548 research outputs found
The Apparent Fractal Conjecture
This short communication advances the hypothesis that the observed fractal
structure of large-scale distribution of galaxies is due to a geometrical
effect, which arises when observational quantities relevant for the
characterization of a cosmological fractal structure are calculated along the
past light cone. If this hypothesis proves, even partially, correct, most, if
not all, objections raised against fractals in cosmology may be solved. For
instance, under this view the standard cosmology has zero average density, as
predicted by an infinite fractal structure, with, at the same time, the
cosmological principle remaining valid. The theoretical results which suggest
this conjecture are reviewed, as well as possible ways of checking its
validity.Comment: 6 pages, LaTeX. Text unchanged. Two references corrected. Contributed
paper presented at the "South Africa Relativistic Cosmology Conference in
Honour of George F. R. Ellis 60th Birthday"; University of Cape Town,
February 1-5, 199
Strain Modulated Superlattices in Graphene
Strain engineering of graphene takes advantage of one of the most dramatic
responses of Dirac electrons enabling their manipulation via strain-induced
pseudo-magnetic fields. Numerous theoretically proposed devices, such as
resonant cavities and valley filters, as well as novel phenomena, such as snake
states, could potentially be enabled via this effect. These proposals, however,
require strong, spatially oscillating magnetic fields while to date only the
generation and effects of pseudo-gauge fields which vary at a length scale much
larger than the magnetic length have been reported. Here we create a periodic
pseudo-gauge field profile using periodic strain that varies at the length
scale comparable to the magnetic length and study its effects on Dirac
electrons. A periodic strain profile is achieved by pulling on graphene with
extreme (>10%) strain and forming nanoscale ripples, akin to a plastic wrap
pulled taut at its edges. Combining scanning tunneling microscopy and atomistic
calculations, we find that spatially oscillating strain results in a new
quantization different from the familiar Landau quantization observed in
previous studies. We also find that graphene ripples are characterized by large
variations in carbon-carbon bond length, directly impacting the electronic
coupling between atoms, which within a single ripple can be as different as in
two different materials. The result is a single graphene sheet that effectively
acts as an electronic superlattice. Our results thus also establish a novel
approach to synthesize an effective 2D lateral heterostructure - by periodic
modulation of lattice strain.Comment: 18 pages, 5 figures and supplementary informatio
Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systems
We consider compositions of the transformations of the time variable and
canonical transformations of the other coordinates, which map completely
integrable system into other completely integrable system. Change of the time
gives rise to transformations of the integrals of motion and the Lax pairs,
transformations of the corresponding spectral curves and R-matrices. As an
example, we consider canonical transformations of the extended phase space for
the Toda lattices and the Stackel systems.Comment: LaTeX2e + Amssymb, 22p
Issues for the Next Generation of Galaxy Surveys
I argue that the weight of the available evidence favours the conclusions
that galaxies are unbiased tracers of mass, the mean mass density (excluding a
cosmological constant or its equivalent) is less than the critical Einstein-de
Sitter value, and an isocurvature model for structure formation offers a viable
and arguably attractive model for the early assembly of galaxies. If valid
these conclusions complicate our work of adding structure formation to the
standard model for cosmology, but it seems sensible to pay attention to
evidence.Comment: 14 pages, 3 postscript figures, uses rspublic.st
Detecting Determinacy in Prolog Programs: 22nd International Conference, ICLP 2006, Seattle, WA, USA, August 17-20, 2006. Proceedings
In program development it is useful to know that a call to a Prolog program will not inadvertently leave a choice-point on the stack. Determinacy inference has been proposed for solving this problem yet the analysis was found to be wanting in that it could not infer determinacy conditions for programs that contained cuts or applied certain tests to select a clause. This paper shows how to remedy these serious deficiencies. It also addresses the problem of identifying those predicates which can be rewritten in a more deterministic fashion. To this end, a radically new form of determinacy inference is introduced, which is founded on ideas in ccp, that is capable of reasoning about the way bindings imposed by a rightmost goal can make a leftmost goal deterministic
Ab Initio Calculations of the Walls Shear Strength of Carbon Nanotubes
The dependence of the energy of interwall interaction in double-walled carbon
nanotubes (DWNT) on the relative position of walls has been calculated using
the density functional method. This dependence is used to evaluate forces that
are necessary for the relative telescopic motion of walls and to calculate the
shear strength of DWNT for the relative sliding of walls along the nanotube
axis and for their relative rotation about this axis. The possibility of
experimental verification of the obtained results is discussed.Comment: 4 pages, 1 figur
Gate-tunable bandgap in bilayer graphene
The tight-binding model of bilayer graphene is used to find the gap between
the conduction and valence bands, as a function of both the gate voltage and as
the doping by donors or acceptors. The total Hartree energy is minimized and
the equation for the gap is obtained. This equation for the ratio of the gap to
the chemical potential is determined only by the screening constant. Thus the
gap is strictly proportional to the gate voltage or the carrier concentration
in the absence of donors or acceptors. In the opposite case, where the donors
or acceptors are present, the gap demonstrates the asymmetrical behavior on the
electron and hole sides of the gate bias. A comparison with experimental data
obtained by Kuzmenko et al demonstrates the good agreement.Comment: 6 pages, 5 figure
The Maupertuis principle and canonical transformations of the extended phase space
We discuss some special classes of canonical transformations of the extended
phase space, which relate integrable systems with a common Lagrangian
submanifold. Various parametric forms of trajectories are associated with
different integrals of motion, Lax equations, separated variables and
action-angles variables. In this review we will discuss namely these induced
transformations instead of the various parametric form of the geometric
objects
Chaos in Static Axisymmetric Spacetimes I : Vacuum Case
We study the motion of test particle in static axisymmetric vacuum spacetimes
and discuss two criteria for strong chaos to occur: (1) a local instability
measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which
is closely related to an unstable periodic orbit in general relativity. We
analyze several static axisymmetric spacetimes and find that the first
criterion is a sufficient condition for chaos, at least qualitatively. Although
some test particles which do not satisfy the first criterion show chaotic
behavior in some spacetimes, these can be accounted for the second criterion.Comment: More comments for the quantitative estimation of chaos are added, and
some inappropriate terms are changed. This will appear on Class. Quant. Gra
Fractal Holography: a geometric re-interpretation of cosmological large scale structure
The fractal dimension of large-scale galaxy clustering has been demonstrated
to be roughly from a wide range of redshift surveys. If correct,
this statistic is of interest for two main reasons: fractal scaling is an
implicit representation of information content, and also the value itself is a
geometric signature of area. It is proposed that the fractal distribution of
galaxies may thus be interpreted as a signature of holography (``fractal
holography''), providing more support for current theories of holographic
cosmologies. Implications for entropy bounds are addressed. In particular,
because of spatial scale invariance in the matter distribution, it is shown
that violations of the spherical entropy bound can be removed. This holographic
condition instead becomes a rigid constraint on the nature of the matter
density and distribution in the Universe. Inclusion of a dark matter
distribution is also discussed, based on theoretical considerations of possible
universal CDM density profiles.Comment: 13 pp, LaTeX. Revised version; to appear in JCA
- âŠ