More information about my papers can be found at my profile on Google Scholar.

Preprints


Variable-order Laplacian and its computations with meshfree methods
Yixuan Wu and Yanzhi Zhang, preprint (2021).

A universal solution scheme for fractional and classical PDEs   (arXiv version)
Yixuan Wu and Yanzhi Zhang, preprint (2021).

Refereed Journal Publications


Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization   (PDF)
Yixuan Wu and Yanzhi Zhang
Discrete and Continuous Dynamical Systems Series S, (2022), to appear.

Pattern selection in the Schnakenberg equations: From normal to anomalous diffusion   (PDF)
Hatim Khudhair, Yanzhi Zhang, and Nobuyuki Fukawa
Numerical Methods for Partial Differential Equations, (2021), 1-18.

Dynamic capability and open-source strategy in the age of digital transformation   (PDF)
Nobuyuki Fukawa, Yanzhi Zhang, and Sunil Erevelles
Journal of Open Innovation: Technology, Market, and Complexity, 7(3) (2021),   175.

Dynamics of plane waves in the fractional nonlinear Schrodinger equation with long-range dispersion   (PDF)
Siwei Duo, Taras I. Lakoba, and Yanzhi Zhang
Symmetry,13(8) (2021),   1394.

A unified meshfree pseudospectral method for solving both classical and fractional PDEs   (PDF)
John Burkardt, Yixuan Wu, and Yanzhi Zhang
SIAM Journal of Scientific Computing, 43 (2021),   pp. A1389-A1411.

Numerical simulations for the energy-supercritical nonlinear wave equation   (PDF)
Jason Murphy and Yanzhi Zhang
Nonlinearity, (2020),   6195.

Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian   (PDF)
Xian-Ming Gu, Hao-Wei Sun, Yanzhi Zhang, and Yong-Liang Zhao
Mathematical Methods in the Applied Sciences, (2020),   pp. 1-23.

Three-dimensional rotation of paramagnetic and ferromagnetic prolate spheroids in simple shear and uniform magnetic field   (PDF)
Christopher A. Sobecki, Yanzhi Zhang, and Cheng Wang
Physics of Fluids, 31 (2019),   102005.
(This paper was selected as Editor's Pick in Physics of Fluids.)

Numerical approximations for the tempered fractional Laplacian: Error analysis and applications   (PDF)
Siwei Duo and Yanzhi Zhang
Journal of Scientific Computing, 81 (2019),   pp. 569-593.

Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications   (PDF)
Siwei Duo and Yanzhi Zhang
Computer Methods in Applied Mechanics and Engineering, 355 (2019),   pp. 639-662.

A comparative study on nonlocal diffusion operators related to the fractional Laplacian   (PDF)
Siwei Duo, Hong Wang, and Yanzhi Zhang
Discrete and Continuous Dynamical Systems B, 24 (2019),   pp. 231-256.

Dynamics of paramagnetic and ferromagnetic ellipsoidal particles in shear flow under a uniform magnetic field   (PDF)
Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, and Cheng Wang
Physical Review Fluids, 3 (2018),   084201.

Numerical investigation of dynamics of elliptical magnetic microparticles in shear flows   (PDF)
Jie Zhang, Christopher A. Sobecki, Yanzhi Zhang, and Cheng Wang
Microfluidics and Nanofluidics, 22 (2018),   83.

A fast algorithm for solving the space–time fractional diffusion equation   (PDF)
Siwei Duo, Lili Ju, and Yanzhi Zhang
Computers & Mathematics with Applications, 446 (2018),   pp. 1230-1254.

A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem   (PDF)
Siwei Duo, Hans Werner van Wyk, and Yanzhi Zhang
Journal of Computational Physics, 355 (2018),   pp. 233-252.

Magnetic control of lateral migration of ellipsoidal microparticles in microscale flows   (PDF)
Ran Zhou, Christopher A. Sobecki, Jie Zhang, Yanzhi Zhang, and Cheng Wang
Physical Review Applied, 8 (2017),   024019.

On the Galerkin approximation for the stochastic reaction-diffusion-advection equation   (PDF)
Li Yang and Yanzhi Zhang
Journal of Mathematical Analysis and Applications, 446 (2017),   pp. 1230-1254.

Mass conservative method for solving the fractional nonlinear Schrödinger equation   (PDF)
Siwei Duo and Yanzhi Zhang
Computers & Mathematics with Applications, 71 (2016),   pp. 2257-2271.

Fractional Schrödinger dynamics and decoherence   (PDF)
Kay Kirkpatrick and Yanzhi Zhang
Physica D: Nonlinear Phenomena, 332 (2016),   pp. 41-54.

Computing the ground and first excited states of fractional Schrodinger equations in an inifinite potential well   (PDF)
Siwei Duo and Yanzhi Zhang
Communications in Computational Physics, 18 (2015),   pp. 321-350.

Profit-sharing between an open-source firm and application developers -- Maximizing profits from applications and in-application advertisements   (PDF)
Nobuyuki Fukawa and Yanzhi Zhang
Industrial Marketing Management, 48 (2015),   pp. 111-120.

An efficient spectral method for computing dynamics of rotating two-component Bose--Einstein condensates via coordinate transformation   (PDF)
Ju Ming, Qinglin Tang, and Yanzhi Zhang
Journal of Computational Physics, 258 (2014),  pp. 538-554.

A simple and efficient numerical method for computing the dynamics of rotating Bose--Einstein condensates via rotating lagrangian coordinates   (PDF)
Weizhu Bao, Daniel Marahrens, Qinglin Tang, and Yanzhi Zhang
SIAM Journal of Scientific Computing, 35 (2013),  pp. A2671-A2675.

Efficient methods for computing ground states of spin-1 Bose--Einstein condensates based on their characterizations   (PDF)
Weizhu Bao, I-Liang Chern and Yanzhi Zhang
Journal of Computational Physics, 253 (2013),   pp. 189-208.

Maximizing critical currents in superconductors by optimization of normal inclusions properties   (PDF)
Yanzhi Zhang, Janet Peterson, and Max Gunzburger
Physica D: Nonlinear Phenomena, 240 (2011),   pp. 1701-1713.

Quadrature-rule type approximations to the quasicontinuum method for long-range interatomic interactions   (PDF)
Yanzhi Zhang and Max Gunzburger
Computer Methods in Applied Mechanics and Engineering, 199 (2010),   pp. 648-659.

A quadrature-rule type approximation to the quasicontinuum method   (PDF)
Max Gunzburger and Yanzhi Zhang
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8 (2010),  pp. 571-590.

Numerical study of vortex interactions in Bose-Einstein condensation   (PDF)
Yanzhi Zhang
Communication in Computational Physics, 8 (2010),   pp. 327-350.

Dynamical laws of the coupled Gross-Pitaevskii qquations for spin-1 Bose-Einstein condensates   (PDF)
Weizhu Bao and Yanzhi Zhang
Methods and Applications of Analysis, 17 (2010),   pp. 49-80.

Efficiently computing vortex lattices in fast rotating Bose-Einstein condensates   (PDF)
Rong Zeng and Yanzhi Zhang
Computer Physics Communication, 180 (2009),   pp. 854-860.

Quantized vortex stability and interaction in the nonlinear wave equation   (PDF)
Weizhu Bao, Rong Zeng, and Yanzhi Zhang
Physica D: Nonlinear Phenomena, 237 (2008),   pp. 2391-2410.

The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schrodinger equation   (PDF)
Yanzhi Zhang, Weizhu Bao, and Qiang Du
SIAM Journal of Applied Mathematics, 67 (2007),   pp. 1740-1775.

Dynamics of vortices in weakly interacting Bose-Einstein condensates   (PDF)
Alexander Klein, Dieter Jaksch, Yanzhi Zhang, and Weizhu Bao
Physics Review A, 76 (2007), 043602.

Dynamics of rotating Two-component Bose-Einstein condensates and its efficient computation   (PDF)
Yanzhi Zhang, Weizhu Bao, and Hailiang Li
Physica D: Nonlinear Phenomena, 234 (2007), pp. 49-69.

Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation   (PDF)
Yanzhi Zhang, Weizhu Bao, and Qiang Du
European Journal of Applied Mathematics, 18 (2007),  pp. 607-630.

Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime   (PDF)
Weizhu Bao, Fong Yin Lim, and Yanzhi Zhang
Bulletin of the Institute of Mathematics, Academia Sinica, 2 (2007),  pp. 495-532.

Dynamics of the center of mass in rotating Bose-Einstein condensates   (PDF)
Yanzhi Zhang and Weizhu Bao
Applied Numerical Mathematics, 57 (2007),  pp. 697-709.

Dynamics of rotating Bose--Einstein condensates and their efficient and accurate numerical computation   (PDF)
Weizhu Bao, Qiang Du, and Yanzhi Zhang
SIAM Journal of Applied Mathematics, 66 (2006),   pp. 758-786.

Dynamics of the Ground state and central vortex states in Bose--Einstein condensation   (PDF)
Weizhu Bao and Yanzhi Zhang
Mathematical Models and Methods in Applied Sciences, 15 (2005), pp. 1863-1896.


Refereed Conference Publications


Uncovering a local trend in consumer eye-tracking data - Application of singular value decomposition in analyzing gaze sequence data
Nobuyuki Fukawa, Yanzhi Zhang, Dave Steward, and John Burkardt
Proceedings of Global Marketing Conference at Tokyo, (2018),   pp. 690.

Open-source strategy to enhance imaginative intensity and profits
Nobuyuki Fukawa, Yanzhi Zhang, and Sunil Erevelles
Proceedings of the Academy of Marketing Science Conference, 38 (2016),   pp. 463.

Understanding B2B relationships between an open-source firm and application developers - Shaing profits from applications and in-application advertisements
Nobuyuki Fukawa and Yanzhi Zhang
Proceedings of the Academy of Marketing Science Conference, Brad Carlson and Todd Donavan (Eds), 37 (2014),   pp. 163.

Approximating the quasicontinuum method using quadrature rules
Yanzhi Zhang and Max Gunzburger
Proceedings of the Fourth International Conference on Multiscale Materials Modeling, (2008),   pp. 57-60.