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Restriction data tranferred 2014-07-01T11:12:11-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only 3645090 http://hdl.handle.net/2142/18870 en Oono, Yoshitsugu Zimmer, Michael Frank 2011-04-25T16:06:56Z 2011-04-25T16:06:56Z 10000-01-01 1993 "In this thesis I investigate some statistical mechanical models that have nonequilibrium features either because of: external time-dependent fields; forces not satisfying detailed balance; nonpotential forces. A large part of this thesis is devoted to the detailed study of the coarse-grained Ising model coupled with a time-dependent magnetic field. The model is the timedependent Ginzburg-Landau equation (i.e., Model A) with an oscillating magnetic field; the mean-field approximation neglects noise and gradient terms. I numerically solve for the time-averaged magnetization, and study the phase boundary as a function of field and temperature. A previous work utilizing an equilibrium scheme (Glauber Dynamics) is argued to be insufficient; it predicts a discontinuous change in the order parameter (for low temperature), whereas my result (which has no equilibrium assumptions) predicts a continuous change. There are very few detailed studies of the role of fluctuations in nonequilibrium systems, especially those with time-dependent fields. One of the most interesting effects of fluctuations occurs near a continuous phase transition, where thermodynamic variables scale with nontrivial exponents. To pursue this, the problem is formulated in a field-theoretic manner, and is investigated in an analogous way. It is found that the oscillating field does not change the (ultraviolet) divergences that appeared without the field. However, it does have the more physical effect of altering the longdistance, long-time behavior of thermodynamic functions such as the susceptibility. On approaching the continuous phase transition line, it is predicted that there will be an anomalously large dissipation. This result is found from a (doubly) resummed perturbation expansion; the corrections to scaling exponents in this expression are also found. Equilibrium systems satisfy identities relating the response and correlation functions, known as fluctuation dissipation theorems (FDTs) of the first kind. In (some) derivations of these identities, use is made of time-reversal symmetry and detailed balance, and so it is expected these identities will break down for nonequilibrium systems. Also, it is known that a field-theoretic formulation of the stochastic models (in ""superspace"") reveals symmetries that lead to sets of Ward-Takahashi identities (WTis); in equilibrium models one of these is the FDT. From this, WTis were found that consisted of the usual FDT, plus a contribution that broke the previously mentioned symmetry. Since they are nonperturbative, they represent a potentially valuable clue to unraveling the mysteries of nonequilibrium statistical mechanics." Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-04-25T16:06:56Z No. of bitstreams: 1 1993_zimmer.pdf: 3112388 bytes, checksum: 5e8e256260deac2615cf5b50d0d4d049 (MD5) Made available in DSpace on 2011-04-25T16:06:56Z (GMT). No. of bitstreams: 1 1993_zimmer.pdf: 3112388 bytes, checksum: 5e8e256260deac2615cf5b50d0d4d049 (MD5) Previous issue date: 1993 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-04-25T16:06:56Z Item is restricted indefinitely. 1993 Michael Frank Zimmer statistical dynamics nonequilibrium systems xternal time-dependent fields nonpotential forces oarse-grained Ising model Statistical dynamics of some nonequilibrium systems Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.