Classification of integrable equations on quad-graphs. The consistency approach

A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional consistency. This property yields, among other features, the existence of the discrete zero curvature with a spectral parameter. For all integrable systems of the obtained exhaustive list, the so called three-leg forms are found. This establishes Lagrangian and symplectic structures for these systems, and the connection to discrete systems of the Toda type on arbitrary graphs. Generalizations of these ideas to the three-dimensional integrable systems and to the quantum context are also discussed

Classification of integrable discrete equations of octahedron type

We use the consistency approach to classify discrete integrable 3D equations of the octahedron type. They are naturally treated on the root lattice $Q(A_3)$ and are consistent on the multidimensional lattice $Q(A_N)$. Our list includes the most prominent representatives of this class, the discrete KP equation and its Schwarzian (multi-ratio) version, as well as three further equations. The combinatorics and geometry of the octahedron type equations are explained. In particular, the consistency on the 4-dimensional Delaunay cells has its origin in the classical Desargues theorem of projective geometry. The main technical tool used for the classification is the so called tripodal form of the octahedron type equations.Comment: 53 pp., pdfLaTe

High transverse momentum suppression and surface effects in Cu+Cu and Au+Au collisions within the PQM model

We study parton suppression effects in heavy-ion collisions within the Parton Quenching Model (PQM). After a brief summary of the main features of the model, we present comparisons of calculations for the nuclear modification and the away-side suppression factor to data in Au+Au and Cu+Cu collisions at 200 GeV. We discuss properties of light hadron probes and their sensitivity to the medium density within the PQM Monte Carlo framework.Comment: Comments: 6 pages, 8 figures. To appear in the proceedings of Hot Quarks 2006: Workshop for Young Scientists on the Physics of Ultrarelativistic Nucleus-Nucleus Collisions, Villasimius, Italy, 15-20 May 200

Lunar elemental analysis obtained from the Apollo gamma-ray and X-ray remote sensing experiment

Gamma-ray and X-ray spectrometers carried in the service modules of the Apollo 15 and Apollo 16 spacecraft were employed for compositional mapping of the lunar surface. The measurements involved the observation of the intensity and characteristic energy distribution of gamma rays and X-rays emitted from the lunar surface. A large-scale compositional map of over 10 percent of the lunar surface was obtained from an analysis of the observed spectra. The objective of the X-ray experiment was to measure the K spectral lines from Mg, Al, and Si. Spectra were obtained and the data were reduced to Al/Si and Mg/Si intensity ratios and ultimately to chemical ratios. Analyses of the results have indicated (1) that the Al/Si ratios are highest in the lunar highlands and considerably lower in the maria, and (2) that the Mg/Si concentrations generally show the opposite relationship. The objective of the gamma-ray experiment was to measure the natural and cosmic-ray-induced activity emission spectrum. At this time, the elemental abundances for Th, U, K, Fe, Ti, Si, and O have been determined over a number of major lunar regions. Regions of relatively high natural radioactivity were found in the Mare Imbrium and Oceanus Procellarum regions

Symmetries of modules of differential operators

Let ${\cal F}\_\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\lambda$ on the circle $S^1$. The space ${\cal D}^k\_{\lambda,\mu}(S^1)$ of $k$-th order linear differential operators from ${\cal F}\_\lambda(S^1)$ to ${\cal F}\_\mu(S^1)$ is a natural module over $\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\cal D}^k\_{\lambda,\mu}(S^1)$, i.e., the linear maps on ${\cal D}^k\_{\lambda,\mu}(S^1)$ commuting with the $\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\mathbb{R}$ (instead of $S^1$) and compare the results in the compact and non-compact cases.Comment: 29 pages, LaTeX, 4 figure

Lunar elemental analysis obtained from the Apollo gamma-ray and X-ray remote sensing experiment

Gamma ray and X-ray spectrometers carried in the service module of the Apollo 15 and 16 spacecraft were employed for compositional mapping of the lunar surface. The measurements involved the observation of the intensity and characteristics energy distribution of gamma rays and X-rays emitted from the lunar surface. A large scale compositional map of over 10 percent of the lunar surface was obtained from an analysis of the observed spectra. The objective of the X-ray experiment was to measure the K spectral lines from Mg, Al, and Si. Spectra were obtained and the data were reduced to Al/Si and Mg/Si intensity ratios and ultimately to chemical ratios. The objective of the gamma-ray experiment was to measure the natural and cosmic ray induced activity emission spectrum. At this time, the elemental abundances for Th, U, K, Fe, Ti, Si, and O have been determined over a number of major lunar regions

Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins

During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description for these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experimental findings. In particular, the temporal period of the oscillations is measured as a function of the cell length and found to be compatible with the theoretical prediction.Comment: 17 pages, 5 figures. Submitted to Physical Biolog

A New Class of Path Equations in AP-Geometry

In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the electromagnetic potential on the motion of the charged particle. This last term may give rise to an effect similar to the Aharanov-Bohm effect. It is to be considered that all extra terms will vanish if the space-time used is torsion-less.Comment: 11 pages, LaTeX fil