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Ken Brakke, Ph.D.

Department: Mathematical Sciences

Professor of Mathematical Sciences

  • Education
  • PHD, Princeton University
  • BS, Univ of Nebraska Lincoln
Ken Brakke

I am a mathematician, and my field of interest is the mathematics of soap films and soap bubbles. I got interested in this in graduate school, where I wandered into a seminar with the imposing title of Geometric Measure Theory, which turned out to be about the shapes that liquid surfaces can form.

It turns out the same mathematics applies to soap films, soap bubbles, foams, raindrops, candle wicks, sponges, liquid solder on circuit boards, and liquid fuel in spacecraft.

My main research activity revolves around computer software I have written called, The Surface Evolver, which does computer models of liquid surfaces. I have made it freely available, and there are hundreds of users of it around the world. I also use it to make a little money, consulting for industrial companies and government laboratories.

I came to Susquehanna University because it is a small school, where I could teach a wide variety of courses and interact with a wide variety of faculty and students. My previous job had been at a large state university, where I was just teaching the same few courses over and over again. Here I can teach not only mathematics courses, but also computer science courses such as Operating Systems, Graphics, and Networks.

My Surface Evolver software gives me a playground for experimentation with all kinds of new mathematics and computer science ideas. I love showing all these ideas to students. Mathematics is the study of patterns, and everyone is a mathematician, whether they think so or not, since everyone sees patterns.

Employment history:

  • August 1983 - Present: Professor of Mathematics, Susquehanna University
  • August 1975 - May 1982: Assistant Professor of Mathematics, Purdue University


  • Ph D in Mathematics, Princeton University, 1975.
  • BA in Mathematics, Physics, University of Nebraska at Lincoln, 1972.

Professional affiliations:

  • 1985 - Present: Association for Computing Machinery
  • 1975 - Present: American Mathematical Society
  • 1968 - Present: Mathematical Association of America


  • Fall 1992 - Spring 1993: Geometry Center, University of Minnesota, Minneapolis, Minnesota.
  • Spring 1995: University of Massachusetts, Amherst, Massachusetts.
  • Spring 2004: Trinity University, Dublin, Ireland.


  • Brakke, K. A. The Surface Evolver.


  • May 16, 2010: John C. Horn Distinguished Service Lectureship, Susquehanna University
  • May 14, 2010: The Dorothy Anderson Faculty Member of the Year Award, Student Government Association
  • 1999: Award for Excellence in Technology Transfer, Federal Laboratory Consortium for Technology Transfer


1 Berthier, J., Brakke, K. A., Gosselin, D., Huet, M., Berthier, E. (in press). Metastable capillary filaments in rectangular cross-section open microchannels. AIMS Biophysics.
2 Xiong, F., Ma, W., Hiscock, T. W., Mosaliganti, K. R., Tetner, A., Brakke, K. A., Rannou, N., Gelas, A., Souhait, L., Swinburne, I., Obholzer, N. D., Megason, S. (2014). Interplay of cell shapes and oriented cell divisions promotes robust morphogenesis of developing epithelia. Cell, 159(2), 415-427.
3 Berthier, J., Brakke, K. A., Gosselin, D., Bourdat, A.-G., Nonglaton, G., Lafitte, G., Boizot, F., Costa, G., Delapierre, G. (in press). Suspended microflows between vertical parallel walls. Microfluidics and Nanofluidics, 10.
4 Brakke, K. A., Berthier, E., Berthier, J. (2013). A general condition for spontaneous capillary flow in uniform cross-section microchannels. Microfluidics and Nanofluidics, online(online), 7.
5 Wakai, F., Brakke, K. A. (2013). Tensorvirial equation of evolving surfaces in sintering of aggregatesof particles by diffusion. Acta Materialia, online.
6 Rezende, R. A., Kasyanov, V., Ovsiankov, A., Pereira, F. D.A.S., Torgeson, J., Gruber, P., Stampfi, J., Brakke, K. A., Nogueira, J. A., Mironov, V., da Silva, J. V.L. (2012). Design, physical prototyping and initial characterisation of `lockyballs'. 7(4), 287-301.
7 Berthier, J., Brakke, K. A. (2012). The Physics of Microdroplets. Martin Scrivener.
8 Brakke, K. A., Shin, D.-Y. (2012). Issues in colour filter fabrication with inkjet printing. Inkjet-based Micromanufacturing. Wiley.
9 Baginski, F., Brakke, K. A. (2012). Deployment of Pneumatic Envelopes Including Ascending Balloons and Inflatable Aerodynamic Decelerators. AIAA J. of Spacecraft and Rockets, 49(2), 17.
10 Gabrielli, R., Meagher, A., Weaire, D., Hutzler, S., Brakke, K. A. (2012). An experimental realisation of the Weaire-Phelan structure in monodisperse liquid foam. Phil. Mag. Letters, 92(1), 1-6.
11 Berthier, J., Brakke, K. A., Mermoz, S., Sanchez, L., DiCioccio, L. (2011). Self-alignment of silicon chips on wafers: a numerical investigation of the effect of spreading and wetting. Sensors & Transducers Journal, 13, 44-52.
12 Brakke, K. A., Kasyanov, V., Moreno-Rodriguez, R., Nagy-Meshesz, A., Ozolanta, I., Markwald, R., Mironov, V. (2011). Toward organ printing: design characteristics for kidney arterial tree. Virtual and Physical Prototyping, 6(4), 197-213.
13 Wakai, F., Brakke, K. A. (2011). Mechanics of sintering for a coupled grain boundary/surface diffusion. Acta Materialia, 59, 5379-5387.
14 Baginski, F., Brakke, K. A. (2011). Estimating the Deployment Pressure in Pumpkin Balloons. AIAA Journal of Aircraft, 48(1), 235-247.
15 Berthier, J., Brakke, K. A., Grossi, F., Sanchez, L., Di Cioccio, L. (2010). Self-alignment of silicon chips on wafers: a capillary approach. Virtual Journal of Nanoscale Science & Technology, 108(online).
16 Baginski, F., Brakke, K. A. (2010). Exploring the stability landscape of constant-stress pumpkin balloon designs. AAIA Journal of Aircraft, 47(3), 849-857.
17 Berthier, J., Brakke, K. A., Grossi, F., Sanchez, L., Di Cioccio, L. (2010). Silicon die self-alignment on a wafer: stable and unstable modes. Sensors & Transducers Journal.
18 Baginski, F., Brakke, K. A. (2010). Simulating clefts in pumpkin balloons. Advances in Space Research, 45, 473-481.
19 Mironov, V., Zhang, J., Gentile, C., Brakke, K. A., Trusk, T., Jakab, K., Forgacs, G., Kasyanov, V., Visconti, R. P., Markwald, R. R. (2009). Designer ‘blueprint' for vascular trees: morphology evolution of vascular tissue constructs. Virtual and Physical Prototyping, 4, 63-74.
20 Swanson, K. W., Brakke, K. A., Breen, D. E. (2009). Physics-based surface modeling using quasi-static liquids. Computer-Aided Design & Applications, 6, 1-4.
21 Shin, D.-Y., Brakke, K. A. (in press). Modelling and analysis of wetting characteristics of ink for display applications with the surface evolution technique. Modelling and Simulation in Materials Science and Engineering.
22 Brakke, K. A., Berthier, J. (2008). The physics of droplets. MIcrodrops and Digital Microfluidics (pp. 75-157). William Andrew.
23 Shearman, G. C., Khoo, B. J., Motherwell, M., Brakke, K. A., Ces, O., Conn, C. E., Seddon, J. M., Templer, R. H. (2007). Calculations of and evidence for chain packing stress in inverse lyotropic bicontinuous cubic phases. Langmuir, 23, 7276-7285.
24 Brakke, K. A. (2007). Theoretical Investigation of Jetting and Wetting Phenomena for the Fabrication of TFT LCD Color Filters (pp. 376-379). Daegu: IMID 2007 Digest of Technical Papers.
25 Brakke, K. A. (2007). Theoretical analysis of jetting and ink filling processes for TFT LCD colour filters. Proceedings of the 10th Asian Symposium on Information Display. Singapore:.
26 Brakke, K. A., Baginski, F., Schur, W. (2006). Cleft formation in pumpkin balloons. Advances in Space Research, 37(11), 2070-2081.
27 Baginski, F., Brakke, K. A., Schur, W. (2006). Stability of cyclically symmetric strained pumpkin balloon configurations and the formation of undesired equilibria. Journal of Aircraft, 43(5), 1414-1423.
28 Baginski, F., Schur, W., Brakke, K. A. (2006). Unstable, cyclically symmetric and stable, asymmetric pumpkin-balloon configurations. Journal of Aircraft, 44(3), 764-773.
29 Anderson, M., Eggar, C., Casci, J., Tiddy, G., Brakke, K. A. (2005). A new minimal surface and the structure of mesoporous silicas. Angew. Chem. Int. Ed., 44, 2-6.
30 Weaire, D., Cox, S., Brakke, K. A. (2005). Liquid Foams. In P. Colombo and M. Scheffler (Ed.), Cellular Ceramics. Weinheim: Wiley-VCH.
31 Brakke, K. A. (2005). Stability, clefting, and other issues related to undesirable equilibria in large pumpkin balloons (pp. 1-13). 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.
32 Brakke, K. A. (2004). Instability of the wet cube cone soap film. Colloids and Surfaces A: Physiochem Eng. Aspects, 263, 4-10.
33 Brakke, K. A. (2002). Instabilities of cylindrical bubble clusters. Eur. Phys. J. E, 9, 453-460.
34 Brakke, K. A., Morgan, F. (1998). Instability of the wet X soap film. Journal of Geometric Analysis, 8(5), 749-768.
35 Brakke, K. A., Baginski, F. (1998). Modeling ascent configurations of strained high-altitude balloons. AIAA Journal, 36, 1901-1910.
36 Francis, G., Sullivan, J. M., Kusner, R., Brakke, K. A., Hartman, C., Chapell, G. (1997). The minimax sphere eversion. In K. Polthier and H. Hege (Ed.), Mathematics and Visualization (pp. 3-20). Berlin: Springer-Verlag.
37 Brakke, K. A., Sullivan, J. (1997). Using symmetry features of the Surface Evolver to study foams. In K. Polthier and H. Hege (Ed.), Mathematics and Visualization (pp. 95-118). Berlin: Springer-Verlag.
38 Brakke, K. A., Singler, T. (1996). Computer simulation of solder bridging phenomena. Transactions of the ASME, 118, 122-126.
39 Brakke, K. A. (1996). The Surface Evolver and the stability of liquid surfaces. Phil. Trans. R. Soc. A, 354, 2143-2157.
40 Brakke, K. A., Phelan, R., Weaire, D. (1995). Computation of equilibrium foam structure using the Surface Evolver. Experimental Mathematics, 4(3), 181-192.
41 Brakke, K. A. (1995). Numerical Solution of Soap Film Dual Problems. Experimental Mathematics, 4(4), 269-287.
42 Brakke, K. A. (1995). Soap films and covering spaces. Journal of Geometric Analysis, 5(4), 445-514.
43 Brakke, K. A. (1992). Minimal Surfaces, Corners, and Wires. Journal of Geometric Analysis, 2(1), 11-36.
44 Brakke, K. A. (1992). The Surface Evolver. Experimental Mathematics, 1(2), 141-165.
45 Brakke, K. A. (1992). The Opaque Cube Problem. American Mathematical Monthly, 99(9), 866-871.
46 Brakke, K. A. (1991). Minimal cones on hypercubes. Journal of Geometric Analysis, 1, 329-338.
47 Brakke, K. A. (1987). Variances of Dihedral Angle Estimators. Metallography, 20, 491-493.
48 Brakke, K. A. Statistics of Three Dimensional Random Voronoi Tessellations.
49 Mantock, J., Fukanaga, K., Brakke, K. A. (1982). Systematic feature extraction. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4, 291-297.
50 Brakke, K. A., Zitron, N. (1980). Some generalizations of the circular city model. Mathematical Modelling, 1, 167-179.
51 Brakke, K. A. (1978). The Motion of a Surface by its Mean Curvature (pp. 252). Princeton, NJ: Princeton University Press.
52 Brakke, K. A., Zitron, N. (1977). Further optimal cost routes in the circular city model. Journal of Optimization Theory and Applications, 4(21), 531-534.
53 Brakke, K. A. (1972). Some new values of Sylvester's function for n noncollinear points. Journal of Undergraduate Mathematics, 4, 11-14.

Courses taught:

  • CSCI-282 Computer Organization
  • CSCI-351 Numerical Computing
  • CSCI-352 Numerical Analysis
  • CSCI-391 Data Communications & Networks I
  • CSCI-392 Data Communication & Networks II
  • CSCI-481 Programming Languages
  • CSCI-483 Compiler Theory
  • CSCI-484 Computer Graphics
  • CSCI-486 Introduction to Operating Systems
  • CSCI-487 Operating Systems
  • CSCI-502 Independent Study
  • INTD-500 Internship
  • MATH-105 Introductory Topics
  • MATH-108 Introduction to Statistics
  • MATH-201 Linear Algebra
  • MATH-211 Multivariate Calculus
  • MATH-331 Geometry
  • MATH-351 Numerical Computing
  • MATH-352 Numerical Analysis
  • MATH-353 Differential Equations
  • MATH-415 Complex Analysis
  • MATH-502 Independent Study