Viral RNAs are unusually compact.

A majority of viruses are composed of long single-stranded genomic RNA molecules encapsulated by protein shells with diameters of just a few tens of nanometers. We examine the extent to which these viral RNAs have evolved to be physically compact molecules to facilitate encapsulation. Measurements of equal-length viral, non-viral, coding and non-coding RNAs show viral RNAs to have among the smallest sizes in solution, i.e., the highest gel-electrophoretic mobilities and the smallest hydrodynamic radii. Using graph-theoretical analyses we demonstrate that their sizes correlate with the compactness of branching patterns in predicted secondary structure ensembles. The density of branching is determined by the number and relative positions of 3-helix junctions, and is highly sensitive to the presence of rare higher-order junctions with 4 or more helices. Compact branching arises from a preponderance of base pairing between nucleotides close to each other in the primary sequence. The density of branching represents a degree of freedom optimized by viral RNA genomes in response to the evolutionary pressure to be packaged reliably. Several families of viruses are analyzed to delineate the effects of capsid geometry, size and charge stabilization on the selective pressure for RNA compactness. Compact branching has important implications for RNA folding and viral assembly

Folding Langmuir Monolayers

The maximum pressure a two-dimensional surfactant monolayer is able to withstand is limited by the collapse instability towards formation of three-dimensional material. We propose a new description for reversible collapse based on a mathematical analogy between the formation of folds in surfactant monolayers and the formation of Griffith Cracks in solid plates under stress. The description, which is tested in a combined microscopy and rheology study of the collapse of a single-phase Langmuir monolayer of 2-hydroxy-tetracosanoic acid (2-OH TCA), provides a connection between the in-plane rheology of LM's and reversible folding

The Critical Behaviour of Potts models with symmetry breaking fields

The $Q$-state Potts model in two dimensions in the presence of external magnetic fields is studied. For general $Q\geq3$ special choices of these magnetic fields produce effective models with smaller $Z(Q')$ symmetry $(Q'< Q)$. The phase diagram of these models and their critical behaviour are explored by conventional finite-size scaling and conformal invariance. The possibility of multicritical behavior, for finite values of the symmetry breaking fields, in the cases where $Q>4$ is also analysed. Our results indicate that for effective models with $Z(Q')$ symmetry $(Q'\leq4)$ the multicritical point occurs at zero field. This last result is also corroborated by Monte Carlo simulations.Comment: 15 pages (standart LaTex), 2 figure (PostScript) available by request to [email protected]

Avoided Critical Behavior in O(n) Systems

Long-range frustrating interactions, even if their strength is infinitesimal, can give rise to a dramatic proliferations of ground or near-ground states. As a consequence, the ordering temperature can exhibit a discontinuous drop as a function of the frustration. A simple model of the doped Mott insulator, where the short-range tendency of the holes to phase separate competes with long-range Coulomb effects, exhibits this "avoided critical" behavior. This model may serve as a paradigm for many other systems.Comment: 4 pages, 2 figure

A Phase-Field Model of Spiral Dendritic Growth

Domains of condensed-phase monolayers of chiral molecules exhibit a variety of interesting nonequilibrium structures when formed via pressurization. To model these domain patterns, we add a complex field describing the tilt degree of freedom to an (anisotropic) complex-phase-field solidification model. The resulting formalism allows for the inclusion of (in general, non-reflection symmetric) interactions between the tilt, the solid-liquid interface, and the bond orientation. Simulations demonstrate the ability of the model to exhibit spiral dendritic growth.Comment: text plus Four postscript figure file

Static Scaling Behavior of High-Molecular-Weight Polymers in Dilute Solution: A Reexamination

Previous theories of dilute polymer solutions have failed to distinguish clearly between two very different ways of taking the long-chain limit: (I) $N \to\infty$ at fixed temperature $T$, and (II) $N \to\infty$, $T \to T_\theta$ with $x \equiv N^\phi (T-T_\theta)$ fixed. I argue that the modern two-parameter theory (continuum Edwards model) applies to case II --- not case I --- and in fact gives exactly the crossover scaling functions for $x \ge 0$ modulo two nonuniversal scale factors. A Wilson-type renormalization group clarifies the connection between crossover scaling functions and continuum field theories. [Also contains a general discussion of the connection between the Wilson and field-theoretic renormalization groups. Comments solicited.]Comment: 10 pages including 1 figure, 181159 bytes Postscript (NYU-TH-93/05/01

Polar Smectic Films

We report on a new experimental procedure for forming and studying polar smectic liquid crystal films. A free standing smectic film is put in contact with a liquid drop, so that the film has one liquid crystal/liquid interface and one liquid crystal/air interface. This polar environment results in changes in the textures observed in the film, including a boojum texture and a previously unobserved spiral texture in which the winding direction of the spiral reverses at a finite radius from its center. Some aspects of these textures are explained by the presence of a Ksb term in the bulk elastic free energy density that favors a combination of splay and bend deformations.Comment: 4 pages, REVTeX, 3 figures, submitted to PR

Hexatic Order and Surface Ripples in Spherical Geometries

In flat geometries, two dimensional hexatic order has only a minor effect on capillary waves on a liquid substrate and on undulation modes in lipid bilayers. However, extended bond orientational order alters the long wavelength spectrum of these ripples in spherical geometries. We calculate this frequency shift and suggest that it might be detectable in lipid bilayer vesicles, at the surface of liquid metals and in multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability induced in the later two systems by an excess of electric charge.Comment: 5 pages, 1 figure; revised version; to appear in Phys. Rev. Let

Towards a Tetravalent Chemistry of Colloids

We propose coating spherical particles or droplets with anisotropic nano-sized objects to allow micron-scale colloids to link or functionalize with a four-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon and germanium. Candidates for such coatings include triblock copolymers, gemini lipids, metallic or semiconducting nanorods and conventional liquid crystal compounds. We estimate the size of the relevant nematic Frank constants, discuss how to obtain other valences and analyze the thermal distortions of ground state configurations of defects on the sphere.Comment: Replaced to improve figures. 4 figures Nano Letter