# Directory

- Ph.D., Chemical Engineering, Rensselaer Polytechnic Institute, Troy, 1978
- M.Sc., Chemical Engineering, University of Dayton, Dayton, 1973
- B.Sc., Chemical Engineering, Vanderbilt University, Tennessee, 1969

## Institutional Expertise

Dr. Morgan was awarded his Ph. D in Chemical Engineering from Rensselaer Polytechnic Institute in 1978, the Master of Science degree in Chemical Engineering from the University of Dayton in 1973, and a Bachelor of Science degree in Chemical Engineering from Vanderbilt University in 1969. He has been a professional chemical engineer for over thirty-nine years that includes thirteen years of industrial experience with General Motors, Monsanto and GE’s Corporate Research and Development Center. Dr. Morgan has also held two academic appointments one with Rensselaer (fourteen years) and the other with Hampton University (past eleven years). Dr. Morgan is the author or co-author of over seventy-five scientific articles, has given over sixty presentations both domestically and internationally, and holds four U.S. Patents.

## Summary of Research Activities: Nonlinear Dynamics

- Digital communication applications are an integral part of modern day society that has accelerated with the growth of wireless telephone technology. A problem of interest in such systems is that of detecting or accessing synchronization levels of signals (time series) arising from divergent sources where the primarily focus has centered on the statistical characterization of binary signals that maybe carrying encoded data. The Hamming distance metric has been used successfully in a variety of applications ranging from developing built-in-error code correcting device for commercial and military communication systems and in personal (iris) discrimination applications. In the present context it is used as a quantitative metric for accessing signals (time series) synchronization levels and performing statistical inferences about information reliability. This Hamming distance based approach that employs the count or difference between two time series is shown to be a quick and effective technique for discrimination. The underlying Hamming distance statistical distribution is determined using bootstrapping, a nonparametric method for providing confidence estimates.
- With regard to inducing synchronization among a network of dynamic systems, two basic problems exist. The first one centers on identifying suitable control variables. Here the recent results of Letellier and Aquire are applicable and provide a theoretical framework for selecting such variables. Their approach involves employing a graphical technique that highlights the interactions among the dynamic variables and their first derivatives. The second problem centers on inducing synchronization via a minimum energy expenditure of the control variables. The stability of these variables is guaranteed by a LaSalle’s Invariance Principle that is necessary and sufficient. The current research is focused on an investigation of the nature or type of synchronization established among a network of functional differential equations and evaluating the robustness of coupling arrangement to sporadic stochastic noise.
- There is also a focus on detection of the changeover or switch point associated with time series that undergo an abrupt change in character. The aim of this work has been to devise robust statistical metrics that accurately and quickly detect a change in the inherent nature of a time series. Such work has broad applications in medicine, process control, electrical power system design, terrorism detection and communications. The present approach employs an adaptive control fitting technique that provides statistical based parameter estimates for experimental time series where the underlying models are not known but must be coupled /synchronized dynamically in the present of stochastic noise that corrupts both time series.
- This research involves a statistical investigation of wavelet methods for analyzing data streams arising from chaotic sources. Currently extensive efforts are being directed toward devising detection algorithms that can distinguish between chaotic and random time series (signals) or detect subtle changes in a chaotic data stream. Such detection algorithms are used for image recognition, speech recognition and diagnostic detection. These schemes have gained popularity because of the need to compress massive data streams. In this work, the Haar wavelets, a subclass of orthogonal functions used for describing square integrable time series (signals) are used to accomplish this task. These wavelets are used to accurately and parsimoniously represent other functions in non-parametric regression applications. The focus of this work is to develop appropriate statistical metrics for such data streams as well as provide nonparametric estimates of population profiles derived fromdeterministic models that mimic random/stochastic processes.
- This effort is concern with developing several statistical metrics for assessing nonlinear time series features, a problem of general interest for complexity measurements of time series. This approach is based on using a metric that is a weighted linear combination of an order pattern statistic and a traditional distance based norm. Similar metrics have been used in the medical profession to assess brain and heart data patterns and to distinguish healthy subjects from sick ones. Examples of such metrics include, but are not limited to, Lyapunov exponents, fractal dimensions and permutation entropies.

## Recent Funded Research Activities

- NASA Pace grant - “Mathematics, Science, Engineering & Technology,” $300,000/3yrs, Co-PI;
- GE Fund-“GETMET”, $150,000/2yrs;
- NASA - “Aero-propulsion”, $4,800,000, Center Director;
- Department of Defense - “Statistical Data Mining and Analysis of Large Drifting Data Streams”, $153,000/2yrs, Co-PI.

## Recent Masters Thesis

- A. Cox, “Stability of a Spouted Bed Combustor,” 2004;
- Lucious Thomas, “Numerical Simulation of Three Dimensional Flow Nesar a Cone with Ribs, with a focus on Drag and Flow Structure”, 2006;
- Clemontina Alexander, “Using a Hamming Distance Metric to determine the effect of Window Size on Error Detection Rates arising from Spread Spectrum and Chaotically generated Binary Time Series”, 2008.

## Patents

- “Electric Spouted Bed Systems,” US Patent # 4,349,967
- “Magnetic Spouted Bed Systems,” US Patent # 4,373,272
- “Automatic Particle Transport System”, US Patent # 5,248,222
- “Coating Apparatus Having Opposed Atomizing Nozzles in a Fluid Bed”, US # 5,254,168