Self-avoiding random walks on multifractal lattices

A renormalisation theory is developed to study the critical behaviour of self-avoiding random walks on multifractals. Critical exponents and connectivity constants are calculated for walks on a class of square multifractal lattices using a finite lattice renormalisation. The effect of the multifractal disorder is considered for both annealed and quenched disorder.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48818/2/jav22i8p1101.pd

Rectangular renormalization

A generalized real-space renormalization scheme is developed for geometrical critical phenomena. The renormalization group is parametrized by the standard length-scaling factor and a new rectangular area-fraction factor. This rectangular renormalization scheme utilizes relatively small rectangular sublattices to effectively renormalize large square lattices. With the area-fraction factor, one can systematically study rectangular generalizations of the conventional square-cell renormalization theories. Application to self-avoiding random walks yields critical descriptors that are comparable to, and in most cases better than previous results obtained from more complex renormalization schemes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48832/2/ja951904.pd

Industry/University Collaboration at the University of Michigan-Dearborn: A Focus on Relevant Technology

https://deepblue.lib.umich.edu/bitstream/2027.42/154106/1/kampfner1998.pd

A weak estimate of the fractal dimension of the Mandelbrot boundary

A technique to compute fractal dimension as defined by the Kolmogorov capacity is discussed. The method is used to compute fractal dimension for several standard curves and the boundary of the Mandelbrot set. This estimate of fractal dimension, although very rough, refutes Milnor's conjecture that the Hausdorff dimension of the Mandelbrot boundary is 2.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27964/1/0000395.pd