Geometric model for motion of curves specified by acceleration Research Proposal

Geometric model for motion of curves specified by acceleration - Research Proposal Example The intention of this study a geometric model generally that deals with the kinematics of a one dimensional manifold in a higher dimensional space. The model is specified by acceleration fields which are local or global functions of the intrinsic quantities of the manifold. This research intends to examine the evolution of one dimensional manifold embedded in the Euclidean space as it evolves under a stochastic flow of diffeomorphisms. Within the manifold, motion depends on the intrinsic invariants immersed in the space. During the course of this research, we will obtain the system of differential equations that governs the motion of the curve, keeping in mind that the processes driving the stochastic flows are chosen to be the most common class of Gaussian processes with stationary increments in time, which is the family of fractional Brownian motions with Hurst parameter. A family of random mappings is called a stochastic (Brownian) flow and is formulated as follows: â€Å"É ¸st, 0 ÍŸ É ¸st, for each s ÍŸ É ¸ut Í ¦ É ¸su = É ¸st, for all s ÍŸ É ¸tt is the identity map on Rn for all t. É ¸s1t1, É ¸s2t2, †¦, É ¸sntn are independent if s1 ÍŸ Using some applications to give geometric meanings to each solution to the governing system of (Partial Differential Equations) PDE,s corresponding to the model length and local time investigated, this profile will also demonstrate how the geometric problem can be transformed to a fully nonlinear parabolic system of equations for the curvature, the position, and orientation. This research will also examine the primary curvature properties developed during the evolution of curves. Another facet of the study will explore the evolution of derive time equations using the Frenet frame. Further derive time equations will be determined regarding the intrinsic quantities satisfied by curves. The investigation will also propose a model using the solution of the evolution equation for the curvature and torsion and the Fundamental theorem for space curves to

5 Page Personal Administrative Project to be done in APA format Essay

5 Page Personal Administrative Project to be done in APA format - Essay Example cy of a university handles the administration of the university and is not that hands on regarding academic matters, the Academic Dean is directly involved in the decision-making and the management of the specific college he or she is assigned to. â€Å"Drawn from the senior faculty ranks, academic deans are seen by many as serving a dual role, that of scholar and administrator† (DiFronzo, 2002). In this sense, the Academic Dean is the symbol of true academic leadership and responsibility. Hence, the Academic Dean is one of the most sought after positions in the university. However true this is, the fact still remains that the Academic Deanship is a position that is riddled with challenges and difficulties as higher education continues to evolve and universities try to keep up with the changing times. On top of this, the Academic Dean is also expected to possess personality traits that are deemed to be necessary in becoming a good and effective academic leader that everyone will respect, â€Å"ranging from a sense of humor to stamina and good listening skills† (Ferren and Stanton, 2004, pp. 1-2). This underlines the importance of the Academic Deanship in the ever-changing world of higher education (DiFronzo, 2002). For this reason, the role of the Academic Dean must be clearly defined through the establishment of the dean’s key responsibilities; for only in knowing completely what the Academic Deanship entails can one become an effective academic leader. The responsibilities of an academic dean are many and complex, with each set varying with every university. In fact, Dean Herbert Hawkes of Columbia College has been quoted in saying that â€Å"there is no such thing as a standardized dean. There is a dean of this and that college, but I have never seen any two deans who could exchange places and retain the same duties† (Gould, 1964, p. 9 as cited in DiFronzo, 2002). This must be remembered in laying down the key responsibilities of the Academic Dean as one duty