Chicken limb formation
Chicken limb formation

Myxobacteria aggregation

From: C.M. Mizutani, Q. Nie, F. Wan, Y.-T. Zhang, P. Vilmos, R. Sousa-Neves, E. Bier, L. Marsh and A. Lander, Formation of the BMP activity gradient in the Drosophila embryo, Developmental Cell, v8, June (2005), pp. 915-924.


Simulations for BMP morphogen gradient formation in the zebrafish embryo.
From: Y.-T. Zhang, A. Lander and Q. Nie, Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo, submitted to Journal of Theoretical Biology, (2006


From: Y.-T. Zhang, H.-K. Zhao and J. Qian,  High order fast sweeping methods for static Hamilton-Jacobi equations, Journal of Scientific Computing, v29 (2006), pp. 25-56.


From: J. Shi, Y.-T. Zhang, and C.-W. Shu, Resolution of High Order WENO Schemes for Complicated Flow Structures, Journal of Computational Physics, v186 (2003), pp.690-696.


Spike amplitude in the RM instability simulations, as functions of time. The conservative tracked amplitude for a coarse grid is in approximate agreement with the non-conservative tracked amplitude for a fine grid.
From: James Glimm, Xiaolin Li, Yingjie Liu, Zhiliang Xu and Ning Zhao, Conservative Front Tracking with Improved Accuracy, Siam J. of Numerical Analysis, 41, No.5, 2003.


Density and grid plots for the spherical RM simulation at time = 0.3. The left frame shows the density plot from AMR front tracking, and the middle frame shows the density plot from uniform grid front tracking. The right frame shows the AMR grid plots.
From: James Glimm Xiaolin Li and Zhiliang Xu,Front Tracking Algorithm Using Adaptively Refined Meshes. Proceedings of the 2003 Chicago Workshop on Adaptive Mesh Refinement Methods, Adaptive Mesh Refinement - Theory and Applications, the Lecture Notes in Computational Science and Engineering, ISSN: 1439-7358


Plot of jet interface at late time with different bubble spacings
From: Zhiliang Xu, M. Kim, T.S. Lu and etc, al, Discrete Bubble Modeling of Unsteady Cavitating Flow, International J. forMultiscale Computational Engineering, accepted for publication (2006).