Skip to main content

Jia Zhao

Profile Picture

Mathematics & Statistics

Assistant Professor

Contact Information

Office Location: ANSC 216
DialPhone: 435-797-1953

Educational Background

PhD, Applied and Computational Mathematics, (Mathematical Biology), University of South Carolina, 2015
Modeling and Computations of Cellular Dynamics Using Complex-fluid Models
BS, Information and Computational Mathematics, Nankai University, 2010


Dr. Zhao is an applied and computational mathematician with a keen interest in interdisciplinary research, aiming to strike a balance among mathematical modeling, numerical analysis, and high-performance computations. His research is highly interdisciplinary, residing at the interface between applied mathematics, scientific computing, soft matter physics, and mathematical biology. His current research projects include numerical analysis of thermodynamically consistent hydrodynamic models, modeling and computation of multiphase complex fluids and complex biological systems (biofilms, cell motility, and liquid-liquid phase separation in intracellular dynamics). Dr. Zhao's research has been supported by the National Science Foundation (NSF), Dean's Dissertation Fellowship, SPARC Research Grant, ASPIRE-II Research Grant at USC, and AMS-Simons Travel Award from the Simons Foundation.

Teaching Interests

Numerical PDEs; Fluid Dynamics; Mathematical Biology; Parallel Computing; Machine Learning; Data Science

Research Interests

Computational Mathematics and Mathematical Biology; Numerical PDEs and High-performance Computing; Modeling and Computation/Simulations of Complex Fluids, Cellular Dynamics, and Complex Biological Systems.


NVIDIA GPU Grant, 2018

NVIDIA Coorporation

NSF Grant DMS-1816783, PI, 2018

National Science Foundation

Research Catalyst (RC) Grant, 2018

Office of Research and Graduate Studies, USU

AMS-Simons Travel Award, 2016

AMS & Simons Foundation

Dean's Dissertation Fellowship, 2014

University of South Carolina

Publications - Abstracts

    Publications - Books & Book Chapters

      Book Chapters

    • Zhao, J., Zhang, T., Wang, Q., (2017). Modeling and simulation of bacterial biofilm treatment with applications to food science: Nanotechnology in Agriculture and Food Science. Wiley *

    * Has not been peer reviewed

    Publications - Fact Sheets

      * Has not been peer reviewed

      Publications - Curriculum

        * Has not been peer reviewed

        Publications - Journal Articles

          Academic Journal

        • Yang, X., Zhao, J., (2019). Efficient linear schemes for the nonlocal Cahn-Hilliard equation of phase field models. Computer Physics Communications, 235, 234--245.
        • Yang, X., Zhao, J., (2019). On linear and unconditionally energy stable algorithms for variable mobility Cahn-Hilliard type equation with logarithmic Flory-Huggins potential. Communications in Computational Physics, 25, 703--728.
        • Zhao, J., Chen, L., Wang, H., (2019). On power law scaling dynamics for time-fractional phase field models during coarsening. Communications in Nonlinear Science and Numerical Simulation, 70, 257--270.
        • Gasior, K., Zhao, J., McLaughlin, G., Forest, G., Gladfelter, A.S, Newby, J., (2019). Partial demixing of RNA-protein complexes leads to intra-droplet patterning in phase-separated biological condensates.
        • Chen, L., Zhao, J., Gong, Y., A Novel Second-order Scheme for the Molecular Beam Epitaxy Model with Slope Selection. Communications in Computational Physics, doi: 10.4208/cicp.OA-2018-0015
        • Chen, L., Zhao, J., Cao, W., Wang, H., Zhang, J., (2018). An accurate and efficient algorithm for the time-fractional molecular beam epitaxy model with slope selection. arXiv preprint arXiv:1803.01963
        • Gong, Y., Zhao, J., Yang, X., Wang, Q., (2018). Fully Discrete Second-Order Linear Schemes for Hydrodynamic Phase Field Models of Binary Viscous Fluid Flows with Variable Densities. SIAM Journal on Scientific Computing, 40:1, B128-B167.
        • Gong, Y., Zhao, J., Wang, Q., (2018). 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, 1573--1600.
        • Yang, X., Zhao, J., He, X., (2018). Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation. Journal of Computational and Applied Mathematics, 343, 80--97.
        • Yang, X., Gong, Y., Li, J., Zhao, J., Wang, Q., (2018). On hydrodynamic phase field models for binary fluid mixtures. Theoretical and Computational Fluid Dynamics, 32:5, 537--560.
        • Chen, L., Zhao, J., Yang, X., (2018). Regularized linear schemes for the molecular beam epitaxy model with slope selection. Applied Numerical Mathematics, 128, 139-156.
        • Gong, Y., Zhao, J., Wang, Q., (2018). 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, B528-B553.
        • Liu, H., Cheng, A., Wang, H., Zhao, J., (2018). Time-fractional Allen--Cahn and Cahn--Hilliard phase-field models and their numerical investigation. Computers \& Mathematics with Applications, 76:8, 1876--1892.
        • Zhao, J., Yang, X., Gong, Y., Wang, Q., (2017). 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, 803–825.
        • Gong, Y., Zhao, J., Wang, Q., (2017). An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities. Computer Physics Communications, 219, 20–34.
        • Zhao, J., Li, H., Wang, Q., Yang, X., (2017). Decoupled energy stable schemes for a phase field model of three-phase incompressible viscous fluid flow. Journal of Scientific Computing, 70:3, 1367–1389.
        • Zhao, J., Wang, Q., Yang, X., (2017). Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach. International Journal for Numerical Methods in Engineering, 110:3, 279–300.
        • Yang, X., Zhao, J., Wang, Q., (2017). Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method. Journal of Computational Physics, 333, 104–127.
        • Yang, X., Zhao, J., Wang, Q., Shen, J., (2017). Numerical approximations of a three components Cahn-Hilliard phase-field model based on invariant energy quadratization method. Mathematical Model and Methods in Applied Sciences, In press
        • Zhao, J., Wang, Q., (2017). Three-dimensional numerical simulations of biofilm dynamics with quorum sensing in a flow cell. Bulltin of Mathematical Biology, 79:4, 884–919.
        • Zhao, J., Seeluangsawat, P., Wang, Q., (2016). Modeling antimicrobial tolerance and treatment of heterogeneous biofilms. Mathematical biosciences282, 1-25.
        • Zhao, J., Wang, Q., (2016). A 3D Multi-Phase Hydrodynamic Model for Cytokinesis of Eukaryotic Cells. Communications in Computational Physics, 19:03, 663–681.
        • Zhao, J., Shen, Y., Haapasalo, M., Wang, Z., Wang, Q., (2016). A 3D numerical study of antimicrobial persistence in heterogeneous multi-species biofilms. Journal of Theoretical Biology, 292, 83-98.
        • Zhao, J., Yang, X., Shen, J., Wang, Q., (2016). 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, 539–556.
        • Zhao, J., Yang, X., Li, J., Wang, Q., (2016). Energy stable numerical schemes for a hydrodynamic model of nematic liquid crystals. SIAM Journal on Scientific Computing, 38:5, A3264–A3290.
        • Shen, Y., Zhao, J., De La Fuente-Nunez, C., Wang, Z., Hancock, R.E, Roberts, C.R, Ma, J., Li, J., Haapasalo, M., Wang, Q., (2016). Experimental and theoretical investigation of multispecies oral biofilm resistance to chlorhexidine treatment. Scientific reports, 6, 27537.
        • Zhao, J., Wang, Q., (2016). Modeling cytokinesis of eukaryotic cells driven by the actomyosin contractile ring. International Journal for Numerical Methods in Biomedical Engineering, 32:12, e02774.
        • Kapustina, M., Tsygankov, D., Zhao, J., Wessler, T., Yang, X., Chen, A., Roach, N., Elston, T.C, Wang, Q., Jacobson, K., Forest, G., (2016). Modeling the Excess Cell Surface Stored in a Complex Morphology of Bleb-Like Protrusions. PLoS Computational Biology, 12:3, e1004841.
        • Zhao, J., Wang, Q., Yang, X., (2016). Numerical approximations to a new phase field model for two phase flows of complex fluids. Computer Methods in Applied Mechanics and Engineering, 310, 77–97.
        • Zhao, J., Wang, Q., (2016). Semi-Discrete Energy-Stable Schemes for a Tensor-Based Hydrodynamic Model of Nematic Liquid Crystal Flows. Journal of Scientific Computing, 68:3, 1241–1266.

        * Has not been peer reviewed

        Publications - Literary Journal

          * Has not been peer reviewed

          Publications - MultiMedia

            * Has not been peer reviewed

            Publications - Technical Reports

              * Has not been peer reviewed

              Publications - Translations & Transcripts

                Publications - Other

                  * Has not been peer reviewed

                  Scheduled Teaching

                  2270 - Linear Algebera, Spring 2018