Publications

See also: Chronological List of Publications.

Table of Contents

1. Electrokinetics
• Encyclopedia Articles
• Induced-Charge Electro-osmosis
• Induced-Charge Electrophoresis
• Electro-osmotic Micropumps
2. Electrochemical Systems
• Diffuse-charge Dynamics / Supercapacitors
• Electrodeposition / Corrosion
• Electrochemical Dynamics / Fuel Cells
• Intercalation Dynamics / Li-ion Batteries
3. Fluid Mechanics (See also Electrokinetics.)
• Conformal Mapping (See also Transport-Limited Aggregation.)
• Granular Flow
• Hydrodynamic Slip
4. Statistical Physics
• Random Walks
• Transport-Limited Aggregation
• Percolation
• Breakdown Phenomena
5. Atomistic Modeling of Materials
• Interatomic Potentials
• Molecular Dynamics Simulations
6. Patents
• Microfluidic Devices
• Pebble-Bed Nuclear Reactors
7. Preprints

1. Electrokinetics

Encyclopedia Articles

• Nonlinear electrokinetic phenomena, M. Z. Bazant, in Li, Dongqing (ed), Encyclopedia of Microfluidics and Nanofluidics, Part 14, pp. 1461-1470 (Springer, Berlin, Heidelberg, New York, 2008). (PDF)
• AC Electro-osmotic flow, M. Z. Bazant, in Li, Dongqing (ed), Encyclopedia of Microfluidics and Nanofluidics, Part I, pp. 8-14 (Springer, Berlin, Heidelberg, New York, 2008). ( PDF)
• Electrokinetic motion of polarizable particles , M. Z. Bazant, in Li, Dongqing (ed), Encyclopedia of Microfluidics and Nanofluidics, Part 5, pp. 522-529 (Springer, Berlin, Heidelberg, New York, 2008). ( PDF)
• Electrokinetic motion of heterogeneous particles, M. Z. Bazant, in Li, Dongqing (ed), Encyclopedia of Microfluidics and Nanofluidics, Part 5, pp. 518-522 (Springer, Berlin, Heidelberg, New York, 2008). (PDF)

Induced-Charge Electro-osmosis

• Induced-charge electro-kinetic phenomena: Theory and microfluidic applications, M. Z. Bazant and T. M. Squires, Phys. Rev. Lett. 92, art. no. 066101 (2004). (This paper triggered a Fast Moving Front of research, according to Thompson Scientific.) (PDF)
• Induced-charge electro-osmosis, T. M. Squires and M. Z. Bazant, J. Fluid. Mech. 509, 217-252 (2004). (PDF)
• Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel, J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires, and M. Z. Bazant, Colloids and Surfaces A 267, 122-132 (2005). (PDF)
• Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane, D. Lacoste, G. I. Menon, M. Z. Bazant, and J. F. Joanny, European Physical Journal E 28, 243-264 (2009). (PDF)
• Nonlinear electrokinetics at large voltages, M. Z. Bazant, M. S. Kilic, B. Storey, and A. Ajdari, New Journal of Physics 11, 075016 (2009). invited article for focus issue on micro- and nanofluidics. (PDF)
• Towards an understanding of induced-charge electrokinetics at large applied voltages, M. Z. Bazant, M S Kilic, B Storey, and A Ajdari, Advances in Colloid and Interface Science, 152, 48-88 (2009). (PDF)
• Effective zero-thickness model for a conductive membrane driven by an electric field, F. Ziebert, M. Z. Bazant, and D. Lacoste. (PDF)

Induced-Charge Electrophoresis

• Breaking symmetries in induced-charge electro-osmosis and electrophoresis, T. M. Squires and M. Z. Bazant, J. Fluid Mech. 560, 65-101 (2006). (PDF)
• Induced-charge electrophoresis of metallo-dielectric particles, S. Gangwal, O. J. Cayre, M. Z. Bazant, and O. D. Velev, Phys. Rev. Lett. 100, 058302 (2008). (PDF)
• Induced-charge electrophoresis near an insulating wall, M. S. Kilic and M. Z. Bazant. (PDF)

Electro-osmotic Micropumps

• Theoretical prediction of fast 3D AC electro-osmotic pumps, M. Z. Bazant and Y. Ben, Lab on a Chip, 6, 1455-1461 (2006). (PDF)
• Fast AC electro-osmotic pumps with non-planar electrodes, J. P. Urbanski, T. Thorsen, J. A. Levitan, and M. Z. Bazant, Applied Physics Letters 89, 143508 (2006). (PDF)
• The effect of step height on the performance of AC electro-osmotic microfluidic pumps, J. P. Urbanski, J. A. Levitan, D. N. Burch, T. Thorsen, and M. Z. Bazant, Journal of Interface and Colloid Science 309, 332-341 (2007). (PDF)
• Electrolyte dependence of AC electro-osmosis, M. Z. Bazant, J. P. Urbanski, J. A. Levitan, K. Subramanian, M. S. Kilic, A. Jones, and T. Thorsen, Proceedings of MicroTAS, Paris (2007). (PDF)
• Experimental study of electrolyte dependence of AC electro-osmotic pumps, K. Subramanian, J. P. Urbanski, J. A. Levitan, T. Thorsen, and M. Z. Bazant, Proceedings of the International Conference on Micro, Meso, and Nanoengineering, Trivandrum, India (2007). (PDF)
• Steric effects on ac electro-osmosis in dilute electrolytes, B. Storey, L. R. Edwards, M. S. Kilic, and M. Z. Bazant, Phys. Rev. E 77, 036317 (2008). (PDF)
• Design principle for improved three-dimensional ac electro-osmotic pumps, D. Burch and M. Z. Bazant, Phys. Rev. E 77, 055303(R) (2008). (PDF)
• Numerical studies of nonlinear kinetics in induced-charge electro-osmosis, M. M. Gregersen, M. Z. Bazant, and H. Bruus, XXII ICTAM Proceedings, Adelaide, Australia (2008). (PDF)
• Topology and shape optimization of induced-charge electro-osmotic micropumps M M Gregersen, F Okkels, M Z Bazant, and H Bruus, New Journal of Physics 11, 075016 (2009). (PDF)
• Ultrafast high-pressure AC electro-osmotic micropumps for portable biomedical microfluidics, C. C. Huang, M. Z. Bazant, and T. Thorsen, Lab on a Chip, accepted, in press. (arxiv.org)

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2. Electrochemical Systems

Diffuse-charge Dynamics / Supercapacitors

• Diffuse-charge dynamics in electrochemical systems, M. Z. Bazant, K. Thornton, and A. Ajdari, Phys. Rev. E 70, 021506 (2004). (PDF)
• Nonlinear electrochemical relaxation around conductors, K. T. Chu and M. Z. Bazant, Phys. Rev. E 74, 011501 (2006). (PDF)
• Steric effects in the dynamics of electrolytes at large applied voltages: I. Double-layer charging, M. S. Kilic, M. Z. Bazant, and A. Ajdari, Phys. Rev. E 75, 021502 (2007). (PDF)
• Steric effects in the dynamics of electrolytes at large applied voltages: II. Modified Nernst-Planck equations, M. S. Kilic, M. Z. Bazant, and A.Ajdari, Phys. Rev. E 75, 021503 (2007). (PDF)
• Surface conservation laws at microscopically diffuse interfaces, K. T. Chu and M. Z. Bazant, J. Colloid and Interface Science 315, 319-329 (2007). (PDF)
• Rational materials design through theory and modeling: capacitive energy storage, M. Z. Bazant, K. Kaneko, L. Pratt, and H. White, Basic Reseach Needs for Electrical Energy Storage, Department of Energy, Panel Report (2007). (PDF)
• Strongly nonlinear dynamics of electrolytes under large AC voltages, L. H. Olesen, H. Bruus, and M. Z. Bazant. (arxiv.org)

Electrodeposition / Corrosion

• Regulation of ramified electrochemical growth by a diffusive wave, M. Z. Bazant, Phys. Rev. E, 52, 1903 (1995). (PDF)
• Front dynamics during diffusion-limited corrosion of ramified electrodeposits, C. Leger, F. Argoul and M. Z. Bazant, J. Phys. Chem. B 103, 5841 (1999). (PDF)
• A Two-species reaction-diffusion problem with one static reactant: the case of higher-order kinetics, H. A. Stone and M. Z. Bazant, in Partial Differential Equations in Models of Superfluidity, Superconductivity and Reactive Flows, ed. by H. Berestycki and Y. Pomeau (1999). (PDF)
• Asymptotics of reaction-diffusion fronts with one static and one diffusing reactant, M. Z. Bazant and H. A. Stone, Physica D 147, 95 (2000). (PDF)

Electrochemical Dynamics / Fuel Cells

• Analysis of diffuse-layer effects on time-dependent interfacial kinetics, A. Bonnefont, F. Argoul and M. Z. Bazant, J. Electroanal. Chem. 500, 52 (2001). (e-print with additional material on AC response) (PDF)
• Current-voltage relations for electrochemical thin films,M. Z. Bazant, K. T. Chu, and B. J. Bayly, SIAM J. Appl. Math 65, 1463-1484 (2005). (PDF)
• Electrochemical thin films at and above the classical limiting current, K. T. Chu and M. Z. Bazant, SIAM J. Appl. Math 65, 1485-1505 (2005). (PDF)
• Diffuse charge effects in fuel-cell membranes, P. M. Biesheuvel, A. A. Franco, and M. Z. Bazant, J. Electrochem. Soc., 156, B225-B233 (2009). (PDF)
• Imposed currents in galvanic cells, P. M. Biesheuvel, M. van Soestbergen, and M. Z. Bazant, Electrochimica Acta 54, 4857-4871 (2009). ( PDF)
• Diffuse charge effects on the transient response of electrochemical cells, M. van Soestbergen, P. M. Biesheuvel, and M. Z. Bazant, Phys. Rev. E, in press. (PDF)
• Nonlinear dynamics of capacitive charging and desalination by porous electrodes, M. Biesheuvel and M. Z. Bazant. (PDF, arXiv).

Intercalation Dynamics / Li-ion Batteries

• Intercalation dynamics in rechargeable battery materials: General theory and phase-transformation waves in LiFePO₄, G. Singh, G. Ceder, and M. Z. Bazant, Electrochimica Acta 53, 7599-7613 (2008). (PDF)
• Phase-transformation wave dynamics in LiFePO₄, D. Burch, G. Singh, G. Ceder, and M. Z. Bazant, Solid State Phenomena 139, 95-100 (2008). (PDF)
• Size-dependent spinodal and miscibility gaps for intercalation in nanoparticles D. Burch and M. Z. Bazant, Nano Letters 9, 3795-3800 (2009). ( PDF)

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3. Fluid Mechanics

Conformal Mapping

• Conformal mapping of some non-harmonic functions in transport theory, M. Z. Bazant, Proc. Roy. Soc. A. 460, 1433-1452 (2004). (PDF)
• Steady advection-diffusion around finite absorbers in two-dimensional potential flows, J. Choi, D. Margetis, T. M. Squires, and M. Z. Bazant, J. Fluid Mech. 536, 155-184 (2005). (PDF)
• Exact solutions of the Navier-Stokes equations having steady vortex structures, M. Z. Bazant and H. K. Moffatt, J. Fluid Mech. 541, 55-64 (2005). (PDF)
• Conformal mapping methods for interfacial dynamics, M. Z. Bazant and D. Crowdy, in the Handbook of Materials Modeling, ed. by S. Yip et al., Vol. I, Art. 4.10 (Springer, 2005). (PDF)
• Interfacial dynamics during transport-limited dissolution, M. Z. Bazant, Phys. Rev. E 73, 060601 (2006). (PDF)

Granular Flow

• Diffusion and mixing in gravity-driven dense granular flows, J. Choi, A. Kudrolli, R. R. Rosales, and M. Z. Bazant, Phys. Rev. Lett. 92, 174301 (2004). (non-technical summary) (PDF)
• Pebble flow experiments for pebble-bed reactors, A. C. Kadak and M. Z. Bazant, Proceedings of the International Meeting on High Temperature Reactor Technology, Beijing, China (2004). (PDF)
• Velocity profile of granular flows in silos and hoppers, J. Choi, A. Kudrolli, and M. Z. Bazant, J. Phys.: Condens. Matter 17, S2533-S2548 (2005). (PDF)
• The Spot Model for random-packing dynamics, M. Z. Bazant, Mechanics of Materials 38, 717-731 (2006). (PDF)
• Dynamics of random packings in granular flow, C. H. Rycroft, M. Z. Bazant, J. Landry, and G. S. Grest, Physical Review E, 73, 051306 (2006). (PDF)
• Analysis of granular flow in a pebble-bed nuclear reactor, C. H. Rycroft, G. S. Grest, M. Z. Bazant, and J. Landry, Phys. Rev. E, 74, 021306 (2006). (PDF)
• Stochastic flow rule for granular materials, K. Kamrin and M. Z. Bazant, Phys. Rev. E 75, 041301 (2007). (PDF)
• The Stochastic Flow Rule: A multiscale model for granular materials, K. Kamrin, C. H. Rycroft and M. Z. Bazant, Modeling and Simulation in Materials Science and Engineering 15, S449-S464 (2007). (PDF)
• Assessing continuum postulates in simulations of granular flow, C. H. Rycro ft, K. Kamrin, and M. Z. Bazant, Journal of the Mechanics and Physics of Solids 7, 828-839 (2009). PDF)
• Fast spot-based multiscale simulations of granular flow, C. H. Rycroft, Y. L. Wong and M. Z. Bazant. (Dry Fluids Lab preprint, PDF)

Hydrodynamic Slip

• Tensorial hydrodynamic slip, M. Z. Bazant and O. I. Vinogradova, Journal of Fluid Mechanics 613, 125-134 (2008). (PDF)
• Effective slip over textured superhydrophobic surfaces, F. Feuillebois, M. Z. Bazant, and O. I. Vinogradova, Phys. Rev. Lett. 102, 026001 (2009). (PDF)
• Anisotropic electro-osmotic flow over super-hydrophobic surfaces, S. Bahga, O. I. Vinogradova, and M. Z. Bazant, J. Fluid Mech., in press (a rxiv.org)
• Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor, K. Kamrin, M. Z. Bazant, and H. A. Stone. (arXiv)

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4. Statistical Physics

Random Walks

• Corrections to the Central Limit Theorem for heavy-tailed probability densities, H. Lam, J. Blanchet, D. Burch, and M. Z. Bazant, preprint (PDF)

Transport-Limited Aggregation

• Dynamics of conformal maps for a class of non-Laplacian growth phenomena, M. Z Bazant, J. Choi, and B. Davidovitch, Phys. Rev. Lett. 91, 045503 (2003). (non-technical summary). (PDF)
• Transport-limited aggregation, M. Z. Bazant, J. Choi, B. Davidovitch, and D. Crowdy, Chaos 14, S6 (2004). (PDF)
• Advection-diffusion-limited aggregation, M. Z. Bazant, J. Choi, and B. Davidovitch, Chaos 14, S7 (2004). (PDF)
• The average shape of transport-limited aggregates, B. Davidovitch, J. Choi, and M. Z. Bazant, Phys. Rev. Lett. 95, 075504 (2005). (PDF)

Percolation

• The largest cluster in subcritical percolation, M. Z. Bazant, Phys. Rev. E 62, 1660 (2000). See also: Related rigorous analysis by van der Hofstad and Redig (2006). (PDF)
• Stochastic renormalization group in percolation, M. Z. Bazant, Physica A 316, 451-477 (2002). (PDF)

Breakdown Phenomena

• Size Effect on Strength and Lifetime Distributions of Quasibrittle Structures Im plied by Interatomic Bond Break Activation, Z. P. Bazant, J.-L. Le, and M. Z. Bazant, Proc., 17th European Conference on Fracture ( ECF-17), held at Technical University Brno, Brno, Czech. Rep., Sept. 2008, publ. by VUTIUM, Brno, J. Pokluda et al., eds.; pp. 78--92 (2008). (PDF)
• Scaling of strength and lifetime distributions of quasibrittle structures based on atomistic fracture mechanics, Z. P. Bazant, J.-L. Le, and M. Z. Bazant, Proceedings of the National Academy of Sciences, 106, 11484-11489 (2009). (PDF)
• Subcritical crack growth law and its consequences for lifetime statistics of quasibrittle structures, J.-L. Le, Z. P. Bazant, and M. Z. Bazant, J. Phys. D: Appl. Phys. 42, 214008 (2009). (PDF)
• Atomistic fracture and nano-macro transition for strength and lifetime statistics of quasibrittle structures, Z. P. Bazant, J.-L. Le, and M. Z. Bazant, Proc. 12th International Conference on Fracture (ICF-12), held in Ottawa, Canada, July 2009, Robert Bell ed., pp. 1-10 (2009). (PDF)
• Lifetime of high-k gate dielectrics and analogy with strength of quasibrittle structures. J.-L. Le, M. Z. Bazant, and Z. P. Bazant, J. Appl. Phys. 106, 104119 (2009). (PDF).

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5. Atomistic Modeling of Materials

Interatomic Potentials

• Derivation of interatomic potentials by inversion of ab initio cohesive energy curves, M. Z. Bazant and E. Kaxiras, Mat. Res. Soc. Proc. 408, 79 (1996). (PDF)
• Modeling covalent bonding in solids by inversion of cohesive energy curves, M. Z. Bazant and E. Kaxiras, Phys. Rev. Lett. 77, 4370 (1996). (PDF)
• Environment-Dependent Interatomic Potential for bulk silicon, M. Z. Bazant, E. Kaxiras, J. F. Justo, Phys. Rev. B 56, 8542 (1997). (PDF)
• Interatomic Forces in Covalent Solids, M. Z. Bazant, Ph.D. Thesis in Physics, Harvard University (1997). (PDF)
• Interatomic potential for condensed phases and bulk defects in silicon, J. F. Justo, M. Z. Bazant, E. Kaxiras, V. V. Bulatov, and S. Yip, Mat. Res. Soc. Proc. 469 (1997). (PDF)
• Interatomic potential for silicon defects and disordered phases, J. F. Justo, M. Z. Bazant, E. Kaxiras, V. V. Bulatov, and S. Yip, Phys. Rev. B 58, 2539 (1998). (PDF)
• A method to extract potentials from the temperature dependence of Langmuir constants for clathrate-hydrates, M. Z. Bazant and B. L. Trout, Physica A 300, 137-173 (2001). (PDF)
• Application of an analytical method to extract molecular potentials from Langmuir curve data, B. Anderson, M. Z. Bazant, and B. L. Trout, Proceedings of the 4th International Conference on Gas Hydrates, Yokohama, Japan (2002). (PDF)
• Application of the cell potential method to predict phase equilibria of multi-component gas hydrate systems, B. J. Anderson, M. Z. Bazant, J. W. Tester, and B. L. Trout, J. Phys. Chem. B 109, 8153-8163 (2005). (PDF)

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Molecular Dynamics Simulations

• The Environment-Dependent Interatomic Potential applied to silicon disordered structures and phase transitions, M. Z. Bazant, E. Kaxiras and J. F. Justo, Mat. Res. Soc. Proc. 491, 339 (1997). (PDF)
• Unstable stacking fault free energies in silicon through empirical modeling, M. de Koning, A. Antonelli, M. Z. Bazant, E. Kaxiras, and J. F. Justo, Mater. Res. Soc. Proc. 539, 175-180 (1998). (PDF)
• Finite temperature molecular-dynamics study of unstable stacking fault energies in silicon, M. de Koning, A. Antonelli, M. Z. Bazant, E. Kaxiras and J. F. Justo, Phys. Rev. B 58 , 12555 (1998). (PDF)
• Energetic, vibrational, and electronic properties of silicon using a nonorthogonal tight-binding model, N. Bernstein, M. J. Mehl, D. A. Papaconstantopoulos, N. I. Papanicolaou, M. Z. Bazant and E. Kaxiras, Phys. Rev. B 62, 4477 (2000). (PDF)
• Thermodynamic behavior of a model covalent material described by the Environment-Dependent Interatomic Potential, P. Keblinski, M. Z. Bazant, J. Dash, and M. Treacy, Phys. Rev. B 66, 064104 (2002). (PDF)
• Defect-induced shifts in the elastic constants of silicon, C. L. Allred, J. T. Borenstein, M. S. Weinberg, X. L. Yuan, M. Z. Bazant, and L. Hobbs, Mat. Res. Soc. Proc. 741, 145-150 (2003). (PDF)
• Statistical error in particle simulations of hydrodynamic phenomena, N. J. Hadjiconstantinou, A. L. Garcia, M. Z. Bazant, and G. He, J. Comp. Phys. 187, 274-297 (2003). (PDF)
• Elastic constants of defected and amorphous silicon with the Environment Dependent Interatomic Potential, C. L. Allred, X. Yuan, M. Z. Bazant, and L. Hobbs, Phys. Rev. B. 70 (13), art. no. 134113 (2004). (PDF)
• Sulfur point defects in crystalline and amorphous silicon, Y. Mo, M. Z. Bazant, and E. Kaxiras, Phys. Rev. B. 70 (20), art. no. 205210 (2004). (PDF)

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6. Patents

Microfluidic Devices

• Microfluidic pumps and mixers driven by induced-charge electro-osmosis, T. M. Squires and M. Z. Bazant, US Patent 7,081,189, issued July 25, 2006, filed in 2002. International patent PCT/US02/40290.
• Fabrication methods and designs for microfluidic devices exploiting induced-charge electro-osmosis, J. A. Levitan, T. Thorsen, M. Schmidt, and M. Z. Bazant, US provisional patent, filed in Oct. 2004. (MIT Case 11683).
• Fast Induced-Charge Electro-Osmotic Pumps for Microfluidics: I. Designs Exploiting Fixed-Potential ICEO, M. Z. Bazant, US Provisional patent, filed Jan 2006 (MIT Case 12056).
• Fast Induced-Charge Electro-Osmotic Pumps for Microfluidics: II. Designs with multilevel pumping surfaces, M. Z. Bazant and Y. Ben, US Provisional patent, filed Jan 2006 (MIT Case 12057).

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Pebble-Bed Nuclear Reactors

• Guide ring to control granular mixing in a pebble-bed nuclear reactor, M. Z. Bazant, US Patent 6,865,245, issued March 8, 2005. filed in 2002. International Patent PCT/US03/31152.
• Bi-disperse pebble-bed nuclear reactor, M. Z. Bazant, US Patent Application 10/932,561 filed in 2004.

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7. Preprints

In Press

• Ultrafast high-pressure AC electro-osmotic micropumps for portable biomedical microfluidics, C. C. Huang, M. Z. Bazant, and T. Thorsen, Lab on a Chip, accepted, in press. (arxiv.org)
• Anisotropic electro-osmotic flow over super-hydrophobic surfaces, S. Bahga, O. I. Vinogradova, and M. Z. Bazant, J. Fluid Mech., in press (a rxiv.org)
• Diffuse charge effects on the transient response of electrochemical cells, M. van Soestbergen, P. M. Biesheuvel, and M. Z. Bazant, Phys. Rev. E, in press. (PDF)

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Under Review

• Corrections to the Central Limit Theorem for heavy-tailed probability densities, H. Lam, J. Blanchet, D. Burch, and M. Z. Bazant, preprint (PDF)
• Induced-charge electrophoresis near an insulating wall, M. S. Kilic and M. Z. Bazant. (PDF)
• Fast spot-based multiscale simulations of granular flow, C. H. Rycroft, Y. L. Wong and M. Z. Bazant. (Dry Fluids Lab preprint)
• Strongly nonlinear dynamics of electrolytes under large AC voltages, L. H. Olesen, H. Bruus, and M. Z. Bazant. (arxiv.org)
• Effective zero-thickness model for a conductive membrane driven by an electric field, F. Ziebert, M. Z. Bazant, and D. Lacoste. (PDF)
• Nonlinear dynamics of capacitive charging and desalination by porous electrodes, M. Biesheuvel and M. Z. Bazant. (PDF, arXiv).
• Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor, K. Kamrin, M. Z. Bazant, and H. A. Stone. (arXiv)

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In Preparation

• Recent advances in induced-charge electrokinetics, M. Z. Bazant and T. M. Squires (invited opinion & review).
• Mosaic instability in rechargeable battery materials, D. Burch, M. Z. Bazant and G. Ceder.
• Transition state theory based on chemical potentials with applications in electrochemistry, M. Z. Bazant, D. Lacoste, and K. Sekimoto.
• A simple model for electrostatic correlation effects in electrochemical dynamics and electrokinetics, B. Storey and M. Z. Bazant.
• Diffusion-limited aggregation on curved surfaces, J. Choi, D. Crowdy, and M. Z. Bazant.

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