846 research outputs found
Rigorous stability results for a Laplacian moving boundary problem with kinetic undercooling
We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of a small bubble in a Hele-Shaw cell with a regularization of kinetic undercooling type, namely a mixed Dirichlet-Neumann boundary condition for the Laplacian field on the moving boundary. Using conformal mapping techniques, linear stability analysis of the uniformly translating disk is recast into a single PDE which is exactly solvable for certain values of the regularization parameter. We concentrate on the physically most interesting exactly solvable and non-trivial case. We show that the circular solutions are linearly stable against smooth initial perturbations. In the transformation of the PDE to its normal hyperbolic form, a semigroup of automorphisms of the unit disk plays a central role. It mediates the convection of perturbations to the back of the circle where they decay. Exponential convergence to the unperturbed circle occurs along a unique slow manifold as time t ! 1. Smooth temporal eigenfunctions cannot be constructed, but excluding the far back part of the circle, a discrete set of eigenfunctions does span the function space of perturbations. We believe that the observed behaviour of a convectively stabilized circle for a certain value of the regularization parameter is generic for other shapes and parameter values. Our analytical results are illustrated by figures of some typical solution
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
Correlation functions of scattering matrix elements in microwave cavities with strong absorption
The scattering matrix was measured for microwave cavities with two antennas.
It was analyzed in the regime of overlapping resonances. The theoretical
description in terms of a statistical scattering matrix and the rescaled
Breit-Wigner approximation has been applied to this regime. The experimental
results for the auto-correlation function show that the absorption in the
cavity walls yields an exponential decay. This behavior can only be modeled
using a large number of weakly coupled channels. In comparison to the
auto-correlation functions, the cross-correlation functions of the diagonal
S-matrix elements display a more pronounced difference between regular and
chaotic systems
The Polarised Valence Quark Distribution from semi-inclusive DIS
The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of
opposite charge has been measured by the COMPASS experiment at CERN. The data
were collected in the years 2002-2004 using a 160 GeV polarised muon beam
scattered off a large polarised ^6LiD target and cover the range 0.006 < x <
0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry
A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an
evaluation of the first moment of Delta u_v + Delta d_v which is found to be
equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at
Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously
measured on the same data, this result favours a non-symmetric polarisation of
light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard
deviations, in contrast to the often assumed symmetric scenario Delta u-bar =
Delta d-bar = Delta s-bar = Delta s.Comment: 7 pages, 3 figures, COMPASS, revised: details added, author list
update
Multiplicities of charged pions and unidentified charged hadrons from deep-inelastic scattering of muons off an isoscalar target
Multiplicities of charged pions and unidentified hadrons produced in
deep-inelastic scattering were measured in bins of the Bjorken scaling variable
, the relative virtual-photon energy and the relative hadron energy .
Data were obtained by the COMPASS Collaboration using a 160 GeV muon beam and
an isoscalar target (LiD). They cover the kinematic domain in the photon
virtuality > 1(GeV/c, , and . In addition, a leading-order pQCD analysis was performed using the
pion multiplicity results to extract quark fragmentation functions
Breeding systems in Tolpis (Asteraceae) in the Macaronesian islands: the Azores, Madeira and the Canaries
Plants on oceanic islands often originate from
self-compatible (SC) colonizers capable of seed set by self fertilization. This fact is supported by empirical studies,
and is rooted in the hypothesis that one (or few) individuals
could find a sexual population, whereas two or more would
be required if the colonizers were self-incompatible (SI).
However, a SC colonizer would have lower heterozygosity
than SI colonizers, which could limit radiation and diver sification of lineages following establishment. Limited
evidence suggests that several species-rich island lineages
in the family Asteraceae originated from SI colonizers with
some ‘‘leakiness’’ (pseudo-self-compatibility, PSC) such
that some self-seed could be produced. This study of Tolpis
(Asteraceae) in Macaronesia provides first reports of the
breeding system in species from the Azores and Madeira,
and additional insights into variation in Canary Islands.
Tolpis from the Azores and Madeira are predominately SI
but with PSC. This study suggests that the breeding sys tems of the ancestors were either PSC, possibly from a
single colonizer, or from SI colonizers by multiple dis seminules either from a single or multiple dispersals. Long distance colonists capable of PSC combine the advantages
of reproductive assurance (via selfing) in the establishment
of sexual populations from even a single colonizer with the
higher heterozygosity resulting from its origin from an
outcrossed source population. Evolution of Tolpis on the
Canaries and Madeira has generated diversity in breeding
systems, including the origin of SC. Macaronesian Tolpis is
an excellent system for studying breeding system evolution
in a small, diverse lineage.info:eu-repo/semantics/publishedVersio
Wavefront error of PHI/HRT on Solar Orbiter at various heliocentric distances
We use wavefront sensing to characterise the image quality of the the High
Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI)
data products during the second remote sensing window of the Solar Orbiter (SO)
nominal mission phase. Our ultimate aims are to reconstruct the HRT data by
deconvolving with the HRT point spread function (PSF) and to correct for the
effects of optical aberrations on the data. We use a pair of focused--defocused
images to compute the wavefront error and derive the PSF of HRT by means of a
phase diversity (PD) analysis. The wavefront error of HRT depends on the
orbital distance of SO to the Sun. At distances \,au, the wavefront error
is small, and stems dominantly from the inherent optical properties of HRT. At
distances \,au, the thermo-optical effect of the Heat Rejection Entrance
Window (HREW) becomes noticeable. We develop an interpolation scheme for the
wavefront error that depends on the thermal variation of the HREW with the
distance of SO to the Sun. We also introduce a new level of image
reconstruction, termed `aberration correction', which is designed to reduce the
noise caused by image deconvolution while removing the aberrations caused by
the HREW. The computed PSF via phase diversity significantly reduces the
degradation caused by the HREW in the near-perihelion HRT data. In addition,
the aberration correction increases the noise by a factor of only
compared to the factor of increase that results from the usual PD
reconstructions
Search for direct stau production in events with two hadronic tau-leptons in root s=13 TeV pp collisions with the ATLAS detector
A search for the direct production of the supersymmetric partners ofτ-leptons (staus) in final stateswith two hadronically decayingτ-leptons is presented. The analysis uses a dataset of pp collisions corresponding to an integrated luminosity of139fb−1, recorded with the ATLAS detector at the LargeHadron Collider at a center-of-mass energy of 13 TeV. No significant deviation from the expected StandardModel background is observed. Limits are derived in scenarios of direct production of stau pairs with eachstau decaying into the stable lightest neutralino and oneτ-lepton in simplified models where the two staumass eigenstates are degenerate. Stau masses from 120 GeV to 390 GeV are excluded at 95% confidencelevel for a massless lightest neutralino
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