(1)
蔡東和 教授
Dong-Ho Tsai, 2:30-3:15 pm
Some New Results for Plane Curves
Expansion
Abstract:
We show that for
embedded or convex plane curves expansion, the
difference u(x,t)-r(t) in
support functions between the expanding curves rt
(with support function u(x,t)) and some
expanding circles Ct (with support
function r(t)) has its anymptotic shape as
t→∞.
Moreover the isoperimetric difference L2
-4�TA
is de-creasing and it converges to a constant б＞0
if the expansion speed is asymptotically a constant and
the initial curve is not a circle. For convex initial
curves, if the ex-pansion speed is asymptotically
infinite, them L2 -4�TA
decrease to б=0 and there exists an asymptotic center of
expansion for rt.
(2)
王偉成 教授
Wei-Cheng Wang, 3:30-4:15 pm
Energy and Helicity Preserving Schemes for Hydro-and
Manetohydro-dynamics flows
with symmetry
Abstract:
We introduce a family of efficient and robust numerical
schemes devised for incompressible flows and MHD
equation that admit a coordinate symmetry, such as the
rotational symmetry.
The conservation of energy and helicity is achieved by
recasting all the nonlinear terms (including the
convection term, the Lorentz force and the electromotive
force) into Jacobians. The conservation of energy and
helicity then becomes transparent by employing the
permutation identities associated with the Jacobians.
This permutation identity is preserved in the discrete
setting by our proposed scheme. In addition, the
conservation property also holds in the vicinity of the
axis of rotation, which is sometimes referred to as a
geometric or pole singularity. The same permutation
identity also gives a priori error estimates of our
scheme. To our knowledge, this is the first rigorous
error estimate of finite difference schemes for
axisymmetric flows in the presence of the pole
singularity.