Instability and front propagation in laser-tweezed lipid bilayer tubules

We study the mechanism of the `pearling' instability seen recently in experiments on lipid tubules under a local applied laser intensity. We argue that the correct boundary conditions are fixed chemical potentials, or surface tensions \Sigma, at the laser spot and the reservoir in contact with the tubule. We support this with a microscopic picture which includes the intensity profile of the laser beam, and show how this leads to a steady-state flow of lipid along the surface and gradients in the local lipid concentration and surface tension (or chemical potential). This leads to a natural explanation for front propagation and makes several predictions based on the tubule length. While most of the qualitative conclusions of previous studies remain the same, the `ramped' control parameter (surface tension) implies several new qualitative results. We also explore some of the consequences of front propagation into a noisy (due to pre-existing thermal fluctuations) unstable medium.Comment: 12 page latex + figures using epsf.sty to be published in Journal de Physique II, January 199

Phase Coexistence of Complex Fluids in Shear Flow

We present some results of recent calculations of rigid rod-like particles in shear flow, based on the Doi model. This is an ideal model system for exhibiting the generic behavior of shear-thinning fluids (polymer solutions, wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We present calculations of phase coexistence under shear among weakly-aligned (paranematic) and strongly-aligned phases, including alignment in the shear plane and in the vorticity direction (log-rolling). Phase coexistence is possible, in principle, under conditions of both common shear stress and common strain rate, corresponding to different orientations of the interface between phases. We discuss arguments for resolving this degeneracy. Calculation of phase coexistence relies on the presence of inhomogeneous terms in the dynamical equations of motion, which select the appropriate pair of coexisting states. We cast this condition in terms of an equivalent dynamical system, and explore some aspects of how this differs from equilibrium phase coexistence.Comment: 16 pages, 10 figures, submitted to Faraday Discussion

Selected highlights from the study of mesons

We provide a brief review of recent progress in the study of mesons using QCD's Dyson-Schwinger equations. Along the way we touch on aspects of confinement and dynamical chiral symmetry breaking but in the main focus upon: exact results for pseudoscalar mesons, including aspects of the eta-eta' problem; a realisation that the so-called vacuum condensates are actually an intrinsic, localised property of hadrons; an essentially nonperturbative procedure for constructing a symmetry-preserving Bethe-Salpeter kernel, which has enabled a demonstration that dressed-quarks possess momentum-dependent anomalous chromo- and electromagnetic moments that are large at infrared momenta, and resolution of a longstanding problem in understanding the mass-splitting between rho- and a1-mesons such that they are now readily seen to be parity partners in the meson spectrum; features of electromagnetic form factors connected with charged and neutral pions; and computation and explanation of valence-quark distribution functions in pseudoscalar mesons. We argue that in solving QCD, a constructive feedback between theory and extant and forthcoming experiments will enable constraints to be placed on the infrared behaviour of QCD's beta-function, the nonperturbative quantity at the core of hadron physics.Comment: 28 pages, 15 figures, 2 tables. Version to appear in the Chinese Journal of Physic

Exclusion zone phenomena in water -- a critical review of experimental findings and theories

The existence of the exclusion zone (EZ), a layer of water in which plastic microspheres are repelled from hydrophilic surfaces, has now been independently demonstrated by several groups. A better understanding of the mechanisms which generate EZs would help with understanding the possible importance of EZs in biology and in engineering applications such as filtration and microfluidics. Here we review the experimental evidence for EZ phenomena in water and the major theories that have been proposed. We review experimental results from birefringence, neutron radiography, nuclear magnetic resonance, and other studies. Pollack and others have theorized that water in the EZ exists has a different structure than bulk water, and that this accounts for the EZ. We present several alternative explanations for EZs and argue that Schurr's theory based on diffusiophoresis presents a compelling alternative explanation for the core EZ phenomenon. Among other things, Schurr's theory makes predictions about the growth of the EZ with time which have been confirmed by Florea et al. and others. We also touch on several possible confounding factors that make experimentation on EZs difficult, such as charged surface groups, dissolved solutes, and adsorbed nanobubbles.Comment: 14 pg

Super- and subradiant emission of two-level systems in the near-Dicke limit

We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction schemes. We show that both models lead to the same result and, in contrast to unrenormalized models, predict that the relative orientation of the (co-aligned) dipoles is unimportant in the Dicke limit. Our master equation is of relevance to any system of dipole-coupled two-level atoms, and gives bounds on the strength of the dipole-dipole interaction for closely spaced atoms. Exact calculations for small atom systems in the near-Dicke limit show the increased emission times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the effect of the dipole-dipole interaction on collective emission is reduced.Comment: 14 pages, 6 figures, published versio

The Hopf Algebra Structure of the Character Rings of Classical Groups

The character ring \CGL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra \Sym$ of symmetric functions. Here we study the character rings \CO and \CSp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that \CO and \CSp also admit natural Hopf algebra structures that are isomorphic to that of \CGL, and hence to \Sym. The isomorphisms are determined explicitly, along with the specification of standard bases for \CO and \CSp analogous to those used for \Sym. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur-Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the \CGL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras \CO and \CSp are not self-dual. The dual Hopf algebras \CO^* and \CSp^* are identified. Finally, the Hopf algebra of the universal rational character ring \CGLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified.Comment: 38 pages, uses pstricks; new version is a major update, new title, new material on rational character

Plethystic Vertex Operators and Boson-Fermion Correspondences

We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape \pi. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each \pi, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.Comment: 21 pages, LaTeX. Minor typos corrected. Added brief survey of related work and new reference