Publication Date


Advisor(s) - Committee Chair

Claus Ernst (Director), Uta Ziegler, Melanie Autin

Degree Program

Department of Mathematics

Degree Type

Master of Science


In this thesis, we study the expected mean of the torsion angle of an n-step
equilateral random walk in 3D. We consider the random walk is generated within a confining sphere or without a confining sphere: given three consecutive vectors e1 , e2 , and e3 of the random walk then the vectors e1 and e2 define a plane and the vectors e2 and e3 define a second plane. The angle between the two planes is called the torsion angle of the three vectors. Algorithms are described to generate random walks which are used in a particular space (both without and with confinement). The torsion angle is expressed as a function of six variables for a random walk in both cases: without confinement and with confinement, respectively. Then we find the probability density functions of these six variables of a random walk and demonstrate an explicit integral expression for the expected mean torsion value. Finally, we conclude that the expected torsion angle obtained by the integral agrees with the numerical average torsion obtained by a simulation of random walks with confinement.


Genetics and Genomics | Mathematics | Probability