As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a non-Hermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g≥1.

In-fiber devices enable a vast array of critical photonic functions ranging from signal conditioning (amplification, dispersion control) to network management (add/drop multiplexers, optical monitoring). These devices have become the mainstays of fiber-optic communication systems because they provide the advantages of low loss, polarisation insensitivity, high reliability, and compatibility with the transmission line. The majority of fiber devices reported to date are obtained by doping, designing or writing gratings in the core of a single mode fiber. Thus, these devices use the fiber only as a platform for propagating light - the device effect itself is due to some extraneously introduced material or structure (dopants for amplification, gratings for phase matching etc).

There exists another, relatively less explored degree of freedom afforded by fibers - the ability to co-propagate more than one mode. Each mode may have a uniquely defined modal dispersion and propagation characteristic. In this talk we will describe the variety of fiber-devices enabled by few-mode fibers - fibers that typically support more than one core- or cladding- guided mode, with suitably tailored dispersive properties. We will show that the unique dispersive properties of various modes in conjunction with the ability to couple between them with gratings, leads to devices that offer novel solutions for dispersion compensation, data modulation, spectral shaping and polarisation control, to name a few applications.

The binding of basic fibroblast growth factor (FGF-2) to its cell surface receptor (CSR) and subsequent signal transduction is known to be enhanced by Heparan Sulfate Proteoglycans (HSPGs). HSPGs bind FGF-2 with low affinity and likely impact CSR-mediated signaling via stabilization of FGF-2-CSR complexes by association with both the ligand and the receptor. However, it is not known whether HSPG associates with CSR in the absence of FGF-2. Using mean-field rate equations, we show that the impact of such pre-formed complexes is significant at (i) high ligand concentrations, and (ii) when [CSR] and [HSPG] are comparable. We test these predictions through numerical simulations, and find quantitative differences with mean-field predictions.

Microtubules are protein polymers found in all eukaryotic cells. These polymers are composed of heterodimeric subunits consisting of two closely-related proteins, alpha- and beta-tubulin. Microtubules are essential for a variety of cellular processes including cell division, intracellular organization and transport, and cell swimming. Defects in microtubule-dependent processes are correlated with a number of human health problems, including cancer, birth defects, neurodegenerative diseases, and sterility. Further, microtubules are common targets for naturally-occurring toxins and synthetic chemotherapy reagents.

The function of microtubules is dependent on the dynamic assembly / disassembly of the polymer, as well as the ability of other proteins, known as microtubule-associated proteins (MAPs), to interact with microtubules. MAPs can be separated into two classes, those that regulate microtubule assembly dynamics and those that act as motors to move cellular contents along microtubule "roadways". Research in my lab focuses on two areas: 1) understanding the mechanisms that control the polymerization / depolymerization of tubulin subunits as part of microtubule turnover, and 2) understanding the role of microtubule motors during cell division, and how different motor proteins work in concert to create and drive the cell division machinery.

In living cells, DNA serves as the template from which mRNA is synthesized. mRNA is then "read," or translated, by ribosomes to produce proteins. Previous studies have shown a nonlinear relationship between mRNA and protein levels, due to the complexity of the translation process. A model is under development to help explain the quantitative relationship between mRNA and protein levels for all genes in Escherichia coli. Statistical physics methods enable a detailed understanding of a single mRNA with a uniform sequence. Realistic, nonuniform sequences are a far more complex case, but mean-field equations provide a good approximation for protein production rates. Details of the model will be discussed, and preliminary results comparing the model to experimental data will be presented.

A number of processes in the development of higher organisms require the generation of a periodic pattern of cell fates. For example, insects must grow from eggs into adults with multiple segments, and vertebrates must form a column of vertebrae along the body axis. One of the best studied and most remarkable examples of such a process occurs in the development of the compound eye of the fruit fly D. melanogaster, where a hexagonal lattice of photoreceptors is specified from an initially undifferentiated sheet of cells. After introducing the basic biology of eye development, I will show how experimental results can be used to infer the network of regulatory interactions responsible for creating the pattern of photoreceptors. This network can be modelled by a system of coupled reaction-diffusion equations. By analyzing a simplified version of the equations, I will argue that the fly eye is one of the clearest known biological examples of pattern formation by local activation with long-range inhibition. In the fly eye, this classic paradigm is augmented by an "epitaxial" mechanism for initially creating the pattern: Rather than growing from an initially uniform state, the hexagonal lattice is formed one row at a time as a front propagates into the undifferentiated region. I will suggest that similar mechanisms may be at work in other biological systems and discuss some experimental consequences of these ideas.

Nematic elastomers are elastic media with the macroscopic symmetry properties of nematic liquid crystals. In addition to the elastic degrees of freedom of ordinary rubber, nematic elastomers possess the internal, orientational degree of freedom of liquid crystals. However, because nematic elastomers cannot flow, their mechanical properties differ significantly from those of standard nematic liquid crystals.

Nematic elastomers have fascinating properties. For example, temperature change or illumination can change the orientational order and cause the elastomer to extend or contract as much as 400%. Nematic elastomers display a soft elasticity characterized by vanishing shear stresses for a range of longitudinal strains applied perpendicular to the nematic direction. They exhibit an anomalous elasticity in which certain bending and shear moduli are length-scale dependent.

After giving an overview of their unique properties, the talk focuses on the theoretic description of nematic elastomers. Basic symmetry arguments are presented that lead to an elastic energy functional for these materials. This elastic energy then allows for an explanation of several of the aforementioned properties.

Simple real-space renormalization techniques are applied to study the criticality of the totally asymmetric simple exclusion process (ASEP) and the three-state driven diffusive lattice gas. Standard block transformation is used for reduction of the degrees of freedom of the models. The flow in the parameter space is obtained by using the master equations for small compact clusters. In the case of the ASEP model computational and analytical approaches are shown, while for the three-state model only the numerical results based on Monte Carlo renormalization are reported.

The organization of cooperating enzymes into macromolecular complexes, or metabolons, is a well-documented, yet often under-appreciated, feature of living cells. This organization provides the means to attain high local substrate concentrations, regulate competition among branch pathways, coordinate the activities of interdependent pathways, and sequester insoluble, toxic, or volatile intermediates. Some metabolons, such as the machinery of protein and nucleic acid biosynthesis, are extremely stable and can be extracted from cells as intact multienzyme structures. Others are organized as "dynamic" complexes that may dissociate and reform in response to environmental or physiological stimuli. In this way, enzyme complexes can provide an important mechanism for controlling cellular metabolism. However, very little known about the molecular basis, or physiological significance, of enzyme complex formation and localization. The Winkel laboratory is using the major plant secondary pathway for the biosynthesis of flavonoids as a model system to examine the role of dynamic enzyme complexes in controlling the amounts, types, and destinations of the metabolites that accumulate in cells. The advent of structural information for several flavonoid enzymes, together with powerful biophysical methods such as small angle neutron scattering, is now leading us to a three-dimensional model of metabolism that can be tested using molecular genetic and biochemical approaches.

The dynamics of a single particle undergoing sliding motion on a surface which is subject to random fluctuations is a non-trivial problem. We use a self-consistent approximation to study this problem in the case of one-dimensional Edwards-Wilkinson surface, where the height correlations are known exactly. This approximation predicts that the passive sliding particle shows anomalous diffusion, with dynamical exponent z=3/2. Numerical simulations are in agreement with this prediction, but only when the particle motion is slow compared to the surface. When the particle moves too fast, particle motion is slaved to surface fluctuations and normal diffusion (z=2) is found. We also discuss possible cross-over scenarios which could account for the change in the observed power law.

The two-species model consists of two types of particles and holes on a square lattice. The particles undergo biased diffusion, with the direction of the bias distinguishing the two types of particle. The particles interact via excluded volume and a nearest-neighbor attraction. Previously, three phases were found by varying a) the fraction of one species relative to the other and b) the 'temperature', which controls the strength of the bias and interactions. Here, we will investigate this phase diagram in greater detail by looking at some larger systems. We also will present preliminary investigations of a different slice of phase space.