# 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
Ω

_{t}in d-dimensional (x_{1}, x_{2}, . . . , x_{d})-space R^{d}. The KCL are derived in a specially defined ray coordinates (ξ_{1}, ξ_{2}, . . . , ξ_{d−1}, t), where ξ_{1}, ξ_{2}, . . . , ξ_{d−1}are surface coordinates on Ω_{t}and t is time. KCL are the most general equations in conservation form, governing the evolution of Ω_{t}with physically realistic singularities. A very special type of singularity is a kink, which is a point on Ω_{t}when Ω_{t}is a curve in R^{2}and is a curve on Ω_{t}when it is a surface in R^{3}. Across a kink the normal**n**to Ω_{t}and normal velocity*m*on Ω_{t}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 Ω_{t}from the governing equations of the medium in which Ω_{t}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 Ω_{t}and numerical results.## Calendar

## Contact

- Scientific Coordinator of the TRR 146
- Dr. Giovanni Settanni
- Staudingerweg 9
- D-55128 Mainz
- trr146rvoPHI@xPcm_tlcOOuni-mainz.de