# Browsing by Subject "fractals"

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Item Chaotic scattering in a molecular system(2009-02) Barr, Alex M.; Na, Kyungsun; Reichl, L. E.; Jung, Christof; Barr, Alex M.; Na, Kyungsun; Reichl, L. E.Show more We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincare surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.Show more Item Effect of pore structure on capillary condensation in a porous medium(2009-02) Deinert, M. R.; Parlange, J. Y.; Deinert, M. R.; Deinert, M. R.Show more The Kelvin equation relates the equilibrium vapor pressure of a fluid to the curvature of the fluid-vapor interface and predicts that vapor condensation will occur in pores or irregularities that are sufficiently small. Past analyses of capillary condensation in porous systems with fractal structure have related the phenomenon to the fractal dimension of the pore volume distribution. Recent work, however, suggests that porous systems can exhibit distinct fractal dimensions that are characteristic of both their pore volume and the surfaces of the pores themselves. We show that both fractal dimensions have an effect on the thermodynamics that governs capillary condensation and that previous analyses can be obtained as limiting cases of a more general formulation.Show more Item Modeling the growth of streamers during liquid breakdown(IEEE, 2008-04) Hebner, R.E.; Kim, M.; Hallock, G.A.Show more Earlier work by Fowler, Davaney, and Hagedorn showed that the morphology of an anode streamer could be modeled as stochastic growth of a branching fractal tree in point-plane geometry. This investigation reproduces the results of that earlier study. Because one of the concerns about the earlier work is that the electric field dependence appeared to be unphysical, the model was modified to operate under assumptions that are consistent with those that have proven useful in earlier investigations. Specifically, linear electric field dependence was assumed and there is an assumed variability in the number density of available electrons. Computations using this assumption also produce the same range of morphologies that has been measured in experiments. In addition, some assessments of sensitivity to other possible variables are made. First, the sharp cutoff in the electric field strength is replaced with a presumably more realistic exponential dependence on energy. Under this assumption, it is also possible to simulate the experimentally observed behavior of anode streamers. It is shown that three possible refinements to the model have small, and likely negligible, effects. The first is using variable streamer step lengths in the calculation rather than the fixed step length used in the earlier work. The second is to assume growth at one point in the streamer makes growth in other parts somewhat less likely. The third is the assumption that the probability of a streamer making the next step in growth is influenced by the distance of the inter-electrode gap that has already been traversed.Show more Item Stochastic Modeling of Streamer Transitions(IEEE, 2008-10) Kim, M.; Murphy, B.; Hebner, R.E.Show more Simulations of the growth of streamers using a model based on the stochastic growth of a branching fractal tree have shown good fidelity in matching the morphology of streamers in liquids. An important aspect that has not yet been simulated is the transition between Type 1 and Type 2 streamers. This work explores the effect of a variation of the applied voltage during streamer growth as well as the effect of differing amounts of available electrons during growth. Neither of these assumptions produced the experimentally observed transitions. These results produced a possible approach that could modify the step length in the simulation in relation to the electric field that may trigger the transition. It also points out that the transition might be due to hydrodynamic instabilities that are not captured by the model.Show more