Harry Dankowicz - US grants

Proposal Title: PECASE: Analysis and Design of Discontinuity-Driven Bifurcations
Institution: Virginia Polytechnic Institute and State University

This award focuses on the analysis and design of nonsmooth dynamical systems, characterized by abrupt and discontinuous changes in the systems' properties, and commonly encountered in mechanical, biological, and electronic models. Of particular significance are the potentially dramatic changes in character and stability of motions of such systems that occur at the onset of weak interactions with the environment, here referred to as discontinuity-driven bifurcations. For example, in the case of human gait, premature, low-velocity ground contact of the swing foot may result in loss of stability of the sustained gait and subsequent fall, particularly in individuals with muscular disorders or the elderly. The objectives of this project are to develop a comprehensive predictive methodology for discontinuity-driven bifurcations of recurrent and transient motions and to formulate design criteria for reducing or eliminating the detrimental effects of unintentional collisions between a mechanical subsystem and its surrounding environment -- in particular, the prevention of fall-related injury due to premature ground contact during gait. The research work will closely integrate with an effort to develop a closed-ended-design course at the junior level emphasizing performance verification tests for mechatronic systems and the evaluation of a system's response in the presence of smooth and discontinuity-driven bifurcations.

This project was originally funded as a CAREER award, and was converted to a Presidential Early Career Award for Engineers and Scientists (PECASE) award in September 2004.

Minimum-contact Tapping-mode Atomic Force Microscopy for Nondestructive Characterization of Soft Nanostructures

Harry Dankowicz, Virginia Polytechnic Institute and State University



Abstract

The invention of the atomic force microscope has paved the way for direct measurements of intermolecular forces and atomic-precision topographical mapping in a wide array of materials including semiconductors, polymers, carbon nanotubes, and biological cells. Of the different imaging modalities, intermittent-contact (TappingModeTM) atomic-force microscopy greatly reduces the effects of adhesion and friction on the probe tip. Here, however, the destabilizing influence of the intermittency of contact may result in probe-tip oscillations with high contact velocity and destructive, nonrepeatable, and unreliable characterization of the nanostructure.

This research effort aims to develop and experimentally demonstrate the feasibility of innovative design and control strategies for minimum-contact, tapping-mode atomic force microscopy to successfully and nonintrusively characterize soft physical structures at the nanoscale. Successful application of the proposed control strategies is expected to dramatically improve the repeatability of structure scans and to provide a more faithful representation of surface properties while significantly reducing damage to the measured structure.

A direct link to industry-relevant problem formulations and a channel for long-term commercialization is provided through a formalized collaboration with Veeco Instruments Inc., a leading provider of nanoscale metrology equipment. This research effort is also integrated with educational and outreach activities of the investigators, through the inclusion of modules on principles of nanoscale characterization in the senior-level undergraduate and first-year graduate-level course "Modeling MEMS and NEMS" and through the creation of a promotional brochure on nanoscale science aimed at local and regional high schools.

The characterization of complex motion patterns in multisegmented biological organisms is typically achieved by the identification and measurement of task-related behaviors and the assessment of deviations from these normative behaviors. The basic hypothesis of this proposal is that there are systematic and quantifiable relationships between observed deviations in motion patterns and underlying physiological limitations. Currently available tools are largely unable to resolve these relationships as they primarily examine discrete events during a specific motion or are based on univariate statistical techniques. Thus, they fall short in quantifying spatiotemporally complex motion patterns and in detecting interactions across multiple segments and joints.
The fundamental objective of this project is to establish a diagnostic, multivariate technique for characterizing complex motion patterns and correlating specific motion patterns with physiological conditions. Specifically, the proposed research will: (i) create an "Integrated Multivariate Motion Analysis" computational tool that combines shape-based analysis techniques with multivariate statistical tools to allow for improved quantification of complex motion patterns; (ii) benchmark the statistical technique against a library of task-specific lower-limb motion patterns generated using numerical optimization techniques applied to a simple mechanical model of the lower limb with unconstrained and constrained joint mobility; and (iii) establish the degree to which the statistical technique is able to identify the presence and degree of constraint in a set of controlled, experimental motion-captured data of human walking without and with braces that artificially constrain the movements at the knee or ankle.
We expect that a successful outcome of the proposed effort will transform studies of gait and other complex motions. The tools developed from this project will significantly advance diagnostic capabilities, aid in the evaluation and treatment of movement conditions, and permit more accurate and comprehensive comparisons of segmental movements in a variety of taxa. These tools will lead to novel inferences about the complexity, performance, efficiency and health of biological and mechanical systems. This project also provides a multidisciplinary research and educational environment for faculty, graduate, and undergraduate students in engineering, anthropology, and psychology with interests in movement analysis, computational simulation of dynamical systems, and the statistical comparison of complex shapes at both the University of Illinois and Stockton College of New Jersey

Dynamical systems methods have had significant impact on the characterization of a range of phenomena in the natural and engineering sciences. More importantly, predictive models have been formulated that enable high-fidelity prediction of complex dynamical responses of natural or man-made mechanisms and systems. This development has supported a deeper understanding of the workings of nature coupled with active intervention and problem solving that has sustained and advanced human society.

With support from the National Science Foundation, a workshop is being held at Cornell University to discuss how dynamical systems can similarly be brought to bear on the cognitive sciences. The workshop features invited speakers and participants from the social, behavioral, cognitive, engineering, and mathematical sciences. Discussions center around the potential for concepts and methods from dynamical systems to shape the research questions and empirical methods asked by cognitive scientists. Benchmark problems and examples from the cognitive sciences are used to help bring clarity and focus to the discussions. The organizers plan to disseminate the results of the workshop by means of an edited volume and a journal article, both designed to reach a broad audience of scientists and engineers.

Across all science and engineering disciplines, research is conducted in theoretical, experimental, and computational modes. In some disciplines, such as meteorology, the dominant mode of research is computational. Yet extant instructional materials for responsible conduct of research focus on ethical issues that arise in experimental research, and do not address specific issues that arise in computational modeling and research. In this project which encompasses a combination of research and education, the PIs will determine empirically the ethical issues and accepted standards for the responsible conduct of computational modeling and research, in a form suitable for teaching graduate students. Specifically, the PIs will articulate the standards for model integrity and validity, model robustness, representations and visualizations, data and code integrity, and intellectual property. They will develop instructional materials, case studies and associated commentaries to teach these standards to graduate students in science and engineering, will assess the quality and effectiveness of the instructional materials, and will disseminate them through conferences, journals, and the Web. The expertise of the project team includes computational dynamics, computational biomechanics, engineering ethics, instructional design, and educational assessment.

Broader Impacts: In collaboration with both graduate and undergraduate students, the PIs will develop cases based on actual situations, and commentaries on the cases for teaching the professional standards of computational modeling to graduate students in science and engineering. These materials will be tested and assessed with students and instructors in two institutions, and with professionals at technical conferences. The materials will be disseminated through academic conferences and archived at the Online Ethics Center of the National Academy of Engineering. The standards will be proposed for inclusion in the publication guidelines of research journals.

Threshold sensors are input-output devices that switch operating state in reaction to the crossing of a threshold value of their input. These are used to monitor and control critical values of temperature, voltage, pressure, etc. in both consumer and industrial settings. The change in operating state might be permanent, such as when a fuse burns out, or capable of being reset, such as with a circuit breaker. This research effort aims to analyze, design, fabricate, and experimentally characterize a class of ultrafast and robust, resettable electromechanical threshold sensors. The fundamental design principle proposed here relies on predicted changes in system response particular to piecewise-smooth dynamical systems including impact- and friction-like discontinuities. The proposed research will validate these theoretical predictions and demonstrate the successful regulation of switch rates using active feedback control in macro- and microscale electromechanical devices.

This research effort makes original contributions to a nascent effort in nonlinear dynamics that will transform the field from a tool for modeling and analysis of observed behavior to a tool of intentional synthesis of engineered systems. The engineering of man-made devices to exhibit desirable nonlinearities has the potential to dramatically broaden the toolbox of the applied engineer and to change the performance characteristics in existing applications by orders of magnitude. The present work is a basic and comprehensive effort to establish the so-called nonsmooth fold bifurcation associated with the onset of low-velocity contact in vibro-impacting systems as an exploitable nonlinear phenomenon in device design, e.g., capacitively-driven circuit protection devices. Preliminary results on the ultrafast response following this bifurcation show a significant potential for dramatic improvement in sensor performance.

This research is an international collaboration with research groups at the Royal Institute of Technology in Stockholm, Sweden and at La Sapienza University in Rome, Italy and will include several extended visits of project graduate research assistants to the international sites.

An Algorithm Suite for Computational Nonlinear Analysis of Power Systems
This effort targets the original development of CNAPS, an innovative suite of numerical algorithms for continuation analysis of multi-segment trajectories in large-scale, nonlinear dynamical systems with multiple slow and fast timescales, coupled components, and with triggers, resets and switches. Continuation methods have proven very successful for analyzing system behavior of low-dimensional systems. In CNAPS, we aim to dramatically scale continuation methods to complex networked systems with hybrid system trajectories and tens of thousands of states, by developing new multiscale, multisegment, trajectory-discretization algorithms based on asynchronous collocation methods; developing new mesh adaptation algorithms suitable for the asynchronous collocation methods, which accommodate segment-specific discretization error bounds; and constructing domain decomposition methods particular to the network topology and the asynchronous collocation formulation, which enable efficient parallel execution.
The core application of CNAPS considered in this multidisciplinary effort is modern power systems that include renewable sources of generation, specifically wind power, and newer forms of load, characterized by multiple coexisting time scales and trigger-induced switching behavior. Analysis of large-disturbance dynamic phenomena in such systems currently relies almost exclusively on forward simulation. While such tools may reveal complex behavior, they offer little help in the design process required to address unacceptable behavior, especially emerging phenomena associated with the increased use of power electronic converters. The development of CNAPS enables intelligent and efficient exploration of transient and steady-state responses of complex power systems, aimed at quantifying design and uncertainty margins for stable, faultless operation.

This INSPIRE award is partially funded by the Perception, Action, and Cognition Program in the Division of Behavioral and Cognitive Sciences in the Directorate for Social, Behavioral and Economic Sciences, the Animal Behavior Program in the Division of Integrative Organismal Systems in the Directorate for Biology, and the Dynamical Systems Program in the Division of Civil, Mechanical & Manufacturing Innovation in the Directorate for Engineering.

The project explores the question of how the activities of individuals become integrated into a smoothly functioning society: What are the dominant mechanisms? How resilient are they? How do they depend on the properties of individual society members? To this end, investigators from engineering, biology, psychology and linguistics will work together to study bee colonies and groups of humans to understand how organization and coordination emerges from these multi-agent systems and the factors that influence their robustness and resilience to perturbations. The project relies on quantitative observations of the dynamic emergence of patterns of interaction and coordination using an unprecedented, 24/7 monitoring system of a beehive as well as in groups of humans under controlled conditions designed to distinguish between failed and successful coordination. The investigators will pursue a combined theoretical, experimental, and computational framework for characterizing the resultant parallel and asynchronous communication systems. The work depends crucially on the interdisciplinary framework and the direct involvement of content expertise from the disciplines represented by the investigators. For example, the human transportation network is designed to resemble the coordinated delivery of nectar through a beehive, but with options for varying the number of different materials transported, the size of arena, the flow rates of the materials, and so on.

The investigators are exploring whether a comprehensive computational framework can be discovered to understand, predict and prevent the collapse of very different types of communities (bees and human networks). The research results are expected to provide insight into how to manipulate the behavior of a complex system, for example to address societal challenges associated with the collapse of pollinating bee colonies or the destructive behavior that is often associated with phases of social transition in groups of humans.