My
research anchors in the field of applied and computational mathematics
involving modeling and computation in a wide range of applications, ranging
from soft matter (complex fluids) and complex biological systems to geophysical,
life, and materials science. Recently, we have invested heavily in data science
ad machine learning, especially, their applications in geophysical and life
science. The digital twin is one of the applications in life science. My group
has also been conducting research on developing efficient and stable numerical
methods for the partial differential equations arising from modeling complex
systems.
My
research focuses on developing state-of-the-art mathematical and computational
models, analysis as well as cutting-edge simulation tools to study the
properties of governing systems of partial differential equations to gain a deeper
understanding of the fascinating phenomena they describe. My research has been
partially supported by grants from various state and federal funding agencies
in the past 30 years.
Current
Projects:
1. Numerical
methods for thermodynamically consistent partial differential equations
2. Fluid
Dynamics and rheology of complex fluids, especially, flows of active liquid
crystals, liquid crystals, phase transition, yield-stress fluids, pattern
formation, and defect dynamics of liquid crystalline polymers.
3. Non-equilibrium
thermodynamics theories for multiphase complex fluids and flows.
4. Modeling
and computation of ion transport in microscale channels.
5. Modeling
and computation of complex biological systems, complex biofluids (biofilms,
biogels, liquid-liquid phase separation), and cellular dynamics (cell motility,
migration, and fusion).
6. Application
of data science and machine learning in materials and life science
7. Digital
twin for health
Research
Laboratory: Computational Science and Mathematical Modeling Laboratory is located in the Sumwalt building on campus (SUM
103).
Computational Facilities: Our
research is supported by a state-of-the-art midrange hybrid HPC node in the
Hyperion hyper-performance compute cluster maintained by the university
Research Computing Institute, which is equipped with state-of-the-art Tesla
GPUs. Cuda, C, C++, Fortran, Open ACC compiler are available together with a
plethora of software packages ranging from FLUENT, POLYFLOW, COMSOL, GAUSSIAN,
Q-CHME, C^2FD (Computational Complex Fluid Dynamics, an in-house software
package developed by my group) etc.
Recent Publications (last 5 years, 2018--):
1.Xiaobo
Jing and Qi Wang, Thermodynamically Consistent Dynamical Boundary Conditions of
Phase Field Models, Communications in Mathematical Sciences, 2022.
2.
Lu Guanyu, Liu Wenqiang, HAO Huiqing, Wang Qi, and HAO Yonghong. Application of
the combined LSTM-GRU model to hydrological simulations. Journal of Hydrology
(Chinese), 2022.
3. Maosheng Jiang, Jia Zhao and Qi
Wang. Linear Energy Stable Numerical Schemes for a General Chemo-Repulsive
Model. Journal of Computational and Applied Mathematics, 2022.
4. Huiqing Hao; Yonghong Hao; Yan Liu; Yan Jim Yeh; Ming
Zhang; Qi Wang; Yonghui Fan. Anomaly of glacier mass balance in different
vertical zones and responses to climate modes: Urumqi Glacier No. 1, China Climate
Dynamics Climate Dynamics, 2022.
6. Xiehui Song, HuiqingHao, Wenqiang
Liu, Qi Wang, Lixing An, Tian-Chyi Jim Yeh, Yonghong Hao. Spatial-temporal
behavior of precipitation driving karst spring discharge in a mountain terrain.
Journal of Hydrology 612 (2022), 128116.
8. Shehani T. Wetthasinghe, Chunyan Li, Huina Lin, Tianyu Zhu, Chuanbing
Tang, Vitaly Rassolov, Qi Wang, Sophya Garashchuk. Investigating stability of substituted
cobaltocenium using deep neural networ Correlation between the Stability of Substituted Cobaltocenium and
Molecular Descriptorsks. Journal
of Physical Chemistry A, 126(1) (2022), 80-87.
9. Hong-Fei Deng, Ming-Wei Sun,Yu Wang, Jun Zeng, Ting
Yuan, Ting Li, Di-Huan Li, Wei Chen, Ping Zhou, Qi Wang, Hua Jiang. Evaluating Machine Learning Moldes for Sepsis
Prediction: A Systematic Review of Methodologies, iScience, in press, 2022.
10. Xiaowen Shen
and Qi Wang. Thermodynamically Consistent Models for Diblock Copolymer Systems
Coupled with an Electric Field. Chinese Phys. B, 31(4), 2022.
11. Lin Lu, Qi Wang, Yongzhong Song and
Yushun Wang, Local structure-preserving algorithms for phase field models of
graphene growth. Journal of Scientific Computing, 90(1) ( 2022).
12. Xin Guo, Xu-sheng Wang, Jun Li,
Tongke Wang, Zhixue Zhao, Huiqing Hao, Hongbin Zhan, Qi Wang, Yonghong Hao. An
approximate analytical solution of depth to water table driven by periodical
precipitation and evapotranspiration in shallow groundwater zones. Advances in
Water Resources, 155 (2021), 104012.
13. Qi Hong, Yuezheng Gong, Jia Zhao and
Qi Wang, Arbitrarily High Order Structure-Preserving Algorithms for the Allen-Cahn
Model with a Nonlocal Constraint. Applied Numerical Mathematics, Volume 170, December
2021, 321-339.
14. Yakun Li, Wenkai Yu, Jia Zhao, and
Qi Wang. Second Order Decoupled Energy Dissipation Rate Preserving Schemes for
an extended Cahn-Hilliard-Darcy Model. Journal of Computational Physics, Volume 444, 1
November 2021, 110561.
15. Wenkai Yu, Jia Zhao, Yakun Li and
Qi Wang. Second-Order Linear Thermodynamically Consistent Approximations to the
Nonlocal Allen-Cahn-Brinkman Model. Computer Methods in Applied Mechanics and
Engineering, Volume 386, 1 December 2021.
16. Xiaowen Shen and Qi Wang, Thermodynamically
Consistent Numerical Algorithms for Models of Diblock Copolymer Solutions with
Variable Mobility, Journal of Computational and Applied Mathematics, Volume 395, 15
October 2021, 113573.
17. Xiaowen Shen and Qi Wang, Thermodynamically
Consistent Algorithms for Models of Block Copolymer Solutions Interacting with
Electric and Magnetic Fields, Journal of Scientific Computing, 88, 43
(2021).
18. Yuezheng Gong, Qi Hong and Qi Wang,
Supplementary Variable Method for Thermodynamically Consistent Partial
Differential Equations. Computer Methods in Applied Mechanics and Engineering, 2021,
381, 113746.
19. Di Wang, Yongyong Cai and Qi Wang, Central
Vortex Steady States and Dynamics of Bose-Einstein Condensates Interacting with
Magnetic Fields. Physica D, Volume 419, May
2021, 132852.
20. Lin Lu, Qi Wang, Yongzhong Song,
Yushun Wang, Local structure-preserving algorithms for the molecular beam epitaxy
model with slope selection. Discrete and Continuous Dynamical System-B, September 2021, 26(9): 4745-4765. doi: 10.3934/dcdsb.2020311
21. Qi Hong, Jia Zhao and Qi Wang, Structure-preserving
Numerical Approximations to Network Generating Partial Differential Equation
Models, Computers and Mathematics with
Applications, 81 (2021), 148-165.
22. Qi Hong, Jun Li and Qi Wang, Supplementary
Variable Method for Structure-Preserving Approximations to Partial Differential
Equations with Deduced Equations. Applied Mathematics Letter, 110 ( 2020),
106576.
23. Cheng Lei, Yu Wang, Jia Zhao, Kexun
Li, Hua Jiang and Qi Wang. A Patient-Specific Predictive Model for Human
Albumin Based on Deep Neural Networks. Computer Methods and Programs in
Biomedicine, 196 (2020), 105555.
24.Shouwen Sun, Jun Li, Jia Zhao, and
Qi Wang, Structure-Preserving Numerical Approximations to Thermodynamically Consistent
Non-isothermal Models of Binary Viscous Fluid Flows. Journal of Scientific Computing, 83 (2020), 50.
25. Yuezheng Gong, Jia Zhao and Qi
Wang. Arbitrarily high-order linear unconditionally energy stable schemes for
gradient ow models. Journal of Computational
Physics, 419 (2020), 109610.
26. Yuezheng Gong, Jia Zhao, Qi Wang, Arbitrarily
high-order unconditionally energy stable SAV schemes for gradient flow models. Computer Physics Communications, 249 (2020),
107033.
27. Xueping Zhao, Tiezheng Qian and Qi
Wang, Thermodynamically Consistent Hydrodynamic Models of Multi-component Fluid
Flows, Communications in Mathematical
Sciences, Vol. 18, No. 5 (2020), 1441-1468.
28. Xiaobo Jing and Qi Wang, Linear Second-Order
Energy Stable Schemes of Phase Field Models with Nonlocal Constraints for
Crystal Growth. Computers &
Mathematics with Applications, 79(3) (2020), 764-788.
29. Yuezheng Gong and Qi Wang and Jia
Zhao. Arbitrarily High-Order Unconditionally Energy Stable Schemes for
Thermodynamically Consistent Gradient Flow Models. Siam Journal on Scientific Computing. 42(1) (2020), B135-B156.
30. Yucan Zhao, Jun Li, Jia Zhao and Qi
Wang, A Linear Energy and Entropy-production-rate Preserving Scheme for
Thermodynamically Consistent Crystal Growth Models. Applied Mathematics Letters, 98, (2019), pp. 142-147.
31. Xueping Zhao and Qi Wang. A Second-Order
Fully-discrete Linear Unconditionally Energy Stable Numerical Scheme for Phase
Field Models of Binary Compressible Fluid Flows. Journal of Computational Physics, 395 (2019), 382-409.
32.Xiaobo Jing, Jun Li, Xueping Zhao
and Qi Wang. Second Order Linear Energy Stable Schemes for Allen-Cahn Equations
with Nonlocal Constraints. Journal of
Scientific Computing, 80 (1) (2019), 500-537.
33.Jun Li, Jia Zhao and Qi Wang. Structure
Preserving Numerical Approximations of Thermodynamically Consistent Crystal
Growth Models. Journal of Computational
Physics, 382 (2019), pp. 202-220.
34. Xiaobo Jing, Xiangya Huang,
Markus Haapasalo, Ya Shen and Qi Wang,
Modeling Oral Multispecies Biofilm Recovery after Antibacterial Treatment, Scientific Reports. 9 (2019), pp. 804.
35. Shouwen Sun, Xiaobo Jing and Qi
Wang, Error Estimates of Energy Stable Numerical Schemes for Allen-Cahn
Equations with Nonlocal Constraints. Journal
of Scientific Computing, Volume 79(1) (2019), pp 593-623.
36. Xiaogang Yang, Jun Li, Yuezheng
Gong, Robert S. Eisenberg, Qi Wang, Quasi-compressible Ionic Fluid Models, Journal of Molecular Liquids, 273
(2019), pp. 677-691.
37. Yuezheng gong, Jia Zhao, and Qi
Wang, Second Order Fully-Discrete Energy Stable Methods on Staggered Grids for
Hydrodynamic Phase Field Models of Binary Viscous Fluids, Siam Journal on Scientific Computing, 40:2, (2018),
pp. B528-B553.
38. Jia Zhao, Xiaofeng Yang, Yuezheng
Gong, Xueping Zhao, Jun Li, Xiaogang Yang and Qi Wang, A General Strategy for
Numerical Approximations of Thermodynamically Consistent Nonequilibrium
Models--Part I: Thermodynamical Systems, International
Journal of Numerical Analysis and Modeling, 15(16) (2018), pp 884-918.
39.Xiaogang Yang, Yuezheng Gong, Jun
Li, Jia Zhao, and Qi Wang, Comparison of Hydrodynamic Phase Field Models for
Binary Fluid Mixtures, Theoretical and
Computational Fluid Dynamics, 32(5) (2018), pp 537-560.
40. Yuezheng Gong, Jia Zhao, and Qi
Wang, Linear Second Order in Time Energy Stable Schemes for Hydrodynamic Models
of Binary Mixtures Based on a Spatially Pseudospectral Approximation，advances
in Computational Mathematics, 44 (5) (2018), pp.1573-1600.
41.Yuezheng Gong, Jia Zhao, Xiaogang
Yang and Qi Wang, Second-order Linear Schemes for Hydrodynamic Phase Field
Models of Binary Viscous Fluids with Variable Densities, Siam Journal on Scientific Computing, 40-1
(2018), pp. B138-B167.