Professor
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
5351 - Mathematical Methods in Science and Engineering I
Mathematical Modeling and Simulation in Materials Science
Machine Learning, Data Science, Image Science
Multiscale and Stochastic Modeling
Partial Differential Equations
Postgraduate Students and Postdocs
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.
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.
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.
10. Y. Xiang, and W.
E, Nonlinear evolution equation
of the stress-driven morphological instability, J. Appl. Phys., 91, 9414-9422, 2002.
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.
1. C.Q. Chen, Y.H. Yang, Y. Xiang,
W.R. Hao, Automatic
Differentiation is Essential in Training Neural Networks for Solving
Differential Equations, arXiv:2405.14099, 2024
2. 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.
3. 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).
4. 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.
5. Y.X. Feng, Y. Lan, L.C. Zhang, Y.
Xiang. ElasticLaneNet:
A Geometry-Flexible Approach for Lane Detection, arXiv:2312.10389, 2023.
6. Y.X. Feng, Y. Lan, L.C. Zhang, Y. Xiang. Elastic Interaction Energy
Loss for Traffic Image Segmentation, arXiv:2310.01449, 2023.
7. 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.
8. B.X. Wang, X.W. Fu, Y. Lan, L.C. Zhang, Y. Xiang, Large
Transformers are Better EEG Learners, arXiv:2308.11654, 2023.
9. 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).
10. 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)
11. C.Q. Chen, Y. Wu, Y. Xiang,
Stability Analysis
Framework for Particle-based Distance GANs with Wasserstein Gradient Flow,
arXiv:2307.01879, 2023.
12. C.Q. Chen, Y. Wu, Y. Xiang,
Elastic Interaction
Energy-Based Generative Model: Approximation in Feature Space,
arXiv:2303.10553, 2023.
13. 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)
14. 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.
15. 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)
16. X. W. Fu, Y. Xiang,
X. Z. Guo, Differentially
private confidence interval on extreme of parameters, arXiv:2303.02892,
2023.
17. 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.
18. 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).
19. 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).
20. 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) .
21. 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.
22. 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.
23. 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.