Event(s) on June 2010

• Friday, 11th June, 2010

  Title:	Numerical simulations of two-dimensional dry foam by the immersed boundary method
  Speaker:	Prof. Lai Ming-Chih, Department of Applied Mathematics, National Chiao Tung University, Taiwan
  Time/Place:	11:00  -  12:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	In this talk, we present an immersed boundary (IB) method to simulate a dry foam, i.e., a foam in which most of the volume is attributed to its gas phase. Dry foam dynamics involves the interaction between a gas and a collection of thin liquid-film internal boundaries that partition the gas into discrete cells or bubbles. The liquid film boundaries are flexible, contract under the influence of surface tension, and are permeable to the gas, which moves across them by diffusion at a rate proportional to the local pressure difference across the boundary. Such problems are conventionally studied by assuming that the pressure is uniform within each bubble. Here, we introduce instead an IB method that takes into account the non-equilibrium fluid mechanics of the gas. To model gas diffusion across the internal liquid-film boundaries, we allow normal slip between the boundary and the gas at a velocity proportional to the (normal) force generated by the boundary surface tension. We implement this method in the two-dimensional case, and test it by verifying the von-Neumann relation, which governs the coarsening of a two-dimensional dry foam. The method is further validated by a convergence study, which confirms its first-order accuracy.

  
  

• Wednesday, 23rd June, 2010

  Title:	Methods and Techniques in the Study of Graph Energy
  Speaker:	Prof. Shao Jia-yu, Department of Mathematics, Tongji University, China
  Time/Place:	11:30  -  12:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
  Abstract:	The energy of a graph is defined to be the sum of the absolute velues of the eigenvalues of the graph. The study of graph energy was originated in theoretical chemistry where the (molecular) graph was used to study the orbital energy levels and the totalπ-energy of the molecule. Now graph energy has become a new research branch of graph theory with many researches and rich results. Various methods and techniques in different branches of mathematics are used to study graph energy, such as algebraic methods, combinatorial methods, analytical methods, as well as the graph theoretical methods. We will mainly introduce some classical methods and some new techniques appeared in the recent research of graph energy, including the classical “quasi-ordering method”, the recent method of combinatorial design (which can be used to find the graphs with maximal energy), the method of singular values of matrices, and also the method of direct comparison.