Browsing by Author "Mulugeta, Yigezu"

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    The Dynamics of a Brownian Particle in a Hookean type Potential and its Effective Diffusion Coefficient in a Ratchet Potential
    (Addis Ababa University, 2007-07) Mulugeta, Yigezu; Bekele, Mulugeta (PhD)
    In the ¯rst part of this work, we use the one dimensional random walk model to simulate the tracings, the autocorrelation function and the Gaussian distribution of the positions of a Brownian particle (a bead of radius Rbead = 240 nm) tethered by a DNA tether of persistence length, lp = 45 nm, whose other end is anchored to a microscope slid. And in the second part, we derive the e®ective di®usion coe±cient analytically and numerically for the one dimensional motion of the Brownian particle in a region where there is a periodic (ratchet) potential pro¯le of period L. To derive the e®ective di®usion coe±cient analytically, we use the known ¯rst passage time (FPT) method. For the simulation part, we use the one dimensional random walk model as in the ¯rst part of our work. The e®ective di®usion coe±cient of the bead obtained both analytically and numerically vanishes at large potential barrier height. However, at the low barrier limit the analytical solution takes the value 2 3D0 ( D0 is the free thermal di®usion of the bead), while the numerical solution takes the expected value, D0. Understanding these physical situations is a practical necessity in many experimental contexts, for instance in single biomolecules