9,342 research outputs found
Theoretical highlights of neutrino-nucleus interactions
The recent theoretical developments in the field of neutrino-nucleus
interactions in the few-GeV region are reviewed based on the presentations made
at the NuInt09 Workshop. The topics of electron scattering and its connections
with neutrino interactions, neutrino induced quasielastic scattering and pion
production (coherent and incoherent) are covered, with special emphasis on the
challenges that arise in the comparison with new experimental data.Comment: Plenary talk at NuFact09, Chicago, July 20-25, 200
A convergent expansion of the Airy's integral with incomplete Gamma functions
There are two main power series for the Airy functions, namely the Maclaurin
and the asymptotic expansions. The former converges for all finite values of
the complex variable, , but it requires a large number of terms for large
values of , and the latter is a Poincar\'{e}-type expansion which is
well-suited for such large values and where optimal truncation is possible. The
asymptotic series of the Airy function shows a classical example of the Stokes
phenomenon where a type of discontinuity occurs for the homonymous multipliers.
A new series expansion is presented here that stems from the method of steepest
descents, as can the asymptotic series, but which is convergent for all values
of the complex variable. It originates in the integration of uniformly
convergent power series representing the integrand of the Airy's integral in
different sections of the integration path. The new series expansion is not a
power series and instead relies on the calculation of complete and incomplete
Gamma functions. In this sense, it is related to the Hadamard expansions. It is
an alternative expansion to the two main aforementioned power series that also
offers some insight into the transition zone for the Stokes' multipliers due to
the splitting of the integration path. Unlike the Hadamard series, it relies on
only two different expansions, separated by a branch point, one of which is
centered at infinity. The interest of the new series expansion is mainly a
theoretical one in a twofold way. First of all, it shows how to convert an
asymptotic series into a convergent one, even if the rate of convergence may be
slow for small values of . Secondly, it sheds some light on the Stokes
phenomenon for the Airy function by showing the transition of the integration
paths at .Comment: 21 pages, 23 figures. Changes in version 2: i) Footnote 10 has been
added, ii) Figure 5 has been added for a deeper analysis of the results, iii)
Reference 15 has been added, iv) Typo: A was missing in (abstract), v) Some font size changes and improved labelling in the
figures Changes in version 3: minor edition change
More On Critical Collapse of Axion-Dilaton System in Dimension Four
We complete our previous study of critical gravitational collapse in the
axion-dilaton system by analysing the hyperbolic and parabolic ans\"atze. As
could be expected, the corresponding Choptuik exponents in four-dimensions
differ from the elliptic case.Comment: 13 pages, Latex file, no figure,v2: to appear in JCA
Airborne collision scenario flight tests: impact of angle measurement errors on reactive vision-based avoidance control
The future emergence of many types of airborne vehicles and unpiloted aircraft in the national airspace means collision avoidance is of primary concern in an uncooperative airspace environment. The ability to replicate a pilot’s see and avoid capability using cameras coupled with vision based avoidance control is an important part of an overall collision avoidance strategy. But unfortunately without range collision avoidance has no direct way to guarantee a level of safety. Collision scenario flight tests with two aircraft and a monocular camera threat detection and tracking system were used to study the accuracy of image-derived angle measurements. The effect of image-derived angle errors on reactive vision-based avoidance performance was then studied by simulation. The results show that whilst large angle measurement errors can significantly affect minimum ranging characteristics across a variety of initial conditions and closing speeds, the minimum range is always bounded and a collision never occurs
Duality in Quantum Field Theory (and String Theory)
These lectures give an introduction to duality in Quantum Field Theory. We
discuss the phases of gauge theories and the implications of the
electric-magnetic duality transformation to describe the mechanism of
confinement. We review the exact results of N=1 supersymmetric QCD and the
Seiberg-Witten solution of N=2 super Yang-Mills. Some of its extensions to
String Theory are also briefly discussed.Comment: 38 pages, 7 figures, LaTeX, revtex, two references added. Based on a
lectures delivered by L. A.-G. at `The Workshop on Fundamental Particles and
Interactions', held in Vanderbilt University, and CERN-La Plata-Santiago de
Compostela School of Physics, both in May 199
Knightian Uncertainty, k-Ignorance, and Optimal Timing
We investigate within a continuous time setting how Knightian uncertainty characterized by k-ignorance affects the optimal timing policies of a risk-neutral and uncertainty averse investor in the case where the exercise payoff is monotonic. We prove that increased Knightian uncertainty unambiguously decreases the value of the optimal timing policy of an uncertainty averse investor. We also show that higher Knightian uncertainty accelerates timing by shrinking the continuation region whenever the termination payoff is independent of Knightian uncertainty. If this independence condition is not fulfilled, then our results indicate that higher Knightian uncertainty may decelerate optimal timing.Knightian uncertainty, k-ambiguity, optimal stopping, diffusions
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