My
research expertise lies within the expansive realm of applied and computational
mathematics, delving into the intricacies of modeling and computation across a
diverse spectrum of applications. These applications span from exploring soft
matter, such as complex fluids and biological systems, to investigations in
geophysical, life, and materials sciences. In recent years, our focus has
significantly expanded to encompass the burgeoning fields of data science and
machine learning, specifically within geophysical and life science domains.
Notably, our work includes pioneering applications of digital twin technology
within life science realms.
Within
my research group, a primary endeavor involves the ongoing exploration and
refinement of highly efficient and stable numerical methods tailored for complex
systems characterized by partial differential equations. This pursuit is
directed toward the development of state-of-the-art mathematical models,
computational analyses, and cutting-edge simulation tools. The overarching aim
is to unravel the fundamental properties governing these differential
equations, thereby unraveling the captivating phenomena they describe.
Over
the past three decades, my research endeavors have received partial support
from diverse state and federal funding agencies. Presently, the focal points of
our current projects include:
1.
Advancements in Numerical Methods:
Addressing over-determined partial differential equation systems.
2.
Fluid Dynamics and Rheology of Complex
Fluids: Specifically investigating active liquid
crystal flows, phase transitions, yield-stress fluids, pattern formation, and
defect dynamics within liquid crystalline polymers.
3.
Non-equilibrium Thermodynamic Theories:
Applied to hybrid materials, multiphase complex fluids, and various flow
scenarios.
4.
Modeling Ion Transport:
Focused on microscale channels.
5.
Exploration of Complex Biological Systems:
Studying complex biofluids, cellular dynamics, and related phenomena such as
biofilms, biogels, and liquid-liquid phase separation.
6.
Data Science and Machine Learning
Applications: Especially relevant to materials and life
science.
7.
Human Digital Twins: A
distinctive application within the field.
These
current projects encapsulate the diverse and cutting-edge research pursued
within my group, emphasizing both theoretical and practical implications across
various scientific disciplines
Research
Laboratory: The Computational Science and Mathematical Modeling Laboratory is located in Sumwalt 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, and 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--Present):
1. Wickramasinghe,
Sachith; Hoehn, Alexandria; Wetthasinghe, Shehani; Lin, Huina; Wang, Qi;
Jakowski, Jacek; Rassolov, Vitaly; Tang, Chuanbing; Garashchuk, Sophya. Theoretical
examination of the hydroxide transport in cobaltocenium-containing
polyelectrolytes. The Journal of Physical Chemistry. In press, 2023.
2.Lin, Huina; Ramos,
Luis; Hwang, JiHyeon; Zhu, Tianyu; Hossain, Md Waliullah; Wang, Qi; Garashchuk,
Sophya; Tang, Chuanbing. Main-Chain Cobaltocenium-Containing Ionomers for
Alkaline Anion-Exchange Membranes. Macromolecules, 2023, 56 (16), 6375-6384.
3. Zhifang Liu, Baocheng
Sun, Xue-Cheng Tai, Qi Wang, and Huibin Chang. A Fast Minimization Algorithm
for the Euler-Elastic Model Based on a Bilinear Decomposition. Siam J Sci Comp.
2023.
4. Qi Hong, Qi Wang, and
Yuzheng Gong. Efficient High-Order Supplementary Variable Methods for
Thermodynamically Consistent Partial Differential Equations. CMAME, 2023.
5. Meirou Sun, Yunhan
Wang, Han-yang Yue, Jianguo Hou, Jun Li, Qiyu Wu, Hua Jiang, and Qi Wang. Dynamical
Monitoring and Causal Inference for Respiratory Metabolic Indicators of Septic
Patients. Precision Nutrition. 2(3): p e00042, September 2023. DOI:
10.1097/PN9.0000000000000042.
6.Jingwei Sun, Jun Li,
Yonghong Hao, Chunmei Ma, Huazhi Sun, Negash Begashaw, Gurcan Comet, Yi Sun,
and Qi Wang. Approximation of the Boundary-to-Solution Operator for the
Groundwater Transport Equation in a Toth Basin. Advances in Water Resources, in
press, 2023.
7.Kaiyan Wang, Jun Li,
Wenke Wang, Zaiyong Zhang, Xusheng Wang, Qi Wang, and Yonghong Hao. Calibrating
a model of depth to water table using Fourier series and Simpson numerical
integration. Journal of Hydrology, 620 (2023), 129516.
8.Yu Wang, Charles Damien
Lu, Wei Chen, Qi Wang, Hua Jiang. Digital Twin-Enabled Personalized Nutrition.
Precision Nutrition, 2(1), March, 2023, e00030.
9.Yakun Li and Qi Wang,
Quasi-incompressible Models for Binary Fluid Flow in Porous Media. Applied
Mathematics Letters, 136, Feb 2023. https://doi.org/10.1016/j.aml.2022.108450.
10.Xiaobo Jing and Qi
Wang, Thermodynamically Consistent Dynamical Boundary Conditions of Phase Field
Models. Communications in Mathematical Sciences. 21 (3), 859-883. 2023. DOI:
https://dx.doi.org/10.4310/CMS.2023.v21.n3.a10.
11.Eric
Stahlberg, Mohamed Abdel-Rahman, Boris Aguilar, Alireza Asadpoure, Robert A.
Beckman, Lynn Borkon, Colleen Cebulla, Young Hwan Chang, Ansu Chatterjee, Jun
Deng, Sepidah Dolatshahi, Olivier Gevaert, Emily Greenspan, Wenrui Hao, Tina
Hernandez-Boussard, Pamela Jackson, Marieke Kuijjer, Adrian Lee, Paul Macklin,
Subha Madhavan, Matthew D. McCoy, Navid Mohammad Mirzaei, Talayeh Razzaghi,
Heber Rocha, Leili Shahriyari, Ilya Shmulevich, Daniel G. Stover, Yi Sun,
Tanveer Syeda-Mahmood, Qi Wang, Jinhua Wang, Ioannis Zervantonakis. Exploring
Approaches for Predictive Cancer Patient Digital Twins: Opportunities for
Collaboration and Innovation. Frontiers in Digital Health, 06 October, 2022. https://doi.org/10.3389/fdgth.2022.1007784.
12.Xiaobo
Jing and Qi Wang, Coupling of Bulk and Surface Dynamics in Thermodynamically
Consistent Models. Entropy, 2022, 24 (11), 1683.
https://doi.org/10.3390/e24111683.
13.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), in press, 2022.
14.Maosheng Jiang, Jia Zhao, and Qi Wang. Linear Energy Stable
Numerical Schemes for a General Chemo-Repulsive Model. Journal of Computational
and Applied Mathematics, 415: 114436 (2022).
15.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 models: Urumqi Glacier No. 1, China
Climate Dynamics Climate Dynamics. May 2022, 60(3), 493-509. DOI:
10.1007/s00382-022-06318-w.
16.Jianguo Hou, Jun Deng, Chunyan Li, and Qi
Wang. Tracing and Forecasting Metabolic Indices of Cancer Patients Using
Patient-Specific Deep Learning Models. Journal of Personalized Medicine, 12
(2022), 742.
17.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.
18.Chunyan Li, Shehani T.
Wetthasinghe, Huina Lin, Tianyu Zhu, Chuanbing Tang, Vitaly Rassolov, Qi Wang,
Sophya Garashchuk. Stability analysis of substituted cobaltocenium
[bis(cyclopentadienyl)cobalt(III)] employing
chemistry-informed neural networks. Journal of Chemical Theory and Computation,
April 11, 2022, https://doi.org/10.1021/acs.jctc.1c01201.
19.Shehani T.
Wetthasinghe, Chunyan Li, Huina Lin, Tianyu Zhu, Chuanbing Tang, Vitaly
Rassolov, Qi Wang, Sophya Garashchuk. Investigating the stability of substituted
cobaltocenium using deep neural network: Correlation between the Stability of
Substituted Cobaltocenium and Molecular Descriptors. Journal of Physical
Chemistry A, 126(1) (2022), 80-87.
20.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
Models for Sepsis Prediction: A Systematic Review of Methodologies, iScience,
2022, 25, 103651. https://doi.org/10.1016/j.isci.2021.103651
21.Xiaowen Shen and Qi
Wang. Thermodynamically Consistent Models for Diblock Copolymer Systems Coupled
with an Electric Field. Chinese Phys. B, 31(4), 2022.
22.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).
23.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.
24.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.
25.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.
26.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.
27.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.
28.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).
29.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.
30.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.
31.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
32.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.
33.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.
34.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.
35.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.
36.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.
37.Yuezheng Gong, Jia Zhao, Qi Wang, Arbitrarily
high-order unconditionally energy stable SAV schemes for gradient flow models. Computer Physics Communications, 249
(2020), 107033.
38.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.
39.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.
40.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.
41.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.
42.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.
43.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.
44.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.
45.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.
46.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), 593-623.
47.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.
48.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.
49.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.
50.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.
51.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.
52.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.