My
research has been on modeling and computation of soft matter and complex fluids
with applications to complex fluid flows, complex biological systems, materials
science and life science. Soft matter and complex fluids are ubiquitous in
nature and in synthesized materials. Modeling and simulation of complex fluids
has been listed as one of the 21st century mathematical challenges by DARPA. My
group has also been conducting research on developing efficient and stable
numerical methods for the partial differential equations arisen from modeling
the complex systems.

My
research focuses on developing the state-of-the-art mathematical and
computational models, analysis as well as cutting-edge simulation tools to
study the properties of the soft matter and complex fluids to gain deeper
understanding of the fascinating phenomena. 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, pattern formation and defect
dynamics of liquid crystalline polymers.

3. Non-equilibrium
thermodynamics theories and analyses for polymer blends, multiphase complex
fluids and flows.

4. Multiscale
theory, kinetic theory and continuum theory for flows of complex fluids and
soft matter.

5. Modeling
and computation of ion transport in microscale channels.

6. Modeling
and computation of complex biological systems, complex biofluids
(biofilms, biogels, liquid-liquid phase separation),
and cellular dynamics (cell motility, migration, and fusion).

7. Application
of data science and machine learning in materials and life science

**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):**

1.Xiaowen Shen and Qi Wang, Thermodynamically
Consistent Algorithms for Models of Block Copolymer Solutions Interacting with
Electric and Magnetic Fields, Journal of Scientific Computing, 2020.

2.Di Wang, Yongyong
Cai and Qi Wang, Central Vortex Steady States and
Dynamics of Bose-Einstein Condensates Interacting with Magnetic Fields. Physica D, in press, 2020.

3.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, in press, 2020.

4.Qi Hong, Jia
Zhao and Qi Wang, Structure-preserving Numerical Approximations to Network
Generating Partial Differential Equation Models, *Computers and Mathematics with Applications*, in press, 2020.

5.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.

6.Cheng Lei, Yu Wang, Jia Zhao, Kexun Li, Hua Jiang and
Qi Wang. A Patient Specific Predicative Model for Human Albumin Based on Deep
Neural Networks. Computer Methods and Programs in Biomedicine, 196 (2020),
105555.

7.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.

8.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.

9.Yuezheng Gong, Jia
Zhao, Qi Wang, Arbitrarily high-order unconditionally energy stable SAV schemes
for gradient flow models. *Computer
Physics Communications*, 249 (2020), 107033.

10.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.

11.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.

12.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.

13.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.

14.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.

15.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.

16.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.

17.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.

18.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.

19.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.

20.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.

21.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.

22.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.

23.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，a*dvances
in Computational Mathematics*, 44 (5) (2018), pp.1573-1600.

24.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.

25.Jia Zhao and Qi Wang, 3-D Numerical
Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell, *Bulletin of Mathematical Biology*, 79(4)
(2017), pp. 884-919.

26.Yi Sun and Qi Wang, In-Silico Analysis on 3D Biofabrication
using Kinetic Monte Carlo Simulations, Advances
in Tissue Engineering and Regenerative Medicine**, **2(5) (2017), pp. 00045.

27.E. A. Bulanova,
E. V. Koudan, J. Degosserie,
C. Heymans, F. D. Pereira, V. A. Parfenov, Yi Sun, Qi
Wang, S. A. Akhmedova , N. S. Sergeeva, G. A. Frank, Y.
D. Khesuani, C. E. Pierreux,
V. A. Mironov. Bioprinting of functional vascularized mouse thyroid
gland construct, *Biofabrication*,
2017, 9(3), 034105.

28.Yuezheng Gong, Jia
Zhao, and Qi Wang, An Energy Stable Algorithm for the Quasi-incompressible
Hydrodynamic Model of Viscous Fluid Mixtures, *Computer Physics Communications*, 219 (2017), pp. 20-34.

29.Xiaofeng Yang, Jia
Zhao, and Qi Wang, Linear and Unconditionally Energy Stable Schemes for
Molecular Beam Epitaxial Growth Model Based on Invariant Energy Quadratization Methods, *Journal
of Computational Physics*, 333
(2017), pp.* *104-127.

30.Jia Zhao, Xiaofeng
Yang, Yuezheng Gong, and Qi Wang, A Novel Linear
Second Order Unconditionally Energy-stable Scheme for a Hydrodynamic Q-tensor
Model of Liquid Crystals, *Computer
Methods in Applied Mechanics and Engineering, *318 (2017), pp. 803-825.

31.Xiaogang Yang and Qi Wang, Structures and
basic patterns in cavity flows of active liquid crystals. *Computers and Fluids*, 155 (2017), pp. 33-49.

32.Xiaofeng Yang, Jia
Zhao, Qi Wang, Jie Shen, Numerical Approximations for
a three-component Cahn-Hilliard phase-field Model based on the Invariant Energy
Quadratization method, *Mathematical Models and Methods in Applied Sciences*, 27(11) (2017),
pp. 1993-2030.

33.Yuezheng Gong, Qi Wang, and Zhu Wang,
Structure-Preserving Galerkin POD Reduced-Order
Modeling of Hamiltonian Systems, *Computer
Methods in Applied Mechanics and Engineering*, 315 (2017), pp. 780-798.

34.Xiaofeng Yang, Jia
Zhao, and Qi Wang, Numerical Approximations for a phase field dendritic Growth
Model Based on the Invariant Energy Quadratization
Approach, *International journal for
Numerical Methods in Engineering*, 110(3) (2017), pp. 279-300.

35.Jia Zhao, Huiyuan
Li, Qi Wang, and Xiaofeng Yang, A Linearly Decoupled
Energy Stable Scheme for Phase Field Models of Three-phase Incompressible
Viscous Fluid Flows, *Journal of
Scientific Computing, *70(3) (2017), 1367-1389*.*

36.Jia Zhao, Tianyu
Zhang, and Qi Wang, Treatment of Biofilms by Nanotechnology and Applications to
Food Science, NANOTECHNOLOGY IN AGRICULTURE AND FOOD SCIENCES, edited by,
Monique A. V. Axelos and Marcel Van de Voorde,
Wiley-VCH, 2017.

37.Yuezheng Gong, Qi Wang, Yushun
Wang, Jiaxiang Cai, A
conservative Fourier pseudospectral method for the
nonlinear Schrodinger equation, *Journal
of Computational Physics*, 328 (2017), pp. 354-370.

38.Yuezheng Gong, Xinfeng
Liu, and Qi Wang, Fully Discretized Energy Stable Schemes for Hydrodynamic
Models of Two-phase Viscous Fluid Flows, *Journal
of Scientific Computing,* 69(3) (2016), 921-945.

39.Norazaliza mohd
Jamil and Qi Wang, CFD-PBE Modelling and Simulation of Enzymatic Hydrolysis of
Cellulose in a Stirred Tank, *Journal of
Mathematics and Statistics*, 12(4) (2016), pp. 225-237.

40.Jia Zhao, Qi Wang, and Xiaofeng Yang, Numerical Approximations to a New Phase
Field Model for Immiscible Mixtures of Nematic Liquid
Crystals and Viscous Fluids, *Computer
Methods in Applied Mechanics and Engineering*, 310 (2016), pp. 77-97.

41.Jia Zhao, P. Seeluangsawat , and Qi Wang,
A hydrodynamic model for biofilms accounting for persisters
and susceptibles, *Mathematics
of Biosciences*, 282 (2016), pp. 1-15.

42.Xiaogang Yang and Qi Wang, Role of Active
Viscosity and Self-propelling Speed on Channel Flows
of Active Polar Liquid Crystals, *Soft
Matter*, 12 (2016), pp. 1262 - 1278.

43.Jia Zhao, Ya
Shen, Markus Haapasalo, Zhejun
Wang, and Qi Wang, A 3D Numerical Study of Antimicrobial Persistence in
Heterogeneous Multi-species Biofilms, *Journal of Theoretical Biology*, 392
(2016), pp. 83-98.

44.Jia Zhao and Qi Wang, Semi-Discrete
Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows, *Journal of Scientific Computing,* 68(3) (2016), pp. 1241-1266.

45.Jia Zhao and Qi Wang, A 3D Hydrodynamic
Model for Cytokinesis of Eukaryotic Cells, *Communication
in Computational Physics*, 19(3) (2016), pp. 663-681.

46.Jia Zhao and Qi Wang, Modeling and
Simulations of Cytokinesis of Eukaryotic Cells, *International Journal for Numerical Methods in Biomedical Engineering*,
32 (12) (2016), pp. e2774.

47.Xiaogang Yang, Jun Li, M. G. Forest, and Qi
Wang, Hydrodynamic Theories for Flows of Active Liquid Crystals and the
Generalized Onsager Principle, *Entropy*,
18 (2016), pp. 202.

48.Kapustina, M., Tsygankov,
J., Zhao, J., Yang, X., Chen, A., Roach, N., Wessler,
T., Elston, T.C., Wang, Q., Jacobson, K., Forest, G.,
Modeling the excess cell surface stored in a complex morphology of bleb-like
protrusions. *PLOS Computational Biology*,
12(3) (2016), pp. e1004841.

49.Jia Zhao, Xiaofeng
Yang, Jun Li and Qi Wang, Energy stable numerical schemes for a hydrodynamic
model of nematic liquid crystals, *Siam J. Sci. Comp.,* 38(5) (2016), pp. 3264-3290.

50.Ya Shen, Jia
Zhao, Cesar de la Fuente-Nunez, Zhejun Wang, Robert
E. W. Hancock, Clive R. Roberts, Jingzhi Ma, Jun Li,
Markus Haapasalo and Qi Wang, Development and
Experimental Validation of a Model for Oral Multispecies Biofilm Recovery after
Chlorhexidine Treatment, *Scientific
Reports*, 6 (2016), pp. 27537.

51.Noraza liza Mohd Jamil and Qi Wang, One-Dimensional Simulation of
Diffusion and Advection Effects in Enzymatic Hydrolysis of Cellulose, *American Journal of Applied Sciences.*
13(7) (2016), pp. 870-876.

52.Jia Zhao, Xiaofeng
Yang, Jie Shen, Qi Wang, A Decoupled Energy Stable
Scheme for a Hydrodynamic Phase-field Model of Mixtures of Nematic
Liquid Crystals and Viscous Fluids, *Journal
of Computational Physics*, 305 (2016), pp. 539-556.