30,407 research outputs found
Cusp Summations and Cusp Relations of Simple Quad Lenses
We review five often used quad lens models, each of which has analytical
solutions and can produce four images at most. Each lens model has two
parameters, including one that describes the intensity of non-dimensional mass
density, and the other one that describes the deviation from the circular lens.
In our recent work, we have found that the cusp and the fold summations are not
equal to 0, when a point source infinitely approaches a cusp or a fold from
inner side of the caustic. Based on the magnification invariant theory, which
states that the sum of signed magnifications of the total images of a given
source is a constant, we calculate the cusp summations for the five lens
models. We find that the cusp summations are always larger than 0 for source on
the major cusps, while can be larger or smaller than 0 for source on the minor
cusps. We also find that if these lenses tend to the circular lens, the major
and minor cusp summations will have infinite values, and with positive and
negative signs respectively. The cusp summations do not change significantly if
the sources are slightly deviated from the cusps. In addition, through the
magnification invariants, we also derive the analytical signed cusp relations
on the axes for three lens models. We find that both on the major and the minor
axes the larger the lenses deviated from the circular lens, the larger the
signed cusp relations. The major cusp relations are usually larger than the
absolute minor cusp relations, but for some lens models with very large
deviation from circular lens, the minor cusp relations can be larger than the
major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA
Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens
An arbitrary surface mass density of gravitational lens can be decomposed
into multipole components. We simulate the ray-tracing for the multipolar mass
distribution of generalized SIS (Singular Isothermal Sphere) model, based on
the deflection angles which are analytically calculated. The magnification
patterns in the source plane are then derived from inverse shooting technique.
As have been found, the caustics of odd mode lenses are composed of two
overlapping layers for some lens models. When a point source traverses such
kind of overlapping caustics, the image numbers change by \pm 4, rather than
\pm 2. There are two kinds of images for the caustics. One is the critical
curve and the other is the transition locus. It is found that the image number
of the fold is exactly the average value of image numbers on two sides of the
fold, while the image number of the cusp is equal to the smaller one. We also
focus on the magnification patterns of the quadrupole (m = 2) lenses under the
perturbations of m = 3, 4 and 5 mode components, and found that one, two, and
three butterfly or swallowtail singularities can be produced respectively. With
the increasing intensity of the high-order perturbations, the singularities
grow up to bring sixfold image regions. If these perturbations are large enough
to let two or three of the butterflies or swallowtails contact, eightfold or
tenfold image regions can be produced as well. The possible astronomical
applications are discussed.Comment: 24 pages, 6 figure
Feedback local optimality principle applied to rocket vertical landing VTVL
Vertical landing is becoming popular in the last fifteen years, a technology known under the acronym VTVL, Vertical Takeoff and Vertical Landing [1,2]. The interest in such landing technology is dictated by possible cost reductions [3,4], that impose spaceshipâs recycling. The rockets are not generally de- signed to perform landing operations, rather their design is aimed at takeoff operations, guaranteeing a very high forward acceleration to gain the velocity needed to escape the gravitational force. In this paper a new control method based on Feedback Local Optimality Principle, named FLOP is applied to the rocket landing problem. The FLOP belongs to a special class of optimal controllers, developed by the mechatronic and vehicle dynamics lab of Sapienza, named Variational Feedback Controllers - VFC, that are part of an ongoing research and are recently applied in different field: nonlinear system [5], marine and terrestrial autonomous vehicles [6,7,8], multi agents interactions and vibration control [9, 10]. The paper is devoted to show the robustness of the nonlinear controlled system, comparing the performances with the LQR, one of the most acknowledged methods in optimal control
Magnification relations of quad lenses and applications on Einstein crosses
In this work, we mainly study the magnification relations of quad lens models
for cusp, fold and cross configurations. By dividing and ray-tracing in
different image regions, we numerically derive the positions and magnifications
of the four images for a point source lying inside of the astroid caustic.
Then, based on the magnifications, we calculate the signed cusp and fold
relations for the singular isothermal elliptical lenses. The signed fold
relation map has positive and negative regions, and the positive region is
usually larger than the negative region as has been confirmed before. It can
also explain that for many observed fold image pairs, the fluxes of the Fermat
minimum images are apt to be larger than those of the saddle images. We define
a new quantity cross relation which describes the magnification discrepancy
between two minimum images and two saddle images. Distance ratio is also
defined as the ratio of the distance of two saddle images to that of two
minimum images. We calculate the cross relations and distance ratios for nine
observed Einstein crosses. In theory, for most of the quad lens models, the
cross relations decrease as the distance ratios increase. In observation, the
cross relations of the nine samples do not agree with the quad lens models very
well, nevertheless, the cross relations of the nine samples do not give obvious
evidence for anomalous flux ratio as the cusp and fold types do. Then, we
discuss several reasons for the disagreement, and expect good consistencies for
more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA
Inter- and Intra-Chain Attractions in Solutions of Flexible Polyelectrolytes at Nonzero Concentration
Constant temperature molecular dynamics simulations were used to study
solutions of flexible polyelectrolyte chains at nonzero concentrations with
explicit counterions and unscreened coulombic interactions. Counterion
condensation, measured via the self-diffusion coefficient of the counterions,
is found to increase with polymer concentration, but contrary to the prediction
of Manning theory, the renormalized charge fraction on the chains decreases
with increasing Bjerrum length without showing any saturation. Scaling analysis
of the radius of gyration shows that the chains are extended at low polymer
concentrations and small Bjerrum lengths, while at sufficiently large Bjerrum
lengths, the chains shrink to produce compact structures with exponents smaller
than a gaussian chain, suggesting the presence of attractive intrachain
interactions. A careful study of the radial distribution function of the
center-of-mass of the polyelectrolyte chains shows clear evidence that
effective interchain attractive interactions also exist in solutions of
flexible polyelectrolytes, similar to what has been found for rodlike
polyelectrolytes. Our results suggest that the broad maximum observed in
scattering experiments is due to clustering of chains.Comment: 12 pages, REVTeX, 15 eps figure
DC Spin Current Generation in a Rashba-type Quantum Channel
We propose and demonstrate theoretically that resonant inelastic scattering
(RIS) can play an important role in dc spin current generation. The RIS makes
it possible to generate dc spin current via a simple gate configuration: a
single finger-gate that locates atop and orients transversely to a quantum
channel in the presence of Rashba spin-orbit interaction. The ac biased
finger-gate gives rise to a time-variation in the Rashba coupling parameter,
which causes spin-resolved RIS, and subsequently contributes to the dc spin
current. The spin current depends on both the static and the dynamic parts in
the Rashba coupling parameter, and , respectively, and is
proportional to . The proposed gate configuration has the
added advantage that no dc charge current is generated. Our study also shows
that the spin current generation can be enhanced significantly in a double
finger-gate configuration.Comment: 4 pages,4 figure
Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions
We study the spectrum of with being the
Wilson-Dirac operator on the lattice with bare mass equal to . The
background gauge fields are generated using the SU(3) Wilson action at
on an lattice. We find evidence that the spectrum of
is gapless for , implying that the physical quark is
massless in this whole region.Comment: 22 pages, LaTeX file, uses elsart.sty, includes 11 figures A
typographical error in one reference has been fixe
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Natural and anthropogenic forest fires recorded in the Holocene pollen record from a Jinchuan peat bog, northeastern China
Pollen and charcoal particles from a Jinchuan peat (northeastern China) were examined to investigate the fire origin and interaction between
climate, vegetation, fire and human activity during the Holocene. Pollen results show that: (i) a broadleaved deciduous forest was dominant during
the early Holocene; (ii) from ~5500 cal. yr B.P. there was a gradual increase in coniferous trees (mainly Pinus), and a decrease in broadleaved
deciduous trees (e.g. Quercus, Juglans, and UlmusâZelkova); (iii) after ~4200 cal. yr B.P., the deciduous forest was replaced by a mixed forest of
coniferous and deciduous trees; (iv) coniferous trees including Pinus, Abies and Picea further increased after ~2000 cal. yr B.P., reflecting a
cooler and drier climate after ~5500â4200 cal. yr B.P. Two layers of abundant microfossil charcoal particles (250â10 ÎŒm) and the coexistence of
macrofossil particles (N2 mm) suggest two local fires: fire event 1 (5120±66 cal. yr B.P.) and fire event 2 (1288±8 cal. yr B.P., AD 662±8).
Charcoal layer 1, with a large amount of Monolete psilate spores, is superimposed on the long-term trend of vegetation changes, indicating a
natural origin for fire event 1 that was probably facilitated by drying environmental conditions since the mid-Holocene. Cerealia-type pollen and a
low percentage of Monolete psilate spores were observed in charcoal layer 2, indicating that fire event 2 was caused by clearing. We suggest that
fire event 2 may be related to the spread of the Han farming culture accompanied by the territorial expansion of the Tang Dynasty to the studied
area in AD 668
Effect of Hydrostatic Pressure on the Superconductivity in NaxCoO2.yH2O
The effect of hydrostatic pressure on the superconducting transition
temperature of Na{0.35}CoO{2}.yH{2}O was investigated by ac susceptibility
measurements up to 1.6 GPa. The pressure coefficient of T{c} is negative and
the dependence T{c}(p) is nonlinear over the pressure range investigated. The
magnitude of the average dlnT{c}/dp=-0.07 GPa^{-1} is comparable to the
pressure coefficient of electron-doped high-T{c} copper oxide superconductors
with a similar value of T{c}. Our results provide support to the assumption of
two-dimensional superconductivity in Na{0.35}CoO{2}.yH{2}O, which is similar to
the cuprate systems, and suggest that intercalation of larger molecules may
lead to an enhancement of T{c}.Comment: Revised Manuscrip
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