@article{kim_ji_bertozzi_sadeghpour_ju_2024, title={A positivity-preserving numerical method for a thin liquid film on a vertical cylindrical fiber}, volume={496}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2023.112560}, abstractNote={When a thin liquid film flows down on a vertical fiber, one can observe the complex and captivating interfacial dynamics of an unsteady flow. Such dynamics are applicable in various fluid experiments due to their high surface area-to-volume ratio. Recent studies verified that when the flow undergoes regime transitions, the magnitude of the film thickness changes dramatically, making numerical simulations challenging. In this paper, we present a computationally efficient numerical method that can maintain the positivity of the film thickness as well as conserve the volume of the fluid under the coarse mesh setting. A series of comparisons to laboratory experiments and previously proposed numerical methods supports the validity of our numerical method. We also prove that our method is second-order consistent in space and satisfies the entropy estimate.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Kim, Bohyun and Ji, Hangjie and Bertozzi, Andrea L. and Sadeghpour, Abolfazl and Ju, Y. Sungtaek}, year={2024}, month={Jan} }
 @article{ji_witelski_2024, title={COARSENING OF THIN FILMS WITH WEAK CONDENSATION\ast}, volume={84}, ISSN={["1095-712X"]}, DOI={10.1137/23M1559336}, abstractNote={A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated which provide insights into the coarsening dynamics for large systems. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.}, number={2}, journal={SIAM JOURNAL ON APPLIED MATHEMATICS}, author={Ji, Hangjie and Witelski, Thomas p.}, year={2024}, pages={362–386} }
 @article{li_ji_tang_2024, title={Numerical Methods for Fourth-Order PDEs on Overlapping Grids with Application to Kirchhoff-Love Plates}, volume={98}, ISSN={["1573-7691"]}, DOI={10.1007/s10915-023-02430-z}, number={2}, journal={JOURNAL OF SCIENTIFIC COMPUTING}, author={Li, Longfei and Ji, Hangjie and Tang, Qi}, year={2024}, month={Feb} }
 @article{taranets_ji_chugunova_2024, title={ON WEAK SOLUTIONS OF A CONTROL-VOLUME MODEL FOR LIQUID FILMS FLOWING DOWN A FIBRE}, volume={2}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2024018}, abstractNote={This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial differential equations, which describe the fluid film's radius and axial velocity. We demonstrate the existence of weak solutions to this coupled system by applying a priori estimates derived from energy-entropy functionals. Additionally, we establish the existence of traveling wave solutions for the system. To illustrate our analytical findings, we present numerical studies that showcase the dynamic solutions of the partial differential equations as well as the traveling wave solutions.}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Taranets, Roman m. and Ji, Hangjie and Chugunova, Marina}, year={2024}, month={Feb} }
 @article{biswal_ji_elamvazhuthi_bertozzi_2024, title={Optimal boundary control of a model thin-film fiber coating model}, volume={457}, ISSN={["1872-8022"]}, DOI={10.1016/j.physd.2023.133942}, abstractNote={This paper considers the control of fluid on a solid vertical fiber, where the fiber radius is larger than the film thickness. The fluid dynamics is governed by a fourth-order partial differential equation (PDE) that models this flow regime. Fiber coating is affected by the Rayleigh-Plateau instability that leads to breakup into moving droplets. In this work, we show that control of the film profile can be achieved by dynamically altering the input flux to the fluid system that appears as a boundary condition of the PDE. We use the optimal control methodology to compute the control function. This method entails solving a minimization of a given cost function over a time horizon. We formally derive the optimal control conditions, and numerically verify that subject to the domain length constraint, the thin film equation can be controlled to generate a desired film profile with a single point of actuation. Specifically, we show that the system can be driven to both constant film profiles and traveling waves of certain speeds.}, journal={PHYSICA D-NONLINEAR PHENOMENA}, author={Biswal, Shiba and Ji, Hangjie and Elamvazhuthi, Karthik and Bertozzi, Andrea L.}, year={2024}, month={Jan} }
 @article{yang_hu_ji_lafata_vaios_floyd_yin_wang_2023, title={A neural ordinary differential equation model for visualizing deep neural network behaviors in multi-parametric MRI-based glioma segmentation}, volume={3}, ISSN={["2473-4209"]}, DOI={10.1002/mp.16286}, abstractNote={Abstract}, journal={MEDICAL PHYSICS}, author={Yang, Zhenyu and Hu, Zongsheng and Ji, Hangjie and Lafata, Kyle and Vaios, Eugene and Floyd, Scott and Yin, Fang-Fang and Wang, Chunhao}, year={2023}, month={Mar} }
 @book{ji_witelski_2023, title={Coarsening of thin films with weak condensation}, DOI={10.48550/arXiv.2303.14728}, abstractNote={A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated which provide insights into the coarsening dynamics for large systems. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.}, number={2303.147282303.14728}, author={Ji, H. and Witelski, T.P.}, year={2023} }
 @article{ji_sanaei_2023, title={Mathematical model for filtration and drying in filter membranes}, volume={8}, ISSN={["2469-990X"]}, url={https://doi.org/10.1103/PhysRevFluids.8.064302}, DOI={10.1103/PhysRevFluids.8.064302}, abstractNote={A filter membrane may be frequently used during its lifetime, with filtration and drying processes occurring in the porous medium for several cycles. As a consequence, the filter performance ultimately deteriorates after several cycles. In this work, we develop a mathematical model that provides insights to the overall porous medium evolution over cycles of filtration and drying processes and predicts the timeline to discard the filter based on its optimum performance.}, number={6}, journal={PHYSICAL REVIEW FLUIDS}, author={Ji, Hangjie and Sanaei, Pejman}, year={2023}, month={Jun} }
 @article{ko_ji_ju_2023, title={Prediction of 3D Velocity Field of Reticulated Foams Using Deep Learning for Transport Analysis}, volume={6}, ISSN={["1573-1634"]}, url={https://doi.org/10.1007/s11242-023-01961-1}, DOI={10.1007/s11242-023-01961-1}, abstractNote={Abstract}, journal={TRANSPORT IN POROUS MEDIA}, author={Ko, Danny D. and Ji, Hangjie and Ju, Y. Sungtaek}, year={2023}, month={Jun} }
 @article{ko_ji_ju_2023, title={Prediction of pore-scale flow in heterogeneous porous media from periodic structures using deep learning}, volume={13}, ISSN={2158-3226}, url={http://dx.doi.org/10.1063/5.0147472}, DOI={10.1063/5.0147472}, abstractNote={Data-driven deep learning models are emerging as a promising method for characterizing pore-scale flow through complex porous media while requiring minimal computational power. However, previous models often require extensive computation to simulate flow through synthetic porous media for use as training data. We propose a convolutional neural network trained solely on periodic unit cells to predict pore-scale velocity fields of complex heterogeneous porous media from binary images without the need for further image processing. Our model is trained using a range of simple and complex unit cells that can be obtained analytically or numerically at a low computational cost. Our results show that the model accurately predicts the permeability and pore-scale flow characteristics of synthetic porous media and real reticulated foams. We significantly improve the convergence of numerical simulations by using the predictions from our model as initial guesses. Our approach addresses the limitations of previous models and improves computational efficiency, enabling the rigorous characterization of large batches of complex heterogeneous porous media for a variety of engineering applications.}, number={4}, journal={AIP Advances}, publisher={AIP Publishing}, author={Ko, Danny D. and Ji, Hangjie and Ju, Y. Sungtaek}, year={2023}, month={Apr} }
 @article{chattopadhyay_ji_2023, title={Thermocapillary thin film flows on a slippery substrate with odd viscosity effects}, volume={455}, ISSN={["1872-8022"]}, url={https://doi.org/10.1016/j.physd.2023.133883}, DOI={10.1016/j.physd.2023.133883}, abstractNote={This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.}, journal={Physica D: Nonlinear Phenomena}, publisher={Elsevier BV}, author={Chattopadhyay, S. and Ji, H.}, year={2023}, month={Dec}, pages={133883} }
 @article{chu_ji_wang_kim_bertozzi_2022, title={Electrohydrodynamics modeling of droplet actuation on a solid surface by surfactant-mediated electrodewetting}, volume={8}, ISSN={["2469-990X"]}, url={https://doi.org/10.1103/PhysRevFluids.8.073701}, DOI={10.1103/PhysRevFluids.8.073701}, abstractNote={Developed to address the drawbacks of electro-wetting, electro-dewetting is a digital microfluidic technique that makes a liquid dewet on a substrate using an electric potential. In this paper, we propose an electrohydrodynamic model to describe the dynamic evolution of a charged slender drop under the influence of an external electric field. We introduce lubrication theory to simplify the model and reproduce fundamental microfluidic operations, including dewetting, rewetting, and droplet shifting.}, number={7}, journal={Physical Review Fluids}, author={Chu, W. and Ji, H. and Wang, Q. and Kim, C.-J. and Bertozzi, A.L.}, year={2022}, month={Jul}, pages={073701} }
 @article{hangjie_taranets_chugunova_2022, title={On travelling wave solutions of a model of a liquid film flowing down a fibre}, volume={33}, url={https://doi.org/10.1017/S0956792521000255}, DOI={10.1017/S0956792521000255}, abstractNote={Abstract}, number={5}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={HANGJIE, JI and TARANETS, ROMAN and CHUGUNOVA, MARINA}, year={2022}, month={Oct}, pages={864–893} }
 @book{taranets_ji_chugunova_2022, title={On travelling waves of a control-volume model for liquid films flowing down a fibre}, DOI={10.48550/arXiv.2301.02720}, abstractNote={This paper analytically investigates the solutions to a control-volume model for liquid films flowing down a vertical fibre. The dynamic evolution of the free surface is governed by a coupled degenerate nonlinear PDE system for the fluid film radius and the axial velocity. We prove the existence of weak solutions to the coupled system based on the application of a priori estimates derived for energy-entropy functionals. Existence of travelling wave solutions to the system is also established. Numerical studies are presented to illustrate the derived analytical results for both the dynamic PDE solutions and the travelling wave structures.}, number={2301.027202301.02720}, author={Taranets, R. and Ji, H. and Chugunova, M.}, year={2022} }
 @article{ji_lafata_mowery_brizel_bertozzi_yin_wang_2022, title={Post-Radiotherapy PET Image Outcome Prediction by Deep Learning Under Biological Model Guidance: A Feasibility Study of Oropharyngeal Cancer Application}, volume={12}, ISSN={["2234-943X"]}, DOI={10.3389/fonc.2022.895544}, abstractNote={PurposeTo develop a method of biologically guided deep learning for post-radiation 18FDG-PET image outcome prediction based on pre-radiation images and radiotherapy dose information.}, journal={FRONTIERS IN ONCOLOGY}, author={Ji, Hangjie and Lafata, Kyle and Mowery, Yvonne and Brizel, David and Bertozzi, Andrea L. and Yin, Fang-Fang and Wang, Chunhao}, year={2022}, month={May} }
 @article{sedighi_zeng_sadeghpour_ji_ju_bertozzi_2021, title={Capillary-Driven Rise of Well-Wetting Liquid on the Outer Surface of Cylindrical Nozzles}, volume={37}, ISSN={0743-7463 1520-5827}, url={http://dx.doi.org/10.1021/acs.langmuir.1c01096}, DOI={10.1021/acs.langmuir.1c01096}, abstractNote={Well-wetting liquids exiting small-diameter nozzles in the dripping regime can partially rise up along the outer nozzle surfaces. This is problematic for fuel injectors and other devices such as direct-contact heat and mass exchangers that incorporate arrays of nozzles to distribute liquids. We report our experimental and numerical study of the rising phenomenon for wide ranges of parameters. Our study shows that the interplay of three dimensionless numbers (the Bond number, the Weber number, and the Ohnesorge number) governs the capillary-driven rise dynamics. In general, as the flow rate or the viscosity increases, the capillary-driven rise height over each dripping period becomes smaller. We identify liquid flow rates below which the temporal evolution of the meniscus positions can be well approximated by a quasistatic model based on the Young-Laplace equation. Our analysis reveals two critical Bond numbers that give nozzle sizes, which correspond to the maximum meniscus rise and the onset of capillary-driven rise cessation. These critical Bond numbers are characterized as a function of the contact angle, regardless of the fluid type. Our study leads to a more efficient and optimized nozzle design in systems using wetting liquids by reducing both the risks of contamination and high pressure drop in such devices.}, number={35}, journal={Langmuir}, publisher={American Chemical Society (ACS)}, author={Sedighi, Erfan and Zeng, Zezhi and Sadeghpour, Abolfazl and Ji, Hangjie and Ju, Y. Sungtaek and Bertozzi, Andrea L.}, year={2021}, month={Aug}, pages={10413–10423} }
 @article{sadeghpour_oroumiyeh_zhu_ko_ji_bertozzi_ju_2021, title={Experimental study of a string-based counterflow wet electrostatic precipitator for collection of fine and ultrafine particles}, volume={71}, ISSN={1096-2247 2162-2906}, url={http://dx.doi.org/10.1080/10962247.2020.1869627}, DOI={10.1080/10962247.2020.1869627}, abstractNote={ABSTRACT Wet electrostatic precipitators (WESP) have been widely studied for collecting fine and ultrafine particles, such as diesel particulate matter (DPM), which have deleterious effects on human health. Here, we report an experimental and numerical simulation study on a novel string-based two-stage WESP. Our new design incorporates grounded vertically aligned polymer strings, along which thin films of water flow down. The water beads, generated by intrinsic flow instability, travel down the strings and collect charged particles in the counterflowing gas stream. We performed experiments using two different geometric configurations of WESP: rectangular and cylindrical. We examined the effects of the WESP electrode bias voltage, air stream velocity, and water flow rate on the number-based fractional collection efficiency for particles of diameters ranging from 10 nm to 2.5 μm. The collection efficiency improves with increasing bias voltages or decreasing airflow rates. At liquid-to-gas (L/G) as low as approximately 0.0066, our design delivers a collection efficiency over 70% even for fine and ultrafine particles. The rectangular and cylindrical configurations exhibit similar collection efficiencies under nominally identical experimental conditions. We also compare the water-to-air mass flow rate ratio, air flow rate per unit collector volume, and collection efficiency of our string-based design with those of previously reported WESPs. The present work demonstrates a promising design for a highly efficient, compact, and scalable two-stage WESPs with minimal water consumption. Implications: Wet Electrostatic Precipitators (WESPs) are highly effective for collecting fine particles in exhaust air streams from various sources such as diesel engines, power plants, and oil refineries. However, their large-scale adoption has been limited by high water usage and reduced collection efficiencies for ultrafine particles. We perform experimental and numerical investigation to characterize the collection efficiency and water flow rate-dependence of a new design of WESP. The string-based counterflow WESP reported in this study offers number-based collection efficiencies >70% at air flow rates per collector volume as high as 4.36 (m3/s)/m3 for particles of diameters ranging from 10 nm – 2.5 μm, while significantly reducing water usage. Our work provides a basis for the design of more compact and water-efficient WESPs.}, number={7}, journal={Journal of the Air & Waste Management Association}, publisher={Informa UK Limited}, author={Sadeghpour, Abolfazl and Oroumiyeh, Farzan and Zhu, Yifang and Ko, Danny D. and Ji, Hangjie and Bertozzi, Andrea L. and Ju, Y. Sungtaek}, year={2021}, month={May}, pages={851–865} }
 @inbook{xia_suliafu_ji_nguyen_bertozzi_osher_wang_2021, title={Heavy ball neural ordinarydifferential equations}, volume={34}, ISBN={9781713845393}, booktitle={Advances in Neural Information Processing Systems}, publisher={Curran Associates Inc.}, author={Xia, H. and Suliafu, V. and Ji, H. and Nguyen, T.M. and Bertozzi, A.L. and Osher, S. and Wang, B.}, editor={Ranzato, M. and Beygelzimer, A. and Dauphin, Y. and Liang, P.S. and Vaughan, J. WortmanEditors}, year={2021}, pages={18646–18659} }
 @article{nguyen_li_ji_2021, title={Stable and accurate numerical methods for generalized Kirchhoff–Love plates}, volume={130}, ISSN={0022-0833 1573-2703}, url={http://dx.doi.org/10.1007/s10665-021-10163-x}, DOI={10.1007/s10665-021-10163-x}, abstractNote={Kirchhoff–Love plate theory is widely used in structural engineering. In this paper, efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff–Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. The generalization stems from the inclusion of additional physics to the classical Kirchhoff–Love model that accounts for bending only. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor–corrector or an implicit Newmark-Beta time-stepping algorithm. Stability analysis is conducted for the schemes, and the results are used to determine stable time steps in practice. A series of carefully chosen test problems are solved to demonstrate the properties and applications of our numerical approaches. The numerical results confirm the stability and 2nd-order accuracy of the algorithms and are also comparable with experiments for similar thin plates. As an application, we illustrate a strategy to identify the natural frequencies of a plate using our numerical methods in conjunction with a fast Fourier transformation power spectrum analysis of the computed data. Then we take advantage of one of the computed natural frequencies to simulate the interesting physical phenomena known as resonance and beat for a generalized Kirchhoff–Love plate.}, number={1}, journal={Journal of Engineering Mathematics}, publisher={Springer Science and Business Media LLC}, author={Nguyen, Duong T. A. and Li, Longfei and Ji, Hangjie}, year={2021}, month={Sep} }
 @article{ji_falcon_sedighi_sadeghpour_ju_bertozzi_2021, title={Thermally-driven coalescence in thin liquid film flowing down a fibre}, volume={916}, ISSN={0022-1120 1469-7645}, url={http://dx.doi.org/10.1017/jfm.2021.198}, DOI={10.1017/jfm.2021.198}, abstractNote={Abstract}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Ji, Hangjie and Falcon, Claudia and Sedighi, Erfan and Sadeghpour, Abolfazl and Ju, Y. Sungtaek and Bertozzi, Andrea L.}, year={2021}, month={Apr} }
 @article{ji_sadeghpour_ju_bertozzi_2020, title={Modelling film flows down a fibre influenced by nozzle geometry}, volume={901}, ISSN={0022-1120 1469-7645}, url={http://dx.doi.org/10.1017/jfm.2020.605}, DOI={10.1017/jfm.2020.605}, abstractNote={Abstract}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Ji, H. and Sadeghpour, A. and Ju, Y. S. and Bertozzi, A. L.}, year={2020}, month={Aug} }
 @article{hangjie_witelski_2020, title={Steady states and dynamics of a thin-film-type equation with non-conserved mass}, volume={11}, url={https://doi.org/10.1017/S0956792519000330}, DOI={10.1017/S0956792519000330}, abstractNote={We study the steady states and dynamics of a thin-film-type equation with non-conserved mass in one dimension. The evolution equation is a non-linear fourth-order degenerate parabolic partial differential equation (PDE) motivated by a model of volatile viscous fluid films allowing for condensation or evaporation. We show that by changing the sign of the non-conserved flux and breaking from a gradient flow structure, the problem can exhibit novel behaviours including having two distinct classes of co-existing steady-state solutions. Detailed analysis of the bifurcation structure for these steady states and their stability reveals several possibilities for the dynamics. For some parameter regimes, solutions can lead to finite-time rupture singularities. Interestingly, we also show that a finite-amplitude limit cycle can occur as a singular perturbation in the nearly conserved limit.}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={HANGJIE, JI and WITELSKI, THOMAS P.}, year={2020}, month={Dec}, pages={1–34} }
 @article{dukler_ji_falcon_bertozzi_2020, title={Theory for undercompressive shocks in tears of wine}, volume={5}, ISSN={2469-990X}, url={http://dx.doi.org/10.1103/physrevfluids.5.034002}, DOI={10.1103/PhysRevFluids.5.034002}, abstractNote={We revisit the tears of wine problem for thin films in water-ethanol mixtures and present a new model for the climbing dynamics. The new formulation includes a Marangoni stress balanced by both the normal and tangential components of gravity as well as surface tension which lead to distinctly different behavior. The prior literature did not address the wine tears but rather the behavior of the film at earlier stages and the behavior of the meniscus. In the lubrication limit we obtain an equation that is already well-known for rising films in the presence of thermal gradients. Such models can exhibit non-classical shocks that are undercompressive. We present basic theory that allows one to identify the signature of an undercompressive (UC) wave. We observe both compressive and undercompressive waves in new experiments and we argue that, in the case of a pre-coated glass, the famous "wine tears" emerge from a reverse undercompressive shock originating at the meniscus.}, number={3}, journal={Physical Review Fluids}, publisher={American Physical Society (APS)}, author={Dukler, Yonatan and Ji, Hangjie and Falcon, Claudia and Bertozzi, Andrea L.}, year={2020}, month={Mar} }
 @article{ji_falcon_sadeghpour_zeng_ju_bertozzi_2019, title={Dynamics of thin liquid films on vertical cylindrical fibres}, volume={865}, url={https://doi.org/10.1017/jfm.2019.33}, DOI={10.1017/jfm.2019.33}, abstractNote={Recent experiments on thin films flowing down a vertical fibre with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of travelling droplets in the experiments and their transition to isolated droplets. This is also supported by stability analysis of the travelling wave solution of the model.}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Ji, H. and Falcon, C. and Sadeghpour, A. and Zeng, Z. and Ju, Y. S. and Bertozzi, A. L.}, year={2019}, month={Apr}, pages={303–327} }
 @article{ji_li_2019, title={Numerical methods for thermally stressed shallow shell equations}, volume={362}, url={https://doi.org/10.1016/j.cam.2018.10.005}, DOI={10.1016/j.cam.2018.10.005}, abstractNote={We develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von Karman type. The governing equations form a fourth-order coupled system of nonlinear biharnomic equations for the transverse deflection and Airy's stress function. A second-order finite difference discretization with three iterative methods (Picard, Newton and Trust-Region Dogleg) are proposed for the numerical solution of the nonlinear PDE system. Three simple boundary conditions and two application-motivated mixed boundary conditions are considered. Along with the nonlinearity of the system, boundary singularities that appear when mixed boundary conditions are specified are the main numerical challenges. Two approaches that use either a transition function or local corrections are developed to deal with these boundary singularities. All the proposed numerical methods are validated using carefully designed numerical tests, where expected orders of accuracy and rates of convergence are observed. A rough run-time performance comparison is also conducted to illustrate the efficiency of our methods. As an application of the methods, a snap-through thermal buckling problem is considered. The critical thermal loads of shell buckling with various boundary conditions are numerically calculated, and snap-through bifurcation curves are also obtained using our numerical methods together with a pseudo-arclength continuation method. Our results are consistent with previous studies.}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier BV}, author={Ji, Hangjie and Li, Longfei}, year={2019}, month={Dec}, pages={626–652} }
 @article{sadeghpour_zeng_ji_ebrahimi_bertozzi_ju_2019, title={Water vapor capturing using an array of traveling liquid beads for desalination and water treatment}, volume={5}, url={https://doi.org/10.1126/sciadv.aav7662}, DOI={10.1126/sciadv.aav7662}, abstractNote={We develop a compact, light-weight, and highly efficient device to capture water vapor for desalination and water harvesting.}, number={4}, journal={Science Advances}, publisher={American Association for the Advancement of Science (AAAS)}, author={Sadeghpour, A. and Zeng, Z. and Ji, H. and Ebrahimi, N. Dehdari and Bertozzi, A. L. and Ju, Y. S.}, year={2019}, month={Apr} }
 @article{hu_li_ji_2018, title={A nodal finite element approximation of a phase field model for shape and topology optimization}, volume={339}, url={https://doi.org/10.1016/j.amc.2018.07.049}, DOI={10.1016/j.amc.2018.07.049}, abstractNote={We propose a nodal finite element method to the problem of finding optimal structural shapes based on a phase field model motivated by the work of Takezawa et al. (2010). Compared to finite differences used in the original study, the proposed method better characterizes optimal configurations and is not sensitive to initial guesses or element shapes. Using nodal finite elements as a basis, we also investigate the application of two semi-implicit time-stepping schemes, the first-order and second-order semi-implicit backward Euler time-stepping schemes (1-SBEM and 2-SBDF), to the optimization problem. We then discuss the stability of these schemes and a classic finite-difference based upwind scheme using benchmark problems of compliance minimization with volume constraints. Numerical evidences show that the nodal FEM approach alleviates the initial dependency problem of structural optimization, and the 1-SBEM scheme is more stable than the other two schemes in tracking the moving boundary.}, journal={Applied Mathematics and Computation}, publisher={Elsevier BV}, author={Hu, Xianliang and Li, Yixin and Ji, Hangjie}, year={2018}, month={Dec}, pages={675–684} }
 @article{gao_ji_liu_witelski_2018, title={A vicinal surface model for epitaxial growth with logarithmic free energy}, volume={23}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85054181122&partnerID=MN8TOARS}, DOI={10.3934/dcdsb.2018170}, abstractNote={We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+\alpha u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ converging to a constant that only depends on the initial data is also investigated both analytically and numerically.}, number={10}, journal={Discrete and Continuous Dynamical Systems - Series B}, author={Gao, Y. and Ji, H. and Liu, J.-G. and Witelski, T.P.}, year={2018}, pages={4433–4453} }
 @article{ji_witelski_2018, title={Instability and dynamics of volatile thin films}, volume={3}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85043242689&partnerID=MN8TOARS}, DOI={10.1103/PhysRevFluids.3.024001}, abstractNote={Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low Reynolds number lubrication approximation incorporating surface tension, intermolecular effects and evaporative fluxes. Parameter ranges for evaporation- dominated and condensation-dominated regimes and a critical case are identified. Interfacial instabilities driven by the competition between the disjoining pressure and evaporative effects are studied via linear stability analysis. Transient pattern formation in nearly-flat evolving films in the critical case is investigated. In the weak evaporation limit unstable modes of finite amplitude non-uniform steady states lead to rich droplet dynamics, including flattening, symmetry breaking, and droplet merging. Numerical simulations show long time behaviors leading to evaporation or condensation are sensitive to transitions between film-wise and drop-wise dynamics.}, number={2}, journal={Physical Review Fluids}, publisher={American Physical Society (APS)}, author={Ji, Hangjie and Witelski, Thomas P.}, year={2018} }
 @inproceedings{sadeghpour_zeng_ji_falcon_ju_bertozzi_2018, title={Video: Dynamics of thin films down vertical fibers}, DOI={10.1103/aps.dfd.2018.gfm.v0005}, booktitle={71th Annual Meeting of the APS Division of Fluid Dynamics - Gallery of Fluid Motion}, publisher={American Physical Society}, author={Sadeghpour, Abolfazl and Zeng, Zezhi and Ji, Hangjie and Falcon, Claudia and Ju, Y. Sungtaek and Bertozzi, Andrea}, year={2018}, month={Nov} }
 @article{ji_witelski_2017, title={Finite-time thin film rupture driven by modified evaporative loss}, volume={342}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85006445289&partnerID=MN8TOARS}, DOI={10.1016/j.physd.2016.10.002}, abstractNote={Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with modified evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term. Several different types of finite-time singularities are observed due to balances between conservative and non-conservative terms. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.}, journal={Physica D: Nonlinear Phenomena}, author={Ji, H. and Witelski, T.P.}, year={2017}, pages={1–15} }
 @article{gao_ji_liu_witelski_2017, title={Global existence of solutions to a tear film model with locally elevated evaporation rates}, volume={350}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85017370200&partnerID=MN8TOARS}, DOI={10.1016/j.physd.2017.03.005}, abstractNote={Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (2014)] for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDE for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and the results are then validated against PDE simulations. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.}, journal={Physica D: Nonlinear Phenomena}, author={Gao, Y. and Ji, H. and Liu, J.-G. and Witelski, T.P.}, year={2017}, pages={13–25} }
 @phdthesis{ji_2017, title={Thin films with non-conservative effects}, school={Duke University}, author={Ji, H.}, year={2017} }