12,703 research outputs found
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
-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
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