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Search Results: 1 - 10 of 192159 matches for " Randall D. Kamien "
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Flory Exponents from a Self-Consistent Renormalization Group
Randall D. Kamien
Physics , 1993, DOI: 10.1051/jp1:1993208
Abstract: The wandering exponent $\nu$ for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the wandering exponent to the exponent in the background field through an $\epsilon$-expansion. We then choose the background field to have the same correlations as the individual polymer, thus self-consistently solving for $\nu$. We find $\nu=3/(d+2)$ for $d<4$ and $\nu=1/2$ for $d\ge 4$, which is exactly the Flory result.
Weak Chirality in Ordered DNA Phases
Randall D. Kamien
Physics , 1996,
Abstract: Recent experiments on aligned DNA show hexatic order with no sign of macroscopic chirality. I make the analogy between smectic liquid crystals and chiral hexatics and show how the absence of chirality cannot occur in a thermodynamic phase of chiral molecules. In addition, I discuss the microscopic origin of chiral mesophases in liquid crystals and show that, within the context of central forces between "atoms" on "molecules", chiral interactions can occur only if there are biaxial correlations between the mesogens. Weak biaxial correlations can therefore lead to small cholesteric pitches.
Force Free Configurations of Vortices in High Temperature Superconductors near H_{c2}
Randall D. Kamien
Physics , 1998, DOI: 10.1103/PhysRevB.58.8218
Abstract: We study force-free configurations of Abrikosov flux lines in the line-liquid and line-crystal limit, near the melting transition at H_m. We show that the condition for zero force configurations can be solved by appealing to the structure of chiral liquid crystalline phases.
Smectic Order in Double-Twist Cylinders
Randall D. Kamien
Physics , 1996, DOI: 10.1051/jp2:1997156
Abstract: I propose a double-twist texture with local smectic order, which may have been seen in recent experiments. As in the Renn-Lubensky TGB phase, the smectic order is broken only through a lattice of screw dislocations. A melted lattice of screw dislocations can produce a double-twist texture as can an unmelted lattice. In the latter case I show that geometry only allows for certain angles between smectic regions. I discuss the possibility of connecting these double-twist tubes together to form a smectic blue phase.
Liquids with Chiral Bond Order
Randall D. Kamien
Physics , 1995, DOI: 10.1051/jp2:1996192
Abstract: I describe new phases of a chiral liquid crystal with nematic and hexatic order. I find a conical phase, similar to that of a cholesteric in an applied magnetic field for Frank elastic constants $K_2>K_3$. I discuss the role of fluctuations in the context of this phase and the possibility of satisfying the inequality for sufficiently long polymers. In addition I discuss the topological constraint relating defects in the bond order field to textures of the nematic and elucidate its physical meaning. Finally I discuss the analogy between smectic liquid crystals and chiral hexatics and propose a defect-riddled ground state, akin to the Renn-Lubensky twist grain boundary phase of chiral smectics.
Local Writhing Dynamics
Randall D. Kamien
Physics , 1997, DOI: 10.1007/s100510050145
Abstract: We present an alternative local definition of the writhe of a self-avoiding closed loop which differs from the traditional non-local definition by an integer. When studying dynamics this difference is immaterial. We employ a formula due to Aldinger, Klapper and Tabor for the change in writhe and propose a set of local, link preserving dynamics in an attempt to unravel some puzzles about actin.
The Geometry of Soft Materials: A Primer
Randall D. Kamien
Physics , 2002, DOI: 10.1103/RevModPhys.74.953
Abstract: 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.
Topology from the Bottom Up
Randall D. Kamien
Physics , 2003,
Abstract: Perspective on cond-mat/0303289
Chiral Mesophases of DNA
Randall D. Kamien
Physics , 1998,
Abstract: In the hexagonal columnar phase of chiral polymers a bias towards cholesteric twist competes with braiding along an average direction. When the chirality is strong, topological defects proliferate, leading to either a tilt grain boundary phase or a new ``moire state'' with twisted bond order. This moire phase can melt leading to a new phase: the chiral hexatic. I will discuss some recent experimental results from the NIH on DNA liquid crystals in the context of these theories.
Decomposition of the Height Function of Scherk's First Surface
Randall D. Kamien
Physics , 2000,
Abstract: We show that Scherk's first surface, a one-parameter family of solutions to the minimal surface equation, may be written as a linear superposition of other solutions with specific parametric values.
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