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Title:  DIFFUSION IN RANDOM MEDIA 
Authors:  SOLOMON, NEGASH ASFAW 
Advisors:  Dr. TATEK YERGOU 
Keywords:  physics 
Copyright:  Jun2010 
Date Added:  10May2012 
Publisher:  AAU 
Abstract:  In this work we present Monte Carlo simulations of particle and polymer diffusion in two
dimensional (2D) media with obstacles distributed randomly. For diffusion of a particle,
the meansquare displacement of the diffusing species is proportional to time for normal
diffusion. But in disordered systems anomalous diffusion may occur, in which the mean
square displacement is proportional to some other power of time. In the presence of
moderate concentration of obstacles, diffusion is anomalous for short times and normal
for long times. Monte Carlo calculations are used to characterize anomalous diffusion
for obstacle concentrations between zero and the percolation threshold. As the obstacle
concentration approaches the percolation threshold, diffusion becomes more anomalous
for long times; the anomalous diffusion exponent increases. In polymer diffusion, we
present a new effective algorithm to simulate dynamic properties of polymeric systems
confined to lattice. The algorithm displays Rouse behavior for all spatial dimensions. The
systems are simulated by bond fluctuation method to study both the static and dynamic
properties of the polymer chains. For static properties we calculated the average mean
2
square endtoend distance R2 (N ) and the meansquare radius of gyration Rg (N ) .
Both the endtoend distance and the radius of gyration are proportional to some power
2
of the number of monomers (N), R2 (N ) ∝ N 3/2 and Rg (N ) ∝ N 3/2 . For dynamical
properties we look at the meansquare displacement of the total chain. For short times
the meansquare displacement of the monomers g1 (t) and the meansquare displacement
of the monomers relative to the chains center of mass g2 (t) show the same behavior and
for long times the meansquare displacement of the center of mass g3 (t) takes over. 
URI:  http://hdl.handle.net/123456789/2942 
Appears in:  Thesis  Physics

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