309 research outputs found
Orbiting Resonances and Bound States in Molecular Scattering
A family of orbiting resonances in molecular scattering is globally described
by using a single pole moving in the complex angular momentum plane. The
extrapolation of this pole at negative energies gives the location of the bound
states. Then a single pole trajectory, that connects a rotational band of bound
states and orbiting resonances, is obtained. These complex angular momentum
singularities are derived through a geometrical theory of the orbiting. The
downward crossing of the phase-shifts through pi/2, due to the repulsive region
of the molecular potential, is estimated by using a simple hard-core model.
Some remarks about the difference between diffracted rays and orbiting are also
given.Comment: 18 pages, 3 figures, to appear in Physical Review
Measuring the Reduced Shear
Neglecting the second order corrections in weak lensing measurements can lead
to a few percent uncertainties on cosmic shears, and becomes more important for
cluster lensing mass reconstructions. Existing methods which claim to measure
the reduced shears are not necessarily accurate to the second order when a
point spread function (PSF) is present. We show that the method of Zhang (2008)
exactly measures the reduced shears at the second order level in the presence
of PSF. A simple theorem is provided for further confirming our calculation,
and for judging the accuracy of any shear measurement method at the second
order based on its properties at the first order. The method of Zhang (2008) is
well defined mathematically. It does not require assumptions on the
morphologies of galaxies and the PSF. To reach a sub-percent level accuracy,
the CCD pixel size is required to be not larger than 1/3 of the Full Width at
Half Maximum (FWHM) of the PSF. Using a large ensemble (> 10^7) of mock
galaxies of unrestricted morphologies, we find that contaminations to the shear
signals from the noise of background photons can be removed in a well defined
way because they are not correlated with the source shapes. The residual shear
measurement errors due to background noise are consistent with zero at the
sub-percent level even when the amplitude of such noise reaches about 1/10 of
the source flux within the half-light radius of the source. This limit can in
principle be extended further with a larger galaxy ensemble in our simulations.
On the other hand, the source Poisson noise remains to be a cause of systematic
errors. For a sub-percent level accuracy, our method requires the amplitude of
the source Poisson noise to be less than 1/80 ~ 1/100 of the source flux within
the half-light radius of the source, corresponding to collecting roughly 10^4
source photons.Comment: 18 pages, 3 figures, 4 tables, minor changes from the previous
versio
The Path-Integral Approach to the N=2 Linear Sigma Model
In QFT the effective potential is an important tool to study symmetry
breaking phenomena. It is known that, in some theories, the canonical approach
and the path-integral approach yield different effective potentials. In this
paper we investigate this for the Euclidean N=2 linear sigma model. Both the
Green's functions and the effective potential will be computed in three
different ways. The relative merits of the various approaches are discussed.Comment: 2 figure
Statistical Theory for Incoherent Light Propagation in Nonlinear Media
A novel statistical approach based on the Wigner transform is proposed for
the description of partially incoherent optical wave dynamics in nonlinear
media. An evolution equation for the Wigner transform is derived from a
nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that
random phase fluctuations of an incoherent plane wave lead to a Landau-like
damping effect, which can stabilize the modulational instability. In the limit
of the geometrical optics approximation, incoherent, localized, and stationary
wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip
Measurement of the Transverse-Longitudinal Cross Sections in the p (e,e'p)pi0 Reaction in the Delta Region
Accurate measurements of the p(e,e?p)pi0 reaction were performed at
Q^2=0.127(GeV/c)^2 in the Delta resonance energy region. The experiments at the
MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam with the
out of plane magnetic spectrometer system (OOPS). In this paper we report the
first simultaneous determination of both the TL and TL? (``fifth" or polarized)
cross sections at low Q^{2} where the pion cloud contribution dominates the
quadrupole amplitudes (E2 and C2). The real and imaginary parts of the
transverse-longitudinal cross section provide both a sensitive determination of
the Coulomb quadrupole amplitude and a test of reaction calculations.
Comparisons with model calculations are presented. The empirical MAID
calculation gives the best overall agreement with this accurate data. The
parameters of this model for the values of the resonant multipoles are
|M_{1+}(I=3/2)|= (40.9 \pm 0.3)10^{-3}/m_pi, CMR= C2/M1= -6.5 \pm 0.3%,
EMR=E2/M1=-2.2 \pm 0.9%, where the errors are due to the experimental
uncertainties.Comment: 10 pages, 3 figures, minor corrections and addition
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Observation of hard scattering in photoproduction events with a large rapidity gap at HERA
Events with a large rapidity gap and total transverse energy greater than 5
GeV have been observed in quasi-real photoproduction at HERA with the ZEUS
detector. The distribution of these events as a function of the
centre of mass energy is consistent with diffractive scattering. For total
transverse energies above 12 GeV, the hadronic final states show predominantly
a two-jet structure with each jet having a transverse energy greater than 4
GeV. For the two-jet events, little energy flow is found outside the jets. This
observation is consistent with the hard scattering of a quasi-real photon with
a colourless object in the proton.Comment: 19 pages, latex, 4 figures appended as uuencoded fil
Refining and regaining skills in fixation/diversification stage performers: The Five-A Model
Technical change is one of many factors underpinning success in elite, fixation/diversification stage performers. Surprisingly, however, there is a dearth of research pertaining to this process or the most efficacious methods used to bring about such a change. In this paper we highlight the emergent processes, yet also the lack in mechanistic comprehension surrounding technical change, addressing issues within the motor control, sport psychology, coaching and choking literature. More importantly, we seek an understanding of how these changes can be made more secure to competitive pressure, and how this can be embedded within the process of technical change. Following this review, we propose The Five-A Model based on successful coaching techniques, psychosocial concomitants, the avoidance of choking and principles of effective behaviour change. Specific mechanisms for each stage are discussed, with a focus on the use of holistic rhythm-based cues as a possible way of internalising changes. Finally, we suggest the need for further research to examine these five stages, to aid a more comprehensive construction of the content and delivery of such a programme within the applied setting
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