Kamien, Randall
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Publication Geometric Theory of Columnar Phases on Curved Substrates(2007-07-06) Santangelo, Christian D.; Vitelli, Vincenzo; Kamien, Randal D.; Nelson, David R.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 (diverge) in regions of positive (negative) Gaussian curvature, in analogy to the focusing of light rays by a lens. We show that the out of plane bending of the cylinders acts as an effective ordering field.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 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 Colloquium: Disclination loops, point defects, and all that in nematic liquid crystals(2012-06-01) Alexander, Gareth P.; Chen, Bryan Gin-ge; Kamien, Randall; Matsumoto, Elisabetta AThe homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet.Publication Chirality in Liquid Crystals: From Microscopic Origins to Macroscopic Structure(1998) Lubensky, Tom C; Harris, A. Brooks; Kamien, Randall D; Yan, GuMolecular chirality leads to a wonderful variety of equilibrium structures, from the simple cholesteric phase to the twist-grain-boundary phases, and it is responsible for interesting and technologically important materials like ferroelectric liquid crystals. This paper will review some recent advances in our understanding of the connection between the chiral geometry of individual molecules and the important phenomenological parameters that determine macroscopic chiral structure. It will then consider chiral structure in columnar systems and propose a new equilibrium phase consisting of a regular lattice of twisted ropes.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 Conformal Smectics and their Many Metrics(2012-05-11) Alexander, Gareth P; Kamien, Randall; Mosna, Ricardo AWe establish that equally spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal structures only found before for smectics on flat substrates.Publication Why is Random Close Packing Reproducible?(2007-10-09) Kamien, Randal D.; Liu, Andrea JWe link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs.We conjecture that the common value of фrcp ≈ 0.64 arises from a divergence in the rate at which accessible states disappear.We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.Publication Elongation and Fluctuations of Semi-flexible Polymers in a Nematic Solvent(2004-03-26) Dogic, Z.; Zhang, J.; Discher, Dennis E; Lau, A. W.C.; Janmey, Paul; Aranda-Espinoza, Helim; Kamien, Randall; Dalhaimer, Paul M; Lubensky, Thomas C.; Yodh, ArjunWe directly visualize single polymers with persistence lengths ranging from lp = 0:05 to 16 µm, dissolved in the nematic phase of rod-like fd virus. Polymers with 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 semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.Publication Elastic-Instability Triggered Pattern Formation(2009-08-12) Matsumoto, Elisabetta A.; Kamien, Randall D.Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple model for determining the orientational order of such patterns using only linear elasticity theory which correctly predicts the outcomes of several experiments. Each element of the pattern is modeled by a “dislocation dipole” located at a point on a lattice, which then interacts elastically with all other dipoles in the system. We explicitly consider a membrane with a square lattice of circular holes under uniform compression and examine the changes in morphology as it is allowed to relax in a specified direction.
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