Enumeration of self avoiding trails on a square lattice using a transfer matrix technique

We describe a new algebraic technique, utilising transfer matrices, for enumerating self-avoiding lattice trails on the square lattice. We have enumerated trails to 31 steps, and find increased evidence that trails are in the self-avoiding walk universality class. Assuming that trails behave like $A \lambda ^n n^{11 \over 32}$, we find $\lambda = 2.72062 \pm 0.000006$ and $A = 1.272 \pm 0.002$.Comment: To be published in J. Phys. A:Math Gen. Pages: 16 Format: RevTe

Coulomb potential from a particle in uniform ultrarelativistic motion

The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional potential solution in the transverse direction. This form makes manifest the source of the energy independence of the interaction.Comment: 5 pages, latex, revtex source, no figure

Hydrodynamic simulations of correlation and scatter in galaxy cluster maps

The two dimensional structure of hot gas in galaxy clusters contains information about the hydrodynamical state of the cluster, which can be used to understand the origin of scatter in the thermodynamical properties of the gas, and to improve the use of clusters to probe cosmology. Using a set of hydrodynamical simulations, we provide a comparison between various maps currently employed in the X-ray analysis of merging clusters and those cluster maps anticipated from forthcoming observations of the thermal Sunyaev-Zel'dovich effect. We show the following: 1) an X-ray pseudo-pressure, defined as square root of the soft band X-ray image times the temperature map is a good proxy for the SZ map; 2) we find that clumpiness is the main reason for deviation between X-ray pseudo-pressure and SZ maps; 3) the level of clumpiness can be well characterized by X-ray pseudo-entropy maps. 4) We describe the frequency of deviation in various maps of clusters as a function of the amplitude of the deviation. This enables both a comparison to observations and a comparison to effects of introduction of complex physical processes into simulation.Comment: 7 pages, A&A in pres

Temperature effects on material characteristics

Some of the physical properties of the main elements of interest in high temperature technology are reviewed. Some general trends emerge when these properties are viewed as a function of melting point, but there are a few notable exceptions. Titanium, zirconium, niobium and tantalum all have disappointingly low moduli; chromium is excellent in many ways, but has a limited ductility at lower temperatures; molybdenum oxidises catastrophically above about 700° C, and niobium suffers from severe oxygen embrittlement. Beryllium and carbon (in the graphitic form) both stand out as exceptional materials, both have very low densities, beryllium a very high modulus but an unfortunately low ductility, while graphite has a relatively low strength at the lower temperatures, although at temperatures of 2000° C and above it emerges as a quite exceptional (and probably as the ultimate) high temperature material. Some of the fundamental factors involved in high temperature material development are examined, in the light, particularly, of past progress with the nickel alloys. If a similar progress can be achieved with other base elements then a considerable margin still remains to be exploited. Protection from oxidation at high temperatures is evidently a factor of major concern, not only with metals, but with graphite also. Successful coatings are therefore of high importance and the questions they raise, such as bonding, differential thermal expansion, and so on, represent aspects of an even wider class covered by the term “composite structures". Such structures appear to offer the only serious solution to many high temperature requirements, and their design, construction and utilization has created a whole series of new exercises in materials assessment. Matters have become so complex, that a very radical and fundamental reassessment is required if we are to change, in any very significant way, the wasteful and ad hoc methods which characterise so much of present-day materials engineering

The 2+2-Signature and the 1+1-Matrix-Brane

We discuss different aspects of the 2+2-signature from the point of view of the quatl theory. In particular, we compare two alternative approaches to such a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime of a string. This analysis also reveals hidden discrete symmetries of the 2+2-brane action associated with the 2+2-dimensional sector of a 2+10-dimensional target background.Comment: 12 pages, Latex, to appear in Mod. Phys. Lett.

Remarks on Weyl invariant p-branes and Dp-branes

A mechanism to find different Weyl invariant p-branes and Dp-branes actions is explained. Our procedure clarifies the Weyl invariance for such systems. Besides, by considering gravity-dilaton effective action in higher dimensions we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the Weyl invariance of p-branes. Our considerations can be extended to the case of super-p-branes.Comment: 18 pages, Late

R^2 Dark Matter

There is a non-trivial four-derivative extension of the gravitational spectrum that is free of ghosts and phenomenologically viable. It is the so called $R^2$-gravity since it is defined by the only addition of a term proportional to the square of the scalar curvature. Just the presence of this term does not improve the ultraviolet behaviour of Einstein gravity but introduces one additional scalar degree of freedom that can account for the dark matter of our Universe.Comment: 6 pages, 1 figure, to appear in the Proceedings of the sixth International Workshop on the Dark Side of the Universe (DSU2010) Leon, Guanajuato, Mexico 1-6 June 201