346 research outputs found
Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
We present examples of rooted tree graphs for which the Laplacian has
singular continuous spectral measures. For some of these examples we further
establish fractional Hausdorff dimensions. The singular continuous components,
in these models, have an interesting multiplicity structure. The results are
obtained via a decomposition of the Laplacian into a direct sum of Jacobi
matrices
170 GBit/s transmission in an erbium-doped waveguide amplifier on silicon
Signal transmission experiments were performed at 170 Gbit/s in an integrated waveguide amplifier to investigate its potential application in high-speed photonic integrated circuits. Net internal gain of up to 11 dB was measured for a continuous-wave 1532 nm signal under 1480 nm pumping, with a threshold pump power of 4 mW. A differential group delay of 2 ps between the TE and TM fundamental modes of the 5.7-cm-long amplifier was measured. When selecting a single polarization open eye diagrams and bit error rates equal to those of the transmission system without the amplifier were observed for a 1550 nm signal encoded with a 170 Gbit/s return-to-zero pseudo-random bit sequence
Areal surface measurement using multidirectional laser line scanning
The overall quality of a machined component has an important association with
the quality of its surface finish. To obtain adequate data for the surface metrology
of machined components, areal scanners are often preferred over stylus based
profile scanners due to their ability to acquire surface data over a relatively large
area. To further improve efficiency, there is a desire to perform on-machine
measurement, and recently, high-resolution areal surface scanners have been
integrated as an on-machine measurement device. Due to the limited areal
coverage, these scanners can require multiple scans to capture data from surfaces
produced on machine tools which requires a sufficient amount of time to
complete a full surface scan. In addition, since these scanners are very sensitive,
scanning delays often cause areal scanners to capture data contaminated with
noise which may arise from within the machining environment such as axes
vibrations, temperature effects, dust, etc. These factors mean such instruments
are typically used in metrology laboratories.
This paper presents a new methodology referred to as multidirectional
scanning (MDS) which is a technique that exploits characteristics of a 2D laser
line scanner (profilometer). The device is used in two directions to scan the
overall component surface ensuring the coverage of a wider surface area
compared to typical areal scanners. Since the scanner is robust and integrated
onto a machine tool, controlled axes feed rates in the orthogonal directions
ensure high spatial resolution which in turn helps to identify and reduce the noise
levels in the data. This methodology has been validated to be both accurate and
rapid to scan the component surface, reducing the cost associated with machine
downtime and also having a wider coverage of 6x6 mm2 for a single scan,
compared to 1 mm2 for most conventional areal surface measurement
instruments having comparable spatial and vertical resolution
Minimal cubic cones via Clifford algebras
We construct two infinite families of algebraic minimal cones in . The
first family consists of minimal cubics given explicitly in terms of the
Clifford systems. We show that the classes of congruent minimal cubics are in
one to one correspondence with those of geometrically equivalent Clifford
systems. As a byproduct, we prove that for any , , there is
at least one minimal cone in given by an irreducible homogeneous cubic
polynomial. The second family consists of minimal cones in , ,
defined by an irreducible homogeneous polynomial of degree . These examples
provide particular answers to the questions on algebraic minimal cones posed by
Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table
Exomoon simulations
We introduce and describe our newly developed code that simulates light
curves and radial velocity curves for arbitrary transiting exoplanets with a
satellite. The most important feature of the program is the calculation of
radial velocity curves and the Rossiter-McLaughlin effect in such systems. We
discuss the possibilities for detecting the exomoons taking the abilities of
Extremely Large Telescopes into account. We show that satellites may be
detected also by their RM effect in the future, probably using less accurate
measurements than promised by the current instrumental developments. Thus, RM
effect will be an important observational tool in the exploration of exomoons.Comment: 5 pages, 2 figures with 9 figure panels, accepted by EM&
Lattice Supersymmetry and Topological Field Theory
It is known that certain theories with extended supersymmetry can be
discretized in such a way as to preserve an exact fermionic symmetry. In the
simplest model of this kind, we show that this residual supersymmetric
invariance is actually a BRST symmetry associated with gauge fixing an
underlying local shift symmetry. Furthermore, the starting lattice action is
then seen to be entirely a gauge fixing term. The corresponding continuum
theory is known to be a topological field theory. We look, in detail, at one
example - supersymmetric quantum mechanics which possesses two such BRST
symmetries. In this case, we show that the lattice theory can be obtained by
blocking out of the continuum in a carefully chosen background metric. Such a
procedure will not change the Ward identities corresponding to the BRST
symmetries since they correspond to topological observables. Thus, at the
quantum level, the continuum BRST symmetry is preserved in the lattice theory.
Similar conclusions are reached for the two-dimensional complex Wess-Zumino
model and imply that all the supersymmetric Ward identities are satisfied {\it
exactly} on the lattice. Numerical results supporting these conclusions are
presented.Comment: 18 pages, 2 figure
A lower limit on the dark particle mass from dSphs
We use dwarf spheroidal galaxies as a tool to attempt to put precise lower
limits on the mass of the dark matter particle, assuming it is a sterile
neutrino. We begin by making cored dark halo fits to the line of sight velocity
dispersions as a function of projected radius (taken from Walker et al. 2007)
for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt
velocity anisotropy profiles, but find that no benefit is gained over constant
velocity anisotropy. In contrast to previous attempts, we do not assume any
relation between the stellar velocity dispersions and the dark matter ones, but
instead we solve directly for the sterile neutrino velocity dispersion at all
radii by using the equation of state for a partially degenerate neutrino gas
(which ensures hydrostatic equilibrium of the sterile neutrino halo). This
yields a 1:1 relation between the sterile neutrino density and velocity
dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn
limit at all radii. By varying the sterile neutrino particle mass, we locate
the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn
limit is not exceeded at any radius (in particular at the centre). We find
sizeable differences between the ranges of feasible sterile neutrino particle
mass for each dwarf, but interestingly there exists a small range 270-280eV
which is consistent with all dSphs at the 1- level.Comment: 13 pages, 2 figures, 1 tabl
Lattice formulation of super Yang-Mills theory
We construct a lattice action for super Yang-Mills theory in
four dimensions which is local, gauge invariant, free of spectrum doubling and
possesses a single exact supersymmetry. Our construction starts from the
observation that the fermions of the continuum theory can be mapped into the
component fields of a single real anticommuting Kahler-Dirac field. The
original supersymmetry algebra then implies the existence of a nilpotent scalar
supercharge and a corresponding set of bosonic superpartners. Using this
field content we write down a -exact action and show that, with an
appropriate change of variables, it reduces to a well-known twist of super Yang-Mills theory due to Marcus. Using the discretization
prescription developed in an earlier paper on the theory in two
dimensions we are able to translate this geometrical action to the lattice.Comment: 15 pages. 1 reference correcte
A Perturbative Calculation of the Electromagnetic Form Factors of the Deuteron
Making use of the effective field theory expansion recently developed by the
authors, we compute the electromagnetic form factors of the deuteron
analytically to next-to-leading order (NLO). The computation is rather simple,
and involves calculating several Feynman diagrams, using dimensional
regularization. The results agree well with data and indicate that the
expansion is converging. They do not suffer from any ambiguities arising from
off-shell versus on-shell amplitudes.Comment: 22 pages, 8 figures. Discussion of effective range theory added,
typos correcte
First results from simulations of supersymmetric lattices
We conduct the first numerical simulations of lattice theories with exact
supersymmetry arising from the orbifold constructions of
\cite{Cohen:2003xe,Cohen:2003qw,Kaplan:2005ta}. We consider the \cQ=4 theory
in dimensions and the \cQ=16 theory in dimensions. We show
that the U(N) theories do not possess vacua which are stable
non-perturbatively, but that this problem can be circumvented after truncation
to SU(N). We measure the distribution of scalar field eigenvalues, the spectrum
of the fermion operator and the phase of the Pfaffian arising after integration
over the fermions. We monitor supersymmetry breaking effects by measuring a
simple Ward identity. Our results indicate that simulations of
super Yang-Mills may be achievable in the near future.Comment: 25 pages, 14 figures, 9 tables. 3 references adde
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