Multi-scale Phenomena in Complex Fluids: Modeling, Analysis by Thomas Y. Hou, Chun Liu, Jian-guo Liu

By Thomas Y. Hou, Chun Liu, Jian-guo Liu

Multi-Scale Phenomena in advanced Fluids is a suite of lecture notes brought throughout the first sequence of mini-courses from Shanghai summer season institution on research and Numerics in sleek Sciences , which used to be held in 2004 and 2006 at Fudan collage, Shanghai, China.

This assessment quantity of five chapters, masking quite a few fields in advanced fluids, areas emphasis on multi-scale modeling, analyses and simulations. will probably be of specific curiosity to researchers and graduate scholars who are looking to paintings within the box of advanced fluids.

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Additional info for Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations (Series in Contemporary Applied Mathematics)

Example text

2 shows the eigenvalue distribution of the matrix M with the setting (N,L,U,(3,t) = (4 x 4,8,0,1,1). In this case, the order of the matrix M is N L = 4 x 4 x 8 = 128. 2 can be used to interpret the distribution. It has a ring structure, centered at (1,0). On every ring there are L = 8 circles. Alternatively, we can also view that the eigenvalues are distributed on L = 8 rays, originated from the point (1,0). The eigenvalues Kij of the matrix K only have 5 different values. There are total 40 circles, which indicate the multiplicity of some eigenvalues.

1, the condition number of M(L) is given by ",(M(L») = Therefore, for large {3, 2. U M(L) = 0 and k < Land Lk = 1 + 4t(3 e . 1 + e- 4t (3 is extremely ill-conditioned. t is an integer. 2. It is anticipated that the bound is still true when Ljk is not an integer. 8 shows condition numbers of M(k) with respect to the reduction factor k when U = O. The computational and estimated condition numbers fit well. 3. 23). 9 shows the condition numbers of sample matrices M(k) (solid lines) for U = 4 and U = 6.

Otherwise, we will have the so-called "sign problem" . al [15] proposed a hybrid method to move x by combining Monte Carlo and molecular dynamics and derived a so-called Hybrid Quantum Monte Carlo (HMQC) method. In the HQMC, an additional auxiliary momentum field P = {pe,i} is introduced. £,iPL+V(x,q,,,)] = (C2)NL7r_3~L j[bXbPb

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