Yang Xiang

 

Professor

Department of Mathematics

Hong Kong University of Science and Technology

Clear Water Bay, Kowloon, Hong Kong   

Office Telephone: (852) 2358-7430, Fax: (852) 2358-1643

Email: maxiang@ust.hk

 

TEACHING:

 

MATH 4351 - Numerical Solutions of Partial Differential Equations

MSDM 5004 - Numerical Methods and Modeling in Science

 

RESEARCH INTERESTS:

         Mathematical Modeling and Simulation in Materials Science

         Machine Learning, Data Science, Image Science

         Multiscale and Stochastic Modeling

         Partial Differential Equations

        

POSTGRADUATE STUDENTS AND POSTDOCS

         Postgraduate Students and Postdocs

 

PUBLICATIONS:

Modeling and simulation of grain boundaries

 

1.     X. X. Qin, L. C. Zhang, Y. Xiang, A Three-Dimensional Continuum Simulation Method for Grain Boundary Motion Incorporating Dislocation Structure, J. Sci. Comput., 90,3, 2022 (arXiv:2102.00386).

 

2.     X. X. Qin, Y. J. Gu, L. C. Zhang, Y. Xiang, Continuum Model and Numerical Method for Dislocation Structure and Energy of Grain Boundaries, Multiscale Model. Simul., 20(1), 323-348, 2022 (arXiv:2101.02596).

 

3.     L. C. Zhang, J. Han, D. J. Srolovitz, Y. Xiang, Equation of motion for  grain boundaries in polycrystals, npj Computational Materials, 7, 64, 2021.

 

4.     L. C. Zhang, X. X. Qin, Y. Xiang, Continuum model for dislocation structures of semicoherent interfaces, Comput. Mater. Sci. 190, 110277, 2021.

 

5.     L. C. Zhang, Y. Xiang, A new formulation of coupling and sliding motions of grain boundaries based on dislocation structure, SIAM J. Appl. Math. 80, 2365-2387, 2020. (arXiv:2001.02082)

 

6.     C. Z. Wei, L. C. Zhang, J. Han, D. J. Srolovitz, Yang Xiang, Grain boundary triple junction dynamics: A continuum disconnection model, SIAM J. Appl. Math. 80, 1101-1122, 2020. (arXiv:1907.13469)

 

7.     C. Z. Wei, S. L. Thomas, J. Han, D. J. Srolovitz, Y. Xiang, A continuum multi-disconnection-mode model for grain boundary migration, J. Mech. Phys. Solids, 133, 103731, 2019.

 

8.     S. L. Thomas, C.Z. Wei, J. Han, Y. Xiang, D. J. Srolovitz, Disconnection description of triple junction motion, Proc. Natl. Acad. Sci. (PNAS), 116, 8756-8765, 2019.

 

9.     Y.J. Gu, Y. Xiang, D.J. Srolovitz, J.A. El-Awady, Self-healing of low angle grain boundaries by vacancy diffusion and dislocation climb, Scripta Mater., 155, 155-159, 2018.

 

10.  L.C. Zhang and Y. Xiang, Motion of grain boundaries incorporating dislocation structure, J. Mech. Phys. Solids, 117, 157-178, 2018. (arXiv:1710.01856, 2017)

 

11.  Y.C. Zhu, J. Luo, X. Guo, Y. Xiang, S.J. Chapman, The role of grain boundaries under long-time radiation, Phys. Rev. Lett., 120, 222501, 2018.

 

12.  L.C. Zhang, J. Han, Y. Xiang, and D.J. Srolovitz, The equation of motion for a grain boundary, Phys. Rev. Lett. 119, 246101, 2017.

 

13.  Y. Xiang and X.D. Yan, Stability of dislocation networks on low angle grain boundaries using a continuum energy formulation, Dis. Cont. Dyn. Sys. B, 23, 2989-3021, 2018.

 

14.  Y.C. Zhu, J. Wang, Y. Xiang, and X. Guo, A three-scale homogenisation approach to the prediction of long-time absorption of radiation induced interstitials by nanovoids at interfaces, J. Mech. Phys. Solids, 105, 1-20,  2017.

 

15.  Y.J. Gu, J. Han, S.Y. Dai, Y.C. Zhu, Y. Xiang, and D. J. Srolovitz, Point defect sink efficiency of low-angle tilt grain boundaries, J. Mech. Phys. Solids, 101, 166-179, 2017.

 

16.  L.C. Zhang, Y.J. Gu, and Y. Xiang, Energy of low angle grain boundaries based on continuum dislocation structure, Acta Mater., 126, 11-24, 2017. (arXiv:1610.04318, 2016)

 

17.  S.Y. Dai, Y. Xiang, and D. J. Srolovitz, Twisted bilayer graphene: Moire with a twist, Nano Lett. 16, 5923-5927, 2016.

 

18.  S.Y. Dai, Y. Xiang, and D. J. Srolovitz, Structure and energetics of interlayer dislocations in bilayer graphene, Phys. Rev. B, 93, 085410, 2016.

 

19.  Y.J. Gu, Y. Xiang, and D.J. Srolovitz, Relaxation of low angle grain boundary structure by climb of the constituent dislocations, Scripta Mater., 114, 35-40, 2016.

 

20.  X.H. Zhu and Y. Xiang, Continuum framework for dislocation structure, energy and dynamics of dislocation arrays and low angle grain boundaries, J. Mech. Phys. Solids, 69, 175-194, 2014.

 

21.  S.Y. Dai, Y. Xiang, and D. J. Srolovitz, Atomistic, generalized Peierls-Nabarro, and analytical models for (111) twist boundaries in Al, Cu and Ni for all twist angles, Acta Mater, 69, 162-174, 2014.

22.  S.Y. Dai, Y. Xiang, and D. J. Srolovitz, Structure and energy of (111) low angle twist boundaries in Al, Cu and Ni, Acta Mater., 61(4), 1327-1337, 2013.

23.  X.H. Zhu, S.Y. Dai, and Y. Xiang, Numerical simulation of dynamics of dislocation arrays and long-range stress fields of nonplanar dislocation arrays, Int. J. Plasticity, 43, 85-100, 2013.

24.  X.H. Zhu and Y. Xiang, A continuum model for the dynamics of dislocation arrays, Commun. Math. Sci., 10(4), 1081-1103, 2012.

25.  S.S. Quek, Y. Xiang, and D. J. Srolovitz, Loss of interface coherency around a misfitting spherical inclusion, Acta Mater., 59(14), 5398-5410, 2011.

26.  S.Y. Dai, Y. Xiang, and T.Y. Zhang, A continuum model for core relaxation of incoherent twin boundaries based on the Peierls-Nabarro framework, Scripta Mater., 64(5), 438-441, 2011.

27.  X.H. Zhu and Y. Xiang, Stabilizing force on perturbed grain boundaries using dislocation model, Scripta Mater., 64(1), 5-8, 2011.

Modeling and simulation of dislocations and solids

1.     X. X.  Qin, A. H.W. Ngan, Y. Xiang, A threshold dislocation dynamics method, Commun. Comput. Phys.35(2), 273-312, 2024. (arXiv:2307.13653).

 

2.     Y. H. Yang, L. C. Zhang, Y. Xiang, Stochastic continuum models for high-entropy alloys with short-range order, Multiscale Model. Simul. 21 (4), 1323-1343, 2023. (arXiv:2205.07186)

 

3.     C. T. Huang, S. Y. Dai, X. H. Niu, T. P. Jiang, Z. J. Yang, Y. J. Gu, Y. Xiang, A continuum model for dislocation climb, International Journal of Plasticity, 168, 103700, 2023. (arXiv:2304.05604).

 

4.     X.H. Niu, Y. Xiang, X.D. Yan, Well-posedness of a modified degenerate Cahn-Hilliard model for surface diffusion, Communications in Mathematical Sciences 22 (2), 487-517, 2024. (arXiv:2202.13492).

 

5.     A. Kalaei, Y. Xiang, A. H.W. Ngan, An efficient and minimalist scheme for continuous dislocation dynamics, International Journal of Plasticity, 158, 103433, 2022.

 

6.     P. C. Zhu, L. Yu, Y. Xiang, Weak solutions to an initial-boundary value problem for a continuum equation of motion of grain boundaries, Discrete and Continuous Dynamical Systems Series B, in press, 2022.

 

7.     T. Luo, Y. Xiang, J. Z. Yang, Finite temperature Cauchy-Born rule and stability of crystalline solids with point defects, Multiscale Model. Simul., 19(4), 1710-1735, 2021.

 

8.     Y. H. Yang, T. Luo, and Y. Xiang, Convergence from Atomistic Model to Peierls-Nabarro Model for Dislocations in Bilayer System with Complex Lattice, Commun. Math. Sci. 20(4), 947-986, 2022 (arXiv:2103.09412).

 

9.     T. Luo, Y. Xiang, J. Z. Yang, C. Yuan, Cauchy-Born rule and stability of crystalline solids at finite temperature, Commun. Math. Sci. 19(6), 1461-1490, 2021.

 

10.  X. H. Niu, Y. Xiang, X.D. Yan, Phase field model for self-climb of prismatic dislocation loops by vacancy pipe diffusion, Int. J. Plasticity, 141, 102977, 2021.

 

11.  S.Y. Dai, F. R. Wang, Y. Xiang, Z.J Yang, and C. Yuan, Boundary Condition for Dislocation Dynamic Simulation in BCC Crystal, CSIAM Trans. Appl. Math., 2, 175-194, 2021.

 

12.  Y. Gao, J.-G. Liu, T. Luo, and Y. Xiang, Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space, Dis. Cont. Dyn. Sys. B, 26, 3177-3207, 2021 (arXiv:1907.07281).

 

13.  T. P. Jiang, Y. Xiang, and L. C. Zhang, Stochastic Peierls-Nabarro model for dislocations in high entropy alloys, SIAM J. Appl. Math. 80(6), 2496-2517, 2020. (arXiv:2004.09375)

 

14.  Z. C. Zhou, Y. C. Zhu, J. Luo, Y. Xiang, and X. Guo, Upscaling dislocation dynamics using machine learning tools guided by a physically-oriented curriculum devised from asymptotic analysis, Int. J. Solids Struct. 198, 57-71, 2020.

 

15.  X.H. Niu, Y.J. Gu, and Y. Xiang, Dislocation dynamics formulation for self-climb of dislocation loops by vacancy pipe diffusion, Int. J. Plasticity, 120, 262-277, 2019. (arXiv:1901.05174, 2019.)

 

16.  L.C. Zhang, Y. Xiang, J. Han, and D.J. Srolovitz, The effect of randomness on the strength of high-entropy alloys, Acta Mater., 166, 424-434, 2019.

 

17.  T. Luo, P. B. Ming, and Y. Xiang, From Atomistic Model to the Peierls-Nabarro Model with Gamma-surface for Dislocations, Arch. Ration. Mech. Anal, 230, 735-781, 2018. (arXiv:1706.03145, 2017)

 

18.  X. H. Niu, Y. C. Zhu, S. Y. Dai, and Y. Xiang, A continuum model for distributions of  dislocations incorporating short-range interactions, Commun. Math. Sci., 16, 491-522, 2018.

 

19.  X. H. Niu, T. Luo, J. F. Lu, and Y. Xiang, Dislocation climb models from atomistic scheme to dislocation dynamics, J. Mech. Phys. Solids, 99, 242-258, 2017. (arXiv:1607.08734, 2016)

 

20.  S. D. Jiang, M. Rachh, and Y. Xiang, An efficient high order method for dislocation climb in two dimensions, SIAM Multiscale Model. Simul, 15, 235-253, 2017.

 

21.  Y.C. Zhu, X.H. Niu, and Y. Xiang, Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes, J. Mech. Phys. Solids, 96, 369-387, 2016.

 

22.  S. J. Chapman, Y. Xiang, and Y. C. Zhu, Homogenisation of a row of dislocation dipoles from discrete dislocation dynamics, SIAM J. Appl. Math., 76(2), 750-775, 2016.

 

23.  Y.C. Zhu, Y. Xiang, and K. Schulz, The role of dislocation pile-up in flow stress determination and strain hardening, Scripta Mater., 116, 53-56, 2016.

 

24.  Y.C. Zhu and Y. Xiang, A continuum model for dislocation dynamics in three dimensions using the dislocation density potential functions and its application to micro-pillars, J. Mech. Phys. Solids, 84, 230-253, 2015.

 

25.  Y.J. Gu, Y. Xiang, S.S. Quek, and D.J. Srolovitz, Three-dimensional formulation of dislocation climb, J. Mech. Phys. Solids, 83, 319-337, 2015.

 

26.  A.Y. Zhu, C.M. Jin, D.G. Zhao, Y. Xiang, and J.F. Huang, A numerical scheme for generalized Peierls-Nabarro model of dislocations based on the fast multipole method and iterative grid redistribution, Commun. Comput. Phys, 18, 1282-1312, 2015.

 

27.  Y.C. Zhu, H.Q. Wang, X.H. Zhu, and Y. Xiang, A continuum model for dislocation dynamics incorporating Frank-Read sources and Hall-Petch relation in two dimensions, Int. J. Plasticity, 60, 19-39, 2014.

28.  H.Q. Wang and Y. Xiang, An adaptive level set method based on two-level uniform meshes and its application to dislocation dynamics, Int. J. Numer. Meth. Engng, 94(6), 573-597, 2013.

29.  D.G. Zhao. H. Wang, and Y. Xiang, Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments, Phil. Mag., 92(18), 2351-2374, 2012.

30.  D.G. Zhao, J.F. Huang, and Y. Xiang, Fast multipole accelerated boundary integral equation method for evaluating the stress field associated with dislocations in a finite medium, Commun. Comput. Phys., 12(1), 226-246, 2012.

31.  C.M. Jin, Y. Xiang, and G. Lu, Dislocation cross-slip mechanisms in aluminum, Phil. Mag., 91(32), 4109-4125, 2011.

32.  X.H. Zhu and Y. Xiang, Continuum model for dislocation dynamics in a slip plane, Phil. Mag., 90 (33), 4409-4428, 2010.

33.  D.G. Zhao, J.F. Huang, and Y. Xiang, A new version fast multipole method for evaluating the stress field of dislocation ensembles, Modelling Simul. Mater. Sci. Eng., 18(4), 045006, 2010.

34.  C.M. Jin, W. Ren, and Y. Xiang, Computing transition rates of thermally activated events in dislocation dynamics, Scripta Mater., 62(4), 206-209, 2010.

35.  S. S. Quek, Y. W. Zhang, Y. Xiang, and D. J. Srolovitz, Dislocation cross-slip in heteroepitaxial multilayer films, Acta Mater., 58(1), 226-234, 2010 .

36.  H. Wei and Y. Xiang, A generalized Peierls-Nabarro model for kinked dislocations, Phil. Mag., 89(27), 2333-2354, 2009.

37.  Y. Xiang, Continuum approximation of the Peach-Koehler force on dislocations in a slip plane, J. Mech. Phys. Solids, 57(4), 728-743, 2009.

38.  H. Wei, Y. Xiang, and P.B. Ming, A generalized Peierls-Nabarro model for curved dislocations using discrete Fourier transform, Commun. Comput. Phys., 4(2), 275-293, 2008.

39.  Y. Xiang, H. Wei, P.B. Ming, and W. E, A generalized Peierls-Nabarro model for curved dislocations and core structures of dislocation loops in Al and Cu, Acta Mater., 56(7), 1447-1460, 2008.

40.  S.S. Quek, Z. Wu, Y.W. Zhang, Y. Xiang, and D.J. Srolovitz, Dislocation junctions as barriers to threading dislocation migration, Appl. Phys. Lett., 90, 011905, 2007.

41.  Y. Xiang and D.J. Srolovitz, Dislocation climb effects on particle bypass mechanisms, Phil. Mag., 86, 3937-3957, 2006.

42.  Y. Xiang, Modeling dislocations at different scales, Commun. Comput. Phys., 1(3), 383-424, 2006.

43.  S.S. Quek, Y. Xiang, Y.W. Zhang, D.J. Srolovitz, and C. Lu, Level set simulation of dislocation dynamics in thin films, Acta Mater., 54(9), 2371-2381, 2006.

44.  Y. Xiang, D.J. Srolovitz, L.T. Cheng, and W. E, Level set simulations of dislocation-particle bypass mechanisms, Acta Mater., 52 (7), 1745-1760 , 2004.

45.  Y. Xiang, L.T. Cheng, D.J. Srolovitz, and W. E, A level set method for dislocation dynamics, Acta Mater., 51(18), 5499-5518, 2003.

Modeling and simulation of epitaxial growth

1.     G. H. Fan, T. Luo, and Y. Xiang, Existence and energy scaling of 2+1 dimensional continuum model for stepped epitaxial surfaces with elastic effects, CSIAM Trans. Appl. Math., 4(3), 419-450, 2023 (arXiv:2103.09157).

 

2.     T. Luo, Y. Xiang, and N. K. Yip, Bunching instability and asymptotic properties in epitaxial growth with elasticity effects: Continuum model, arXiv:2204.10051, 2022.

 

3.     T. Luo, Y. Xiang, and N. K. Yip, Energy scaling and asymptotic properties of one-dimensional discrete system with generalized Lennard--Jones (m,n) interaction, J. Nonlinear Sci. 31, 43, 2021. (arXiv:2004.12279)

4.     T. Luo, Y. Xiang, and N. K. Yip, Energy scaling and asymptotic properties of step bunching in epitaxial growth with elastic effects, Multiscale Model. Simul., 44(2),  737-771, 2016.

5.     X.H. Zhu, H.Y. Xu and Y. Xiang, Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in 2+1 dimensions, Phys. Rev. B, 79(12), 125413, 2009.

6.     H.Y. Xu and Y. Xiang, Derivation of a continuum model for the long-range elastic interaction on stepped epitaxial surfaces in 2+1 dimensions, SIAM J. Appl. Math., 69(5), 1393-1414, 2009.

7.     J.F. Huang, M.C. Lai, and Y. Xiang, An integral equation method for epitaxial step-flow growth simulations, J. Comput. Phys., 216(2), 724-743, 2006.

8.     Y. Xiang and W. E, Misfit elastic energy and a continuum model for epitaxial growth with elasticity, Phys. Rev. B, 69, 035409, 2004.

9.     Y. Xiang, Derivation of a continuum model for epitaxial growth with elasticity, SIAM J. Appl. Math., 63(1), 241-258, 2002.

10.  Y. Xiang, and W. E, Nonlinear evolution equation of the stress-driven morphological instability, J. Appl. Phys., 91,  9414-9422, 2002.

 Optics

1.     T. P. Jiang and Y. Xiang, Computation of transverse-electric polarized optical eigenstates in dielectric systems based on perfectly matched layer, Phys. Rev. E 105, 045309, 2022

2.     T. P. Jiang and Y. Xiang, Perfectly matched layer method for optical modes in dielectric cavities, Phys. Rev. A 102, 053704, 2020.

3.     T. P. Jiang and Y. Xiang, Perturbation method for optical modes in deformed disks, Phys. Rev. A 99, 023847, 2019.

 Machine learning, data science and image science

1.     J. An, J. Lu, Y. Wu, Y. Xiang, Why does the two-timescale Q-learning converge to different mean field solutions? A unified convergence analysis, arXiv:2404.04357, 2024.

2.     J.Y. Fan, Y.X Han, J.L Zeng, J.-F. Cai, Y. Wang, Y. Xiang, J.H. Zhang, RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model, International Conference on Artificial Intelligence and Statistics (AISTATS) 2024, PMLR, 238: 2035-2043, 2024 (arXiv:2403.11544).

3.     G.H. Fan, T.Y. Jin, Y. Lan, Y. Xiang, L.C. Zhang, Energy stable neural network for gradient flow equations, arXiv:2309.10002, 2023.

4.     Y.X. Feng, Y. Lan, L.C. Zhang, Y. Xiang.  ElasticLaneNet: A Geometry-Flexible Approach for Lane Detection, arXiv:2312.10389, 2023.

5.     Y.X. Feng, Y. Lan, L.C. Zhang, Y. Xiang. Elastic Interaction Energy Loss for Traffic Image Segmentation, arXiv:2310.01449, 2023.

6.     Y.H. Yang, Y. Wu, H.Z. Yang, Y. Xiang, Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces, arXiv:2310.10766, 2023.

7.     B.X. Wang, X.W. Fu, Y. Lan, L.C. Zhang, Y. Xiang, Large Transformers are Better EEG Learners, arXiv:2308.11654, 2023.

8.     Y.H. Yang, H.Z. Yang, Y. Xiang, Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives, Conference on Neural Information Processing Systems (NeurIPS) 2023. (arXiv:2305.08466, 2023).

9.     J.F. Lu, Y. Wu, Y. Xiang, Score-based Transport Modeling for Mean-Field Fokker-Planck Equations, Journal of Computational Physics, 503, 112859, 2024. (arXiv:2305.03729)

10.  C.Q. Chen, Y. Wu, Y. Xiang, Stability Analysis Framework for Particle-based Distance GANs with Wasserstein Gradient Flow, arXiv:2307.01879, 2023.

11.  C.Q. Chen, Y. Wu, Y. Xiang, Elastic Interaction Energy-Based Generative Model: Approximation in Feature Space, arXiv:2303.10553, 2023.

12.  Y. Lan, Z. Li, J. Sun, Y. Xiang, DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting, Journal of Computational Physics, 491, 112343, 2023. (arXiv:2212.05571, 2022)

13.  C. T. Huang, Z. J. Liu, S. Y. Bai, L. W. Zhang, C. C. Xu, Y. Xiang, Y. P. Xiong, PF-ABGen: A Reliable and Efficient Antibody Generator via Poisson Flow, ICLR 2023 Machine Learning for Drug Discovery (MLDD) Workshop, 2023.

14.  Y. X. Han, J. L. Zeng, Y. Wang, Y. Xiang, J. H. Zhang, Optimal Contextual Bandits with Knapsacks under Realizibility via Regression Oracles, International Conference on Artificial Intelligence and Statistics (AISTATS) 2023, PMLR 206:5011-5035, 2023. (arXiv:2210.11834)

15.  X. W. Fu, Y. Xiang, X. Z. Guo, Differentially private confidence interval on extreme of parameters, arXiv:2303.02892, 2023.

16.  Y. Lan, L. Qin, Z.Y. Sun, Y. Xiang, J. Sun, GOLLIC: Learning global context beyond patches for lossless high-resolution image compression, arXiv:2210.03301, 2022.

17.  Y. H. Yang and Y. Xiang, Approximation of Functionals by Neural Network without Curse of Dimensionality, J. Mach. Learn., 1(4), 342-372, 2022 (arXiv:2205.14421).

18.  Y. Wu, Y. Lan, L. Zhang, Y. Xiang, Feature Flow Regularization: Improving Structured Sparsity in Deep Neural Networks, Neural Networks, 161, 598-613, 2023 (arXiv:2106.02914).

19.  Y. Lan, Y. Xiang, L. C. Zhang, An elastic interaction based loss function for medical image segmentation, The 23rd International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2020), Lima, Peru, October 4-8, 2020. MICCAI 2020. Lecture Notes in Computer Science, vol 12265, pp 755-764. (arXiv: 2007.02663) .

20.  Y. Xiang, A.C.S. Chung, and J. Ye, An active contour model for image segmentation based on elastic interaction, J. Comput. Phys., 219(1), 455-476, 2006.

21.  A.C.S. Chung, Y. Xiang, J. Ye, and W.K. Law, Elastic interaction models for active contours and surfaces, The International Workshop on Computer Vision for Biomedical Image Applications: Current Techniques and Future Trends, The Tenth IEEE International Conference on Computer Vision (CVBIA 2005), Beijing, China, Oct, 2005, LNCS 3765, pp. 314-323.

22.  Y. Xiang, A.C.S. Chung, and J. Ye, A new active contour method based on elastic interaction, IEEE International Conference on Computer Vision and Pattern Recognition 2005 (CVPR 2005), San Diego, CA, USA, June 20-26, 2005, Vol. 1, 452-457.