# Randall Kamien

- Vicki and William Abrams Professor in the Natural Sciences (2006-)
- Simons Investigator (2013)
- Associate Editor for Soft Condensed Matter, Reviews of Modern Physics (2006-2010)
- Associate Editor, Physical Review E (2000-2003)
- Post-Doctoral Research Associate, University of Pennsylvania (1995-1997)
- Member, Institute for Advanced Study, Princeton, NJ (1992-1995)

Ph.D, Harvard University (1992)

B.S., M.S., California Institute of
Technology (1988)

My research interests center on problems in soft condensed matter theory.

#### Minimal Surfaces and Crystal Structure

Great advances in synthetic chemistry have produced a new class of monodisperse, yet highly complex, molecules. These molecules self-assemble into a variety of crystalline lattices with lattice constants on the order of 10nm. Unlike colloidal crystals, these materials form lattices that are not close-packed such as the face-centered-cubic (FCC) lattice. Instead the body-centered-cubic (BCC) lattice as well as the more exotic beta-Tungsten lattice form. While detailed modeling can lead to precise intermolecular potentials, progress has been made on a generic approach to crystal formation based on the mathematics of minimal surfaces. By considering the interface between the Voronoi cells that contain each molecule, one can argue that the complex molecular coats favor a minimum area. This leads to the BCC lattice among others. Minimal surfaces have a long history of lying in the interface between Physics and Mathematics. Their use has had somewhat of a revival due to the ever increasing complexity of lyotropic phases of matter. Block copolymers and amphiphiles form structures that resemble doubly- and triply-periodic minimal surfaces. This is no surprise: because physics problems can be posed as extremal problems and because the mean curvature is the lowest-degree, rotationally-invariant scalar, minimal surfaces arise as solutions. However, nonlinearities should play an important role as the lengthscales of the structures become comparable to molecular sizes.

#### Liquid Crystals

The theory of liquid crystals and liquid crystalline polymers runs the gamut from the rheology of complex fluids to the esoterica of homotopy and topological defects. All aspects of theory are intimately influenced and connected with experiment. This places liquid crystal physics in an exciting position: it is driven by both theory and experiment and by both the abstract and the applied. Specifically, chiral molecules are ubiquitous in nature and exhibit many liquid crystal phases. They are extensively studied by biologists, chemists and biophysicists. There is still much theoretical work to be done on the wealth of experimental data. I have studied a new class of chiral liquid crystals which, in addition to their directional liquid crystalline order, have hexatic bond-orientational order in the plane perpendicular to the director. Aside from finding new twisted phases, based on symmetry arguments and Landau theory, I would like to understand better the topological and geometric constraints that liquid crystals and liquid crystalline polymers must satisfy. Smectic liquid crystals as well as columnar liquid crystals have the analogue of the Meissner phase in superconductors, in which chirality is excluded from the bulk (just as the magnetic field is expelled in a superconductor). The constraints imposed by topology and geometry can screen out chirality as well.

- "Making the Cut: Lattice Kirigami Rules", T. Castle, Y. Cho, X. Gong, E. Jung, D.M. Sussman, S. Yang, and R.D. Kamien, Phys. Rev. Lett. 113 (2014) 245502.
- "Geometry of the Cholesteric Phase", D.A. Beller, T. Machon, S. Čopar,
D.M. Sussman, G.P. Alexander, R.D. Kamien, and R.A. Mosna,
*Phys. Rev. X*4 (2014) 031050. - "Focal Conic Flower Textures at Curved interfaces", D.A. Beller, M.A.
Gharbi, A. Honglawan, K.J. Stebe, S. Yang, and R.D. Kamien,
*Phys. Rev. X*3 (2013) 041026. - "Generating the Hopf Fibration Experimentally in Nematic Liquid Crystals", B.G. Chen, P.J. Ackerman, G.P. Alexander, R.D. Kamien, and I.I. Smalyukh,
*Phys. Rev. Lett.*110 (2013) 237801. - "Topographically-Induced Hierarchical Assembly and Geometrical Transformation of Focal Conic Domain", A. Honglawan, D.A. Beller, M. Cavallaro, Jr., R.D. Kamien, K.J. Stebe, and S. Yang,
*Proc. Natl. Acad.*Sci. 110 (2013) 34. - "Topological Colloids", B. Senyuk, Q. Liu, S. He, R.D. Kamien, R.B. Kusner, T.C. Lubensky, and I.I. Smalyukh,
*Nature*493 (2013) 200. - "Developed Smectics: When Exact Solutions Agree", G.P. Alexander, C.D.
Santangelo, and R.D. Kamien,
*Phys. Rev. Lett.*108 (2012) 047802. - "The Power of Poincaré: Elucidating the Hidden Symmetries in Focal Conic
Domains", G.P. Alexander, B.G. Chen, E.A. Matsumoto, and R.D. Kamien,
*Phys. Rev. Lett.*104 (2010) 257802. - "Symmetry Breaking in Smectics and Surface Models of Their Singularities",
B.G. Chen, G.P. Alexander, and R.D. Kamien,
*Proc. Natl. Acad. Sci.*106 (2009) 15577. - "Hard Discs on the Hyperbolic Plane", C.D. Modes and R.D. Kamien,
*Phys. Rev. Lett.*99 (2007) 235701. - "Why is Random Close Packing Reproducible?", R.D. Kamien and A.J. Liu, Phys. Rev. Lett. 99 (2007) 155501.
- "Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain
Boundaries", C.D. Santangelo and R.D. Kamien, Phys.
*Rev. Lett.*96 (2006). - "Entropically Driven Helix Formation", Y. Snir and R.D. Kamien,
*Science*307 (2005) 1067. - "Soap Froths and Crystal Structures", P. Ziherl and R.D. Kamien,
*Phys. Rev. Lett.*85 (2000) 3528. - "Molecular Chirality and Chiral Parameters", A.B. Harris, R.D. Kamien and
T.C. Lubensky,
*Rev. Mod. Phys.*71 (1999) 1745. - "Liquids with Chiral Bond Order", R.D. Kamien,
*J. Phys. II France*6 (1996) 461.

Phys 500: Mathematical Methods of Physics

Phys 528: Liquid Crystals

Phys 611: Statistical Mechanics

Phys 612: Advanced Statistical Mechanics