mathematical materials science, mathematical fluid dynamics, mathematical biology, computational mathematics, cancer modeling, nanomaterials, quantum dots, complex fluids
7/09–Present Chancellor’s Professor
Sept 1991–June 1992 Member
School of Mathematics, Institute for Advanced Study
June 1990–June 1993 NSF Postdoctoral Fellow
Stanford Advisor: Professor Joseph Keller
Minnesota Advisor: Professor Mitchell Luskin
July 1989–Sept 1992 Szego Assistant Professor
Department of Mathematics, Stanford University
Sept 1988–June 1989 Visiting Member
Courant Institute of Mathematical Sciences, New York University
1. The Convergence of the Vortex Method for Vortex Sheets, with R.C. Caflisch, SIAM J. Num. Anal., 26, pp. 1060-1080, 1989.
2. The Convergence of the Vortex Method for Vortex Sheets, Mathematical Aspects of Vortex Dynamics, ed. R.C. Caflisch, SIAM, pp. 120-127, 1989.
3. The Convergence of the Point Vortex Method for the 2-D Euler Equations, with J. Goodman and T.Y. Hou, Comm. Pure Appl. Math, XLIII, pp. 415-430, 1990.
4. The Convergence of the Point Vortex Method for the 3-D Euler Equations, with T.Y. Hou, Comm. Pure Appl. Math, XLIII, pp. 965-981, 1990.
5. Smooth Grid Methods for the Vorticity Formulation of the Euler Equations, with M.J. Shelley, in Vortex Dynamics and Methods, ed. C. Anderson and C. Greengard, Lectures in Applied Mathematics, 28, AMS, pp. 423-432, 1991.
6. The Convergence of an Exact Desingularization and Local Regridding for Vortex Methods, with T.Y. Hou and M.J. Shelley, in Vortex Dynamics and Methods, ed. C. Anderson and C. Greengard, Lectures in Applied Mathematics, v. 28, AMS, pp. 341-362, 1991.
7. The Convergence of a Point Vortex Method for Vortex Sheets, with T.Y. Hou and R. Krasny, SIAM J. Num. Anal., 28, pp. 308-320, 1991.
8. On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension, with J.T. Beale and T.Y. Hou, in Singularities in Fluids, Plasmas and Optics, ed. R. Caflisch and G. Papanicolaou, NATO ASI Series, Kluwer Publishers, pp. 11-38, 1992.
9. Asymptotic and Numerical Results for Blowing-up Solutions to Semi-Linear Heat Equations, with J.B. Keller, in Singularities in Fluids, Plasmas and Optics, ed. R.C. Caflisch and G. Papanicolaou, NATO ASI Series, Kluwer Publishers, pp. 111-130, 1992.
10. The Convergence of an Exact Desingularization for Vortex Methods, with T.Y. Hou and M.J. Shelley, SIAM J. Sci. Comp., 14, pp. 1-18, 1993.
11. High Order and Efficient Methods for the Vorticity Formulation of the Euler Equations, with M.J. Shelley and B. Merriman, SIAM J. Sci. Comp., 14, pp. 1107-1142, 1993.
12. Growth Rates for the Linearized Motion of Fluid Interfaces away from Equilibrium, with J.T. Beale and T.Y. Hou, Comm. Pure Appl. Math., XLVI, pp. 1269-1301, 1993.
13. Removing the Stiffness from Interfacial Flows with Surface Tension, with T.Y. Hou and M.J. Shelley, J. Comp. Phys., 114, No. 2, pp. 312-338, 1994.
14. Spatial and Temporal Stability Issues for Interfacial Flows with Surface Tension, with J.T. Beale, T.Y. Hou and M.J. Shelley, J. Math. and Comp. Modelling, 20, No. 10/11, pp. 1-27, 1994.
15. Numerical Calculations of Precipitate Shape Evolution in Elastic Media, with H.-J. Jou and P. Leo, to appear in Proceedings of an International Conference on Solid-Solid Phase Transformations, ed. W.C. Johnson, J.M. Howe, D.E. Laughlin, W.A. Soffa, The Minerals, Metals and Materials Society, Warrendale, PA, pp. 635-640, 1994.
16. Convergence of Boundary Integral Methods for Water Waves, with J.T. Beale and T.Y. Hou, SIAM J. Num. Anal., 33, 1797, 1996.
17. The long time motion of vortex sheets with surface tension, with T.Y. Hou and M.S. Shelley, Phys. Fluids, 9, pp. 1933-1954, 1997.
18. Microstructural Evolution in Inhomogeneous Elastic Media, with H.J.-Jou and P.H. Leo, J. Comp. Phys., 131, pp. 109-148, 1997.
19. Stability of Boundary Integral Methods for Water Waves, with J.T. Beale and T.Y. Hou, AMS/IP Stud. Adv. Math, 3 (Nonlinear Evolutionary Partial Differential Equations, Beijing 1993), pp. 107-127, 1997.
20. A Diffuse Interface Model for Microstructural Evolution in Elastically Stressed Solids, with P.H. Leo and H.-J. Jou, Acta Materialia, 46, pp. 2113-2130, 1998.
21. Quasi-incompressible Cahn-Hilliard Fluids and Topological Transitions, with L. Truskinovsky, Proc. Roy. Soc. London A 454, pp. 2617-2654, 1998.
22. Almost Optimal Convergence of the Point Vortex Method for Vortex Sheets using Numerical Filtering, with R.C. Caflish and T.Y. Hou, Math. Comp., 68, pp. 1465-1496, 1999.
23. Topological Transitions in Liquid/Liquid Interfaces, with J. Goodman, H. Lee, E. Longmire, M.J. Shelley and L. Truskinovsky, Chapman & Hall/CRC Res. Notes Math, 409 (Free Boundary Problems: Theory and Applications, Crete 1997), pp. 221-236, 1999.
24. Microstructural Evolution in Orthotropic Elastic Media, with P.H. Leo and Q. Nie, J. Comp. Phys., 157, pp. 44-88, 2000.
25. A Comparison of Experiments and Simulations on Pinch-Off in Round Jets, with E.K. Longmire and D.L. Gefroh, in Proceedings of the 1999 ASME/JSME Meeting, San Francisco.
26. Measurement and modeling of latent heat release during freezing in a small container, with R. V. Devireddy, J.C. Bischof, P.H. Leo, ASME IMECE HTD-368/BED-47 (2000), 23-31.
27. Boundary Integral Methods for Multicomponent Fluids and Multicomponent Materials, with T.Y. Hou and M.J. Shelley, J. Comp. Phys. 169 (2001), 302-362.
28. Focusing of an elongated hole in porous medium flow, with S.B. Angenent, D.G. Aronson and S.I. Betelu, Physica D 151 (2001), 228-252.
29. Modeling multiphase flows using a novel 3D adaptive remeshing algorithm, with R. Hooper V. Cristini, S. Shakya, C. W. Macosko and J. J. Derby, In Computational Methods in Multiphase Flow, Eds.: C.A. Brebbia and H. Power, Series: Advances in Fluid Mechanics, Vol. 29, Wessex Institute of Technology Press, UK, 2001.
30. On an Elastically Induced Splitting Instability, with P.H. Leo and Q. Nie, Acta Mater. 49 (2001), 2761-2772.
31. Modelling Pinchoff and Reconnection in a Hele-Shaw Cell Part I: The Models and their Calibration, with H. Lee and J. Goodman, Phys. Fluids 14 (2002), 492-513.
32. Modelling Pinchoff and Reconnection in a Hele-Shaw Cell Part II: Analysis and Simulation in the Nonlinear Regime, with H. Lee and J. Goodman, Phys. Fluids 14 (2002), 514-545.
33. Measurement and numerical analysis of freezing in solutions enclosed in a small container, R. Devireddy, P. Leo and J. Bischof, Int. J. Heat Mass Transfer 45 (2002), 1915-1931.
34. Three dimensional crystal growth. I. Linear analysis and self-similar evolution, with V. Cristini, J. Crystal Growth, 240 (2002) 267.
35. Nonlinear simulation of tumor growth, with V. Cristini and Q. Nie, J. Math. Biol. 46 (2003) 191.
36. Microstructure evolution in three-dimensional inhomogeneous elastic media, with X. Li, Q. Nie, P.H. Leo and V. Cristini, Met. Mater. Trans. A 34A (2003) 1421.
37. Conservative multigrid methods for Cahn-Hilliard fluids, with J.-S. Kim, K. Kang, J. Comp. Phys. 193 (2004) 511-543.
38. Three dimensional crystal growth II. Nonlinear simulation and control of the Mullins-Sekerka instability, with V. Cristini, J. Crystal Growth 266 (2004) 552.
39. Conservative multigrid methods for ternary Cahn-Hilliard systems, with J.-S. Kim and K. Kang, Comm. Math. Sci. 2 (2004) 53.
40. Nonlinear theory of self-similar growth and melting, with S. Li, P.H. Leo and V. Cristini, J. Crystal Growth 267 (2004) 703.
41. A surfactant conserving volume-of-fluid method for interfacial flows with insoluble surfactant, with A. James, J. Comp. Phys. 201 (2004) 685-722.
42. Two- and three dimensional equilibrium morphology of a misfitting particle and the Gibbs-Thomson effect , with X. Li, K. Thornton, Q. Nie and P.W Voorhees, Acta Metall. 52 (2004) 5829-5843.
43. Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film, with S.M. Wise, J.S. Kim and W.C. Johnson, J. Superlattices and Microstructures 36 (2004) 293-304.
44. Experiments and computations on drop impact at a liquid/liquid interface, with Z. Mohamed Kassim, E.K. Longmire, J.-S. Kim, X. Zheng , Proc. 5th Int. Conf. Multiphase Flow, paper no. 122 (2004) in press.
45. Phase-field modeling of step dynamics, with Z. Hu, S.M. Wise, J.S. Kim and A. Voigt, MRS Proceedings 859E (JJ8.6), J. Evans, C. Orme, M. Asta and Z. Zhang eds., 2004.
46. Evolving interfaces via gradients of geometry dependent interior Poisson problems: Application to tumor growth, with P. Macklin, J. Comp. Phys. 203 (2005) 191-220.
47. Nonlinear stability analysis of self-similar crystal growth: Control of the Mullins-Sekerka Instability, with S. Li, P.H. Leo and V. Cristini, J. Crystal Growth 277 (2005) 578-592.
48. Modeling coarsening dynamics using interface tracking methods, invited review, Handbook of Materials Modeling, vol 1., S. Yip ed., Kluwer Acad. Press (2005) in press.
49. Interfaces and multicomponent fluids, with J.-S. Kim, Encyclopedia of Math. Phys., J.-P. Francoise, G. Naber and T.-S. Tsun eds., Elsevier (2005), invited review, to appear.
50. Adaptive unstructured volume remeshing algorithms II: Application to two- and three- dimensional level-set simulations of multiphase flows, with X. Zheng, A. Anderson and V. Cristini, J. Comp. Phys., 208 (2005) 626-650.
51. Phase field modeling and simulation of three phase flows, with J.-S. Kim, Int. Free Bound. 7 (2005) 435-466.
52. Nonlinear morphological control of growing crystals, with S.W. Li and P.H. Leo, Physica D 208 (2005) 209-219.
53. Quantum dot formation on a strain-patterned epitaxial thin film, with S.M. Wise, J.S. Kim, K. Thornton, P.W. Voorhees and W.C. Johnson, Appl. Phys. Lett. 87 (2005) 133102.
54. A level-set method for interfacial flows with surfactant, with J.J. Xu, Z.L. Li and H.-K. Zhao, J. Comp. Phys. 212 (2006) 590-616.
55. Phase reconstruction by the weighted least action principle, with C.M. Lee J. Rubinstein and X.M. Zheng, J. Optics A- Pure Appl. Optics 8 (2006) 279-289.
56. An improved geometry-aware curvature discretization for level set methods: Application to tumor growth, with P. Macklin, J. Comp. Phys. 215 (2006) 392-401.
57. Analysis of cell growth in three-dimensional scaffolds, with J.C.Y. Dunn, W.Y. Chan, V. Cristini, J.S. Kim, S. Singh, B.M. Wu, Tissue Eng. 12 (2006) 705-716.
58. Numerical evidence of nonuniqueness in the evolution of vortex sheets, with M.C. Lopes, H.J.N. Lopes and Y. Zheng, ESAIM-Math. Model. Numer. Anal. 40 (2006) 225-237.
59. An adaptive coupled level-set/volume of fluid interface tracking method for unstructured triangular grids, with X. Yang, A. James, X. Zheng and V. Cristini, J. Comp. Phys. 217 (2006) 364-394.
60. Non-monotone temperature boundary conditions in dendritic growth, with M.E. Glicksman and S. Li, Proc. Modelling of Casting, Welding and Adv. Solid Processes XI, ed. C.A. Gandin, M. Bellet, (2006) 512-528.
61. A deterministic mechanism for dendritic solidification kinetics, with M.E. Glicksman and S. Li, JOM 59 (2007) 27-34.
62. Nonlinear three-dimensional simulation of solid tumor growth, with X. Li, V. Cristini and Q. Nie, Discrete Contin. Dyn. System B 7 (2007) 581-604.
63. Nonlinear simulation of the effect of the microenvironment on tumor growth, with P. Macklin, J. Theor. Biol. 245 (2007) 677-704.
64. A rescaling scheme with application to the long time simulation of viscous fingering in a Hele-Shaw cell, with S. Li and P.H. Leo, J. Comp. Phys. 225 (2007) 554-567.
65. Surface phase separation and flow in a simple model of multicomponent drops and vesicles, with J.-J. Xu and A. Voigt, Fluid Dyn. Mater. Proc., 3 (2007) 1-19.
66. Computer simulation of glioma growth and morphology, with H.B. Frieboes, S. Wise, X. Zheng, P. Macklin, E. Bearer, V. Cristini, NeuroImage 37 (2007) S59-S70.
67. Morphological stability analysis of the epitaxial growth of a circular island: Application to nanoscale shape control, with Z. Hu and S. Li, Physica D 233 (2007) 151-166.
68. Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method, with S.M. Wise and J.-S. Kim, J. Comp. Phys. 226 (2007) 414-446.
69. A linear stability analysis for step meandering instabilities including the effects of elastic interactions and ES Barriers, with D.-H. Yeon, P.-R. Cha, A. Voigt and K. Thornton, Phys. Rev. E 76 (2007) 011601.
70. A deterministic mechanism for side-branching in dendritic growth, with S. Li, X. Li and M. Glicksman, Fluid Dyn. Mater. Proc. 2 (2007) 1-8.
71. Nonlinear modeling and simulation of tumor growth , with V. Cristini, H.B. Frieboes, X. Li, P. Macklin, S. Sanga, S.M. Wise and X. Zheng, in Modeling and Simulation in Science, Engineering and Technology, ed. N. Bellomo, M. Chaplain and E. DeAngelis, Birkhauser, Boston, (2008) 113-181.
72. A ghost-cell/level-set method for nonlinear moving boundary problems, with P. Macklin, J. Sci. Comput. 35 (2008) 266-299.
73. Three-dimensional multispecies nonlinear tumor growth-I. Model and numerical method, with S.M. Wise, H.B. Frieboes and V. Cristini, J. Theor. Biol. 253 (2008) 524-543.
74. A new method for simulating strongly anisotropic Cahn-Hilliard equations , with S. Torabi, S. Wise, A. Ratz and A. Voigt, Proc. Mater. Sci. Tech. 2007.
75. Phase-field modeling of nanoscale island dynamics , with Z. Hu, S. Li, S. Wise and A. Voigt, Proc. TMS 2008 (137th meeting) Supplemental Proceedings: Materials Processing and Properties (2008) 111-16.
76. Nonlinear simulations of solid tumor growth using a mixture model: Invasion and branching, with V. Cristini, X. Li and S.M. Wise, J. Math. Biol. 58 (2009) 723-763.
77. Multiscale modeling and nonlinear simulation of vascular tumour growth , with P. Macklin, S. McDougall, A.R.A. Anderson, M.A.J. Chaplain and V. Cristini, J. Math. Biol. 58 (2009) 765-798.
78. Multiparamter computational modeling of tumor invasion, with E.L. Bearer, Y.-L. Chuang, H.B. Frieboes, F. Jin, S.M. Wise, M. Ferrari, D.B. Agus, V. Cristini, Cancer Res. 69 (2009) 4493-4501.
79. Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding and fission, with A. Rätz and A. Voigt, Phys. Rev. E 79 (2009) 031926.
80. A new phase-field model for strongly anisotropic systems, with S. Torabi, A. Voigt and S.M. Wise, Proc. R. Soc. London A 465 (2009) 1337-1359
81. Geometric evolution laws for thin crystal line films: Modeling and numerics, with B. Li, A. Rätz and A. Voigt, Comm. Comp. Phys. 6 (2009) 433-482. (invited review)
82. Stable and efficient finite-difference nonlinear multigrid schemes for the phase-field crystal equation, with Z. Hu, S.M. Wise, C. Wang, J. Comput. Phys. 228 (2009) 5323-5339.
83. An energy stable and convergent finite-difference scheme for the phase-field crystal equation, with S.M. Wise and C. Wang, SIAM J. Numer. Anal. 47 (2009) 2269-2288.
84. Solving PDES in complex geometries: A diffuse domain approach, with X. Li, A. Ratz and A. Voigt, Commun. Math. Sci. 7 (2009) 81-107.
85. Control of viscous fingering patterns in a radial Hele-Shaw cell , with S. Li, J. Fontana and P. Palffy-Muhoray, Phys. Rev. Lett. 102 (2009) 174501.
86. Coarsening of 3D thin films under the influence of strong surface anisotropy, elastic stresses, with P. Zhou and S.M. Wise, TMS 2009 (138th annual meeting), Supplemental Proceedings: Materials Characterization, Computation and Modeling (2009) 39-46.
87. Dynamics of multicomponent vesicles in a viscous fluid, with J.-S. Sohn, Y.-H. Tseng, S. Li, A. Voigt, J. Comput. Phys. 229 (2010) 119-144.
88. A diffuse-interface approach for modeling transport, diffusion and adsorption/desorption of material quantities on a deformable interface, with K.E. Teigen, X. Li, F. Wang and A. Voigt, Comm. Math. Sci., to appear.
89. Selection in spatial stochastic models of cancer: Migration as a key modulator of fitness, with C.J. Thalhauser, D. Stupack and N.L. Komarova, Biology Direct (2009), to appear.
90. Nonlinear modeling of cancer: Bridging the gap between cells and tumors, with H.B. Frieboes, F. Jin, Y.-L. Chuang, X. Li, P. Macklin, S.M. Wise and V. Cristini, Nonlinearity (2010) to appear. (invited review).
Oct 2009- Sept 2011 Grand Opportunity Award
Feedback, lineages and cancer: A multidisciplinary approach National Institutes of Health (co-PI Arthur Lander, UCI)
June 2008 Chancellor’s award for Excellence in Fostering Undergraduate Research
April 2008 Distinguished Mid-Career Faculty Award for Research
June 2006 - May 2009 NSF Grant in the Division of Materials Research
New epitaxial nanostructures in the limited adatom mobility regime (co-PI, with Professor Robert Hull, U. Va.(PI))
August 2005 - July 2009 NSF Grant in the Division of Materials Research
NSF-EC Cooperative Activity in Computational materials research: Bridging the atomistic to the continuum– Multiscale investigation of self-assembling magnetic dots during epitaxial growth (co-PI, with Professors M. Asta (co-PI), P.W. Voorhees (co-PI) and K. Thornton (PI))
Jul 1994-Aug 2012 NSF Grants in the Division of Mathematical Sciences
(1) Multiscale modeling of solid tumor growth
(2) Computational problems in heterogeneous nanomaterials
(3) Morphological control of material microstructures
Jul 2006-June 2007 University of California, Irvine Research Experience for Undergraduates
Agent-based models of tumor growth (awarded for Aaron Abajian). Also awarded Henry Samueli Engineering School Undergraduate Fellowship.
June 2006-Sept 2006 University of California, Irvine Research Experience for Undergraduates
Turing instability for irregular domains (awarded for Katiya Pavlova)
Jul 2004-June 2005 University of California, Irvine Research Experience for Undergraduates
Nonlinear 3D modeling of tumor growth (awarded for Genevieve Brown)
Jan 2002-July 2003 University of Minnesota Research Experience for Undergraduates
The development of a three dimensional adaptive tetrahedal mesh (awarded for Tony Anderson)
July 2001-June 2002 Minnesota Supercomputer Institute Research Scholarship
Numerical Simulation of Microstructured Materials (awarded for Dr. Vittorio Cristini)
Jan 1998-Dec 2004 DOE Grants in the Basic Energy Sciences Division
Fundamental Studies of Topological Transitions in Liquid/Liquid Flows (PI, with Professor E.K. Longmire (co-PI)).
Nov 1998 Francois Frenkiel Award
American Physical Society, Fluid Dynamics Division
Sept 1996-2001 NSF Group Infrastructure Grant
Infrastructural Needs for Preparing Students for the Industrial and Business Workforce (co-PI, with Professors B.Cockburn (co-PI), A. Friedman (co-PI), and F. Santosa (PI))
Sept 1995-1997 Sloan Foundation Fellowship
July 1994-1996 McKnight Foundation Professorship
University of Minnesota
June 1990-1993 NSF Postdoctoral Fellowship
University of Minnesota 1992—1995
University of Minnesota 1995—1999
University of Minnesota 1999—2003
University of North Carolina 1999—2001
Mathematical and Computational Biology
Center for Complex Biological Systems (CCBS)
Mathematical, Computational and Systems Biology (MCSB)