101,693 research outputs found
Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap
Rapidly scanning magnetic and optical dipole traps have been widely utilised
to form time-averaged potentials for ultracold quantum gas experiments. Here we
theoretically and experimentally characterise the dynamic properties of
Bose-Einstein condensates in ring-shaped potentials that are formed by scanning
an optical dipole beam in a circular trajectory. We find that unidirectional
scanning leads to a non-trivial phase profile of the condensate that can be
approximated analytically using the concept of phase imprinting. While the
phase profile is not accessible through in-trap imaging, time-of-flight
expansion manifests clear density signatures of an in-trap phase step in the
condensate, coincident with the instantaneous position of the scanning beam.
The phase step remains significant even when scanning the beam at frequencies
two orders of magnitude larger than the characteristic frequency of the trap.
We map out the phase and density properties of the condensate in the scanning
trap, both experimentally and using numerical simulations, and find excellent
agreement. Furthermore, we demonstrate that bidirectional scanning eliminated
the phase gradient, rendering the system more suitable for coherent matter wave
interferometry.Comment: 10 pages, 7 figure
Planet Signatures in Collisionally Active Debris Discs: scattered light images
Planet perturbations are often invoked as a potential explanation for many
spatial structures that have been imaged in debris discs. So far this issue has
been mostly investigated with collisionless N-body numerical models. We
numerically investigate how the coupled effect of collisions and radiation
pressure can affect the formation and survival of radial and azimutal
structures in a disc perturbed by a planet. We consider two set-ups: a planet
embedded within an extended disc and a planet exterior to an inner debris ring.
We use the DyCoSS code of Thebault(2012) and derive synthetic images of the
system in scattered light. The planet's mass and orbit, as well as the disc's
collisional activity are explored as free parameters.
We find that collisions always significantly damp planet-induced structures.
For the case of an embedded planet, the planet's signature, mostly a density
gap around its radial position, should remain detectable in head-on images if
M_planet > M_Saturn. If the system is seen edge-on, however, inferring the
presence of the planet is much more difficult, although some planet-induced
signatures might be observable under favourable conditions.
For the inner-ring/external-planet case, planetary perturbations cannot
prevent collision-produced small fragments from populating the regions beyond
the ring: The radial luminosity profile exterior to the ring is close to the
one it should have in the absence of the planet. However, a Jovian planet on a
circular orbit leaves precessing azimutal structures that can be used to
indirectly infer its presence. For a planet on an eccentric orbit, the ring is
elliptic and the pericentre glow effect is visible despite of collisions and
radiation pressure, but detecting such features in real discs is not an
unambiguous indicator of the presence of an outer planet.Comment: Accepted for Publication in A&A (NOTE: Abridged abstract and
(very)LowRes Figures. Better version, with High Res figures and full abstract
can be found at http://lesia.obspm.fr/perso/philippe-thebault/planpapph.pdf
Method and apparatus for phasing segmented mirror arrays
A method and an apparatus are disclosed for edge phasing an array of segments in a segmented primary telescope mirror using white light from a far field source and starting with the inner edge of each segment in the first ring of segments. The segments are individually phased for zero piston and tilt error with respect to the edge of a reference surface in the open center position of the telescope mirror. After edge phasing of all segments in the telescope mirror array is completed, full surface phasing can be achieved by using a conventional Shack-Hartmann technique followed by finding the RMS best fit for each segment of the mirror array
Signatures of massive collisions in debris discs
Violent stochastic collisional events have been invoked as a possible
explanation for some debris discs displaying pronounced asymmetries or having a
great luminosity excess. So far, no thorough modelling of the consequences of
such events has been carried out, mainly because of the extreme numerical
challenge of coupling the dynamical and collisional evolution of dust.
We perform the first fully self-consistent modelling of the aftermath of
massive breakups in debris discs. We follow the collisional and dynamical
evolution of dust released after the breakup of a Ceres-sized body at 6 AU from
its central star. We investigate the duration, magnitude and spatial structure
of the signature left by such a violent event, as well as its observational
detectability.
We use the recently developed LIDT-DD code (Kral et al., 2013), which handles
the coupled collisional and dynamical evolution of debris discs. The main focus
is placed on the complex interplay between destructive collisions, Keplerian
dynamics and radiation pressure forces. We use the GRaTer package to estimate
the system's luminosity at different wavelengths.
The breakup of a Ceres-sized body at 6 AU creates an asymmetric dust disc
that is homogenized, by the coupled action of collisions and dynamics, on a
timescale of a few years. The luminosity excess in the breakup's
aftermath should be detectable by mid-IR photometry, from a 30 pc distance,
over a period of years that exceeds the duration of the asymmetric
phase of the disc (a few years). As for the asymmetric structures, we
derive synthetic images for the SPHERE/VLT and MIRI/JWST instruments, showing
that they should be clearly visible and resolved from a 10 pc distance. Images
at 1.6m (marginally), 11.4 and 15.5m would show the inner disc
structures while 23m images would display the outer disc asymmetries.Comment: 16 pages, 14 figures, abstract shortened, accepted for publication in
A&
An Improvement over the GVW Algorithm for Inhomogeneous Polynomial Systems
The GVW algorithm is a signature-based algorithm for computing Gr\"obner
bases. If the input system is not homogeneous, some J-pairs with higher
signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead,
GVW have to compute some J-pairs with lower signatures but higher degrees.
Consequently, degrees of polynomials appearing during the computations may
unnecessarily grow up higher and the computation become more expensive. In this
paper, a variant of the GVW algorithm, called M-GVW, is proposed and mutant
pairs are introduced to overcome inconveniences brought by inhomogeneous input
polynomials. Some techniques from linear algebra are used to improve the
efficiency. Both GVW and M-GVW have been implemented in C++ and tested by many
examples from boolean polynomial rings. The timings show M-GVW usually performs
much better than the original GVW algorithm when mutant pairs are found.
Besides, M-GVW is also compared with intrinsic Gr\"obner bases functions on
Maple, Singular and Magma. Due to the efficient routines from the M4RI library,
the experimental results show that M-GVW is very efficient
Twisted Blanchfield pairings, twisted signatures and Casson-Gordon invariants
This paper decomposes into two main parts. In the algebraic part, we prove an
isometry classification of linking forms over and
. Using this result, we associate signature functions to
any such linking form and thoroughly investigate their properties. The
topological part of the paper applies this machinery to twisted Blanchfield
pairings of knots. We obtain twisted generalizations of the Levine-Tristram
signature function which share several of its properties. We study the behavior
of these twisted signatures under satellite operations. In the case of
metabelian representations, we relate our invariants to the Casson-Gordon
invariants and obtain a concrete formula for the metabelian Blanchfield
pairings of satellites. Finally, we perform explicit computations on certain
linear combinations of algebraic knots, recovering a non-slice result of
Hedden, Kirk and Livingston.Comment: 81 pages, 1 figur
Hard isogeny problems over RSA moduli and groups with infeasible inversion
We initiate the study of computational problems on elliptic curve isogeny
graphs defined over RSA moduli. We conjecture that several variants of the
neighbor-search problem over these graphs are hard, and provide a comprehensive
list of cryptanalytic attempts on these problems. Moreover, based on the
hardness of these problems, we provide a construction of groups with infeasible
inversion, where the underlying groups are the ideal class groups of imaginary
quadratic orders.
Recall that in a group with infeasible inversion, computing the inverse of a
group element is required to be hard, while performing the group operation is
easy. Motivated by the potential cryptographic application of building a
directed transitive signature scheme, the search for a group with infeasible
inversion was initiated in the theses of Hohenberger and Molnar (2003). Later
it was also shown to provide a broadcast encryption scheme by Irrer et al.
(2004). However, to date the only case of a group with infeasible inversion is
implied by the much stronger primitive of self-bilinear map constructed by
Yamakawa et al. (2014) based on the hardness of factoring and
indistinguishability obfuscation (iO). Our construction gives a candidate
without using iO.Comment: Significant revision of the article previously titled "A Candidate
Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the
constructions by giving toy examples, added "The Parallelogram Attack" (Sec
5.3.2). 54 pages, 8 figure
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