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Publication List

(Note: * indicates graduate student under my supervision)

  1.  X.-H. Zhou*, J. Han, M.I. Zafar*, C.J. Roy, H. Xiao. Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state simulations. [arXiv]: 2312.11842.

  2. H.-C. Wang*, M. Yu, H. Xiao. First-principle-like reinforcement learning of nonlinear numerical schemes for conservation laws. [arXiv]:2312.13260.

Journal Papers in Process

Journal Publications

  1. X.-L. Zhang, H. Xiao, S. Jee, G. He. Physical interpretation of neural network-based nonlinear eddy viscosity models. Aerospace Science and Technology, 142, 108632, 2023.  [arXiv]

  2. X.-L. Zhang, H. Xiao, X. Luo, G. He. Combining direct and indirect sparse data for learning generalizable turbulence models. Journal of Computational Physics, 489, 112272, 2023.  [arXiv]

  3. X.-H. Zhou*, H. Wang*, J.E. McClure, C. Chen, H. Xiao. Inference of relative permeability curves in reservoir rocks with ensemble Kalman method. European Physical Journal E, 46, 44, 2023.   [arXiv]

  4. J. Han, X.-H. Zhou*, H. Xiao, An equivariant neural operator for developing nonlocal tensorial constitutive models. Journal of Computational Physics, 488, 112243, 2023.  [arXiv]

  5. Y. Lu, X.-H. Zhou*, H. Xiao, Q. Li. Using machine learning to predict urban canopy flows for land surface modeling. Geophysical Research Letters, 50, e2022GL102313, 2023.

  6. X.-L. Zhang*, H. Xiao, X. Luo, G. He. Ensemble Kalman method for learning turbulence models from indirect observation data. Journal of Fluid Mechanics, 949(A26), 2022.  [arXiv] 

  7. M. I. Zafar*, J. Han, X.-H. Zhou*, H. Xiao. Frame invariance and scalability of neural operators for partial differential equations. Communication in Computational Physics, 32(2), 336-363, 2022.  [arXiv]

  8. ​R. Xu*, X.-H. Zhou*, J. Han, R. P. Dwight, H. Xiao. A PDE-free, neural network-based eddy viscosity model coupled with RANS equations. International Journal of Heat and Fluid Flow, 98, 109051, 2022.  [arXiv]

  9. X.-H. Zhou*, J. Han, H. Xiao. Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids. Computer Methods in Applied Mechanics and Engineering, 388, 114211, 2022.  [arXiv]

  10. X.-H. Zhou*, J. McClure, C. Chen, H. Xiao.  Neural network based pore flow field prediction in porous media using super resolution. Physical Review Fluids, 7(7), 074302 (20 pages), 2022.  [arXiv]

  11. X.-L. Zhang, H. Xiao, G. He.  Assessment of regularized ensemble  Kalman inversion of turbulence quantity fields. AIAA Journal, 60(1), 3-13, 2022.

  12. X.-L. Zhang, H. Xiao, T. Wu, G. He. Acoustic Inversion for Uncertainty Reduction in Reynolds-Averaged Navier-Stokes-Based Jet Noise Prediction. AIAA Journal, 60(4), 2407-2422, 2022. 

  13. J. Schaefer*,  A. Cary, M. Mani, Th. Grandine, C.J. Roy, H. Xiao.  Uncertainty quantification across design space using spatially accurate polynomial chaos. AIAA Journal, 60(3), 1482-1504, 2022. 

  14. C. Michelén-Ströfer*, X.-L. Zhang, H. Xiao. Ensemble gradient for learning turbulence models from indirect observations. Communications in Computational Physics, 30, 1269-1289, 2021.  [arXiv]

  15. M. I. Zafar*, M. M. Choudhari, P. Paredes, H. Xiao. Recurrent neural network for end-to-end modeling of laminar-turbulent transition. Data Centric Engineering, 2, 2021.

  16. C. Michelén-Ströfer*, H. Xiao. End-to-end differentiable learning of turbulence models from indirect observations. Theoretical and Applied Mechanics Letters, 11(4), 100280, 2021.

  17. X.-H. Zhou*, J. Han, H. Xiao. Learning nonlocal constitutive models with neural networks. Computer Methods in Applied Mechanics and Engineering. 384, 113927 (27 pages), 2021.  [arXiv]

  18. X.-L. Zhang, H. Xiao, G.W. He, S.Z. Wang. Assimilation of disparate data for enhanced reconstruction of turbulent mean flows. Computers and Fluids, 224, 104962 (14 pages), 2021.  [arXiv]

  19. Y. Zeng*, J.-L. Wu*, H. Xiao. Enforcing imprecise constraints on generative adversarial networks for emulating physical systems. Communications in Computational Physics, 30(3), 635-665, 2021.  [arXiv]

  20. C. Michelén-Ströfer*, X.-L. Zhang, H. Xiao. DAFI: An open-source framework for ensemble-based data assimilation and field inversion. Communications in Computational Physics, 29, 1583-1622, 2021.  [arXiv]

  21. K. Kashinath, M. Mustafa, A. Albert, J.-L. Wu*, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, R. Wang, A. Chattopadhyay, A. Singh, A. Manepalli, D. Chirila, R. Yu, R. Walters, B. White, H. Xiao, H.A. Tchelepi, P. Marcus, A. Anandkumar, P. Hassanzadeh, Prabhat. Physics-informed machine learning: case studies for weather and climate modelling. Philosophical Transactions of the Royal Society A, 379(2194), 20200093 (36 pages), 2021.

  22. M. I. Zafar*, H. Xiao, M. M. Choudhari, F. Li, C.-L. Chang, P. Paredes, B. Venkatachari. Convolutional neural network for transition modeling based on linear stability theory. Physical Review Fluids, 5(11), 113903 (21 pages), 2020.  [arXiv]

  23. X.-L. Zhang*, C. Michelén-Ströfer*, H. Xiao. Regularized ensemble Kalman methods for inverse problems. Journal of Computational Physics, 416, 109517 (26 pages), 2020.  [arXiv]

  24. C. Michelén-Ströfer*, X.-L. Zhang*, H. Xiao, O. Coutier-Delgosha. Enforcing boundary conditions on physical fields in Bayesian inversion, Computer Methods in Applied Mechanics and Engineering, 367, 113097 (20 pages), 2020.  [arXiv]

  25. X.-L. Zhang*, H. Xiao, Th. Gomez, O. Coutier-Delgosha. Evaluation of ensemble methods for quantifying uncertainties in steady-state CFD applications with small ensemble sizes. Computers and Fluids, 203, 104530, 2020.  [arXiv]

  26. J.-L. Wu*, K. Kashinath, A. Alberta, D. Chirila, M. Prabhat, H. Xiao. Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems. Journal of Computational Physics, 406, 109209 (20 pages), 2020.  [arXiv]

  27. P. Paredes, B. Venkatachari, M. M. Choudhari, F. Li, C.-L. Chang, M. I. Zafar*, H. Xiao. Physics-based transition modeling in a hypersonic boundary layer at flight conditions. AIAA Journal, 58(10), 4475-4484, 2020.

  28. H. Xiao, J.-L. Wu*, S. Laizet, L. Duan. Flows over periodic hills of parameterized geometries: a dataset for data-driven turbulence modeling from direct simulations. Computers and Fluids, 200, 104431, 2020.  [arXiv]

  29. K. Duraisamy, G. Iaccarino, and H. Xiao. Turbulence modeling in the age of data. Annual Review of Fluid Mechanics, 51, 357-377, 2019.  [arXiv] (Invited review article: all authors contributed equally and are listed alphabetically)

  30. H. Xiao and P. Cinnella. Quantification of model uncertainty in RANS simulations: A review. Progress in Aerospace Sciences, 108, 1-31, 2019.  [arXiv] (Invited review article)

  31. J.-L. Wu*, C. Michelén-Ströfer*, H. Xiao. Physics-informed covariance kernel for model-form uncertainty quantification with application to turbulent flows. Computers and Fluids, 193, 104292 (11 pages), 2019.

  32. J.-L. Wu*, H. Xiao, R. Sun*, and Q. Wang. Reynolds averaged Navier-Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned. Journal of Fluid Mechanics, 869, 553-586, 2019.  [arXiv]

  33. X.I.A. Yang, S. Zafar, J.-X. Wang, H. Xiao. Predictive LES wall modeling via physics-informed neural networks. Physical Review Fluids, 4(3), 034602 (22 pages), 2019. 

  34. J.-X. Wang*, J. Huang, L. Duan and H. Xiao. Predicting Reynolds stresses in high-Mach-number turbulent boundary layers with physics-informed machine learning. Theoretical and Computational Fluid Dynamics. 33(1), 1-19, 2019. 

  35. J.-L. Wu*, R. Sun*, S. Laizet, H. Xiao. Representation of Reynolds stress perturbations with application in machine-learning-assisted turbulence modeling. Computer Methods in Applied Mechanics and Engineering, 346, 707-726, 2019.  [arXiv]

  36. X.-L. Zhang*, J.-L. Wu*, O. Coutier-Delgosha, H. Xiao. Recent progress in augmenting turbulence models with physics-informed machine learning. Journal of Hydrodynamics, 31(6), 1153-1158, 2019.

  37. C. Michelén-Ströfer*, J.-L. Wu*, H. Xiao and E. G. Paterson. Data-driven, physics-based feature extraction from fluid flow fields with convolutional neural networks. Communications in Computational Physics, 25(3), 625-650, 2019.  [arXiv]

  38. J.-L. Wu*, X. Yin, and H. Xiao. Seeing permeability from images: Fast prediction with convolutional neural networks. Science Bulletin, 63(18), 1215-1222, 2018. (Invited paper)

  39. J.-L. Wu*, H. Xiao and E. G. Paterson. Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework. Physical Review Fluids, 3(7), 074602 (28 pages), 2018.  [arXiv]

  40. R. Sun*, H. Xiao, H. Sun. Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations. Advances in Water Resources, 111, 406-422, 2018.  [arXiv]

  41. J.-X. Wang*, H. Tang, H. Xiao, and R. Weiss. Inferring tsunami flow depth and flow speed from sediment deposits based on ensemble Kalman filtering. Geophysical Journal International, 212(1), 646-658, 2018.  [arXiv]

  42. J.-X. Wang*, C. J. Roy and H. Xiao. Propagation of input uncertainty in presence of model-form uncertainty: A multi-fidelity approach for CFD applications. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 4(1), 011002 (8 pages), 2018.  [arXiv]

  43. H. Tang, J.-X. Wang*, R. Weiss and H. Xiao. TSUFLIND-EnKF: Inversion of tsunami flow depth and flow speed from deposits with quantified uncertainties. Marine Geology,  396, 15-26, 2018.  [arXiv]

  44. R. Sun*, H. Xiao and H. Sun. Realistic representation of grain shapes in CFD-DEM simulations of sediment transport with a bonded-sphere approach. Advances in Water Resources, 107, 421-438, 2017.  [arXiv]

  45. J.-L. Wu*, J.-X. Wang*, H. Xiao, J. Ling. A Priori assessment of prediction confidence for data-driven turbulence modeling. Flow, Turbulence and Combustion, 99(1), 25-46, 2017.  [arXiv]

  46. J.-X. Wang*, J.-L. Wu*, and H. Xiao. Physics informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Physical Review Fluids, 2(3), 034603 (21 pages), 2017.  [arXiv]

  47. H. Xiao, J.-X. Wang* and P. Jenny. An implicitly consistent formulation of a dual-mesh hybrid LES/RANS method. Communications in Computational Physics, 21(2), 570-599, 2017.

  48. H. Xiao, J.-X. Wang* and R. G. Ghanem. A random matrix approach for quantifying model-form uncertainties in turbulence modeling. Computer Methods in Applied Mechanics and Engineering, 313, 941-965, 2017.  [arXiv]

  49. H. Xiao, J.-L. Wu*, J.-X. Wang*, R. Sun*, and C. J. Roy. Quantifying and reducing model-form uncertainties in Reynolds averaged Navier–Stokes equations: A data-driven, physics-informed Bayesian approach. Journal of Computational Physics, 324, 115-136, 2016.  [arXiv]

  50. R. Sun* and H. Xiao. Sediment micromechanics in sheet flows induced by asymmetric waves: A CFD-DEM study. Computers and Geosciences, 96, 35-46, 2016.  [arXiv]

  51. J.-X. Wang*, R. Sun*, H. Xiao. Quantification of uncertainty in RANS models: A comparison of physics-based and random matrix theoretic approaches. International Journal of Heat and Fluid Flow, 62, 577-592, 2016.  [arXiv]

  52. J.-X. Wang* and H. Xiao. Data-driven CFD modeling of turbulent flows through complex structures. International Journal of Heat and Fluid Flow, 62(Part B), 138-149, 2016.  [arXiv]

  53. J.-X. Wang*, J.-L. Wu*, and H. Xiao. Incorporating prior knowledge for quantifying and reducing model-form uncertainty in RANS simulations. International Journal of Uncertainty Quantification, 6(2), 109-126, 2016.  [arXiv]

  54. R. Sun* and H. Xiao. CFD-DEM simulations of current-induced dune formation and morphological evolution. Advances in Water Resources, 92, 228-239, 2016. [arXiv]

  55. J.-L. Wu*, J.-X. Wang*, and H. Xiao. A Bayesian calibration-prediction method for reducing model-form uncertainties with application in RANS simulations. Flow, Turbulence and Combustion, 97, 761-786, 2016. [arXiv]

  56. R. Sun* and H. Xiao. SediFoam: A general-purpose, open-source CFD-DEM solver for particle-laden flows with emphasis on sediment transport. Computers and Geosciences, 89, 207-219, 2016. [arXiv]

  57. R. Sun* and H. Xiao. Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests. International Journal of Multiphase Flow, 77, 142-157, 2015. [arXiv]

  58. R. Sun* and H. Xiao. Diffusion-based coarse graining in hybrid continuum–discrete solvers: Applications in CFD-DEM. International Journal of Multiphase Flow, 72, 233-247, 2015. [arXiv]

  59. R. Sun* and H. Xiao. Eulerian-Lagrangian modeling of current-induced coastal sand dune migration. Geotechnical Engineering Journal of the SEAGS & AGSSEA, 45(4), 2014. (Invited paper)

  60. Q. Lei, Y. Wu, H. Xiao, L. Ma. Analysis of four-dimensional Mie imaging using fiber-based endoscopes. Applied Optics, 53(28), 6389-6398, 2014.

  61. H. Xiao, J.-X. Wang* and P. Jenny. Dynamic evaluation of mesh resolution and its application in hybrid LES/RANS methods. Flow, Turbulence and Combustion, 93(1), 141-170, 2014.

  62. H. Xiao, Y. Sakai*, R. Henniger, M. Wild, P. Jenny. Coupling of solvers with non-conforming computational domains in a dual-mesh hybrid LES/RANS framework. Computers and Fluids, 88, 653-662, 2013.

  63. H. Xiao and P. Jenny. A consistent dual-mesh framework for hybrid LES/RANS modeling. Journal of Computational Physics, 231(4), 1848-1865, 2012.

  64. H. Xiao and J. Sun. Algorithms in a robust hybrid CFD-DEM solver for particle-laden flows. Communications in Computational Physics, 9(2), 297-323, 2011.

  65. Y. L. Young, H. Xiao, T. Maddux. Hyro-and morpho-dynamic modeling of breaking solitary waves over sand beach. Part I: Experimental Modeling. Marine Geology, 269, 107-118, 2010.

  66. H. Xiao, Y. L. Young, J. H. Prévost. Hyro-and morpho-dynamic modeling of breaking solitary waves over sand beach. Part II: Numerical Simulation. Marine Geology, 269, 119-131, 2010.

  67. H. Xiao, Y. L. Young, J. H. Prévost. Scaling of dynamic wave-soil interaction experiments. Int. J. Numerical & Analytical Methods in Geomechanics, 34(8), 839-858, 2010.

  68. H. Xiao, Y. L. Young, J. H. Prévost. Time scale analysis in unsaturated porous media under external wave loads. Int. J. Numerical & Analytical Methods in Geomechanics, 34(18), 1935–1959, 2010.

  69. H. Xiao, Y. L. Young, J. H. Prévost. Parametric study of breaking solitary wave induced liquefaction of coastal sandy slopes. Ocean Engineering, 34(17), 1546-1553, 2010.

  70. J. Sun, H. Xiao and D. Gao. Numerical study of segregation using multi-scale models. Int. J. of Computational Fluid Dynamics, 23(2), 81-92, 2009.

  71. Y. L. Young, J. A. White, H. Xiao, R. I. Borja. Liquefaction potential of coastal slopes induced by solitary waves. Acta Geotechnica, 4(1), 17-34, 2009.

Dissertations

  1. Carlos A. C. Michelén-Ströfer. Machine Learning and Field Inversion approaches to Data-Driven Turbulence Modeling. Doctoral Dissertation, Virginia Tech, 2021.

  2. Jin-Long Wu. Predictive Turbulence Modeling with Bayesian Inference and Physics-Informed Machine Learning. Doctoral Dissertation, Virginia Tech, 2018.

  3. Rui Sun. Particle-Resolving Simulations of Dune Migration: Novel Algorithms and Physical Insights. Doctoral Dissertation, Virginia Tech, 2017.

  4. Jian-Xun Wang. Physics-Informed, Data-Driven Framework for Model-Form Uncertainty Estimation and Reduction in RANS Simulations. Doctoral Dissertation, Virginia Tech, 2017.

Conference Proceedings and Book Chapters

  1. H. Xiao. Physics-Informed Machine Learning for Predictive Turbulence Modeling: Status, Perspectives, and Case Studies. NASA Langley Workshop on Machine Learning Technologies and Their Applications to Scientific and Engineering Domains. Hampton, VA. August 16-18, 2016. (Invited) Download Slides

  2. H. Xiao. A Data-Driven, Physics-Informed Approach for Predictive Turbulence Modeling: From Data Assimilation to Machine Learning. Applied Numerical Analysis Seminar, Department of Mathematics, Virginia Tech. September 23, 2016. Download Slides

  3. R. Sun*, H. Xiao. Study of interactions between sediment particles in sheet flow using CFD--DEM, in the 68th Annual Meeting of the APS Division of Fluid Dynamics. Boston, Massachusetts, November 22–24, 2015.

  4. H. Xiao, J.-L. Wu*, J.-X. Wang*, R. Sun*, C. J. Roy. Quantifying Model-Form Uncertainties in Reynolds Averaged Navier-Stokes Equations: An Open-Box, Physics-Based, Bayesian Approach, in the 68th Annual Meeting of the APS Division of Fluid Dynamics. Boston, Massachusetts, November 22–24, 2015.

  5. J.-L. Wu*, J.-X. Wang*, H. Xiao. Model-Form Uncertainty Quantification in RANS Simulation of Wing-Body Junction Flow, in the 68th Annual Meeting of the APS Division of Fluid Dynamics. Boston, Massachusetts, November 22–24, 2015.

  6. H. Xiao, J.-L. Wu*, J.-X. Wang*, R. Sun*, C. J. Roy. Quantifying Model Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations, in the first international conference on Quantification of Uncertainty in Engineering, Sciences and Technology (QUEST). Beijing, October 19-21, 2015.

  7. H. Tang, J.-X. Wang*, R. Weiss, H. Xiao. TSUFLIND-EnKF: Inversion of tsunami flow condition with quantified uncertainty, in the YCSEC meeting. Newark, DE, 27-29 July, 2015.

  8. R. Sun* and H. Xiao. CFD-DEM Simulations of Sediment Transport Based on a Novel Coarse-Graining Algorithm, in the 13th US National Congress on Computational Mechanics (USNCCM 13), San Diego, California. July 26-31, 2015.

  9. H. Xiao, J.-L. Wu*, J.-X. Wang*, R. Sun*, C. J. Roy. Quantifying Model Form Uncertainties in Reynolds-Averaged Navier-Stokes Equations: An Open-Box, Physics-Informed, Bayesian Approach, in the 13th US National Congress on Computational Mechanics (USNCCM 13), San Diego, California. July 26-31, 2015.

  10. J.-X. Wang*, H. Xiao. A multi-model approach for uncertainty propagation and model calibration in CFD applications. SIAM Computational Science and Engineering Conference. Salt Lake City, Utah, March 14-18, 2015.

  11. H. Tang, J.-X. Wang*, R. Weiss, H. Xiao. Inversion of tsunami characteristics: Estimation of transient flow depth and speed with quantified uncertainties, in 2014 AGU Fall meeting.. San Francisco, California., December 13-17, 2014.

  12. Q. Wang, P. Constantine, H. Xiao. Uncertainty quantification of chaotic and turbulent dynamical systems. in SIAM Uncertainty Quantification Conference. Savannah, Georgia, April 1-4, 2014.

  13. Y. Liu and H. Xiao. Numerical simulation of annular flow using volume of fluid method, 2013 ANS Winter Meeting and Nuclear Technology Expo. Washington, DC, November 10-14, 2013.

  14. H. Xiao and P. Jenny. A dual-mesh hybrid LES/RANS framework with implicit consistency, Direct and Large Eddy Simulations 9, Dresden, Germany, April 4-5, 2013. 

  15. H. Xiao, L. Duan, R. Sui and T. Rösgen. Experimental investigations of turbulent wake behind porous disks, Proceedings of The 1st Marine Energy Technology Symposium, Washington, DC, 2013. 

  16. H. Xiao, Y. Sakai, R. Henniger and P. Jenny. Simulating Flow over Periodic Hills Using a Dual-Mesh Hybrid Solver with High-Order LES, ICCFD7-1604, Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 9-13, 2012.

  17. H. Xiao, M. Wild and P. Jenny. Preliminary evaluation and applications of a consistent hybrid LES-RANS method. S. Fu et al. (Eds.): Progress in Hybrid RANS-LES Modeling, NNFM 117. Springer, 2011.

  18. Y. L. Young, H. Xiao and J. H. Prévost. Numerical and physical modeling of nearshore wave-soil interactions, 16th US National Congress of Theoretical and Applied Mechanics, June 27-July 2, 2010.

  19. Y. L. Young, H. Xiao and J. H. Prevost, Transient Responses of Coastal Sandy Slopes during Extreme Wave Runups and Drawdowns, NEES 7th Annual Meeting: Seismic Mitigation in a Flat World, Honolulu, Hawaii, June 23-25, 2009.

  20. Y. L. Young, J. H. Prévost, J. A. Smith, H. Xiao, S. Sanborn, M.-L. Baeck and N. Lin. Numerical modeling of hurricanes and storm surges, nearshore wave-soil interactions, and slope instability failures, 2009 NSF Engineering Research and Innovation Conference, Honolulu, Hawaii, June 22-25, 2009. 

  21. Y. L. Young and H. Xiao. Erosion and liquefaction failure of coastal sandy slopes caused by breaking solitary wave runup and drawdown. Proceedings of 2009 NSF Engineering Research and Innovation Conference, Honolulu, Hawaii, June 22-25, 2009. 

  22. H. Xiao, Y. L. Young and J. H. Prévost. Dynamic interactions between the vadose and phreatic zones during breaking solitary wave runup and drawdown. Proceedings of ASME 28th International Conference on Ocean, Offshore and Arctic Engineering, Honolulu, HI, May 31-June 5, 2009.

  23. H. Xiao and Y. L. Young. Solitary wave runup on movable bed: experimental and numerical investigations. NEES 6th Annual Meeting: The Value of Earthquake Engineering Research, Portland, Oregon, June 18-20, 2008.

  24. Y. L. Young, H. Xiao, J. White and R. I. Borja. Can tsunami lead to liquefaction failure of coastal sandy slopes, 14th World Conference on Earthquake Engineering, Beijing, China, October 12-17, 2008.

  25. H. Xiao and Y. L. Young. Enhanced Sediment Transport due to Wave-Soil Interactions, Proceedings of NSF Engineering Research and Innovation Conference, Knoxville, Tennessee, January 8-10, 2008.

  26. H. Xiao and Y. L. Young. Modeling of solitary waves over a movable bed. 9th US National Congress on Computational Mechanics, San Francisco, California, July 23-26, 2007.

  27. H. Xiao and A. Eriksson. Co-rotational thin membrane elements. 5th International Conference on Computation of Shell and Spatial Structures, Salzburg, Austria, June 1-4, 2005.

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