Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models

5-branes of nontrivial topology are associated in the Diaconescu-Hanany-Witten-Witten (DHWW) approach with the Seiberg-Witten (SW) theory of low-energy effective actions. There are two different "pictures", related to the IIA and IIB phases of M-theory. They differ by the choice of $6d$ theory on the 5-brane world volume. In the IIB picture it is just the 6d SUSY Yang-Mills, while in the IIA picture it is a theory of SUSY self-dual 2-form. These two pictures appear capable to describe the (non-abelian) Lax operator and (abelian) low-energy effective action respectively. Thus IIB-IIA duality is related to the duality between Hitchin and Whitham integrable structures.Comment: LaTeX, 12pp, 4 figs in ps-format requiring psfig.te

Molecular Motors Interacting with Their Own Tracks

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models. Molecular motors are viewed as diffusing particles that can asymmetrically break or rebuild periodically distributed weak links when passing over them. Our explicit calculations of dynamic properties show that coupling the transport of the unbiased molecular motor with the bridge-burning mechanism leads to a directed motion that lowers fluctuations and produces a dynamic transition in the limit of low concentration of weak links. Interaction between the backward biased molecular motor and the bridge-burning mechanism yields a complex dynamic behavior. For the reversible dissociation the backward motion of the molecular motor is slowed down. There is a change in the direction of the molecular motor's motion for some range of parameters. The molecular motor also experiences non-monotonic fluctuations due to the action of two opposing mechanisms: the reduced activity after the burned sites and locking of large fluctuations. Large spatial fluctuations are observed when two mechanisms are comparable. The properties of the molecular motor are different for the irreversible burning of bridges where the velocity and fluctuations are suppressed for some concentration range, and the dynamic transition is also observed. Dynamics of the system is discussed in terms of the effective driving forces and transitions between different diffusional regimes

Microdisk Resonators with Two Point Scatterers

Optical microdisk resonators exhibit modes with extremely high Q-factors. Their low lasing thresholds make circular microresonators good candidates for the realization of miniature laser sources. They have, however, the serious drawback that their light emission is isotropic, which is inconvenient for many applications. In our previous work, we showed that the presence of a point scatterer inside the disk can lead to highly directional modes in various frequency ranges while preserving the high Q-factors. In the present paper we generalize this idea to two point scatterers. The motivation for this work is that the strength of a point scatterer is difficult to control in experiments, and the presence of a second scatterer leads to a higher dimensional parameter space which permits to compensate this deficiency. Similar to the case of a single scatterer in a circular disk, the problem of finding the resonance modes in the presence of two scatterers is to a large extent analytically tractable.

Phase behaviour of block copolymer melts with arbitrary architecture

The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for microphase separation in AB block copolymer melts is generalized for systems with arbitrary topology of molecules. A diagrammatic technique for calculation of the monomeric correlation functions is developed. The free energies of various mesophases are calculated within the second-harmonic approximation. Model highly-branched tree-like structures are considered as an example and their phase diagrams are obtained. The topology of molecules is found to influence the spinodal temperature and asymmetry of the phase diagrams, but not the types of phases and their order. We suggest that all model AB block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also http://rugmd4.chem.rug.nl/~morozov/research.htm

New matrix model solutions to the Kac-Schwarz problem

We examine the Kac-Schwarz problem of specification of point in Grassmannian in the restricted case of gap-one first-order differential Kac-Schwarz operators. While the pair of constraints satisfying $[{\cal K}_1,W] = 1$ always leads to Kontsevich type models, in the case of $[{\cal K}_1,W] = W$ the corresponding KP $\tau$-functions are represented as more sophisticated matrix integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the 29th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, German