Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version (PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902 (2001) (E

Model for the unidirectional motion of a dynein molecule

Cytoplasmic dyneins transport cellular organelles by moving on a microtubule filament. It has been found recently that depending on the applied force and the concentration of the adenosine triphosphate (ATP) molecules, dynein's step size varies. Based on these studies, we propose a simple model for dynein's unidirectional motion taking into account the variations in its step size. We study how the average velocity and the relative dispersion in the displacement vary with the applied load. The model is amenable to further extensions by inclusion of details associated with the structure and the processivity of the molecule.Comment: 10 pages, 5 figure

Spacetimes with Longitudinal and Angular Magnetic Fields in Third Order Lovelock Gravity

We obtain two new classes of magnetic brane solutions in third order Lovelock gravity. The first class of solutions yields an $(n+1)$-dimensional spacetime with a longitudinal magnetic field generated by a static source. We generalize this class of solutions to the case of spinning magnetic branes with one or more rotation parameters. These solutions have no curvature singularity and no horizons, but have a conic geometry. For the spinning brane, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters, while the static brane has no net electric charge. The second class of solutions yields a pacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. Although the second class of solutions may be made electrically charged by a boost transformation, the transformed solutions do not present new spacetimes. Finally, we use the counterterm method in third order Lovelock gravity and compute the conserved quantities of these spacetimes.Comment: 15 pages, no figur

Non-linear Brane Dynamics in 6 Dimensions

We consider a dynamical brane world in a six dimensional spacetime containing a singularity. Using the Israel conditions we study the motion of a 4-brane embedded in this setup. We analize the brane behavior when its position is perturbed about a fixed point and solve the full non-linear dynamics in the several possible scenarios. We also investigate the possible gravitational shortcuts and calculate the delay between graviton and photon signals and the ratio of the corresponding subtended horizons.Comment: 5 pages, 2 figures. Contribution to the Proceedings of "Renormalization Group and Anomalies in Gravitation and Cosmology", Ouro Preto, Brazil, March 200

Duality and phase diagram of one dimensional transport

The observation of duality by Mukherji and Mishra in one dimensional transport problems has been used to develop a general approach to classify and characterize the steady state phase diagrams. The phase diagrams are determined by the zeros of a set of coarse-grained functions without the need of detailed knowledge of microscopic dynamics. In the process, a new class of nonequilibrium multicritical points has been identified.Comment: 6 pages, 2 figures (4 eps files

Finite Size Correction In A Disordered System - A New Divergence

We show that the amplitude of the finite size correction term for the $n$th moment of the partition function, for randomly interacting directed polymers, diverges (on the high temperature side) as $(n_c - n)^{-r}$, as a critical moment $n_c$ is approached. The exponent $r$ is independent of temperature but does depend on the effective dimensionality. There is no such divergence on the low temperature side ($n>n_c)$.Comment: 8 pages, Revtex, 5 figures. For figs, send mail to [email protected]

Nonlocality in kinetic roughening

We propose a phenomenological equation to describe kinetic roughening of a growing surface in presence of long range interactions. The roughness of the evolving surface depends on the long range feature, and several distinct scenarios of phase transitions are possible. Experimental implications are discussed.Comment: Replaced with the published version (Phys. Rev. Lett 79, 2502 (1997)). Eq. 1 written in a symmetrical form, references update

Dynamic instability of microtubules: effect of catastrophe-suppressing drugs

Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very rapidly; this phenomenon is known as ``catastrophe''. However, often a shrinking microtubule is ``rescued'' and starts polymerizing again. Here we develope a model for the polymerization-depolymerization dynamics of microtubules in the presence of {\it catastrophe-suppressing drugs}. Solving the dynamical equations in the steady-state, we derive exact analytical expressions for the length distributions of the microtubules tipped with drug-bound tubulin subunits as well as those of the microtubules, in the growing and shrinking phases, tipped with drug-free pure tubulin subunits. We also examine the stability of the steady-state solutions.Comment: Minor corrections; final published versio

Vicinal Surfaces, Fractional Statistics and Universality

We propose that the phases of all vicinal surfaces can be characterized by four fixed lines, in the renormalization group sense, in a three-dimensional space of coupling constants. The observed configurations of several Si surfaces are consistent with this picture. One of these fixed lines also describes one-dimensional quantum particles with fractional exclusion statistics. The featureless steps of a vicinal surface can therefore be thought of as a realization of fractional-statistics particles, possibly with additional short-range interactions.Comment: 6 pages, revtex, 3 eps figures. To appear in Physical Review Letters. Reference list properly arranged. Caption of Fig. 1 slightly reworded. Fig 3 (in color) is not part of the paper. It complements Fig.