19,132 research outputs found
Finite Symmetry of Leptonic Mass Matrices
We search for possible symmetries present in the leptonic mixing data from
SU(3) subgroups of order up to 511. Theoretical results based on symmetry are
compared with global fits of experimental data in a chi-squared analysis,
yielding the following results. There is no longer a group that can produce all
the mixing data without a free parameter, but a number of them can accommodate
the first or the second column of the mixing matrix. The only group that fits
the third column is . It predicts and
, in good agreement with experimental results.Comment: Version to appear in Physical Review
Asymptotic theory for torsional convection in rotating fluid spheres
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper is concerned with the classical, well-studied problem of convective instabilities in rapidly rotating, self-gravitating, internally heated Boussinesq fluid spheres. Sanchez et al. (J. Fluid Mech., vol. 791, 2016, R1) recently found, unexpectedly via careful numerical simulation, that non-magnetic convection in the form of axially symmetric, equatorially antisymmetric torsional oscillation is physically preferred in a special range of small Prandtl number for rapidly rotating fluid spheres with the stress-free boundary condition. We derive an asymptotic solution describing convection-driven torsional oscillation – whose flow velocity and pressure are fully analytical and in closed form – that confirms the result of the numerical analysis and is in quantitative agreement with the numerical solution. We also demonstrate, through the derivation of a different asymptotic solution, that convection-driven torsional oscillation cannot occur in rapidly rotating fluid spheres with the no-slip boundary condition.KZ is supported by Leverhulme Trust Research Project Grant RPG-2015-096, by
Macau FDCT grants 007/2016/A1 and 001/2016/AFJ, and by the CAS grant XDB1801020
Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma
The equations governing a collisionless obliquely-flowing plasma around an
ion-absorbing object in a strong magnetic field are shown to have an exact
analytic solution even for arbitrary (two-dimensional) object-shape, when
temperature is uniform, and diffusive transport can be ignored. The solution
has an extremely simple geometric embodiment. It shows that the ion collection
flux density to a convex body's surface depends only upon the orientation of
the surface, and provides the theoretical justification and calibration of
oblique `Mach-probes'. The exponential form of this exact solution helps
explain the approximate fit of this function to previous numerical solutions.Comment: Four pages, 2 figures. Submitted to Phys. Rev. Letter
Maximal quadratic modules on *-rings
We generalize the notion of and results on maximal proper quadratic modules
from commutative unital rings to -rings and discuss the relation of this
generalization to recent developments in noncommutative real algebraic
geometry. The simplest example of a maximal proper quadratic module is the cone
of all positive semidefinite complex matrices of a fixed dimension. We show
that the support of a maximal proper quadratic module is the symmetric part of
a prime -ideal, that every maximal proper quadratic module in a
Noetherian -ring comes from a maximal proper quadratic module in a simple
artinian ring with involution and that maximal proper quadratic modules satisfy
an intersection theorem. As an application we obtain the following extension of
Schm\" udgen's Strict Positivstellensatz for the Weyl algebra: Let be an
element of the Weyl algebra which is not negative semidefinite
in the Schr\" odinger representation. It is shown that under some conditions
there exists an integer and elements such
that is a finite sum of hermitian squares. This
result is not a proper generalization however because we don't have the bound
.Comment: 11 page
K2-265 b: a transiting rocky super-Earth
We report the discovery of the super-Earth K2-265 b detected with K2 photometry. The planet orbits a bright (V_(mag) = 11.1) star of spectral type G8V with a period of 2.37 days. We obtained high-precision follow-up radial velocity measurements from HARPS, and the joint Bayesian analysis showed that K2-265 b has a radius of 1.71 ± 0.11 R⊕ and a mass of 6.54 ± 0.84 M⊕, corresponding to a bulk density of 7.1 ± 1.8 g cm^(−3). Composition analysis of the planet reveals an Earth-like, rocky interior; this object has a rock mass fraction of ~80%. The short orbital period and small radius of the planet puts it below the lower limit of the photoevaporation gap, where the envelope of the planet could have eroded owing to strong stellar irradiation, leaving behind an exposed core. Knowledge of the planet core composition allows us to infer the possible formation and evolution mechanism responsible for its current physical parameters
Biased EPR entanglement and its application to teleportation
We consider pure continuous variable entanglement with non-equal correlations
between orthogonal quadratures. We introduce a simple protocol which equates
these correlations and in the process transforms the entanglement onto a state
with the minimum allowed number of photons. As an example we show that our
protocol transforms, through unitary local operations, a single squeezed beam
split on a beam splitter into the same entanglement that is produced when two
squeezed beams are mixed orthogonally. We demonstrate that this technique can
in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure
Stability of Filters for the Navier-Stokes Equation
Data assimilation methodologies are designed to incorporate noisy
observations of a physical system into an underlying model in order to infer
the properties of the state of the system. Filters refer to a class of data
assimilation algorithms designed to update the estimation of the state in a
on-line fashion, as data is acquired sequentially. For linear problems subject
to Gaussian noise filtering can be performed exactly using the Kalman filter.
For nonlinear systems it can be approximated in a systematic way by particle
filters. However in high dimensions these particle filtering methods can break
down. Hence, for the large nonlinear systems arising in applications such as
weather forecasting, various ad hoc filters are used, mostly based on making
Gaussian approximations. The purpose of this work is to study the properties of
these ad hoc filters, working in the context of the 2D incompressible
Navier-Stokes equation. By working in this infinite dimensional setting we
provide an analysis which is useful for understanding high dimensional
filtering, and is robust to mesh-refinement. We describe theoretical results
showing that, in the small observational noise limit, the filters can be tuned
to accurately track the signal itself (filter stability), provided the system
is observed in a sufficiently large low dimensional space; roughly speaking
this space should be large enough to contain the unstable modes of the
linearized dynamics. Numerical results are given which illustrate the theory.
In a simplified scenario we also derive, and study numerically, a stochastic
PDE which determines filter stability in the limit of frequent observations,
subject to large observational noise. The positive results herein concerning
filter stability complement recent numerical studies which demonstrate that the
ad hoc filters perform poorly in reproducing statistical variation about the
true signal
An experimental investigation of criteria for continuous variable entanglement
We generate a pair of entangled beams from the interference of two amplitude
squeezed beams. The entanglement is quantified in terms of EPR-paradox [Reid88]
and inseparability [Duan00] criteria, with observed results of and , respectively. Both results clearly beat the standard quantum
limit of unity. We experimentally analyze the effect of decoherence on each
criterion and demonstrate qualitative differences. We also characterize the
number of required and excess photons present in the entangled beams and
provide contour plots of the efficacy of quantum information protocols in terms
of these variables.Comment: 4 pages, 5 figure
XAX: a multi-ton, multi-target detection system for dark matter, double beta decay and pp solar neutrinos
A multi-target detection system XAX, comprising concentric 10 ton targets of
136Xe and 129/131Xe, together with a geometrically similar or larger target of
liquid Ar, is described. Each is configured as a two-phase
scintillation/ionization TPC detector, enhanced by a full 4pi array of
ultra-low radioactivity Quartz Photon Intensifying Detectors (QUPIDs) replacing
the conventional photomultipliers for detection of scintillation light. It is
shown that background levels in XAX can be reduced to the level required for
dark matter particle (WIMP) mass measurement at a 10^-10 pb WIMP-nucleon cross
section, with single-event sensitivity below 10^-11 pb. The use of multiple
target elements allows for confirmation of the A^2 dependence of a coherent
cross section, and the different Xe isotopes provide information on the
spin-dependence of the dark matter interaction. The event rates observed by Xe
and Ar would modulate annually with opposite phases from each other for WIMP
mass >~100 GeV/c^2. The large target mass of 136Xe and high degree of
background reduction allow neutrinoless double beta decay to be observed with
lifetimes of 10^27-10^28 years, corresponding to the Majorana neutrino mass
range 0.01-0.1 eV, the most likely range from observed neutrino mass
differences. The use of a 136Xe-depleted 129/131Xe target will also allow
measurement of the pp solar neutrino spectrum to a precision of 1-2%.Comment: 16 pages with 17 figure
Isolating Geometry in Weak Lensing Measurements
Given a foreground galaxy-density field or shear field, its cross-correlation
with the shear field from a background population of source galaxies scales
with the source redshift in a way that is specific to lensing. Such a
source-scaling can be exploited to effectively measure geometrical distances as
a function of redshift and thereby constrain dark energy properties, free of
any assumptions about the galaxy-mass/mass power spectrum (its shape, amplitude
or growth). Such a geometrical method can yield a ~ 0.03 - 0.07 f_{sky}^{-1/2}
measurement on the dark energy abundance and equation of state, for a
photometric redshift accuracy of dz ~ 0.01 - 0.05 and a survey with median
redshift of ~ 1. While these constraints are weaker than conventional weak
lensing methods, they provide an important consistency check because the
geometrical method carries less theoretical baggage: there is no need to assume
any structure formation model (e.g. CDM). The geometrical method is at the most
conservative end of a whole spectrum of methods which obtain smaller errorbars
by making more restrictive assumptions -- we discuss some examples. Our
geometrical approach differs from previous investigations along similar lines
in three respects. First, the source-scaling we propose to use is less
demanding on the photometric redshift accuracy. Second, the scaling works for
both galaxy-shear and shear-shear correlations. Third, we find that previous
studies underestimate the statistical errors associated with similar
geometrical methods, the origin of which is discussed.Comment: 13 pages, 4 figures, submitted to Ap
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