On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

Molecules, ices and astronomy

Molecules in interstellar gas and in interstellar ices play a fundamental role in astronomy. However, the formation of the simplest molecule, molecular hydrogen, is still not fully understood. Similarly, although interstellar ice analogues have received much attention in the laboratory, the evolution of ices in the interstellar medium still requires further study. At UCL we have developed two separate experiments to address these issues and explore the following questions: How is H formed on dust-grain surfaces? What is the budget between internal, kinetic and surface energies in the formation process? What are the astronomical consequences of these results? For ices, we ask: How do molecules desorb from pure and from mixed ices in regions warmed by newly formed stars? What can molecules released from ices tell us about the star-formation process? We put our results in the context of other laboratory work and we describe their application to current problems in astronomy

An analytical and experimental assessment of flexible road ironwork support structures

This paper describes work undertaken to investigate the mechanical performance of road ironwork installations in highways, concentrating on the chamber construction. The principal aim was to provide the background research which would allow improved designs to be developed to reduce the incidence of failures through improvements to the structural continuity between the installation and the surrounding pavement. In doing this, recycled polymeric construction materials (Jig Brix) were studied with a view to including them in future designs and specifications. This paper concentrates on the Finite Element (FE) analysis of traditional (masonry) and flexible road ironwork structures incorporating Jig Brix. The global and local buckling capacity of the Jig Brix elements was investigated and results compared well with laboratory measurements. FE models have also been developed for full-scale traditional (masonry) and flexible installations in a surrounding flexible (asphalt) pavement structure. Predictions of response to wheel loading were compared with full-scale laboratory measurements. Good agreement was achieved with the traditional (masonry) construction but poorer agreement for the flexible construction. Predictions from the FE model indicated that the use of flexible elements significantly reduces the tensile horizontal strain on the surface of the surrounding asphaltic material which is likely to reduce the incidence of surface cracking

Agricultural interpretation technique development

There are no author-identified significant results in this report

Energy distribution in a BTZ black hole spacetime

We evaluate the energy distribution associated with the (2+1)-dimensional rotating BTZ black hole. The energy-momentum complexes of Landau-Lifshitz and Weinberg are employed for this computation. Both prescriptions give exactly the same form of energy distribution. Therefore, these results provide evidence in support of the claim that, for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions, as it is the case in four dimensions.Comment: 16 pages, LaTeX; v2: comments, clarifications and references added, version to appear in Int.J.Mod.Phys.

Bifurcated polarization rotation in bismuth-based piezoelectrics

ABO3 perovskite-type solid solutions display a large variety of structural and physical properties, which can be tuned by chemical composition or external parameters such as temperature, pressure, strain, electric, or magnetic fields. Some solid solutions show remarkably enhanced physical properties including colossal magnetoresistance or giant piezoelectricity. It has been recognized that structural distortions, competing on the local level, are key to understanding and tuning these remarkable properties, yet, it remains a challenge to experimentally observe such local structural details. Here, from neutron pair-distribution analysis, a temperature-dependent 3D atomic-level model of the lead-free piezoelectric perovskite Na0.5Bi0.5TiO3 (NBT) is reported. The statistical analysis of this model shows how local distortions compete, how this competition develops with temperature, and, in particular, how different polar displacements of Bi3+ cations coexist as a bifurcated polarization, highlighting the interest of Bi-based materials in the search for new lead-free piezoelectrics

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.Comment: 19 pages, 5 figures. accepted to Int. J. Mod. Phys. B (April 2006

Fast Collisionless Reconnection Condition and Self-Organization of Solar Coronal Heating

I propose that solar coronal heating is a self-regulating process that keeps the coronal plasma roughly marginally collisionless. The self-regulating mechanism is based on the interplay of two effects. First, plasma density controls coronal energy release via the transition between the slow collisional Sweet-Parker regime and the fast collisionless reconnection regime. This transition takes place when the Sweet--Parker layer becomes thinner than the characteristic collisionless reconnection scale. I present a simple criterion for this transition in terms of the upstream plasma density (n_e), the reconnecting (B_0) and guide (B_z) magnetic field components, and the global length (L) of the reconnection layer: L < 6.10^9 cm [n_e/(10^{10}/cm^3)]^(-3) (B_0/30G)^4 (B_0/B_z)^2. Next, coronal energy release by reconnection raises the ambient plasma density via chromospheric evaporation and this, in turn, temporarily inhibits subsequent reconnection involving the newly-reconnected loops. Over time, however, radiative cooling gradually lowers the density again below the critical value and fast reconnection again becomes possible. As a result, the density is highly inhomogeneous and intermittent but, statistically, does not deviate strongly from the critical value which is comparable with the observed coronal density. Thus, in the long run, the coronal heating process can be represented by repeating cycles that consist of fast reconnection events (i.e., nanoflares), followed by rapid evaporation episodes, followed by relatively long periods (1-hour) during which magnetic stresses build up and simultaneously the plasma cools down and precipitates.Comment: 17 pages, no figures; accepted to the Astrophysical Journal; replaced to match the accepted versio