Many cells employ cadherin complexes (c-sites) on the cell membrane to attach to neighboring cells, as well as integrin complexes (i-sites) to attach to a substrate in order to accomplish cell migration. This paper analyzes a model for the motion of a group of cells connected by c-sites. We begin with two cells connected by a single c-site and analyze the resultant motion of the system. We find that the system is irrotational. We present a result for reducing the number of c-sites in a system with c-sites between pairs of cells. This greatly simplifies the general system, and provides an exact solution for the motion of a system of two cells and several c-sites.Then a method for analyzing the general cell system is presented. This method involves 0-row-sum, symmetric matrices. A few results are presented as well as conjectures made that we feel will greatly simplify such analyses. The thesis concludes with the proposal of a framework for analyzing a dynamic cell system in which stochastic processes govern the attachment and detachment of c-sites.

The dropped objects are identified as one of the top ten causes of fatalities and serious injuries in the oil and gas industry. It is of importance to understand dynamics of dropped objects under water in order to accurately predict the motion of dropped objects and protect the underwater structures and facilities from being damaged. In this thesis, we study nondimensionalization of dynamic equations of dropped cylindrical objects. Nondimensionalization helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of dynamics of dropped cylindrical objects under water. The resulting simulations of dimensionless trajectory confirms that drop angle, trailing edge and drag coefficient have the significant effects on dynamics of trajectories and landing location of dropped cylindrical objects under water.