Elasticity Theory of a Twisted Stack of Plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.Comment: 19 pages, plain LaTeX, 1 included eps figur

Quantum geometry from 2+1 AdS quantum gravity on the torus

Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved figures and extra figures. To appear GER

Shockley-Ramo theorem and long-range photocurrent response in gapless materials

Scanning photocurrent maps of gapless materials, such as graphene, often exhibit complex patterns of hot spots positioned far from current-collecting contacts. We develop a general framework that helps to explain the unusual features of the observed patterns, such as the directional effect and the global character of photoresponse. We show that such a response is captured by a simple Shockley-Ramo-type approach. We examine specific examples and show that the photoresponse patterns can serve as a powerful tool to extract information about symmetry breaking, inhomogeneity, chirality, and other local characteristics of the system.Comment: 7 pgs, 3 fg

Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant

We relate the geometrical and the Chern-Simons description of (2+1)-dimensional gravity for spacetimes of topology $R\times S_g$, where $S_g$ is an oriented two-surface of genus $g>1$, for Lorentzian signature and general cosmological constant and the Euclidean case with negative cosmological constant. We show how the variables parametrising the phase space in the Chern-Simons formalism are obtained from the geometrical description and how the geometrical construction of (2+1)-spacetimes via grafting along closed, simple geodesics gives rise to transformations on the phase space. We demonstrate that these transformations are generated via the Poisson bracket by one of the two canonical Wilson loop observables associated to the geodesic, while the other acts as the Hamiltonian for infinitesimal Dehn twists. For spacetimes with Lorentzian signature, we discuss the role of the cosmological constant as a deformation parameter in the geometrical and the Chern-Simons formulation of the theory. In particular, we show that the Lie algebras of the Chern-Simons gauge groups can be identified with the (2+1)-dimensional Lorentz algebra over a commutative ring, characterised by a formal parameter $\Theta_\Lambda$ whose square is minus the cosmological constant. In this framework, the Wilson loop observables that generate grafting and Dehn twists are obtained as the real and the $\Theta_\Lambda$-component of a Wilson loop observable with values in the ring, and the grafting transformations can be viewed as infinitesimal Dehn twists with the parameter $\Theta_\Lambda$.Comment: 50 pages, 6 eps figure

Environmental modeling and recognition for an autonomous land vehicle

An architecture for object modeling and recognition for an autonomous land vehicle is presented. Examples of objects of interest include terrain features, fields, roads, horizon features, trees, etc. The architecture is organized around a set of data bases for generic object models and perceptual structures, temporary memory for the instantiation of object and relational hypotheses, and a long term memory for storing stable hypotheses that are affixed to the terrain representation. Multiple inference processes operate over these databases. Researchers describe these particular components: the perceptual structure database, the grouping processes that operate over this, schemas, and the long term terrain database. A processing example that matches predictions from the long term terrain model to imagery, extracts significant perceptual structures for consideration as potential landmarks, and extracts a relational structure to update the long term terrain database is given

The Nuclear Outflow in NGC 2110

We present a HST/STIS spectroscopic and optical/radio imaging study of the Seyfert NGC 2110 aiming to measure the dynamics and understand the nature of the nuclear outflow in the galaxy. Previous HST studies have revealed the presence of a linear structure in the Narrow-Line Region (NLR) aligned with the radio jet. We show that this structure is strongly accelerated, probably by the jet, but is unlikely to be entrained in the jet flow. The ionisation properties of this structure are consistent with photoionisation of dusty, dense gas by the active nucleus. We present a plausible geometrical model for the NLR, bringing together various components of the nuclear environment of the galaxy. We highlight the importance of the circum-nuclear disc in determining the appearance of the emission line gas and the morphology of the jet. From the dynamics of the emission line gas, we place constraints on the accelerating mechanism of the outflow and discuss the relative importance of radio source synchrotron pressure, radio jet ram pressure and nuclear radiation pressure in accelerating the gas. While all three mechanisms can account for the energetics of the emission line gas, gravitational arguments support radio jet ram pressure as the most likely source of the outflow.Comment: 15 pages, 7 figures; accepted to MNRA