Date of Graduation
We use numerical modeling and scaling theory methods to investigate the time evolution of three types of condensed matter systems far from equilibrium. We study buckling instability of flexible chains of molecules, buckling instability of tethered membranes and Molecular Beam Epitaxy (MBE) Growth Model. We find that the buckling of the flexible chain is similar to coarsening phenomena such as the spinodal decomposition. Evolving chain profile is like a wave with a wavelength Î»(t) that grows, via coarsening, as a power of time. The evolving chain is like a rough object with transversal roughness w(t) growing as a power of time. We find that Î»(t) âˆ¼ w( t) âˆ¼ tÂ¼. These power laws are associated with a chaotic coarsening of the chain dynamics that is statistically self-similar in time. In the second part we study the buckling instability of compressed tethered membranes. We relate the membrane buckling dynamics to phase ordering phenomena. We find that the evolving membrane develops a growing wavelike pattern. The membrane evolves via a stochastic coarsening process that has associated with it power law growth of length scales that characterize the evolving membrane. Membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena. In the third part, we study a continuum model of MBE growth. The growth on the isotropic and hexagonal symmetry surfaces it is shown to exhibit a scaling behavior characterized by the presence of a single characteristic length scale that grows in time as a power law. The coarsening exponent is the same for both isotropic and hexagonal surfaces. A scaling theory that predicts this scaling behavior is proposed. The growth on the square symmetry (001) surfaces was shown to exhibit a multi-scaling behavior as there are two characteristic length-scales that grow in time with two different coarsening exponents. A kinetic scaling theory that predicts the coarsening exponents for the square symmetry (001) surfaces is proposed.
Moldovan, Dorel I., "Studies of far from equilibrium condensed matter systems: Euler buckling instability and molecular beam epitaxy." (1999). Graduate Theses, Dissertations, and Problem Reports. 9443.