# Faculty Profile

## Donald Kouri

Cullen Distinguished Professor

**Department of Physics**

**Office:** Science & Research 1, 606B

**Contact:** kouri@uh.edu - (713) 743-3245

**Education:** Ph.D., University of Wisconsin

## Theoretical and Mathematical Chemistry

Fundamental quantum theory; generalized coherent states; quantum theory of atomic and molecular collisions; few body problems; approximate methods for calculating cross sections, theory of reactive scattering, nonequilibrium statistical mechanics; real-time Feynman path integral studies; wavepacket treatments of quantum dynamics; digital signal processing; wavelet theory; multiresolution analysis.

We are continuing to carry out research in the formal and computational aspects of molecular collision dynamics. Our current focus is on combining our recently developed time-independent wavepacket formulation of reactive scattering with various approximations. The basic idea is to use our "divide-and conquer" approach (using absorbing and emitting potentials as formulated by my former student John Zhang, and modified by myself) so that different appropriate approximations can be used in the various separate dynamical regions (e.g., the entrance channel, strong-interaction region, and various exit channels). A key part of the research is the use of different coordinates in each region so that the equations are most nearly separable in each region. This will facilitate the choice of the optimal approximation in each region.

A second major area of research is in what might be called "mathematical chemistry and physics." We have developed a new approach to functional approximations called the "distributed approximating functionals" (DAFs) and used them to solve a variety of both linear and nonlinear partial differential equations. We also have used them to develop new "filters" for denoising experimental and computational data. We shall be continuing this research, looking at a broad range of problems generally known as "digital signal processing", in addition to an enormous range of areas, including imaging, data compression, pattern recognition, neural networks, wavelet theory, etc.

The third major area of research we are currently pursuing is in the fundamentals of quantum theory. Of particular interest is a new generalization of the Heisenberg uncertainty principle, so as to include the idea of multiresolution analysis. This is important for nonlinear optics (e.g., preparation of optimal coherent light pulses), Bose-Einstein condensation and confinement of material particles, quantum computing, and many other areas. It has led to the development of generalized Gaussian and coherent quantum states. These promise to be important both theoretically and experimentally.

- B. G. Bodmann, D. K. Hoffman, D. J. Kouri and M. Papadakis, Hermite distributed approximating functionals as almost-ideal low-pass filters, Journal of Sampling Theory in Image and Signal Processing, 7, 15 (2008).
- F. Shi, P. Sharma, D. J. Kouri, F. Hussain and G. H. Gunaratne, Nanostructures with long-range order in monolayer self-assembly, Phys. Rev. E, 78, 025203-1 to 4 (2008).
- I. S. Walimuni, D. J. Kouri, M. Papadakis and B. G. Bodmann, Polychromatic method to enhance the soft tissue contrast of CT images using a saddle point approximation, in IEEE ISBI-2007, pp. 828-831.
- S. Hu, G. Nathan, F. Hussain, D. J. Kouri, P. Sharma and G. H. Gunaratne, On stability of self-assembled nanoscale patterns, J. Mech. and Phys. of Solids, 55, 1357 (2007).
- S. Gertz, D. Vela, I. Aboshady, L. Frazier, J. L. Conyers, L. Gavish, B. Bodmann, M. Papadakis, S. Alexander, D. Kouri, G. Gladish, D. Cody, J. Willerson and S. Cassells, Imaging of vulnerable plaque: Indications, challenges and future directions, in Proc. 13th World Congress on Heart Disease, H728R9060, pp. 121-127 (2007).
- L. Shen, M. Papadakis, I. A. Kakadiaris, I. Konstantinidis, D. Kouri and D. Hoffman, Image denoising using a tight frame, IEEE Trans. Image Processing, 15, 1254 (2006).
- L. Shen, M. Papadakis, I. A. Kakadiaris, I. Konstantinidis, D. Kouri and D. Hoffman, Image denoising using a tight frame, in IEEE ICASSP, II-641, (2005).
- M. Papadakis, G. Gogoshin, I. A. Kakadiaris, D. J. Kouri, and D. K. Hoffman, Non-separable radial frame multiresolution analysis in multidimensions, Numerical Functional Analysis and Optimization, 24 (2003), p.907-928.
- I. A. Kakadiaris, M. Papadakis, L. Shen, D. J. Kouri, and D. K. Hoffman, g-HDAF mulriresolution deformable models, in Proceedings Lecture Notes in Computer Science, 2492, 21-31 (2002).
- I. A Kakadiaris, M. Papadakis, L. X. Shen, D. J. Kouri and D. K. Hoffman, g-HDAF multiresolution deformable models for shape modeling and reconstruction, in Proceedings of the British Machine Vision Conference, Eds. P. L. Rosin, A. D. Marshall, BMVC2002, p. 303-312 (2002).
- "A method to Fourier filter textured images," D. K. Hoffman, G. W. Wei, D. S. Zhang and D. J. Kouri, Chaos, 10, 240 (2000).
- "Distributed approximating functional treatment of noising signals," D. S. Zhang, D. J. Kouri, D. K. Hoffman, and G.H.Gunaratne, Computer Phys. Commun., 120, 1 (1999).
- "Numerical Solutions of Nonlinear Wave Equations," D. J. Kouri, D. S. Zhang, G. W. Wei, T. Konshak, and D. K. Hoffman, Phys. Rev. E, 59, 1274 (1999).
- "Generalized symmetric interpolating wavelets," Z. Shi, D. J. Kouri, G. W. Wei, and D. K. Hoffman, Comuter Phys. Commun., 119, 194 (1999)
- "A variaional approach to the Dirichlet-Gabor wavelet-distributed approximating functional," D. K. Hoffman , G. W. Wei, and D. J. Kouri, J. Math, Chem., 25, 235 (1999).
- "Interpolating Distributed Approximating Functionals," D. K. Hoffman, G. W. Wei, D. S. Zhang and D. J. Kouri, Phys. Rev. Lett. 57, 6152 (1998).