Lingyun Ding. Shear dispersion of multispecies electrolyte solutions in the channel domain. Journal of Fluid Mechanics, 970:A27, 2023. doi: https://doi.org/10.1017/jfm.2023.626
I derived a reduced model for transport multispecies electrolytes by fluid flows, taking into account the interactions among flow, diffusion, and electric potential. This model reveals nontrivial phenomena driven by diffusion-induced electric potentials, such as the upstream migration of species and spontaneous ion separation. These findings suggest novel applications in microseparators and mixers, as well as a potential method for measuring concentration ratios using optical measurements. This work was featured in the ’Focus on Fluids’ section of JFM, underscoring its potential significance in the field.
Lingyun Ding. Diffusion-driven flows in a non-linear stratified fluid layer. Journal of Fluid Mechanics, 2024. doi: https://doi.org/10.48550/arXiv.2311.17386
The classical asymptotic method, expanding quantities as power series of parameters, is inadequate for approximating the fluid system addressed in this paper. I introduce a novel asymptotic expansion method based on the system’s slow manifold. This method expands quantities in terms of derivatives of the cross-sectional averaged density field, thereby yielding accurate approximations for the velocity, density, and pressure fields. This innovative approach offers a robust framework for modeling systems characterized by slow manifolds, including natural convection in curved pipes and thin film fluid flow.
Jim Thomas and Lingyun Ding. Upscale transfer of waves in one-dimensional rotating shallow water. Journal of Fluid Mechanics, 961:A2, 2023. doi: https://doi.org/10.1017/jfm.2023.114
We explore the inverse wave cascade in one-dimensional rotating shallow water equations, revealing that waves injected at smaller scales upscale primarily through resonant quartic interactions between modes. This process, marked by intermittent bursts, results in a shallower wave spectrum and amplified wave fields. Our study uncovers complex features in a simple geophysical fluid dynamic model, highlighting previously unrecognized aspects of wave transfer. This work, featured in the ’Focus on Fluids’ section of the Journal of Fluid Mechanics (JFM), underscores its potential significance in the field.
In the publication marked with ∗, authors listed in alphabetical order in accordance with the 2009 American Mathematical Society statement about the Culture of Research and Scholarship in Mathematics.
Lingyun Ding. Long-time asymptotics of passive scalar transport in periodically modulated channels. arXiv preprint arXiv:2504.14733, 2025a Accepted by Journal of Fluid Mechanics
James Teague, Lingyun Ding, and Francesca Bernardi. Adapting taylor dispersion to measure the dispersion coefficient of electrolyte solutions via an accessible microfluidic setup. Journal of Visualized Experiments, 2025. doi: https://doi:10.3791/69040
Lingyun Ding, Sarah Burnett, and Andrea Bertozzi. Equilibrium theory of bidensity particle-laden suspensions in thin-film flow down a spiral separator, Physics of Fluids, 2025 doi: https://arxiv.org/abs/2410.23568
Sirui Zhu, Zhi Lin, Liang Li, and Lingyun Ding. Optimal stirring strategies for passive scalars in a domain with a general shape and no-flux boundary condition. Advances in Applied Mathematics and Mechanics, 2024. doi: https://arxiv.org/abs/2401.05684
Wing Pok Lee, Jonathan D. Woo, Luke F. Triplett, Yifan Gu, Sarah Burnett, Lingyun Ding, and Andrea Bertozzi. A comparative study of dynamic models for gravity-driven particle-laden flows. Applied Mathematics Letters, 2024 in press, https://arxiv.org/abs/2410.23561
Lingyun Ding. Diffusion-driven flows in a non-linear stratified fluid layer. Journal of Fluid Mechanics, 2024. doi: https://doi.org/10.1017/jfm.2024.870 arxiv https://doi.org/10.48550/arXiv.2311.17386
*Russell Arnold, Roberto Camassa, and Lingyun Ding. Hamiltonian shocks. Studies in Applied Mathematics, page e12733, 2024. doi: https://doi.org/10.1111/sapm.12733
*Lingyun Ding and Richard M McLaughlin. Correlation function of a random scalar field evolving with a rapidly fluctuating gaussian process. Journal of Statistical Physics, 190(12):201, 2023a. doi: https://doi.org/10.1007/s10955-023-03191-7
Lingyun Ding. Shear dispersion of multispecies electrolyte solutions in the channel domain. Journal of Fluid Mechanics, 970:A27, 2023. doi: https://doi.org/10.1017/jfm.2023.626
Jared Weed, Lingyun Ding, Jingfang Huang, and Min Hyung Cho. Quadrature by two expansions for evaluating helmholtz layer potentials. Journal of Scientific Computing, 95(3):96, 2023. doi: https://doi.org/10.1007/s10915-023-02222-5
*Lingyun Ding and Richard M. McLaughlin. Dispersion induced by unsteady diffusion-driven flow in a parallel-plate channel. Phys. Rev. Fluids, 8:084501, Aug 2023b. doi:https://doi.org/10.1103/PhysRevFluids.8.084501
Jim Thomas and Lingyun Ding. Upscale transfer of waves in one-dimensional rotating shallow water. Journal of Fluid Mechanics, 961:A2, 2023. doi: https://doi.org/10.1017/jfm.2023.114
Zhi Lin, Sirui Zhu, and Lingyun Ding. Stirring by anisotropic squirming. Theoretical and Applied Mechanics Letters, page 100358, 2022. doi: https://doi.org/10.1016/j.taml.2022.100358
*Lingyun Ding and Richard M McLaughlin. Determinism and invariant measures for diffusing passive scalars advected by unsteady random shear flows. Physical Review Fluids, 7(7):074502, 2022a. doi: https://doi.org/10.1103/PhysRevFluids.7.074502
*Roberto Camassa, Lingyun Ding, Richard M McLaughlin, Robert Overman, Richard Parker, and Ashwin Vaidya. Critical density triplets for the arrestment of a sphere falling in a sharply stratified fluid. Recent Advances in Mechanics and Fluid-Structure Interaction with Applications: The Bong Jae Chung Memorial Volume, page 69, 2022. doi: https://doi.org/10.1007/978-3-031-14324-3
*Lingyun Ding and Richard M McLaughlin. Ergodicity and invariant measures for a diffusing passive scalar advected by a random channel shear flow and the connection between the Kraichnan-Majda model and Taylor-Aris dispersion. Physica D: Nonlinear Phenomena, 432:133118, 2022b. doi: https://doi.org/10.1016/j.physd.2021.133118
*Roberto Camassa, Lingyun Ding, Zeliha Kilic, and Richard M McLaughlin. Persisting asymmetry in the probability distribution function for a random advection–diffusion equation in impermeable channels. Physica D: Nonlinear Phenomena, 425:132930, 2021a. doi: https://doi.org/10.1016/j.physd.2021.132930
*Lingyun Ding, Robert Hunt, Richard M McLaughlin, and Hunter Woodie. Enhanced diffusivity and skewness of a diffusing tracer in the presence of an oscillating wall. Research in theMathematical Sciences, 8(3):1–29, 2021b. doi: https://doi.org/10.1007/s40687-021-00257-4
*Lingyun Ding, Jingfang Huang, Jeremy L Marzuola, and Zhuochao Tang. Quadrature by two expansions: Evaluating laplace layer potentials using complex polynomial and plane wave expansions. Journal of Computational Physics, 428:109963, 2021a. doi: https://doi.org/10.1016/j.jcp.2020.109963
Qinghai Zhang and Lingyun Ding. Lagrangian flux calculation through a fixed planar curve for scalar conservation laws. SIAM Journal on Scientific Computing, 41(6):A3596–A3623, 2019. doi:https://doi.org/10.1137/18M1210885
Lingyun Ding, Shuang Hu, Baiyun Huang, Qinghai Zhang, Lagrangian flux calculation through a time-dependent surface for scalar conservation laws
Lingyun Ding and Terry Wang, Marcus Roper, Thin gap approximations for microfluidic device design
Lingyun Ding. Semi-implicit-explicit runge-kutta method for nonlinear differential equations. arXiv preprint arXiv:2504.09969, 2025b
*Dylan Bruney, Roberto Camassa, Lingyun Ding, Richard McLaughlin, Taylor Dispersion Induced by Stokes Flow in a Straight Channel with Periodically Varying Cross-Section