## Kamien, Randall

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Publication Direct Determination of DNA Twist-Stretch Coupling(1996-11-01) Kamien, Randall; Lubensky, Tom; Nelson, Philip C; O'Hern, Corey S.The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this important material parameter. We extract its value from a recent experiment of Strick et al. [Science 271 (1996) 1835] and find rough agreement with an independent experimental estimate recently given by Marko. We also present a very simple microscopic theory predicting a value comparable to the one observed.Publication Bubble Kinetics in a Steady-State Column of Aqueous Foam(2006-10-13) Feitosa, K.; Kamien, Randall D; Halt, O. L; Durian, Douglas JWe measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.Publication Dynamics of Shallow Impact Cratering(2005-10-01) Kamien, Randall D; Ambroso, M. A; Durian, Douglas JWe 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 position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.Publication Molecular Chirality and Chiral Parameter(1999-10-01) Harris, A. Brooks; Kamien, Randal D; Lubensky, Thomas CThe fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. The authors show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations that only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. The authors illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, the chiral parameter of the constituent molecules that determines the macroscopic pitch of cholesterics is identified.Publication Helical Tubes in Crowded Environments(2007-05-18) Snir, Yehuda; Kamien, Randal D.When placed in a crowded environment, a semiflexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semiflexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.Publication Hard Disks on the Hyperbolic Plane(2007-12-03) Modes, Carl D.; Kamien, Randall D.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 theory and the virial expansion to this regime, deriving the equation of state for the system, and compare its predictions with simulation near an isostatic packing in the curved space.Publication Triply Periodic Smectic Liquid Crystals(2007-01-18) Santangelo, Christian D.; Kamien, Randal D.Twist-grain-boundary phases in smectics are the geometrical analogs of the Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear elasticity is important in evaluating their energetics. We analytically construct the height function of a π/2 twist-grain-boundary phase in smectic-A liquid crystals, known as Schnerk’s first surface. This construction, utilizing elliptic functions, allows us to compute the energy of the structure analytically. By identifying a set of heretofore unknown defects along the pitch axis of the structure, we study the necessary topological structure of grain boundaries at other angles, concluding that there exist a set of privileged angles and that the π/2 and π/3 grain boundary structures are particularly simple.Publication Helical Nanofilaments and the High Chiralty Limit of Smectics A(2009-12-18) Matsumoto, Elisabetta A.; Alexander, Gareth P.; Kamien, Randal D.Liquid crystalline systems exhibiting both macroscopic chirality and smectic order experience frustration resulting in mesophases possessing complex three-dimensional order. In the twist-grainboundary phase, defect lattices mediate the propagation of twist throughout the system. We propose a new chiral smectic structure composed of a lattice of chiral bundles as a model of the helical nanofilament (B4) phase of bent-core smectics.Publication Microscopic Origin of Cholesteric Pitch(1997-02-24) Harris, A. Brooks; Kamien, Randall D; Lubensky, Tom CWe present a microscopic analysis of the instability of the nematic phase to chirality when molecular chirality is introduced perturbatively. We show that for central-force interactions the previously neglected short–range biaxial correlations play a crucial role in determining the cholesteric pitch. We propose a pseudoscalar strength which quantifies the chirality of a molecule.Publication Breaking the rules for topological defects: Smectic order on conical substrates(2012-07-18) Mosna, Ricardo A.; Beller, Daniel A.; Kamien, RandallOrdered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are grown on real surfaces; eventually, surface imperfections are on the same scale as the lattice constant. Here, we gain insights into this general problem by studying two-dimensional smectic order on substrates with highly localized intrinsic curvature, constructed from cones and their intersections with planes. In doing so we take advantage of fully tractable “paper and tape” constructions, allowing us to understand, in detail, the induced cusps and singularities.

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