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We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

- Zvonimir Dogic, J Zhang, +7 authors Arjun G. Yodh
- Physical review letters
- 2004

We directly visualize single polymers with persistence lengths l(p), ranging from 0.05 to 16 microm, dissolved in the nematic phase of rodlike fd virus. Polymers with a sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of… (More)

Direct Determination of DNA Twist-Stretch Coupling Randall D. Kamien, Tom C. Lubensky, Philip Nelson, and Corey S. O'Hern Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104 USA The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent… (More)

- Carl D. Modes, Randall D. Kamien
- Physical review. E, Statistical, nonlinear, and…
- 2008

We examine a simple hard-disk fluid with no long-range interactions on the two-dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable, one-parameter model of disordered monodisperse hard disks. We extend… (More)

- Carl D. Modes, Randall D. Kamien
- Physical review letters
- 2007

We examine a simple hard disk fluid with no long range interactions on the two-dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is frustrated, allowing us to construct a tractable model of disordered monodisperse hard disks. We extend free-area… (More)

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic… (More)

The molecules in lyotropic membranes are typically aligned with the surface normal. When these molecules are chiral, there is a tendency for the molecular direction to twist. These competing effects can reach a compromise by producing helicoidal defects in the membranes. Unlike thermotropic smectics, the centers of these defects are hollow and thus their… (More)

- Christian D. Santangelo, Vincenzo Vitelli, Randall D. Kamien, David R. Nelson
- Physical review letters
- 2007

We study thin self-assembled columns constrained to lie on a curved, rigid substrate. The curvature presents no local obstruction to equally spaced columns in contrast with curved crystals for which the crystalline bonds are frustrated. Instead, the vanishing compressional strain of the columns implies that their normals lie on geodesics which converge… (More)

- Bryan Gin-ge Chen, Gareth P Alexander, Randall D. Kamien
- Proceedings of the National Academy of Sciences…
- 2009

The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the interaction between translations and… (More)

- Michael Ambroso, Randall D. Kamien, Douglas J. Durian
- Physical review. E, Statistical, nonlinear, and…
- 2005

We present data for the time dependence of wooden spheres penetrating into a loose noncohesive packing of glass beads. The stopping time is a factor of 3 longer than the time d/v0 needed to travel the total penetration distance d at the impact speed v0. The acceleration decreases monotonically throughout the impact. These kinematics are modeled by a… (More)