Research Activities

1. Data science combined with dynamical systems
2. Data-driven stochastic dynamics
3. Stochastic dynamical systems & stochastic partial differential equations
4. Numerical methods for nonlocal PDEs, computational fluid dynamics, computational materials science, computational acoustics, boundary elements method
5. Numerical methods for non-equilibrium systems, interfacial instabilities, morphologies, pattern formation, crystal growth and nanostructure patterning in thin films
6. Computational & stochastic modeling for geophysical systems and biophysical systems
7. Nonlinear dynamical systems and applications
8. Data assimilation and predicting dynamical behaviors

Research Funding

1. NSF/CBMS Regional Conference in the Mathematical Sciences (Supported by NSF) Nonlocal Dynamics: Theory, Computation and Applications, Jinqiao Duan & Xiaofan Li, 2016--2020
2. NSF NSF-DMS 1620449 "Theoretical and Numerical Studies of Nonlocal Equations Derived from Stochastic Differential Equations with Levy Noises". Xiaofan Li & Jinqiao Duan, 2016--2019.

Lab Seminars

1. Stochastic & Multiscale Modeling and Computation Seminar

Publications

1. An Introduction to Stochastic Dynamics, Cambridge University Press, 2015.
2. Effective Dynamics of Stochastic Partial Differential Equations (with Wei Wang), Elsevier, 2014.
3. Nonlocal PDEs & Non-Gaussian Stochastic Dynamics Institute for Pure and Applied Mathematics,
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Visiting Professors

1. Professor Ludiwg Arnold, Bremen University, Germany
2. Professor Bjorn Schmalfuss, Jena University, Germany
3. Professor Wei Yan, Henan Normal University, China
4. Professor Hongjun Gao, Nanjing Normal University, China

Graduate Students

1. Zhuan Cheng, PHD candidate, Illinois Institute of Technology, Email: zcheng9@hawk.iit.edu
2. Hansen Ha, PhD candidate, Illinois Institute of Technology, Email: hha3@hawk.iit.edu
3. Senbao Jiang, PhD candidate, Illinois Institute of Technology

Postdocs

Meetings

• SIAM Conference on Applications of Dynamical Systems , May 2021, Portland, Oregon
• NSF-CBMS conference on Nonlocal Dynamics: Theory, Computation and Applications (Supported by NSF),Chicago , June 4--9, 2017
• SIAM Conference on Applications of Dynamical Systems , May 2019, Snowbird, Utah
• The 5th International Conference on Random Dynamical Systems --- Celebrating Ludwig Arnold's 80th birthday, June 2017, Wuhan, China
• AMS Fall Central Section meeting, Chicago, October 3-4, 2015. Special Session: "Nonlocal Diffusions and Non-Gaussian Stochastic Dynamics"
• NSF-CBMS Regional Conference on Recent Advances in the Numerical Approximation of Stochastic Partial Differential Equations, August 9-13, 2010, Chicago, USA
• AMS Fall West Section meeting, April 9--10, 2016, Univ of Utah, USA

Book Series and Journals

• Book Series: "Interdisciplinary Mathematical Sciences"
• Journal: "Stochastics and Dynamics"

Computing Resources

• PCs and Sun Workstations are available in this Laboratory and in other university computer laboratories
• Beowulf Linux Cluster "Menger" is a computer cluster consisting of one master node and eight slave nodes. Each node is equipped with dual 1.7 GHz Pentium 4 Xeon processors and 2GB RDRAM. All nodes are connected to each other via fast ehternet switch.