Bipartite partial duals and circuits in medial graphs

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.Comment: v2: minor changes. To appear in Combinatoric

Nonlinear effects in optical data processing Final progress report

Nonlinearity effects in optical data processing, and FORTRAN program for analyzing nonlinearities in spectroscopic photographic plate

The effect of non-linearities on optical correlation processing

Analytical method using series expansion to determine effect of nonlinearities on output of coherent optical correlato

On knotted streamtubes in incompressible hydrodynamical flow and a restricted conserved quantity

For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a very precise topological meaning viz, measure of the degree of knottedness or linkage of streamtubes.As a consequence, stream-helicity emerges as a robust topological invariant.Comment: This extended version is the basically a more clarified version of the previous submission physics/0611166v

Geometrical statistics and vortex structures in helical and nonhelical turbulences

In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and nonhelical turbulences generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the antisymmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe the following in both helical and nonhelical turbulences: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 with both the most contractive and the most extensive eigendirections of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3336012

Bibliography on Optical Information and Data Processing

Bibliography on optical information and data processin

The fantastic in Spain during the late- nineteenth and early-twentieth centuries

This thesis has as its primary objective the drawing together and subsequent theorisation of diverse texts which can be understood to be examples of Spanish fantastic literature. It demonstrates that from nineteenth-century Realism and Naturalism (exemplified in narratives by Pérez Galdós, Alarcón and Pardo Bazán), through turn-of-the-century modernismo (Valle-Inclán and Zamacois) to twentieth- century proto-existentialism (Unamuno), a significant number of texts were produced which, in spite of the obvious differences between them, refute the widely held idea that 'the fantastic' and Spanish literature share little common ground. The thesis is therefore one more step along the journey of establishing that Spanish fantastic literature is as important and integral to the whole swathe of Spanish cultural production as it is in many other European countries. The critical analyses of the narratives push at the boundaries of previous interpretative strategies both in terms of the fantastic and of the texts themselves. The exception to this interrogation and reinvigoration of earlier interpretations is to be found in the approach to the narratives by Zamacois, which have hitherto received very little critical attention. These detailed readings draw out the complexities and intriguing perspectives which the fantastic in Spain presents to the attentive reader. By means of these textual analyses, the thesis also explores some of the various possibilities presented by the fantastic itself, putting flesh on the theoretical bones of several different critical discourses. Ultimately, this thesis charts a dynamic and coherent corpus of material which represents the process of the psychologisation of the supernatural from Romanticism onwards. Each successive text more starkly expresses the unreal horrors of the fractured human mind, as well as the mutations of the body. As such, the evolutionary history of the fantastic in Spain is shown to be more gripping and relevant than has hitherto been understood to be the case

Evaluations of topological Tutte polynomials

We find new properties of the topological transition polynomial of embedded graphs, $Q(G)$. We use these properties to explain the striking similarities between certain evaluations of Bollob\'as and Riordan's ribbon graph polynomial, $R(G)$, and the topological Penrose polynomial, $P(G)$. The general framework provided by $Q(G)$ also leads to several other combinatorial interpretations these polynomials. In particular, we express $P(G)$, $R(G)$, and the Tutte polynomial, $T(G)$, as sums of chromatic polynomials of graphs derived from $G$; show that these polynomials count $k$-valuations of medial graphs; show that $R(G)$ counts edge 3-colourings; and reformulate the Four Colour Theorem in terms of $R(G)$. We conclude with a reduction formula for the transition polynomial of the tensor product of two embedded graphs, showing that it leads to additional relations among these polynomials and to further combinatorial interpretations of $P(G)$ and $R(G)$.Comment: V2: major revision, several new results, and improved expositio