STOCHASTIC PROCESSES IN SURFACE GROWTH AND IN POLYMER

The study of fluctuations in physical systems is of interest in many disciplines. These disciplines include physics, chemistry, biology, astronomy and mathematics. The stochastic methods used to describe fluctuations have grown enormously in the last few decades and continue to be the subject of very active research. This project aims to apply stochastic methods to the study of processes in surface growth. These processes include deposition, sedimentation, diffusion and epitaxial growth. Such studies can lead to fundamental understanding in thin film growth, which is an important technique in the Fabrication of solid-state devices. Another area of interest is in the application of stochastic methods to study the dynamics of polymer solutions.In this area, Lam and Bagayoko have generalized the influence of uncorrelated white noise on the dynamics of polymer solutions to the case where the correlations depend on both space and time. A noise with space and time dependent correlation is referred to as colored noise. We found that colored noise leads to measurable effects in the dynamic light scattering in polymer solutions.This result sheds light on the dynamics of polymers in solutions. Our studies of stochastic processes have equally been fruitful and led to significant publications in the last two years. This work is supported in part by the Louisiana Education Quality Support Fund (Contract No. LEQSF(1993-94)-ENH-TR-29). It is also supported, through the Timbuktu Academy, by the National Science Foundation (NSF Grant# HRD-9108590) and by the Department of the Navy, Office of Naval Research (ONR Grant# N00014-93-1-1368).

References:
1. Dynamic scaling of The island-size distribution and percolation in a model of submonolayer molecular beam epitaxy, J. G. Amar, F. Family and P.M. Lam, Phys. Rev. B50, 8781 (1994).
   
   
2. Ward identities for surface growth models with diffusion, P.M. Lam and D. Bagayoko Phys.Rev. E50, 2488 (1994).
   
   
3. Dynamics of concentration fluctuations in polymer solutions with spatiotemporal correlated noise, P.M. Lam and D. Bagayoko, Phys. Rev. E50, 437 (1994).
   
   
4. Polymer brushes with density dependent excluded volume parameters, P. Anderson, D.C. Hong, P.M. Lam and B.E. Vugmeister, J. Physique II4, 1157(1994).
   
   
5. Spatiotemporal correlations in colored noise, P.M. Lam and D. Bagayoko, Phys. Rev. E48, 3267 (1993).
   
   
6. Renormalization group and simulation studies of groove instabilities in surface growth,l F. Family and P.M. Lam, Physica A205, 272 (1994).
   
   
7. Groove instabilities in surface growth with diffusion, J. G. Amar, P.M. Lam and F. Family, Phys. Rev. E47, 3242 (1993).
   
   
8. Mode-coupling theory and simulation of a running sandpile model of self-organized criticality, P.M. Lam and F. Family, Phys. Rev. E47, 1570 (1993).