Xiangdong Liang Research Scientist I am currently a reserach scientist at Aramco Boston Research Center. I am interested in physicsbased mathematical modeling and highperformance numerical computation. I obtained my Ph.D in Applied Mathematics from MIT, under the supervision of Prof. Steven Johnson. Before coming to MIT, I studied at City University of Hong Kong, under the supervision of Prof. Roderick Wong. 

Publications
[1]  Z. Lin, X. Liang, M. Lončar, S. G. Johnson, and A. W. Rodriguez. Cavityenhanced secondharmonic generation via nonlinearoverlap optimization. Optica, 3(3):233+, March 2016. [ bib  DOI  http  .pdf ] 
[2]  X. Liang. Modeling of fluids and waves with analytics and numerics. Ph.D. Thesis. [ .pdf ] 
[3]  X. Liang and S. G. Johnson. Formulation for scalable optimization of microcavities via the frequencyaveraged local density of states. Optics Express, 21(25):30812+, December 2013. [ bib  DOI  http  .pdf ] 
[4]  J. J. Kaufman, R. Ottman, G. Tao, S. Shabahang, EH Banaei, X. Liang, S. G. Johnson, Y. Fink, R. Chakrabarti, and A. F. Abouraddy. Infiber production of polymeric particles for biosensing and encapsulation. Proceedings of the National Academy of Sciences, 110(39):15549–15554, September 2013. [ bib  DOI  http  .pdf ] 
[5]  B. Zhen, S.L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira. Enabling enhanced emission and lowthreshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals. Proceedings of the National Academy of Sciences, 110(34):13711–13716, August 2013. [ bib  DOI  http  .pdf] 
[6]  A. Gumennik, L. Wei, G. Lestoquoy, A. M. Stolyarov, X. Jia, P. H. Rekemeyer, M. J. Smith, X. Liang, B. Grena, S. G. Johnson, S. Gradečak, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink. Siliconinsilica spheres via axial thermal gradient infibre capillary instabilities. Nature Communications, 4, July 2013. [ bib  DOI  http  .pdf ] 
[7]  J. J. Kaufman, G. Tao, S. Shabahang, EH Banaei, D. S. Deng, X. Liang, S. G. Johnson, Y. Fink, and A. F. Abouraddy. Structured spheres generated by an infibre fluid instability. Nature, 487(7408):463–467, July 2012. [ bib  DOI  http  .pdf ] 
[8]  D. S. Deng, J. C. Nave, X. Liang, S. G. Johnson, and Y. Fink. Exploration of infiber nanostructures from capillary instability. Optics Express, 19(17):16273+, August 2011. [ bib  DOI  http  .pdf ] 
[9]  X. Liang, D. S. Deng, J. C. Nave, and S. G. Johnson. Linear stability analysis of capillary instabilities for concentric cylindrical shells. Journal of Fluid Mechanics, 683:235–262, 2011. [ bib  DOI  http  .pdf  
[10]  X. Liang and R. Wong. On a Nested BoundaryLayer Problem. Communications on Pure and Applied Analysis, 8(1):419–433, January 2009. [ bib  DOI  http  .pdf ] 
Research
Project I: Capillary Instability of Concentric Cylindrical Shells
Keywords: Computational Fluid Dynamics, LevelSet Methods, Capillary Instability, Linear Stability Analysis
Computational Tools: C, MATLAB, MEX, OpenMP, FFTW, Lapack.
A classic example of capillary instability (PlateauRayleigh instability) is the breakup of a fluid thread into droplets due to surface tension force. Motivated by complex multifluid geometries currently being explored in fibredevice manufacturing, we theoretically and computationally studied capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full NavierStokes problem.
The mathematical model we built can quickly predict the breakup lengthscale and timescale of concentric cylindrical fluids, and provides useful guidance for material selections in fiberdrawing experiments. For example, in our experimental collaborators' recent work published in Nature, they developed a technique to produce uniform sized, structured coreshell particles by capillary instability, and our model captured the main physics in this experiment and predicted correct lengthscale of these spherical particles.
In addition to the theoretically linear stability analysis, we also implemented a full 3D Stokes simulation by spectral and levelset methods to understand the physics from a computational perspective. One interesting example is to predict which interface (inner or outer) breaks up first in a threefluid system. For various surface tensions of the outer interface γ_{2}, the following simulation movies confirmed the prediction from the mathematical analysis that the inner interface breaks up first when γ_{2}=6 (figure a), the outer interface breaks up first for γ_{2}=25 (figure c), and nearsimultaneous breakup occurs for γ_{2}=15 (figure b).
Project II: LargeScale Microcavity Topology Optimization
Keywords: Computational Electromagnetism, Parallel Computing, Nonlinear PDEConstrained Optimization
Computational Tools: C, PETSc, MPI, NLOPT, PaStiX, Mumps.
Applications such as lasers and nonlinear devices require optical microcavities with long lifetimes Q and small modal volumes V. We formulate and solve a full 3d optimization scheme, over all possible 2dlithography patterns in a thin dielectric film. The key to our formulation is a frequencyaveraged local density of states (LDOS), where the frequency averaging corresponds to the desired bandwidth, evaluated by a novel technique: solving a single scattering problem at a complex frequency. To compute the objective LDOS, we implement a full 3D Maxwell's equation frequency domain parallel solver in C (PETSc). For the optimization, we use gradientbased algorithms from the optimization library NLOPT. The optimized structure we obtained for 3D slab is four times better (same order of Q, but much smaller V) than previous hand designs in the literature.
The optimization of a 2D microcavity for TM polarization from photonic crystal initial guess (blue for air and red for silicon):
Teaching
Fall 2010 18.03 Differential Equations
Fall 2008 18.305 Advanced Analytic Methods