test techniques and results.

##### Wednesday, Febraury 16, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Spectral Multidomain Penalty Methods For Accurate Simulation Of Fluid Turbulence

##### Peter Diamessis

Department of Aerospace and Mechanical Engineering

USC

Los Angeles, CA

Spectral multidomain techniques have strong advantages in the numerical investigation of localized, time-dependent, multiscale phenomena that combine non-linearity and physical dissipation. The immediate advantages are: high order accuracy, flexibility in local spatial resolution and straightforward parallel implementation. Although accurate and convenient in this respect, in the absence of artificial numerical dissipation, spectral methods are prone towards catastrophic numerical instability in cases of extreme non-linearity and/or weak dissipation–such as high Reynolds number turbulence. The design of more robust spectral discretization methods for under-resolved simulations has broad application not only in computational fluid dynamics, but also in combustion, acoustics and solid mechanics.

This talk will outline the fundamental components of a novel spectral multidomain penalty method developed for the numerically stable, and spectrally accurate, simulation of high Reynolds number, stratified turbulence. Results will be compared with corresponding laboratory data. An application to internal solitary wave-induced global instability in shallow water benthic boundary layers will then be presented, and extension to more complex boundary conditions, and to fields outside fluid mechanics will be discussed.

##### Thursday, February 17, 2005

11:00 AM

Von KleinSmid Center, Room 150 (VKC 150)

Refreshments will be served at 3:15 pm.

#### Pop-up Reflector Structures

##### Sergio Pellegrino

Professor

Department of Engineering

University of Cambridge

This talk will present a novel approach to the design of ultra-lightweight foldable precision structures of very low mass. One particular idea is to make a foldable box with singly-curved faces; one or more of these faces provide the required precision surface. A box is a stable and efficient structural form, which can be constructed from paper-thin sheets of high modulus composite materials. By ensuring that the profiles of the edges of the sheets satisfy certain geometric rules, to allow compact folding of the assembled structure, a range of useful shapes can be achieved. The practical realization of these structures has posed a number of structural mechanics challenges. A particular problem is, how tightly can a thin sheet of woven carbon-fibre reinforced plastic be folded without breaking? The answer is, in the most extreme cases, twice as tightly as conventional thinking would suggest.

##### Wednesday, February 23, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Optical MEMS Based Micro-sensors for Aerodynamic Measurements: Development and Experimental Results

##### Dr. Dominique Fourguette

Senior Scientist

VioSense Corporation

Pasadena, CA

Integrated optics and optical MEMS can achieve the same functions of bulky optics but in an extremely compact size. With this technology and in collaboration with Caltech and JPL, a series of sensors were developed for aerodynamic applications. The development of these micro-sensors will be presented along with experimental results obtained with these sensors. Current developments and future applications of this technology will be discussed. In addition, optical MEMS technology and the resulting diffractive optical elements that are key to the development of these sensors will also be described.

##### Monday, February 28, 2005

11:00 AM

Laufer Library (RRB 208)

Refreshments will be served at 3:15 pm.

#### Small Scale Statistics in High Resolution DNS of Turbulence with up to 4096^{3} Grid Points

##### Yukio Kaneda

Department of Computational Science and Engineering

Graduate School of Engineering

Nagoya University, Japan

High resolution direct numerical simulations (DNS) of incompressible homogeneous turbulence in a periodic box with the number of the grid points up to 4096^{3} and Taylor microscale Reynolds number about 1131 were performed on the Earth Simulator, with sustained performance up to 16.4 TFlops. The simulations are based on a spectral method free from aliasing errors. The numbers of the degrees of freedom and the nonlinear interactions in the 4096^{3}-DNS are about M =4096^{3} ×4 ˜ 2.75 ×10^{11}, and M^{2} ˜7.6 ×10^{22}, respectively.

Small scale statistics of turbulence is now being studied by using the DNS data. The data analysis has so far shown some new aspects regarding the Reynolds number dependence of the statistics including

(i) the inertial subrange energy spectrum, and the dissipation range spectrum,

(ii) the normalized mean energy dissipation rate, and

(iii) probability distribution function of velocity gradients, moments of velocity gradients including skewness and flatness factor, and the squares of the energy dissipation rate, enstrophy and pressure gradients.

The visualization of the flow field suggests the importance of the understanding the inertial subrange structure. Studies based on the DNS data have been also made on

(i) the statistics of energy transfer,

(ii) quantitative examination of Kolmogorv’s log-normal hypothesis, and

(iii) eddy viscosity.

##### Wednesday, March 2, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Noise Generation by Low Mach Number Shear Flows

##### Marios C. Soteriou

United Technologies Research Center

East Hartford, CT 06108

Noise generation by subsonic shear flows is investigated using Computational Aeroacoustics (CAA) models of varying degrees of complexity and fidelity. Particular emphasis is paid to the directive noise field generated by the coherent large vortical structures that characterize these flows. The first and major part of the presentation will deal with the more fundamental aspects of the problem and will focus on results obtained from a CAA model based on the Expansion about Incompressible Flow (EIF) method. This is a methodology that we helped develop and employs high fidelity CFD to capture the flow near field, and an acoustic model for the computation of the far field noise that naturally accounts for flow-acoustic interactions in the near field. Results from a variety of flows including shear layers and wakes will be presented and will be contrasted to analytical, experimental and computational evidence. Particular emphasis will be given to the ability of the approach to capture the directive nature of the sound field. The second part of the presentation will present the application of a lower fidelity CAA model to the problem of jet-noise suppression. The focus is on identifying relatively minor changes to the jet inlet conditions that result in noise suppression. The work is motivated by the need to explain the experimentally observed impact of jet nozzle tabs. The CAA model employs the Vortex Filament method to reproduce the unsteady three dimensional large scale flow features in the near field, and Lighthill’s acoustic analogy to compute the far field sound field. Results qualitatively reproduce the experimentally observed behavior and help explain how specific patterns of very weak streamwise vorticity at the jet inlet impact the flow and far field noise fields.

##### Monday, March 7, 2005

11:00 AM

Laufer Library, Rapp Research Bldg., Room 208 (SLH 208)

Refreshments will be served at 3:15 pm.

#### Interactive Computing in Engineering Education

##### Bingen Yang

Professor

Department of Aerospace & Mechanical Engineering

USC

The recent technological advancements in computers, software, and telecommunications make it possible for individuals to enjoy an interactive and mobile computing environment in their study and work. This talk is intended to show that interactive computing (IC) can greatly enhance the learning of various topics in science and technology, and surely help increase the efficiency and accuracy of engineering designs. The talk explains why IC capabilities are needed in engineering education, addresses several important issues on how to establish such capabilities, and outlines a plan for possible IC-related technology transfer. Additionally, through an example, the enhancement and innovation of a curriculum on solid mechanics and structural dynamics by IC is illustrated.

##### Wednesday, March 9, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Wave Generation by Intrusive Gravity Currents

##### Bruce R. Sutherland

Professor

Dept. Mathematical and Statistical Sciences

University of Alberta

A gravity current forms, for example, when dense fluid is released into a uniform but less dense ambient – a circumstance which has been well-studied theoretically, experimentally and numerically. By comparison, relatively little is known about the dynamics of intrusive gravity currents, which form when intermediate-density fluid is released into a stratified ambient.

This talk will present the results of laboratory experiments focussing upon the generation of internal waves by intrusive gravity currents in a variety of circumstances. In a two-layer fluid, interfacial internal waves can be excited with such large amplitudes that the propagation speed is poorly predicted by a steady-state theory. By contrast, an intrusion over-riding a continuously stratified fluid excites vertically propagating internal waves, but their associated momentum flux is small compared with that of the current. Nonetheless, the frequency of the waves relative to the background buoyancy frequency lies in a narrow band implying that waves are generated through a resonant, albeit weak, interaction with the intrusion.

##### Wednesday, March 23, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Nanomechanics: A Continuum Theory Based On The Interatomic Potential

##### Yonggang Young Huang

Shao Lee Soo Professor

Department of Mechanical and Industrial Engineering

University of Illinois at Urbana-Champaign

It is commonly believed that continuum mechanics theories may not be applicable on the nanometer scale due to the discrete nature of atoms. Here we develop a nano-continuum theory based on the interatomic potential for nanostructured materials. The interatomic potential is directly incorporated into the continuum theory through the constitutive models. The nano-continuum theory is then applied to study the mechanical deformation of carbon nanotubes, including (1) the pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation; (5) electrical property change due to mechanical deformation; (6) binding energy between carbon nanotubes; (7) coefficient of thermal expansion; and (8) specific heat. The nano-continuum theory agrees very well with the atomistic models without any parameter fitting, and therefore has the potential to be applied to complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).

##### Friday, March 25, 2005

11:00 AM

Location TBD

#### Evolution of the Blended Wing Body

##### Blaine K. Rawdon

Technical Fellow

The Boeing Company

Huntington Beach, CA

The Blended Wing Body (BWB) is an aircraft configuration that blends a pure flying wing with a broad central fuselage, providing aerodynamic and structural benefits for transonic transport missions. An overview of the development and features of this configuration at Boeing will be presented. Aspects described include aerodynamics, structure, comparison with conventional configurations, interior arrangement and emergency egress, testing, ride quality, commonality, performance and risk.

##### Wednesday, March 30, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Spectral Multidomain Penalty Methods For Accurate Simulation Of High Reynolds Number Fluid Flow

##### Peter Diamessis

Department of Aerospace and Mechanical Engineering

University of Southern California

Los Angeles, CA

Spectral multidomain techniques have distinct advantages in the numerical investigation of localized, time-dependent, multiscale phenomena that combine non-linearity and physical dissipation. The immediate advantages are: high order accuracy, flexibility in local spatial resolution and straightforward parallel implementation. Although accurate and convenient in this respect, in the absence of artificial numerical dissipation, spectral methods are prone towards catastrophic numerical instability in cases of extreme non-linearity and/or weak dissipation–such as high Reynolds number fluid flow. The design of more robust spectral discretization methods for under-resolved simulations has broad application not only in computational fluid dynamics, but also in combustion, acoustics and solid mechanics.

This talk will outline the fundamental components of a novel spectral multidomain penalty method developed for the numerically stable, and spectrally accurate, simulation of high Reynolds number, stratified flows. Results will be compared with corresponding laboratory data. An application to internal solitary wave-induced global instability in shallow water benthic boundary layers will then be presented, and extension to more complex geometries, and to fields outside fluid mechanics will be discussed.

##### Tuesday, April 5, 2005

12:00 Noon

Laufer Library, Rapp Research Building

#### Time-Resolved Photometry For Sensing Biological Tissues

##### Laurent Pilon

Assistant Professor

Mechanical and Aerospace Engineering Department

University of California, Los Angeles

Los Angeles, CA

Lasers are currently used in numerous biomedical applications as a tool for surgery, therapy, or diagnostics. Practical examples range from eye surgery and tissue welding to photodynamic therapy and optical tomography. Biological tissues can be treated as absorbing and scattering media in which light transport is commonly modeled using the diffusion approximation. However, it has been shown that the diffusion approximation is not valid for very short time scales and for some specific tissues. Therefore, the complete transient radiation transfer equation (RTE) must be solved to simulate ultra-short pulsed laser transport through tissues.

Moreover, some biological tissues (e.g., skin and arterial walls), contain various endogenous fluorophores such as NADH, collagen, elastin, and flavins uniquely characterized by their quantum yield and lifetime(s). The fluorescence signal depends on the age and health of the tissue investigated. Thus, fluorescence spectroscopy can be used as a diagnostic and monitoring tool and already showed tremendous potential for acne, aging, skin cancer, or atherosclerotic lesions.

This talk focuses on ultra-short pulse laser transport through biological tissues as a non-invasive sensing technique for retrieving physiological and morphological information. First, the modified method of characteristics is presented as an efficient and accurate method for simulating transient radiation transfer in absorbing, scattering, and fluorescing media. Particular attention is paid to directional time-resolved reflectance and autofluorescence of human skin. Finally, preliminary experimental data for human subjects will be presented along with potential applications.

##### Wednesday, April 6, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Mathematical Theory of AeroElasticity

##### Dr. A.V. Balakrishnan

Professor of Applied Mathematics and Electrical Engineering

Director

Flight Test Laboratory F S R C

UCLA

The central problem of AeroElasticity involves an endemic safety issue – the determination of the ‘Flutter Boundary’– the speed at which the wing structure becomes unstable at any given altitude. Currently all the theoretical work is computational – wedding the Lagrangian FEM Structure codes to the Euler CFD codes to produce a ‘time-marching’ solution. While they can handle ‘real life’ nonlinear complex-geometry structures and viscous flows, they are based on approximation by Ordinary Differential Equations, and limited to specific numerical parameters. In turn this limits the generality of the results and understanding of phenomena involved; and of course inadequate for Control Design for possible stabilization (‘Flutter Suppression’). In this presentation, we show that the problem can be formulated, retaining the full continuum models without approximation, as a Boundary-Value Problem for coupled Nonlinear Partial Differential Equations. The flutter speed can then be characterized as a Hopf bifurcation point for a nonlinear convolution-evolution equation in the time domain, which – and this is the crucial point – is then determined completely by the linearized equations – linearized about the equilibrium state. A key step in this approach is a singular integral equation, discovered by Camillo Possio in 1938, and bearing his name, linking the aerodynamics to the structure dynamics. A challenge here is to choose models which are amenable to analysis, taking advantage of recent advances in Boundary-Value problems, and yet can display the phenomena of interest. The presentation will emphasise Problem Formulation but will include recent results both analytical and experimental (flight-tests).

##### Wednesday, April 13, 2005

##### 3:30 PM

##### Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Geometric Mechanics and Biomorphic Locomotion in Fluids

##### Scott Kelly

Professor

Mechanical Engineering

University of Illinois, Urbana-Champaign

Biomorphic designs for aquatic and aerial vehicles offer advantages in energy efficiency, agility, and stealth. Animals which swim or fly, however, often derive superior performance through subtle, controlled interactions with their environments. The realization of engineering systems which enjoy similar performance requires the development of appropriate modeling, analysis, and control methods as well as novel sensors and actuators. Differential geometric concepts unify the realization and analysis of reduced-order models for complex mechanical systems and the treatment of nonlinear control problems, but the fluid-structure interactions central to macroscopic swimming and flying fall outside the traditional scope of geometric mechanics. This talk will describe the treatment of phenomena like lift generation through vortex shedding in the context of Lagrangian and Hamiltonian systems, the formulation of control problems for energy-efficient underwater locomotion, and the development of a robotic platform for autonomous mobile aquatic sensor networks.

##### Thursday, April 14, 2005

12:00 Noon

Laufer Library, Rapp Research Bldg.

#### MEMS and Microfluidic Systems for Biomolecular Manipulation and Characterization

##### Qiao Lin

Assistant Professor

Department of Mechanical Engineering

Carnegie Mellon University

Pittsburgh, PA

Microelectromechanical systems (MEMS) and microfluidics technologies hold potential to vitally impact biology and medicine. We have been pursuing MEMS and micro/nanofluidic systems as innovative tools for biological manipulation and characterization, with a primary interest in controlling the motion and measuring the dynamic behavior, such as conformational transitions, interactions, and reactions, of biomolecules in solution. Such miniaturized systems will allow biomolecules to be interrogated in controlled micro/nano environments with orders-of-magnitude reduction in the consumption of biological material. Functional and structural integration will allow multi-mode analysis of complex biomolecular processes with improved sensitivity, reliability and automation. Arrays of devices integrated in a single system will afford parallelized, high-throughput processing of samples. Ultimately, such systems will enable novel biomolecular investigations that are unattainable with conventional technologies.

This presentation will give a highlight of our efforts in designing and creating such MEMS and micro/nanofluidic systems. We pursue manipulation of biomolecular solution by exploiting polymers as micro/nanofluidic functional materials. For example, highly compliant microstructures of elastomeric polymers have been used as passive flow control devices, while surface-grafted, thermally responsive polymer nanolayers are being exploited to enable active, intelligent biofluid handling and chromatographic separations. We address biomolecular characterization with microsystems that integrate MEMS sensors with microfluidics. These include integrated calorimetric devices for measuring metabolic reactions as well as conformational changes and interactions of DNA and proteins, and integrated vibrational sensors for detecting hydrodynamic property changes induced by biomolecular events. We will present experimental results from prototype devices, as well as models that afford in-depth understanding of the device physics.

##### Wednesday, April 20, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Dynamics of Micro-machined Gyroscopes

##### Eva Kanso

Control and Dynamical Systems

Caltech

Pasadena, CA

We present a model for the response of a micro-machined rotary gyroscope to general input motions. The governing equations are formulated for weakly non-linear oscillations of the rotor, which is suspended above the moving substrate via elastic beams. The method of multiple scales is used to separate the slow and fast responses. This approach allows to quickly compute the long-term behavior of the rotor without the need to integrate over fast oscillations. The power of the model to evince cross-coupling errors is demonstrated through examples.

##### Tuesday, April 26, 2005

12:00 Noon

Laufer Libray, Rapp Research Bldg.

#### Local High-Order Galerkin Methods For Geophysical Fluid Dynamics

##### Francis X. Giraldo

Marine Meteorology Division

Naval Research Laboratory

Monterey. CA

For the past thirty years global atmospheric models (hydrostatic primitive equations) have been based on global methods such as the spectral transform method. Because the current trend in high-performance computing has moved towards clustered systems having tens of thousands of processors it is anticipated that ST methods will meet their doom due because they may not be able to take full advantage of such large processor-count systems. In addition, with the ever increasing computing power it will soon be possible to run global atmospheric models at sufficiently high resolution such that the hydrostatic approximation breaks down. At this resolution the models then need to use the non-hydrostatic equations (i.e. the Euler equations). This then means that the global and regional models can be unified into one model. To properly handle fine-scale regions such as hurricanes, the GFD models then need to be much more similar to CFD models than in the past. For example, constructing not just globally but also locally conservative methods becomes important.

In this talk, we discuss the types of numerical discretization methods being developed and implemented for the purpose of constructing: global hydrostatic atmospheric models, regional non-hydrostatic atmospheric models, and non-hydrostatic coastal ocean models. We describe in particular characteristic-based time-integrators, spectral element and discontinuous Galerkin spatial discretization methods.

##### Wednesday, April 27, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Simulation of Progressive Failure in Multidirectional Laminates

##### Anthony M. Waas

Professor of Aerospace Engineering

Composite Structures Laboratory

Department of Aerospace Engineering

University of Michigan

Ann Arbor, MI 41809-2140

A new mechanism based methodology is developed and used to perform progressive failure analyses (PFA) of fiber reinforced laminated composites under predominantly compressive loading. Current methods that are implemented in finite element based codes rely on defining ‘strength’ based failure indices at the lamina level. When any of these indices exceeds a predefined critical value, the material at that point is said to have failed. When a material point has failed (in tension due to fiber breaking, or matrix cracking, in compression due to fiber kink-banding or by shear due to fiber/matrix debonding), different elastic moduli are set to zero. Further, material behavior is assumed to be linear elastic throughout the analysis.

Index based failure analysis methods cannot account for mechanisms of degradation and failure, and thus are not well suited for progressive failure analyses of composite structures. The presence of a local multiaxial stress state is shown to affect, in particular, the ‘maximum’ sustainable compressive axial stress at a material point. Thus, ‘strength’ at a material point is influenced to a great extent by the current stress-state and is predicated on the mechanism of failure. The present approach considers fiber kinking as the main failure mechanism for fiber reinforced laminates under compression dominated general multiaxial stress states. The available body of analytical, experimental and micromechanical studies show that the two main events associated with fiber kinking are the rotation of fibers and the degradation of the shear properties of the lamina. These two phenomena establishes a positive feedback loop where, a small imperfection at the beginning of loading leads to fiber rotation, which in turn degrades the in-situ shear properties. This degradation reduces the material resistance to fiber rotation and allows the fibers to rotate easily which in turn increases the rate of shear degradation. The culmination of these events is a limit load type instability, which limits the compressive load carrying capability of the axially loaded plies. In the present PFA approach, these two events are incorporated in a lamina level numerical scheme to model the compression-dominated response of composite structural laminates. Degradation of the lamina is manifested via the degradation of the in-situ transverse and shear moduli. The axial direction response is assumed to be linear elastic. The commercially available FE code, ABAQUS, is used for the FE analyses. The predictive capability of the current approach is validated using experimental results for compression loaded double-notched thick (70 ply) panels, and a shear loaded thin (16 ply) panel, stressed into the deep postbuckling regime.

##### Tuesday, May 10, 2005

11:00 AM

Laufer Library (RRB 208)

#### Modeling of Strong Discontinuities in Solids at Failure

##### Francisco Armero

Structural Engineering, Mechanics and Materials

Department of Civil and Environmental Engineering

University of California

Berkeley, CA 94720

The modeling of the failure of solids and structures requires detailed analyses at several levels or scales of observation. These include the characterization of the physical mechanisms involved in the response of the material at the micromechanical or lower scales and their incorporation in the mathematical problem describing the global response of the solid or structure. The involvement of highly non-smooth solutions, exhibiting from thin localization bands to actual discontinuous displacements as in cracks, makes this mathematical modeling and its numerical resolution a difficult challenge for the large-scale mechanical/structural systems of interest. We present in this talk an overview of the strong discontinuity approach, which we have developed in both its theoretical and computational components to address this challenge. The approach is based on the characterization and resolution of the discontinuous displacements (the strong discontinuities) associated with the deformations of the solids at failure in the large-scale limit. The consideration of these limit discontinuous solutions allows, in particular, the incorporation of cohesive softening laws between displacement jumps and driving tractions, hence capturing the localized dissipation observed at failure and avoiding the well-known difficulties associated with local continuum models with strain softening. Crucial to our developments is the multi-scale treatment of these considerations, by which the large-scale problem at hand (a local continuum or structural theory) does not change in structure, requiring only the introduction of the effects of the small scales active at failure locally. These considerations lead naturally to the formulation of finite elements enhanced locally with the discontinuities, resulting in objective and very efficient computational tools for the analysis of localized failures of solids and structures in typical engineering applications.

After presenting a summary of several analyses that show the regularization and other mathematical properties of the introduction of strong discontinuities in the continuum, we discuss some of the cases that we have considered to date, which include the modeling of shear banding in finite strain plasticity, cracking in brittle materials, strain localization in coupled thermomechanical and poroplastic solids, as well as inelastic structural models of beams, rods, plates and shells. The latter cases have proven to be an especially challenging task given the more involved kinematics in the underlying structural theories, all the way to the consideration of finite rotations in nonlinear Cosserat shells. The strong discontinuities include also discontinuous rotations in this case, recovering the classical notion of softening hinges in these structural members too. The design of enhanced finite element methods that avoid a number of well-known limitations (like volumetric, shear and stress locking, among others) has been addressed in detail. The range of application of the proposed models and the performance of the new finite element methods are evaluated with several examples.

##### Thursday, May 12, 2005

2:30 PM

Laufer Library, RRB 208

## Fall, 2005

#### Carbon nanoparticles in the environment: A multiscale perspective

##### Angela Violi

Department of Mechanical Engineering

University of Michigan

Ann Arbor, MI

and

Departments of Chemistry and Chemical Engineering

University of Utah

Salt Lake City, UT

The process of combustion is the dominant pathway through which mankind continuously injects particulate matter into the atmosphere. These combustion-generated particles are present not only in very large amounts, but they are produced, at the smallest scale, in the form of clusters with nanometric dimensions. Although the total mass of particulate emissions has been significantly reduced with improvement of combustion efficiency and emissions control systems, the very small nanoparticles are exceedingly difficult to control by the emission systems typically installed on vehicles. In addition, the current emissions regulations are mass-based and do not address the presence of nanoparticles. Predictive models of nanoparticle formation and oxidation that provide detailed chemical structures of the particles currently do not exist, a fact that greatly limits our ability to control this important chemical process. The objectives of this work are focused on gaining a clearer understanding of the chemical and physical processes occurring in the formation of carbon nanoparticles in combustion conditions and their fate in the environment. The primary focus is to provide a detailed multi-scale characterization of nanoparticle formation in combustion environments, through the use of novel simulation methodologies operating across disparate (spatial/temporal) regimes. The use of atomistic models, such as the Kinetic Monte Carlo technique and Molecular Dynamics simulation, allow us to follow the transformations that occur during nanoparticle formation in a chemically specific way, thereby providing information on both the chemical structure and the configuration of the nanoparticles and their agglomeration. This approach establishes a connection between the various time scales in the nanoparticle self-assembly problem, together with an unprecedented opportunity for the understanding of the atomistic interactions underlying carbonaceous nanoparticle structures and growth. Preliminary results will also be given from atomistic-scale simulations of the nanoparticles interacting with model cell membranes.

##### Wednesday, August 31, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Making Electrical Power With Microbes: Putting the Bio- in Biofuelcells

##### Kenneth Nealson

Wrigley Professor of Geobiology

USC

For many years, biofuel cells have consisted of bacteria (grown on any of a variety of substrates) linked to anodes via chemical electron mediators like methylene blue. These bioreactors, while of some curiosity and pleasure (and useful for teaching), have been very inefficient and of little real use. This seminar will introduce you to bacteria in the group Shewanella that generate current in fuel cells with no mediator added. These bacteria, originally isolated for their ability to reduce the Fe(III) to Fe(II) in solid metal oxides, attach directly to the graphite electrode, using it as an “oxygen substitute” for respiration. Studies with these bacteria suggest that electron transfer (to both iron oxides and to the electrode of the fuel cell) occurs via multiheme cytochromes located on the outside of the bacterial cell, and mutants in any of several electron transport components result in decreased fuel cell performance, and decreased ability to reduce iron oxides. The implications of this ability, and the potential for exploiting such bacteria for useful purposes will be discussed.

##### Wednesday, September 7, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Nanomaterials for Aerospace Applications

##### Yuntian T. Zhu

Technical Staff Member

Materials Science and Technology Division

Los Alamos National Laboratory, Los Alamos, NM 87545

Materials for aerospace applications such as airplanes and space shuttles are required to have high strength and light weight. After decades of extensive research and development, conventional materials have reached their limits in terms of their strengths. Nanomaterials are significantly stronger than conventional, coarse-grained materials and offer potentials for improving current aerospace structures and for enabling new space adventures. In this talk I’ll present nanostructured metals and long carbon nanotubes, both of which are promising new aerospace materials.

Nanostructured metals can have strengths that are several times higher than their coarse-grained counterparts. However, they often have low ductility, with only a few exceptions. Both high strength and good ductility are desired for structural applications. To tailor nanostructured metals for both high strength and good ductility, we need to first understand their deformation physics. I will present our recent work on the deformation physics of nanostructured metals as well as preliminary evidences that nano-metals can be tailored to have both high strength and good ductility. Carbon nanotubes are 100 times stronger than steel but only one-sixth as heavy. Long carbon nanotubes are the key to utilize their high strength. I’ll present the synthesis of 40-mm-long carbon nanotubes and intramolecular nanotube junctions as well as their potential applications in aerospace and other advanced applications.

##### Wednesday, September 14, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Internal-Wave Breaking Over Obstacles

##### Olivier Eiff

Institut de Mecanique des Fluides

Toulouse, France

The presentation of PIV measurements obtained in a large towing tank of stably stratified flow over Gaussian-shaped obstacles leading to internal-wave breaking, is made with two objectives: first, to investigate the effect of side-wall confinement as well as the width of the obstacles on the occurrence of wave-breaking, and second, to give a first description of the turbulence generated by the breaking waves at high Re. The first study, performed with small obstacles (Re=600) to significantly alleviate side-wall confinement, shows that breaking occurs neither for unconfined nor for confined axisymmetric mountains.

For quasi-2D obstacles with ridge-to-height ratios above about 3, increased confinement induces breaking, while for very low confinement, an increased width-to-height ratio above about 9, is the factor which induces wave breaking. The high Re results (Re=9000) confirm that the flow evolution and the ensuing large-scale flow structures in the wave-breaking region are essentially the same as observed in the low Re laboratory experiments and direct numerical simulations. The statistics in a horizontal plane intersecting the wave-breaking region reveal a turbulent flow with intensities up to 20% and spatial distributions which indicate that the underlying large-scale flow structures—toroidal vortices—are quasi-steadily aligned in the spanwise direction and that they might be shed downstream.

##### Tuesday, September 9, 2005

12:30 PM

Laufer Library (RRB 208)

#### Transport, Mixing and Coherent Structures in Chaotic Flows

##### Francois Lekien

Princeton University

Department of Mechanical and Aerospace Engineering

In this talk, I will describe a dynamical systems framework for studying Lagrangian transport in time-chaotic systems. Numerous experiments have revealed the presence of coherent structures that govern transport and mixing in such systems. These mixing templates are invisible to the naked eye but can be extracted, for example, by computing finite-time Lyapunov exponents. Their presence indicates alleyways and barriers to transport and provide a geometric description of the mixing processes in the system. I will discuss the properties of these Lagrangian coherent structures and illustrate their use in several problems.

Applications range from space missions to molecular fragmentation. In recent years, there has been much effort in applying this approach to the study of mixing in fluids. I will describe fluid transport near the Atlantic coast of Florida using a velocity field observed experimentally from high frequency radar measurements, a new technology that produces detailed velocity maps near the surface of coastal waters. Dynamical barriers and alleyways in this system reveal the existence of optimal release windows in which contaminants can be efficiently advected away from the coast, reducing their negative impact on the marine environment. Identification of Lagrangian coherent structures can also enhance the performance of adaptive sampling networks. I will introduce the Autonomous Ocean Sampling Network II project that coordinates the effort of high-frequency radar, ships, airplanes, satellites, buoys and underwater vehicles for the purpose of improving the observation and the prediction of ocean processes in Monterey Bay, CA. Lagrangian coherent structures can be used to locate biological and sampling “hot spots.” We are also exploring their application in determining efficient routes for vehicles and in identifying regions of high stretching that may adversely affect the stability of a vehicle formation.

Transport and mixing near the surface of an airfoil or a coastline can also be studied in terms of separation and re-attachment near the boundary. I will discuss the recent development of exact criteria to detect and extract separation points and related separation profiles. The existence of such analytic criteria permits the design of separation controllers. I will describe how separation can be controlled in jet-actuated systems. Such a mechanism permits a fine control of the lift on an airfoil or the efficient transport of fuel along separation profiles.

##### Wednesday, September 28, 2005

12:00 PM

Laufer Library (RRB 208)

#### On The Dynamics Of Linear And Nonlinear Periodic Structures

##### Dr. Francesco Romeo

Faculty of Engineering

University of Rome, “La Sapienza”

The dynamics of both linear and nonlinear multi-coupled periodic structures is addressed by means of transfer matrices of single units.

As far as linear structures is considered, general bi- and three-coupled periodic systems are first dealt with showing that free wave propagation properties depend upon the solutions of the transfer matrix reflexive characteristic polynomial. By discussing them in terms of invariant quantities, an exhaustive description of the free wave propagation patterns is given on invariant spaces where propagation domains with qualitatively different character are identified. Next, as applications, several periodic mechanical models are considered such as bi-coupled beams resting on elastic supports and three-coupled truss beams, thin-walled beams and stiffened pipes; a nonlinear mapping from the invariants’ plane to the physical parameters plane provides a concise representation of the pattern of the propagation domains. Moreover, a mechanical interpretation associated with the bounding frequencies of these regions is given.

Next, the dynamics of nonlinear multi-coupled periodic systems is addressed by means of two different approaches. In one hand, a transfer matrix perturbation approach is presented to analyze chains of continuous nonlinear elements; the procedure is applied to determine frequency-response relationship, under free and forced vibrations, of chains of continuous nonlinear shear indeformable beams. On the other hand, a nonlinear map approach is presented to analyze chains of discrete nonlinear elements; the procedure is applied to determine free-wave propagation properties in one-dimensional chains of multi-coupled nonlinear oscillators.

##### Wednesday, September 28, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Optimal Design under Uncertainty: Single- and Multi-level Systems

##### Michael Kokkolaras

Department of Mechanical Engineering

University of Michigan

Ann Arbor, MI

Deterministic optimal design assumes that complete information is available, and that design decisions can be implemented exactly. These assumptions imply that optimization results are as good (and therefore useful) as the design and simulation/analysis models used to obtain them, and that they are meaningful only if they can be realized. However, we are rarely in a position to represent a physical system without using approximations, know the exact numerical values of all of its parameters, or manufacture it with high precision. Therefore, uncertainty must be taken into account during the design optimization process. The method for solving an optimal design problem under uncertainty depends on how the latter is quantified. When sufficient information is available the popular probabilistic approach can be adopted. In reality however, we often do not have sufficient data to infer appropriate probability distributions. The amount of available information may be limited to ranges of values for the uncertain quantities. In this case, a possibilistic approach can be employed to reformulate and solve the optimal design problem. In this talk, we will use an engine design example to demonstrate both approaches while addressing challenging issues and highlighting advantages and disadvantages. In the second part of the talk, we will consider design optimization of complex engineering systems (also referred to as “systems of systems”), which can more often than not be accomplished only by decomposition. In particular, we will consider hierarchically decomposed multilevel systems, and extend our previously developed deterministic multilevel optimization methodology for optimal and consistent design of such systems to account for the presence of uncertainties. We will address the important issue of uncertainty propagation, and use a simple yet illustrative simulation-based bi-level example to demonstrate the presented methodology.

Bio: Dr. Michael Kokkolaras is an Associate Research Scientist in the Department of Mechanical Engineering at the University of Michigan. He has a Diploma in Aerospace Engineering from the Technical University of Munich (1992) and a Ph.D. in Mechanical Engineering from Rice University (1997). His research interests lie primarily in the areas of multidisciplinary design optimization and systems engineering, in particular optimal system design under uncertainty, decomposition and coordination, and design of product families. Earlier and other research activities include development of optimization techniques for coordinating multidisciplinary analysis, numerical methods that utilize parallel optimization algorithms for solving differential equations, and multilevel optimization-based methodologies for tolerance allocation in multistation assembly systems. He is co-author of numerous journal and conference articles and two book chapters. His research is funded by the Automotive Research Center and the General Motors Collaborative Research Laboratory, both at the University of Michigan, as well as NSF, ONR, Ford, International, and General Dynamics Land Systems.

##### Thursday, September 29, 2005

11:30 AM

Laufer Library (RRB 208)

#### Stochastic Modeling and Computation of Micro-Physical Processes in Gas Turbine Combustion

##### Chong M. Cha

Affiliate Faculty

Indiana University-Purdue University

Indianapolis, IN

and

Senior Research Engineer

Rolls-Royce

Indianapolis, IN

Combinations of classic continuum simulations with particle dynamics, lattice mechanics, stochastic descriptions of infrequent events, and/or Monte Carlo methods have defined new computational paradigms to treat systems which span a large range of scales. Although such multi-scale simulation techniques are popularly associated with MEMS applications, they also offer a means for improving both the physical modeling and computational turn-around of many long-existing problems of engineering interest where more traditional CFD techniques are used for analysis and design improvement. In this seminar, some novel applications of the techniques in modeling and computing the micro-physical processes in gas turbine combustors will be described. Such processes occur at scales well below the resolution of the RANS or LES, but still have a leading-order impact on the large-scale dynamics. The unresolved micro-physical flow processes generally involve multi-phase and multi-component fluids and include liquid droplet breakup and evaporation, chemically-reacting gaseous flow, and solid-phase smoke particle interactions.

##### Wednesday, October 5, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Near-Field Tsunami Waveforms from Submarine Slumps and Slides

##### Mihailo D. Trifunac

Professor

Department of Civil Engineering

University Southern California

Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, but which consider the effects of source finiteness and directivity. First the nature of tsunami sources is reviewed, including source duration, displacement amplitudes, and areas and volumes of selected past earthquakes, slumps and slides that have or may have generated a tsunami. This review shows that the velocity of spreading of submarine slides and slumps is comparable to the long wavelength tsunami velocity *c _{T} = (gh)^{1/2}*. Then, examples of simple two-dimensional kinematic models of submarine slumps and slides are explored, described mathematically as combinations of sliding constant or sloping uplift functions. Tsunami waveforms for these models are computed using linearized shallow-water theory for constant water depth and transform method of solution (Lapace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, in the near-field, for a time window of the order of the source duration.

The results show that, at the time when the source process is completed, for slides that spread rapidly (*c*_{R}/*c*_{T} ≥ 20, where *c*_{R} is the velocity of predominant spreading), the displacement of the free surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity, the tsunami waveform has progressively larger amplitude, and with higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for c_{R}/c_{T} ~1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.

##### Wednesday, October 12, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

#### Efficiency of Nonequilibrium Plasma for the Enhancement of Ignition and Combustion

##### Svetlana Starikovskaia

Physics of Nonequilibrium Systems Laboratory

Moscow Institute of Physics and Technology

This talk reviews investigations of the detailed spatial and temporal structure of a high-voltage pulsed nanosecond discharge implemented in the form of a fast ionization wave. Distinctive features of this type of discharge include a high propagation velocity (1-10 cm/ns), and good reproducibility of both the discharge parameters and spatial homogeneity over a large gas volume. The time and spatially resolved electric field, electron and excited state concentrations are analyzed on the basis of experimental data within the framework of a unified kinetic approach. The efficiencies of nonequilibrium plasma resulting from pulsed gas discharges, which have potentially important practical applications in ignition and combustion, will be discussed; and examples of experimental data and the results of numerical simulations for the verification of the main concepts will be represented.

##### Wednesday, October 26

12:00 NOON

Olin Hall of Engineering, Room 230 (OHE 230)

#### Max-Plus Methods in Nonlinear Control and the Curse-of-Dimensionality

##### William M. McEneaney

Depts. of Math. and of Mech. and Aero. Eng.

University of California, San Diego

Control of nonlinear systems has long posed a very difficult challenge. The most general approach for handling this class of problems is the method of dynamic programming. For continuous problems, this approach leads to a need to solve a Bellman PDE. This PDE must be solved over a space whose dimension is the dimension of the state space in the control problem. Grid-based methods for the solution of such problems are subject to the well-known curse-of-dimensionality.

In recent years, the fields of max-plus algebra and analysis have appeared and grown tremendously. One of the original motivations was to discrete event systems. However, our motivation is the optimal control of continuous systems. The study of such control problems from a max-plus algebraic point-of-view has led to entirely new classes of numerical methods for Bellman PDEs. Some of these methods, for certain classes of PDEs, are not subject to the curse-of-dimensionality.

In the max-plus algebra, the “addition” operation is maximization, and the “multiplication” operation is standard-sense addition. This makes it a very natural algebra when one is studying control problems. We will consider problems which may be cast as optimal control problems where the dynamics are governed by ordinary differential equations (possibly plus a switching process). Applying dynamic programming to such a problem, one obtains the dynamic programming principle (DPP) as well as an associated first-order Hamilton-Jacobi-Bellman partial differential equation (HJB PDE). The PDE is generally fully nonlinear. The DPP can be interpreted as a nonlinear semigroup with generator given by the HJB PDE.

Interestingly, this semigroup is max-plus linear, and this linearity can be exploited in constructing numerical methods. For instance, one can reduce an infinite time-horizon, nonlinear optimal control problem to a max-plus eigenvector problem. One max-plus numerical method constructs the associated matrix, and then computes its max-plus eigenvector.

As indicated above, one of the most vexing problems in nonlinear control has been the curse-of-dimensionality. While linear PDEs may be easily solved, even a single nonlinearity in the PDE generally reduces one to using finite element methods where the curse-of-dimensionality reigns supreme. Interestingly, the max-plus linearity can be employed in producing a curse-of-dimensionality-free numerical method for a nontrivial class of HJB PDEs. Such results have already been demonstrated for problems combining linear/quadratic elements with a discrete event switching process.

##### Wednesday, November 2, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.

#### Tools for Tiny Tech

##### J. Clarke

Assistant Professor

Electrical and Computer Engineering

Wayne State University, MI

A revolution in information technology is coming into view. It involves ubiquitous computing, wireless communications, distributed sensors, actuators, and a host of other tiny technologies which will profoundly impact the quality of our lives. A bottleneck in the realization and application of complex micro- and nano-scale innovations come from the lack of adequate metrology and modeling tools for such multidisciplinary systems. In this seminar you will learn about a paradigm shift toward the enabling metrology and computer aided engineering tools, which aim to increase the scope and bandwidth of innovations and applications for this new and exciting era.

A major underlying problem is the numerous uncertain properties. These roughly-known parameters often lead to unconfident results in both measurement and predicted simulation, which impede our understanding of the physical phenomena and our advancement toward more sophisticated micronanosystems. Adequate metrology at this scale has been elusive. Metrology is typically done by adapting macro-scale methods to the micro-scale. However, nonidealities in geometry and material properties, which are typically ignored at the macro-scale, become significant at micro- and nano-scales. Due to large effective uncertainties, conventional metrology techniques often yield just one or two significant digits of accuracy, which does not justify their high cost and time for either laboratories on a budget or production-scale organizations. Different metrology techniques often yield different nominal values. Such problems in measurement adversely impact international commerce – making it difficult for customers to specify their needs. To date, only two ASTM standards exist at the micro-scale, which are for measuring the length and strain gradient of a cantilever. Currently, there is no consensus on the methods to measure other properties such as Young’s modulus, beam width, etc., which may have a much more substantial effect on the performance of micronanosystems. In addition to these large effective uncertainties associated with conventional measurement methods, the problems are further compounded by large sensitivities due to process variations. This implies that two seemingly identical runs will most likely produce two nonidentical sets of microdevices. Slight differences in properties often translate into substantial differences in dynamic performance. Indeed, the issues are formidable.

Vertical advancements in metrology and computer aided engineering will be discussed. Electro Micro-Metrology (EMM) is an innovative methodology for precision sensing and actuation at the micro- and nano-scale. It is well-suited for tiny technology because it leverages off the electromechanical benefits of the scale. Unlike conventional tools, EMM is quick, accurate, inexpensive, easy to employ, automatable, and tiny. We have discovered that by examining the unique relationships between the electrostatics and mechanics of simple microdevices, a multitude of geometric, dynamic, and material properties may be formulated as functions of electrical measurands. The formulations account for the nonidealities in going from layout to fabrication – i.e. coarse sidewall surfaces, rounded corners, over/under cuts, webbed fillets at all acute angles, and stress-induced asymmetry. It will be shown that by measuring the change in capacitance, change in voltage, and/or resonant frequency of a few structures, over two-dozen geometric, dynamic, and material properties can be extracted with a much higher precision and relative error than conventional methods. A fully characterized device becomes a precise measurement and actuation tool for the tiny technologist. Applications may include: calibration of atomic force microscopes, measurements of molecular bond strengths, nano-manipulations, post-packaged recharacterization after environmental change or long-term dormancy, quality control, etc. In regards to developing industry standards, EMM’s performance-based measurements may be preferable to direct measurements because macroscopic notions (e.g. beam width) are not well-defined at this scale. Last, we will discuss what these precise measurements mean for model-building. In particular, we will consider a unifying modeling tool for complex systems.

**Jason V. Clark** will receive his Ph.D. in Applied Science and Technology from the University of California at Berkeley on December 20, 2005. He received a B.S. in Physics from California State University Hayward. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering at Wayne State University. He has developed a new graduate course called Modeling and Simulation of Multidisciplinary Systems, and he also teaches an undergraduate course called Materials Science for Engineers. His research interests are in the areas of design, modeling, simulation, and realization of complex engineered systems. He has published several refereed articles on computer aided engineering and metrology, and he has two patents pending. Previous positions include the Berkeley Sensor and Actuator Center (BSAC) and the Center for Information Technology Research in the Interest of Society (CITRIS), where he was the key developer of the first modified nodal analysis computer aided engineering package for MEMS; the U. C. Berkeley Biomedical Microdevices Center, where he applied BioMEMS to oncology; the U.C. Berkeley Materials Science Department, as a Graduate Student Instructor; the Lawrence Berkeley National Laboratory’s Weak-Interactions Group, where he laser-cooled radioactive atoms; Coventor Inc., as a Reverse-Engineering CAE developer; and the Lawrence Livermore National Laboratory in the Atmospheric Sciences Division.

##### Tuesday, November 8, 2005

11:30 AM

Laufer Library (RRB 208)

#### Tension-Field Theory

##### David Steigmann

Department of Mechanical Engineering

University of California, Berkeley

Berkeley, CA

A version of the method of dynamic relaxation is developed to analyze equilibrium configurations of partly wrinkled membranes. In this method equilibria are regarded as long-time limits of the solutions to a damped dynamical problem. The membrane theory considered is based on the concept of a relaxed strain-energy function that automatically incorporates the tension-field effect associated with membrane wrinkling. For neo-Hookean materials, existence theorems of nonlinear elasticity are used to show that the relaxed potential energy possesses minimizers in a certain function space. Moreover, solutions to the equilibrium equations furnish global minima of the energy, for certain classes of boundary data. Such deformations are automatically stable according to the minimum-energy criterion. Several examples of two- and three-dimensional deformations are presented. These are shown to exhibit many of the complex qualitative features observed in simple experiments.

##### Friday, November 11, 2005

1:30 PM

SGM 101

#### Ship Shock Trial Modeling and Simulation

##### Young S. Shin

Professor of Mechanical Engineering

Department of Mechanical and Astronautical Engineering

Naval Postgraduate School

Monterey, California 93943

(831) 646-2568

During World War II many surface combatants were damaged or severely crippled by close-proximity underwater explosions from ordnance that had actually missed their target. Since this time all new classes of combatants have been required to conduct shock trial tests on the lead ship of the class in order to test the survivability of mission essential equipment in a severe shock environment. While these tests are extremely important in determining the vulnerabilities of a surface ship, they require an extensive amount of preparation, man-hours, and money. Furthermore, these tests present an obvious danger to the crew on board, the ship itself, and any marine life in the vicinity. Creating a virtual shock environment by use of a computer to model the ship structure and the surrounding fluid presents a valuable design tool and an attractive alternative to these tests. The research work shown in this paper investigated the accuracy of shock simulation using the shock trials conducted on DDG class ship. The ship shock modeling and simulation strategy is discussed and the effects of fluid volume size, mesh density, mesh quality are also investigated.

##### Wednesday, November 16, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Molecular Surgery through Electrical Impedance Tomography of Electroporation

##### Rafael Davalos

Senior Member of the Technical Staff

Sandia National Laboratories

Livermore, CA

Electroporation is a method to introduce molecules, such as gene constructs or small drugs, into cells by temporarily permeating the cell membrane with electric pulses. In molecular medicine and biotechnology, tissue electroporation is performed with electrodes placed in the target area of the body. Currently, tissue electroporation, as with all other methods of molecular medicine, is performed without real-time control or near-term information regarding the extent and degree of electroporation. We hypothesize that permeabilization of the normally electrically nonconductive cell membrane should lead to a change in the bulk electrical properties of the tissue and would be detectable with a bioimpedance imaging technique. We quantified the change in conductivity of an individual cell during electroporation using a microelectromechanical chip that incorporated a live biological cell within an electric circuit. In addition, experiments conducted on ex vivo tissue samples yielded a clear correlation between the electric field and the normalized conductivity change and, therefore, permeabilization state of the cell membrane. The experimental data was incorporated into numerical simulations of therapeutic electroporation and images were generated using a reconstruction algorithm to demonstrate that electrical impedance tomography (EIT) can produce an image of the electroporated area. Combining EIT with electroporation could become an important biotechnological tool to introduce therapeutic molecules into cells in tissue at predetermined areas of the body for the treatment of genetic diseases and cancer.

##### Monday, November 21, 2005

10:30 AM

Laufer Library, RRB 208

#### Molecular Dynamics with Molecular Temperature (MDMT):

A New Technique For Simulating The Interactions Of Certain Types Of Large Molecules

##### Arun Srinivasa

Associate Professor

Mechanical Engineering Department

Texas A&M University

College Station, Texas

One of the fundamental difficulties of doing molecular dynamics simulations of large organic molecules (e.g., Chlorobenze) is the fact that there are widely different time scales involved. Since MD simulations are unstable if the time step is too large, it is prohibitively expensive and difficult to simulate the behavior of such large molecules. In this talk I will present a new technique, (Phares and Srinivasa, *J. Phys. Chemistry A* **108** (29): 6100-6108, 2004) for doing molecular dynamics simulations using the notion of a molecular temperature to model the internal degrees of freedom of large molecules. After a brief overview of different types of MD simulations, I will show how MDMT can be used to simulate the photofragmentation of Chlorobenzene as an example. I will also indicate how to combine the technique with certain macroscopic continuum models so that detailed MD simulations can be carried out in small regions while the surrounding regions are modeled as a continuum, and the challenges and opportunities in this regard.

##### Wednesday, November 23, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 100 (SLH 100)

Refreshments will be served at 3:15 pm.

#### Invariant Dynamical Systems Embedded In The N-Vortex Problem On A Sphere With Pole Vortices

##### Takashi Sakajo

Associate Professor

Department of Mathematics

Hokkaido University

We are going to give a reduction method of the N-vortex point problem on a sphere. The reduction is based on the linear stability analysis for the polygonal ring configuration (N-ring) of the vortex points. We show that mathematically there exists the 2p-dimensional invariant dynamical system for arbitrary factor p of N. We use these invariant systems to describe the motion of the unstable N-ring when it is perturbed.

##### Wednesday, November 30, 2005

3:30 PM

Stauffer Science Lecture Hall, Room 102 (SLH 102)

Refreshments will be served at 3:15 pm.