Coxeter group structure of cosmological billiards on compact spatial manifolds

We present a systematic study of the cosmological billiard structures of Einstein-p-form systems in which all spatial directions are compactified on a manifold of nontrivial topology. This is achieved for all maximally oxidised theories associated with split real forms, for all possible compactifications as defined by the de Rham cohomology of the internal manifold. In each case, we study the Coxeter group that controls the dynamics for energy scales below the Planck scale as well as the relevant billiard region. We compare and contrast them with the Weyl group and fundamental domain that emerge from the general BKL analysis. For generic topologies we find a variety of possibilities: (i) The group may or may not be a simplex Coxeter group; (ii) The billiard region may or may not be a fundamental domain. When it is not a fundamental domain, it can be described as a sequence of pairwise adjacent chambers, known as a gallery, and the reflections in the billiard walls provide a non-standard presentation of the Coxeter group. We find that it is only when the Coxeter group is a simplex Coxeter group, and the billiard region is a fundamental domain, that there is a correspondence between billiard walls and simple roots of a Kac-Moody algebra, as in the general BKL analysis. For each compactification we also determine whether or not the resulting theory exhibits chaotic dynamics.Comment: 51 pages. Typos corrected. References added. Submitted for publicatio

Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

Electronic friction and liquid-flow-induced voltage in nanotubes

A recent exciting experiment by Ghosh et al. reported that the flow of an ion-containing liquid such as water through bundles of single-walled carbon nanotubes induces a voltage in the nanotubes that grows logarithmically with the flow velocity v0. We propose an explanation for this observation. Assuming that the liquid molecules nearest the nanotube form a 2D solid-like monolayer pinned through the adsorbed ions to the nanotubes, the monolayer sliding will occur by elastic loading followed by local yield (stick-slip). The drifting adsorbed ions produce a voltage in the nanotube through electronic friction against free electrons inside the nanotube. Thermally excited jumps over force-biased barriers, well-known in stick-slip, can explain the logarithmic voltage growth with flow velocity. We estimate the short circuit current and the internal resistance of the nanotube voltage generator.Comment: 8 pages, 3 figures; published on PRB (http://link.aps.org/abstract/PRB/v69/e235410) and on the Virtual Journal of Nanoscale Science and Technology (http://www.vjnano.org, July 14, 2002, Vol. 10, Iss. 2

How do liquids confined at the nanoscale influence adhesion?

Liquids play an important role in adhesion and sliding friction. They behave as lubricants in human bodies especially in the joints. However, in many biological attachment systems they acts like adhesives, e.g. facilitating insects to move on ceilings or vertical walls. Here we use molecular dynamics to study how liquids confined at the nanoscale influence the adhesion between solid bodies with smooth and rough surfaces. We show that a monolayer of liquid may strongly affect the adhesion.Comment: 5 pages, 9 color figures. Some figures are in Postscript Level 3 format. Minimal changes with respect to the previous version. Added doi and reference to the published article also inside the pape

Fluid flow at the interface between elastic solids with randomly rough surfaces

I study fluid flow at the interface between elastic solids with randomly rough surfaces. I use the contact mechanics model of Persson to take into account the elastic interaction between the solid walls and the Bruggeman effective medium theory to account for the influence of the disorder on the fluid flow. I calculate the flow tensor which determines the pressure flow factor and, e.g., the leak-rate of static seals. I show how the perturbation treatment of Tripp can be extended to arbitrary order in the ratio between the root-mean-square roughness amplitude and the average interfacial surface separation. I introduce a matrix D(Zeta), determined by the surface roughness power spectrum, which can be used to describe the anisotropy of the surface at any magnification Zeta. I present results for the asymmetry factor Gamma(Zeta) (generalized Peklenik number) for grinded steel and sandblasted PMMA surfaces.Comment: 16 pages, 14 figure

Quantum-dot thermometry

We present a method for the measurement of a temperature differential across a single quantum dot that has transmission resonances that are separated in energy by much more than the thermal energy. We determine numerically that the method is accurate to within a few percent across a wide range of parameters. The proposed method measures the temperature of the electrons that enter the quantum dot and will be useful in experiments that aim to test theory which predicts quantum dots are highly-efficient thermoelectrics.Comment: 3 pages, 4 Figure