Browsing by Subject "probability"
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Item Modeling the growth of streamers during liquid breakdown(IEEE, 2008-04) Hebner, R.E.; Kim, M.; Hallock, G.A.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.Item Quantum Contextuality As A Measurement Disturbance Effect(2009-03) La Cour, B. R.; La Cour, Brian R.The question of quantum contextuality in the Mermin-Peres square is considered. It is shown that a deterministic, noncontextual hidden variable model of this problem is not inconsistent with quantum mechanics, contrary to the Kochen-Specker theorem. The key idea is that measurement outcomes may be viewed as deterministic functions of hidden variable states which are disturbed through the process of measurement. This, in turn, implies that the outcome of measuring the product of two commensurate observables need not be equal to the product of the outcomes that would have been obtained had they been measured individually. A critical analysis of some recent and proposed experimental tests of contextuality is also provided.Item Relaxation Of Brownian Particles In A Gravitational Field(2009-03) Saka, Halil; Bengtson, Roger D.; Reichl, Linda E.; Saka, Halil; Bengtson, Roger D.; Reichl, Linda E.We describe an upper level undergraduate experiment on the time-dependent behavior of a suspension of Brownian particles under gravitational attraction. We employed the Fokker-Planck equation in the strong friction limit and measured the time-evolution of the probability distribution for 1.0 mu m diameter latex Brownian particles in water at room temperature and pressure. The experiment provides evidence of the atomic nature of water.Item The Texas Mathematics Teachers' Bulletin, Volume XXII(University of Texas at Austin, 1938-04-01) The University of Texas