Department Seminars & Colloquia
When you're logged in, you can subscribe seminars via e-mail
| 일시: 2009. 5. 27(수), 오후 4:30 장소 : 산업경영동 3층 세미나실 연사:Dr. Sarah L. Mitchell (MACSI, University of Limerick, Ireland) 제목:Improving the accuracy of heat balance integral methods (HBIMs) applied to thermal and Stefan problems 요약:This talk concerns the study of conventional and refined heat balance integral methods applied to a variety of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We give an overview of the development of this method, originally used for analysing boundary layers. Although this method has made the greatest impact on Stefan problems, where very few exact solutions exist, we begin by considering standard thermal problems to highlight the original method and to explain how we have significantly improved the accuracy of these approximate solutions. The method involves choosing an approximating function for the temperature, which is usually a polynomial. The most contentious aspect of the HBIM is the choice of power of the highest order term. Our work has developed a method where the exponent is determined during the solution process, and it produces significantly better results than all previous models. We also show that an extra improvement can be made by including a logarithmic term in the approximating function. Finally, we show how this method can be applied to more practical problems including the 1D melting of a finite thickness layer, solidification from an incoming fluid, removal of mass from an object by vaporization (known as ablation), determining travelling wave solutions to the Korteweg-de Vries equation, unsteady contact melting and boundary layer flow of a power law fluid over a flat plate. |
E6-1, ROOM 1409
Discrete Math
Maria Chudnovsky (Columbia University, New York)
Discrete Math Seminar (Maria Chudnovsky, Columbia Univ.,2PM)
E6-1, ROOM 1409
Discrete Math
***** KAIST Discete Math Semianr *****
DATE: May 21, *Thursday*
TIME: *2PM-3PM*
PLACE: E6-1, ROOM 1409
SPEAKER: Maria Chudnovsky, Columbia University, New York
TITLE: Packing seaguls in graphs with no stable set of size three
http://mathsci.kaist.ac.kr/~sangil/seminar/entry/20090521/
Hadwiger’s conjecture is a well known open problem in graph theory. It states that every graph with chromatic number k, contains a certain structure, called a “clique minor” of size k. An interesting special case of the conjecture, that is still wide open, is when the graph G does not contain three pairwise non-adjacent vertices. In this case, it should be true that G contains a clique minor of size t where t=\lceil |V(G)|/2 \rceil. This remains open, but Jonah Blasiak proved it in the subcase when |V(G)| is even and the vertex set of G is the union of three cliques. Here we prove a strengthening of Blasiak’s result: that the conjecture holds if some clique in G contains at least |V(G)|/4 vertices.
This is a consequence of a result about packing “seagulls”. A seagull in G is an induced three-vertex path. It is not known in general how to decide in polynomial time whether a graph contains k pairwise disjoint seagulls; but we answer this for graphs with no stable sets of size three.
This is joint work with Paul Seymour.