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Professor
Research Interests
Mathematical Modeling and Simulation in Materials Science; Numerical Analysis and Scientific Computing; Image ProcessingTeaching
 MATH5352 Mathematical Methods in Science and Engineering II
 MATH6914S Reading Course: Introduction to Reinforcement Learning Models
 MATH6914T Reading Course: Introduction to Computational Stochastic PDEs
 MATH6915 Scientific Computation Seminar
 MATH6915A Scientific Computation Seminar
 MATH6916 Student Seminars on Computation Related Research
Awards & Honors

Invited Speaker for 2021 SIAM Conference on Mathematical Aspects of Materials Science
(2021)
Selected Publications
Article

A ThreeDimensional Continuum Simulation Method for Grain Boundary Motion Incorporating Dislocation Structure
 Author(s): Qin, Xiaoxue; Zhang, Luchan; Xiang, Yang
 Source: Journal Of Scientific Computing, v. 90, (1), January 2022, article number 3
 Year: 2022

Boundary condition for dislocation dynamic simulation in BCC crystal
 Author(s): Dai, Shuyang; Wang, Fengru; Xiang, Yang; Yang, Jerry Zhijian; Yuan, Cheng
 Source: CSIAM Transactions on Applied Mathematics, v. 2, (1), March 2021, p. 175194
 Year: 2021

Cauchy–Born rule and stability of crystalline solids at finite temperature
 Author(s): Luo, Tao; Xiang, Yang; Yang, Jerry Zhijian; Yuan, Cheng
 Source: Communications in Mathematical Sciences, v. 19, (6), August 2021, p. 14611490
 Year: 2021

Energy Scaling and Asymptotic Properties of OneDimensional Discrete System with Generalized LennardJones (m, n) Interaction
 Author(s): Luo, Tao; Xiang, Yang; Yip, Nung Kwan
 Source: Journal of Nonlinear Science, v. 31, (2), April 2021, article number 43
 Year: 2021

Equation of motion for grain boundaries in polycrystals
 Author(s): Zhang, Luchan; Han, Jian; Srolovitz, David J.; Xiang, Yang
 Source: npj Computational Materials, v. 7, (1), December 2021, article number 64
 Year: 2021

Phase field model for selfclimb of prismatic dislocation loops by vacancy pipe diffusion
 Author(s): Niu, Xiaohua; Xiang, Yang; Yan, Xiaodong
 Source: International Journal of Plasticity, v. 141, June 2021, article number 102977
 Year: 2021

Continuum model for dislocation structures of semicoherent interfaces
 Author(s): Zhang, Luchan; Qin, Xiaoxue; Xiang, Yang
 Source: Computational Materials Science, v. 190, April 2021, article number 110277
 Year: 2021

Revisit of the peierlsnabarro model for edge dislocations in Hilbert space
 Author(s): Gao, Yuan; Liu, Jian Guo; Luo, Tao; Xiang, Yang
 Source: Discrete and Continuous Dynamical Systems  Series B, v. 26, (6), June 2021, p. 31773207
 Year: 2020

Perfectly matched layer method for optical modes in dielectric cavities
 Author(s): Jiang, Tianpeng ; Xiang, Yang
 Source: Physical Review A, v. 102, (5), 5 November 2020, article number 053704
 Year: 2020

A new formulation of coupling and sliding motions of grain boundaries based on dislocation structure
 Author(s): Zhang, Luchan; Xiang, Yang
 Source: SIAM Journal on Applied Mathematics, v. 80, (6), November 2020, p. 23652387
 Year: 2020

Stochastic PeierlsNabarro model for dislocations in high entropy alloys
 Author(s): Jiang, Tianpeng; Xiang, Yang; Zhang, Luchan
 Source: SIAM Journal on Applied Mathematics, v. 80, (6), December 2020, p. 24962517
 Year: 2020

Characterisation of dislocation patterning behaviour with a continuum dislocation dynamics model on two parallel slip planes equipped with a deep neural network resolving local microstructures
 Author(s): Zhou, Zhengcheng; Zhu, Yichao; Luo, Jing; Xiang, Yang; Guo, Xu
 Source: International Journal of Solids and Structures, v. 198, August 2020, p. 5771
 Year: 2020

Grain Boundary Triple Junction Dynamics: A Continuum Disconnection Model
 Author(s): Wei, Chaozhen ; Zhang, Luchan; Han, Jian; Srolovitz, David J.; Xiang, Yang
 Source: SIAM Journal on Applied Mathematics, v. 80, (3), 2020, p. 11011122
 Year: 2020

A Continuum MultiDisconnectionMode model for grain boundary migration
 Author(s): Wei, Chaozhen ; Thomas, Spencer L.; Han, Jian; Srolovitz, David J.; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids, v.133, December 2019, article number 103731
 Year: 2019

Dislocation dynamics formulation for selfclimb of dislocation loops by vacancy pipe diffusion
 Author(s): Niu, Xiaohua ; Gu, Yejun; Xiang, Yang
 Source: International Journal of Plasticity, v. 120, September 2019, p. 262277
 Year: 2019

Perturbation model for optical modes in deformed disks
 Author(s): Jiang, Tianpeng ; Xiang, Yang
 Source: Physical Review. A, v. 99, (2), February 2019, article number 023847, p. 02384710238477
 Year: 2019

Disconnection description of triplejunction motion
 Author(s): Thomas, Spencer L.; Wei, Chaozhen ; Han, Jian; Xiang, Yang ; Srolovitz, David J.
 Source: Proceedings of the National Academy of Sciences of the United States of America, v. 116, (18), April 2019, p. 87568765
 Year: 2019

Perturbation method for optical modes in deformed disks
 Author(s): Jiang, Tianpeng ; Xiang, Yang
 Source: Physical Review. A, v. 99, (2), 25 February 2019, article number 023847
 Year: 2019

The effect of randomness on the strength of highentropy alloys
 Author(s): Zhang, Luchan ; Xiang, Yang ; Han, Jian; Srolovitz, David J.
 Source: Acta Materialia, v. 166, March 2019, p. 424434
 Year: 2019

Stability of dislocation networks of low angle grain boundaries using a continuum energy formulation
 Author(s): Xiang, Yang ; Yan, Xiaodong
 Source: Discrete and Continuous Dynamical Systems Series B. , v. 23, (8), October 2018, p. 29893021
 Year: 2018

A Continuum Model for Distributions of Dislocations Incorporating Shortrange Interactions
 Author(s): Niu, Xiaohua ; Zhu, Yichao; Dai, Shuyang; Xiang, Yang
 Source: Communications in Mathematical Sciences. , v. 16, (2), 2018, p. 491522
 Year: 2018

Role of Grain Boundaries under LongTime Radiation
 Author(s): Zhu, Yichao; Guo, Xu; Luo, Jing; Xiang, Yang ; Chapman, Stephen Jonathan
 Source: Physical Review Letters. , v. 120, (22), May 2018, article number 222501
 Year: 2018

Selfhealing of low angle grain boundaries by vacancy diffusion and dislocation climb
 Author(s): Gu, Y.; Xiang, Yang ; Srolovitz, D.J.; ElAwady, J.A.
 Source: Scripta Materialia. , v. 155, October 2018, p. 155159
 Year: 2018

Motion of Grain Boundaries Incorporating Dislocation Structure
 Author(s): Zhang, Luchan ; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 117, August 2018, p. 157178
 Year: 2018

From Atomistic Model to the PeierlsNabarro Model with Gammasurface for Dislocations
 Author(s): Luo, Tao ; Ming, Pingbing; Xiang, Yang
 Source: Archive for Rational Mechanics and Analysis. , v. 230, (2), November 2018, p. 735781
 Year: 2018

An Efficient High Order Method for Dislocation Climb in Two Dimensions
 Author(s): Jiang, Shidong; Rachh, Manas; Xiang, Yang
 Source: Multiscale Modeling and Simulation. , v. 15, (1), 2017, p. 235253
 Year: 2017

A ThreeScale Homogenisation Approach to the Prediction of LongTime Absorption of Radiation Induced Interstitials by Nanovoids at Interfaces
 Author(s): Zhu, Yichao; Wang, Jian; Xiang, Yang; Guo, Xu
 Source: Journal of the Mechanics and Physics of Solids. , v. 105, August 2017, p. 120
 Year: 2017

Equation of Motion for a Grain Boundary
 Author(s): Zhang, Luchan; Han, Jian; Xiang, Yang; Srolovitz, David J
 Source: Physical Review Letters. , v. 119, (24), 12 December 2017, article number 246101
 Year: 2017

Dislocation Climb Models from Atomistic Scheme to Dislocation Dynamics
 Author(s): Niu, Xiaohua ; Luo, Tao ; Lu, Jianfeng; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 99, February 2017, p. 242258
 Year: 2017

Point Defect Sink Efficiency of Lowangle Tilt Grain Boundaries
 Author(s): Gu, Yejun PHYS; Han, Jian; Dai, Shuyang; Zhu, Yichao ; Xiang, Yang ; Srolovitz, David J.
 Source: Journal of the Mechanics and Physics of Solids. , v. 101, 2017, p. 166179
 Year: 2017

Energy of Low Angle Grain Boundaries Based on Continuum Dislocation Structure
 Author(s): Zhang, Luchan ; Gu, Yejun PHYS; Xiang, Yang
 Source: Acta Materialia. , v. 126, March 2017, p. 1124
 Year: 2017

Structure and Energetics of Interlayer Dislocations in Bilayer Graphene
 Author(s): Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
 Source: Physical Review B. , v. 93, (8), February 2016, article number 085410
 Year: 2016

Twisted Bilayer Graphene: Moire with a Twist
 Author(s): Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
 Source: Nano Letters. , v. 16, (9), September 2016, p. 59235927
 Year: 2016

The Role of Dislocation PileUp in Flow Stress Determination and Strain Hardening
 Author(s): Zhu, Yichao; Xiang, Yang; Schulz, Katrin V.
 Source: Scripta Materialia. , v. 116, April 2016, p. 5356
 Year: 2016

Continuum Dynamics of the Formation, Migration and Dissociation of SelfLocked Dislocation Structures on Parallel Slip Planes
 Author(s): Zhu, Yichao; Niu, Xiaohua; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 96, November 2016, p. 369387
 Year: 2016

Homogenization of a Row of Dislocation Dipoles from Discrete Dislocation Dynamics
 Author(s): Chapman, Stephen Jonathan; Xiang, Yang; Zhu, Yichao
 Source: SIAM Journal on Applied Mathematics. , v. 76, (2), April 2016, p. 750775
 Year: 2016

Energy Scaling and Asymptotic Properties of Step Bunching in Epitaxial Growth with Elasticity Effects
 Author(s): Luo, Tao; Xiang, Yang; Yip, Nung Kwan
 Source: Multiscale Modeling and Simulation. , v. 14, (2), May 2016, p. 737771
 Year: 2016

Relaxation of LowAngle Grain Boundary Structure by Climb of the Constituent Dislocations
 Author(s): Gu, Yejun; Xiang, Yang; Srolovitz, David J.
 Source: Scripta Materialia. , v. 114, March 2016, p. 3540
 Year: 2016

A Numerical Scheme for Generalized PeierlsNabarro Model of Dislocations Based on the Fast Multipole Method and Iterative Grid Redistribution
 Author(s): Zhu, Aiyu; Jin, Congming; Zhao, Degang; Xiang, Yang; Huang, Jingfeng
 Source: Communications in Computational Physics. , v. 18, (5), November 2015, p. 12821312
 Year: 2015

A Continuum Model for Dislocation Dynamics in Three Dimensions Using the Dislocation Density Potential Functions and its Application to MicroPillars
 Author(s): Zhu, Yichao; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 84, November 2015, p. 230253
 Year: 2015

Threedimensional formulation of dislocation climb
 Author(s): Gu, Yejun; Xiang, Yang; Quek, Siu Sin; Srolovitz, David J.
 Source: Journal of the Mechanics and Physics of Solids. , v. 83, October 2015, p. 319337
 Year: 2015

A Continuum Model for Dislocation Dynamics Incorporating FrankRead Sources and HallPetch Relation in Two Dimensions
 Author(s): Zhu, Yongchang; Wang, Hanquan; Zhu, Xiaohong; Xiang, Yang
 Source: International Journal of Plasticity. , v. 60, September 2014, p. 1939
 Year: 2014

Continuum Framework for Dislocation Structure, Energy and Dynamics of Dislocation Arrays and Low Angle Grain Boundaries
 Author(s): Zhu, Xiaohong; Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 69, (1), September 2014, p. 175194
 Year: 2014

Atomistic, Generalized PeierlsNabarro and Analytical Models for (1 1 1) Twist Boundaries in Al, Cu and Ni for All Twist Angles
 Author(s): Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
 Source: Acta Materialia. , v. 69, May 2014, p. 162174
 Year: 2014

An Adaptive Level Set Method Based on TwoLevel Uniform Meshes and its Application to Dislocation Dynamics
 Author(s): Wang, Hanquan; Xiang, Yang
 Source: International Journal for Numerical Methods in Engineering. , v. 94, (6), May 2013, p. 573597
 Year: 2013

Structure and Energy of (111) LowAngle Twist Boundaries in Al, Cu and Ni
 Author(s): Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
 Source: Acta Materialia. , v. 61, (4), February 2013, p. 13271337
 Year: 2013

Numerical Simulation of Dynamics of Dislocation Arrays and LongRange Stress Fields of Nonplanar Dislocation Arrays
 Author(s): Zhu, Xiaohong; Dai, Shuyang; Xiang, Yang
 Source: International Journal of Plasticity. , v. 43, April 2013, p. 85100
 Year: 2013

A Continuum Model for the Dynamics of Dislocation Arrays
 Author(s): Zhu, Xiaohong; Xiang, Yang
 Source: Communications in Mathematical Sciences. , v. 10, (4), 2012, p. 10811103
 Year: 2012

Fast Multipole Accelerated Boundary Integral Equation Method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium
 Author(s): Zhao, Degang; Huang, Jingfang; Xiang, Yang
 Source: Communications in Computational Physics. , v. 12, (1), July 2012, p. 226246
 Year: 2012

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments
 Author(s): Zhao, Degang; Wang, Hanquan; Xiang, Yang
 Source: Philosophical Magazine. , v. 92, (18), June 2012, p. 23512374
 Year: 2012

Stabilizing Force on Perturbed Grain Boundaries Using a Dislocation Model
 Author(s): Zhu, Xiaohong; Xiang, Yang
 Source: Scripta Materialia. , v. 64, (1), January 2011, p. 58
 Year: 2011

Loss of Interface Coherency Around a Misfitting Spherical Inclusion
 Author(s): Quek, Siu Sin; Xiang, Yang; Srolovitz, David J.
 Source: Acta Materialia. , v. 59, (14), August 2011, p. 53985410
 Year: 2011

Dislocation CrossSlip Mechanisms in Aluminum
 Author(s): Jin, Congming; Xiang, Yang; Lu, Gang
 Source: Philosophical Magazine. , v. 91, (32), November 2011, p. 41094125
 Year: 2011

A Continuum Model for Core Relaxation of Incoherent Twin Boundaries Based on the PeierlsNabarro Framework
 Author(s): Dai, Shuyang; Xiang, Yang; Zhang, Tongyi
 Source: Scripta Materialia. , v. 64, (5), March 2011, p. 438441
 Year: 2011

Continuum Model for Dislocation Dynamics in a Slip Plane
 Author(s): Zhu, Xiaohong; Xiang, Yang
 Source: Philosophical Magazine. , v. 90, (33), November 2010, p. 44094428
 Year: 2010

Dislocation CrossSlip in Heteroepitaxial Multilayer Films
 Author(s): Quek, Siu Sin; Zhang, Yongwei; Xiang, Yang; Srolovitz, David J.
 Source: Acta Materialia. , v. 58, (1), January 2010, p. 226234
 Year: 2010

Computing Transition Rates of Thermally Activated Events in Dislocation Dynamics
 Author(s): Jin, Congming; Ren, Weiqing; Xiang, Yang
 Source: Scripta Materialia. , v. 62, (4), February 2010, p. 206209
 Year: 2010

A New Version Fast Multipole Method for Evaluating the Stress Field of Dislocation Ensembles
 Author(s): Zhao, Degang; Huang, Jingfang; Xiang, Yang
 Source: Modelling and Simulation in Materials Science and Engineering. , v. 18, (4), June 2010, article number 045006
 Year: 2010

A generalized Peierls–Nabarro model for kinked dislocations
 Author(s): Wei, He; Xiang, Yang
 Source: Philosophical Magazine. , v. 89, (27), September 2009, p. 23332354
 Year: 2009

Continuum approximation of the Peach–Koehler force on dislocations in a slip plane
 Author(s): Xiang, Yang
 Source: Journal of the Mechanics and Physics of Solids. , v. 57, (4), April 2009, p. 728743
 Year: 2009

Continuum Model for the LongRange Elastic Interaction on Stepped Epitaxial Surfaces in 2+1 Dimensions
 Author(s): Zhu, Xiaohong; Xu, Haoyun; Xiang, Yang
 Source: Physical Review B: Condensed Matter and Materials Physics. , v. 79, (12), March 2009, article number 125413
 Year: 2009

A Generalized PeierlsNabarro Model for Curved Dislocations and Core Structures of Dislocation Loops in Al and Cu
 Author(s): Xiang, Yang; Wei, He; Ming, Pingbing; E, Weinan
 Source: Acta Materialia. , v. 56, (7), April 2008, p. 14471460
 Year: 2008

A Generalized PeierlsNabarro Model for Curved Dislocations Using Discrete Fourier Transform
 Author(s): Wei, He; Xiang, Yang; Ming, Pingbing
 Source: Communications in Computational Physics. , v. 4, (2), August 2008, p. 275293
 Year: 2008

Derivation of a Continuum Model for the LongRange Elastic Interaction on Stepped Epitaxial Surfaces in 2+1 Dimensions
 Author(s): Xu, Haoyun; Xiang, Yang
 Source: SIAM Journal on Applied Mathematics. , v. 69, (5), 2009, p. 13931414
 Year: 2008

Dislocation Junctions as Barriers to Threading Dislocation Migration
 Author(s): Quek, Siu Sin; Wu, Zhaoxuan; Zhang, YongWei; Xiang, Yang; Srolovitz, David J.
 Source: Applied Physics Letters. , v. 90, (1), January 2007, article number 011905
 Year: 2007

Level set simulation of dislocation dynamics in thin films
 Author(s): Quek, Siu Sin; Xiang, Yang; Zhang, Yongwei; Srolovitz, David J.; Lu, Chun
 Source: Acta Materialia. , v. 54, (9), May 2006, p. 23712381
 Year: 2006

Modeling Dislocations at Different Scales
 Author(s): Xiang, Yang
 Source: Communications in Computational Physics. , v. 1, (3), June 2006, p. 383424
 Year: 2006

Dislocation Climb Effects on Particle Bypass Mechanisms
 Author(s): Xiang, Yang; Srolovitz, D.J.
 Source: Philosophical Magazine. , v. 86, (2526), September 2006, p. 39373957
 Year: 2006

An active contour model for image segmentation based on elastic interaction
 Author(s): Xiang, Yang; Chung, Albert Chi Shing; Ye, Jian
 Source: Journal of Computational Physics. , v. 219, (1), November 2006, p. 455476
 Year: 2006

An Integral Equation Method for Epitaxial StepFlow Growth Simulations
 Author(s): Huang, Jingfang; Lai, Mingchih; Xiang, Yang
 Source: Journal of Computational Physics. , v. 216, (2), August 2006, p. 724743
 Year: 2006

Misfit Elastic Energy and a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces
 Author(s): Xiang, Yang; E, Weinan
 Source: Physical Review B  Condensed Matter and Materials Physics. , v. 69, (3), January 2004, article number 035409
 Year: 2004

Level Set Simulations of Dislocationparticle Bypass Mechanisms
 Author(s): Xiang, Yang; Srolovitz, D.J.; Cheng, L.T.; E, Weinan
 Source: Acta Materialia. , v. 52, (7), April 2004, p. 17451760
 Year: 2004

A Level Set Method for Dislocation Dynamics
 Author(s): Xiang, Yang; Cheng, LiTien; Srolovitz, David J.; E, Weinan
 Source: Acta Materialia. , v. 51, (18), October 2003, p. 54995518
 Year: 2003

Nonlinear evolution equation for the stressdriven morphological instability
 Author(s): Xiang, Yang; E, Weinan
 Source: Journal of Applied Physics. , v. 91, (11), June 2002, p. 94149422
 Year: 2002

Derivation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surface
 Author(s): Xiang, Yang
 Source: SIAM Journal on Applied Mathematics. , v. 63, (1), July 2002, p. 241258
 Year: 2002

Comparison principle for viscosity solutions with high growth at infinity
 Author(s): Xiang, Yang
 Source: Journal of Partial Differential Equations. , v. 10, (2), 1997, p. 107122
 Year: 1997

Existence for Viscosity Solutions of Nonlinear Degenerate Elliptic Equations in RN
 Author(s): Xiang, Yang
 Source: Acta Mathematicae Applicatae Sinica. , v. 20, 1997, p. 209220
 Year: 1997
Book chapter

Dislocation Dynamics in 2 + epsilon Dimensions: Slip Planes, Thin Films, and Grain Boundaries
 Author(s): Xiang, Yang; Quek, SiuSin; Zhang, YongWei; Lim, Adele; Srolovitz, David J.
 Source: Multiscale Modeling and Analysis for Materials. , / Edited by Weizhu Bao, Qiang Du. Singapore ; Hackensack, NJ : World Scientific, c2012, p.194
 Year: 2012

Level Set Dislocation Dynamics Method
 Author(s): Xiang, Yang; Srolovitz, David J.
 Source: Handbook of Materials Modeling. , / Edited by Sidney Yip. Netherlands : Springer, 2005, pp 23072323
 Year: 2005
Conference paper

An elastic interaction based loss function for medical image segmentation
 Author(s): Lan, Yuan ; Xiang, Yang; Zhang, Luchan
 Source: Lecture Notes in Computer Science, v. 12265, 2020, p. 755764
 Year: 2020

A New Active Contour Method Based on Elastic Interaction
 Author(s): Xiang, Yang; Chung, Albert Chi Shing; Ye, Jian
 Source: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. , v. 1, 2005, p. 452457
 Year: 2005

Elastic Interaction Models for Active Contours and Surfaces
 Author(s): Chung, Albert Chi Shing; Xiang, Yang; Ye, Jian; Law, Max Wai Kong
 Source: Lecture Notes in Computer Science. , v. 3765, 2005, p. 314323
 Year: 2005

An efficient step flow simulation scheme using potential theory
 Author(s): Huang, Jingfang; Xiang, Yang
 Source: Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics, Elsevier. , 2001, p. 861864
 Year: 2001