John S. LowengrubChancellor’s Professor, Mathematics Professor, Biomedical Engineering Professor, Chemical Engineering & Materials Science 
Research Interests 
mathematical materials science, mathematical fluid dynamics, mathematical biology, computational mathematics, cancer modeling, nanomaterials, quantum dots, complex fluids  
URL  www.math.uci.edu/~lowengrb  
Academic Distinctions  7/09–Present Chancellor’s Professor  
Appointments 
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 

Publications  1. The Convergence of the Vortex Method for Vortex Sheets, with R.C. Caflisch, SIAM J. Num. Anal., 26, pp. 10601080, 1989.  
2. The Convergence of the Vortex Method for Vortex Sheets, Mathematical Aspects of Vortex Dynamics, ed. R.C. Caflisch, SIAM, pp. 120127, 1989.  
3. The Convergence of the Point Vortex Method for the 2D Euler Equations, with J. Goodman and T.Y. Hou, Comm. Pure Appl. Math, XLIII, pp. 415430, 1990.  
4. The Convergence of the Point Vortex Method for the 3D Euler Equations, with T.Y. Hou, Comm. Pure Appl. Math, XLIII, pp. 965981, 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. 423432, 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. 341362, 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. 308320, 1991.  
8. On the WellPosedness 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. 1138, 1992.  
9. Asymptotic and Numerical Results for Blowingup Solutions to SemiLinear 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. 111130, 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. 118, 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. 11071142, 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. 12691301, 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. 312338, 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. 127, 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 SolidSolid Phase Transformations, ed. W.C. Johnson, J.M. Howe, D.E. Laughlin, W.A. Soffa, The Minerals, Metals and Materials Society, Warrendale, PA, pp. 635640, 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. 19331954, 1997.  
18. Microstructural Evolution in Inhomogeneous Elastic Media, with H.J.Jou and P.H. Leo, J. Comp. Phys., 131, pp. 109148, 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. 107127, 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. 21132130, 1998.  
21. Quasiincompressible CahnHilliard Fluids and Topological Transitions, with L. Truskinovsky, Proc. Roy. Soc. London A 454, pp. 26172654, 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. 14651496, 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. 221236, 1999.  
24. Microstructural Evolution in Orthotropic Elastic Media, with P.H. Leo and Q. Nie, J. Comp. Phys., 157, pp. 4488, 2000.  
25. A Comparison of Experiments and Simulations on PinchOff 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 HTD368/BED47 (2000), 2331.  
27. Boundary Integral Methods for Multicomponent Fluids and Multicomponent Materials, with T.Y. Hou and M.J. Shelley, J. Comp. Phys. 169 (2001), 302362.  
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), 228252.  
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), 27612772.  
31. Modelling Pinchoff and Reconnection in a HeleShaw Cell Part I: The Models and their Calibration, with H. Lee and J. Goodman, Phys. Fluids 14 (2002), 492513.  
32. Modelling Pinchoff and Reconnection in a HeleShaw Cell Part II: Analysis and Simulation in the Nonlinear Regime, with H. Lee and J. Goodman, Phys. Fluids 14 (2002), 514545.  
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), 19151931.  
34. Three dimensional crystal growth. I. Linear analysis and selfsimilar 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 threedimensional 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 CahnHilliard fluids, with J.S. Kim, K. Kang, J. Comp. Phys. 193 (2004) 511543.  
38. Three dimensional crystal growth II. Nonlinear simulation and control of the MullinsSekerka instability, with V. Cristini, J. Crystal Growth 266 (2004) 552.  
39. Conservative multigrid methods for ternary CahnHilliard systems, with J.S. Kim and K. Kang, Comm. Math. Sci. 2 (2004) 53.  
40. Nonlinear theory of selfsimilar growth and melting, with S. Li, P.H. Leo and V. Cristini, J. Crystal Growth 267 (2004) 703.  
41. A surfactant conserving volumeoffluid method for interfacial flows with insoluble surfactant, with A. James, J. Comp. Phys. 201 (2004) 685722.  
42. Two and three dimensional equilibrium morphology of a misfitting particle and the GibbsThomson effect , with X. Li, K. Thornton, Q. Nie and P.W Voorhees, Acta Metall. 52 (2004) 58295843.  
43. Efficient phasefield 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) 293304.  
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. Phasefield 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) 191220.  
47. Nonlinear stability analysis of selfsimilar crystal growth: Control of the MullinsSekerka Instability, with S. Li, P.H. Leo and V. Cristini, J. Crystal Growth 277 (2005) 578592.  
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 levelset simulations of multiphase flows, with X. Zheng, A. Anderson and V. Cristini, J. Comp. Phys., 208 (2005) 626650.  
51. Phase field modeling and simulation of three phase flows, with J.S. Kim, Int. Free Bound. 7 (2005) 435466.  
52. Nonlinear morphological control of growing crystals, with S.W. Li and P.H. Leo, Physica D 208 (2005) 209219.  
53. Quantum dot formation on a strainpatterned 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 levelset method for interfacial flows with surfactant, with J.J. Xu, Z.L. Li and H.K. Zhao, J. Comp. Phys. 212 (2006) 590616.  
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) 279289.  
56. An improved geometryaware curvature discretization for level set methods: Application to tumor growth, with P. Macklin, J. Comp. Phys. 215 (2006) 392401.  
57. Analysis of cell growth in threedimensional scaffolds, with J.C.Y. Dunn, W.Y. Chan, V. Cristini, J.S. Kim, S. Singh, B.M. Wu, Tissue Eng. 12 (2006) 705716.  
58. Numerical evidence of nonuniqueness in the evolution of vortex sheets, with M.C. Lopes, H.J.N. Lopes and Y. Zheng, ESAIMMath. Model. Numer. Anal. 40 (2006) 225237.  
59. An adaptive coupled levelset/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) 364394.  
60. Nonmonotone 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) 512528.  
61. A deterministic mechanism for dendritic solidification kinetics, with M.E. Glicksman and S. Li, JOM 59 (2007) 2734.  
62. Nonlinear threedimensional simulation of solid tumor growth, with X. Li, V. Cristini and Q. Nie, Discrete Contin. Dyn. System B 7 (2007) 581604.  
63. Nonlinear simulation of the effect of the microenvironment on tumor growth, with P. Macklin, J. Theor. Biol. 245 (2007) 677704.  
64. A rescaling scheme with application to the long time simulation of viscous fingering in a HeleShaw cell, with S. Li and P.H. Leo, J. Comp. Phys. 225 (2007) 554567.  
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) 119.  
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) S59S70.  
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) 151166.  
68. Solving the regularized, strongly anisotropic CahnHilliard equation by an adaptive nonlinear multigrid method, with S.M. Wise and J.S. Kim, J. Comp. Phys. 226 (2007) 414446.  
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 sidebranching in dendritic growth, with S. Li, X. Li and M. Glicksman, Fluid Dyn. Mater. Proc. 2 (2007) 18.  
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) 113181.  
72. A ghostcell/levelset method for nonlinear moving boundary problems, with P. Macklin, J. Sci. Comput. 35 (2008) 266299.  
73. Threedimensional multispecies nonlinear tumor growthI. Model and numerical method, with S.M. Wise, H.B. Frieboes and V. Cristini, J. Theor. Biol. 253 (2008) 524543.  
74. A new method for simulating strongly anisotropic CahnHilliard equations , with S. Torabi, S. Wise, A. Ratz and A. Voigt, Proc. Mater. Sci. Tech. 2007.  
75. Phasefield 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) 11116.  
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) 723763.  
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) 765798.  
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) 44934501.  
79. Phasefield 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 phasefield model for strongly anisotropic systems, with S. Torabi, A. Voigt and S.M. Wise, Proc. R. Soc. London A 465 (2009) 13371359  
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) 433482. (invited review)  
82. Stable and efficient finitedifference nonlinear multigrid schemes for the phasefield crystal equation, with Z. Hu, S.M. Wise, C. Wang, J. Comput. Phys. 228 (2009) 53235339.  
83. An energy stable and convergent finitedifference scheme for the phasefield crystal equation, with S.M. Wise and C. Wang, SIAM J. Numer. Anal. 47 (2009) 22692288.  
84. Solving PDES in complex geometries: A diffuse domain approach, with X. Li, A. Ratz and A. Voigt, Commun. Math. Sci. 7 (2009) 81107.  
85. Control of viscous fingering patterns in a radial HeleShaw cell , with S. Li, J. Fontana and P. PalffyMuhoray, 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) 3946.  
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) 119144.  
88. A diffuseinterface 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).  
Grants  Oct 2009 Sept 2011 Grand Opportunity Award Feedback, lineages and cancer: A multidisciplinary approach National Institutes of Health (coPI Arthur Lander, UCI)  
June 2008 Chancellor’s award for Excellence in Fostering Undergraduate Research UC Irvine  
April 2008 Distinguished MidCareer Faculty Award for Research UC Irvine  
June 2006  May 2009 NSF Grant in the Division of Materials Research New epitaxial nanostructures in the limited adatom mobility regime (coPI, with Professor Robert Hull, U. Va.(PI))  
August 2005  July 2009 NSF Grant in the Division of Materials Research NSFEC Cooperative Activity in Computational materials research: Bridging the atomistic to the continuum– Multiscale investigation of selfassembling magnetic dots during epitaxial growth (coPI, with Professors M. Asta (coPI), P.W. Voorhees (coPI) and K. Thornton (PI))  
Jul 1994Aug 2012 NSF Grants in the Division of Mathematical Sciences Current Grants: (1) Multiscale modeling of solid tumor growth (2) Computational problems in heterogeneous nanomaterials (3) Morphological control of material microstructures  
Jul 2006June 2007 University of California, Irvine Research Experience for Undergraduates Agentbased models of tumor growth (awarded for Aaron Abajian). Also awarded Henry Samueli Engineering School Undergraduate Fellowship.  
June 2006Sept 2006 University of California, Irvine Research Experience for Undergraduates Turing instability for irregular domains (awarded for Katiya Pavlova)  
Jul 2004June 2005 University of California, Irvine Research Experience for Undergraduates Nonlinear 3D modeling of tumor growth (awarded for Genevieve Brown)  
Jan 2002July 2003 University of Minnesota Research Experience for Undergraduates The development of a three dimensional adaptive tetrahedal mesh (awarded for Tony Anderson)  
July 2001June 2002 Minnesota Supercomputer Institute Research Scholarship Numerical Simulation of Microstructured Materials (awarded for Dr. Vittorio Cristini)  
Jan 1998Dec 2004 DOE Grants in the Basic Energy Sciences Division Fundamental Studies of Topological Transitions in Liquid/Liquid Flows (PI, with Professor E.K. Longmire (coPI)).  
Nov 1998 Francois Frenkiel Award American Physical Society, Fluid Dynamics Division  
Sept 19962001 NSF Group Infrastructure Grant Infrastructural Needs for Preparing Students for the Industrial and Business Workforce (coPI, with Professors B.Cockburn (coPI), A. Friedman (coPI), and F. Santosa (PI))  
Sept 19951997 Sloan Foundation Fellowship  
July 19941996 McKnight Foundation Professorship University of Minnesota  
June 19901993 NSF Postdoctoral Fellowship  
Other Experience 
Assistant Professor University of Minnesota 1992—1995 

Associate Professor University of Minnesota 1995—1999 

Professor University of Minnesota 1999—2003 

Professor University of North Carolina 1999—2001 

Graduate Programs 
Mathematical and Computational Biology 

Research Centers  Center for Complex Biological Systems (CCBS)  
Mathematical, Computational and Systems Biology (MCSB)  
Link to this profile  http://www.faculty.uci.edu/profile.cfm?faculty_id=5697  
Last updated  12/02/2009  