Seminar
KCL - A mathematical model to describe evolution of curves and surfaces
Monday, December 15, 2014 2:15 PM;
JGU Mainz, Mathematics, Room 05-426
Speaker: Phoolan Prasad; Indian Institute of Science, Bangalore
In a large number of physical phenomena, we find propagating surfaces which need mathematical
treatment. d-D kinematical conservation laws (KCL) are equations of evolution of a moving surface
Ωt in d-dimensional (x1 , x2 , . . . , xd )-space Rd . The KCL are derived in a specially defined ray
coordinates (ξ1 , ξ2 , . . . , ξd−1 , t), where ξ1 , ξ2 , . . . , ξd−1 are surface coordinates on Ωt and t is time.
KCL are the most general equations in conservation form, governing the evolution of Ωt with
physically realistic singularities. A very special type of singularity is a kink, which is a point on
Ωt when Ωt is a curve in R2 and is a curve on Ωt when it is a surface in R3 . Across a kink the
normal n to Ωt and normal velocity m on Ωt are discontinuous. Since the KCL system contains
only kinematical relations, it is an under-determined system of equations. In order to complete the
system, we need to find additional equations representing the dynamics of Ωt from the governing
equations of the medium in which Ωt propagates. The mathematical analysis of 3-D KCL system
and computation with its help present a challenge since the eigenspace is not complete and there
are geometric solenoidal constrains. We present a few examples of Ωt and numerical results.
Calendar
Contact
- Scientific Coordinator of the TRR 146
- Dr. Giovanni Settanni
- Staudingerweg 9
- D-55128 Mainz
- trr146E@CmVaoMYEzruni-mainz.de