arXiv subjects
Publications and source records attributed to Christian Muenkel.
We discuss an elementary problem in electrostatics: What does the charge distribution look like for a free charge on a strictly one-dimensional wire of finite length? To the best of our knowledge this question has so far not been discussed anywhere. One notices that a solution of this problem is not as simple as it might appear at first sight.
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and compared to the results of percolation theory. We also describe the dependence of the typical cluster structures on the reaction rate.