Office: Room 1549W in the Science Building No. 1, Peking University.
北京大学理科1号楼1549W
Tel: 86-10-62757592
Fax: 86-10-62751801
Email: tieli{at} math {dot} pku {dot} edu {dot} cn
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Workshop on Multi-Stoch09, July 4-5, 2009, Beijing
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ICIAM 2011, July 18-22, 2011, Vancouver, Canada
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The Second Brazil-China Conference on Scientific Computing,
, June 27-July 1, Beijing
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KITPC Program on Interdisciplinary Applications of Statistical Physics & Complex Networks
, March 1-April 1, 2011, Beijing
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China-Norway-Sweden workshop on computational mathematics, June 8-10, 2010, Bergen, Norway
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Joint China-Germany Conference on "Mathematics and Industry", Mar. 15-17, 2010, Beijing
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Multiscale Modeling and Simulation in Science, Nov. 16-19, 2009, Stockholm
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Program on Mathematical Theory and Numerical Methods for Computational Materials Simulation
and Design, Aug. 9-21, 2009, Singapore
- Annual meeting of Chinese Math. Soc. 2009 (Invited speaker), Apr 21-24, 2009, Xiamen
- Adaptivity, robustness and complexity of multiscale algorithms, Mar. 30-Apr. 3, 2009, Edinburgh, UK
- Rheology of complex fluids, Jan. 5-9, 2009, Paris, France
- 973 project meeting, Nov. 15-17, 2008, Xiamen
- 973 group meeting, Nov. 8-9, 2008, Shanghai
- Frontiers of CompMath, July 19-22, 2008, Hefei
- FoCM08, June 16-26, 2008, City Univ. of Hong Kong
- 973 project meeting, Nov. 10-11, 2007, Beijing
- The 8th Annual Meeting of CompMath in China (Invited plenary speaker), Oct. 25-29, 2007, Chengdu
- 973 group meeting, Sep. 22-24, 2007, Xiangtan
- Frontiers of CompMath, Aug. 4-5, 2007, Beijing
- ICIAM07, July 16-20, 2007, Zurich, Switzerland
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Chemical Reaction Kinetics: Currently we focus our research on the understanding of the
tau-leaping algorithm and constructing more accurate and stabilized schemes based on solid mathematical analysis. I mainly collaborate with
Assyr Abdulle (EPFL) and my students Yucheng Hu and Bin Min (PKU) in this research field.
- Analysis of explicit tau-leaping schemes for simulating chemically
reacting systems, Multi. Mod. Simul. 6 (2007), 417-436.
- S-ROCK methods for stiff Ito SDEs,
with Assyr Abdulle, Comm. Math. Sci. 6 (2008), 845-868.
- Highly accurate tau-leaping methods for simulating chemically
reacting systems, with Yucheng Hu, J. Chem. Phys 130 ( 2009), 124109.
- The weak convergence analysis of tau-leaping methods: revisited,
with Yucheng Hu and Bin Min, to appear in Comm. Math. Sci., 2009.
- Chebyshev methods with discrete noise: the tau-ROCK methods,
with Assyr Abdulle and Yucheng Hu, J. Comp. Math. 28 (2009), 195-217.
Multiscale modeling of complex fluids: We have done some theoretical analysis for the
multiscale models of complex fluids, such as the wellposedness of the equations, convergence analysis of the BCF method, and HMM methods.
This is an exciting area. I mainly collaborate with Weinan E (Princeton), Eric Vanden-Eijnden (Courant), Hui Zhang (BNU) and Pingwen Zhang (PKU)
in this field.
- Stochastic models of polymeric liquids at small Deborah number
, with Eric Vanden-Eijnden, Pingwen Zhang, and Weinan E, J. Non-Newtonian Fluid Mech.
121 (2004), 117-125.
- Analysis of 1+1 dimensional stochastic models
of liquid crystal polymer flows, with Pingwen Zhang and Xiang Zhou, Comm. Math. Sci. 2 (2004), 295-316.
- Local existence for the dumbbell model of
polymeric fluids, with Hui Zhang and Pingwen Zhang, Comm. PDE, 29 (2004), 903-923.
- Well-posedness for the dumbbell model of polymeric liquids
, with Weinan E and Pingwen Zhang, Comm. Math. Phys. 248 (2004), 409-427.
- Convergence analysis of BCF methods for Hookean dumbbell model
, with Pingwen Zhang, Multi. Model. Simul. 5 (2006), 205-234.
- Mathematical analysis of multiscale models of complex fluids
, with Pingwen Zhang, Comm. Math. Sci. 5 (2007), 1-51.
Statistical data analysis: The data is emerging each second in our time. How to
extract the information from the data? We consider this problem from different interesting backgrounds such as the complex networks,
quantum optics, Netflix problems etc.
- Model reduction of complex networks: Complex networks usually have huge amount
of nodes and edges. How to optimally reduce this type of models to explore its essential behavior? This covers the problems from
Sociology, Biology and dynamical system theory. We try to do this rationally based on Markov chain theory.
- Optimal partition and effective dynamics of complex networks, with Weinan E and Eric Vanden-Eijnden, Proc. Nat. Acad. Sci., 105 (2008), 7907-7912.
SI
- Probabilistic framework for network partition,
with Weinan E and Jian Liu, Phys. Rev. E 80 (2009), 026106.
- A validity index approach to network partition, with Jian Liu, submitted to Phys. A, 2010.
- Other fields:
Miscs: Though diversified, most of them have one central theme: STOCHASTICS.
- Localized basis of eigen-subspaces and operator
compression, with Weinan E and Jianfeng Lu, Proc. Nat. Acad. Sci. 107 (2010), 1273.
- A note on the analysis of heterogeneous rod like chain in DNA
modeling, with Yan Ding, Int. J. Mod. Phys. B, 22 (2008), 2213-2224.
- On the Poisson approximation for photon distribution for
faint lasers, with Yucheng Hu, Xiang Peng and Hong Guo, Phys. Lett. A, 367 (2007), 173-176.
- Effectiveness of implicit methods for stiff stochastic
differential equations, with Assyr Abdulle and Weinan E, Comm. Comp. Phys. 3 (2008), 295-307.
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Last modified: Dec. 6th, 2010.
