7,857 research outputs found
Extended Derivative Dispersion Relations
It is shown that, for a wide class of functions with physical interest as
forward scattering amplitudes, integral dispersion relations can be replaced by
derivative forms without any high-energy approximation. The applicability of
these extended derivative relations, in the investigation of forward
proton-proton and antiproton-proton elastic scattering, is exemplified by means
of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics",
Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa,
Italy, Jan. 26-27, 200
Derivative dispersion relations above the physical threshold
We discuss some formal and practical aspects related to the replacement of
Integral Dispersion Relations (IDR) by derivative forms, without high-energy
approximations. We first demonstrate that, for a class of functions with
physical interest as forward scattering amplitudes, this replacement can be
analytically performed, leading to novel Extended Derivative Dispersion
Relations (EDDR), which, in principle, are valid for any energy above the
physical threshold. We then verify the equivalence between the IDR and EDDR by
means of a popular parametrization for total cross sections from proton-proton
and antiproton-proton scattering and compare the results with those obtained
through other representations for the derivative relations. Critical aspects on
the limitations of the whole analysis, from both formal and practical points of
view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358
(2007
Eikonal zeros in the momentum transfer space from proton-proton scattering: An empirical analysis
By means of improved empirical fits to the differential cross section data on
elastic scattering at GeV and making use of a
semi-analytical method, we determine the eikonal in the momentum transfer space
(the inverse scattering problem). This method allows the propagation of the
uncertainties from the fit parameters up to the extracted eikonal, providing
statistical evidence that the imaginary part of the eikonal (real part of the
opacity function) presents a zero (change of signal) in the momentum space, at
GeV. We discuss the implication of this change of
signal in the phenomenological context, showing that eikonal models with one
zero provide good descriptions of the differential cross sections in the full
momentum transfer range, but that is not the case for models without zero.
Empirical connections between the extracted eikonal and results from a recent
global analysis on the proton electric form factor are also discussed, in
special the Wu-Yang conjecture. In addition, we present a critical review on
the differential cross section data presently available at high energies.Comment: Two references and some misprints corrected, 22 pages; final version
to be published in Eur.Phys. J. C (2008
High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations
We present the results of several parametrizations to two different ensemble
of data on total cross sections at the highest
center-of-mass energies (including cosmic-ray information). The results are
statistically consistent with two distinct scenarios at high energies. From one
ensemble the prediction for the LHC ( TeV) is mb and from the other, mb. From each
parametrization, and making use of derivative analyticity relations (DAR), we
determine (ratio between the forward real and imaginary parts of the
elastic scattering amplitude). A discussion on the optimization of the DAR in
terms of a free parameter is also presented.In all cases good descriptions of
the experimental data are obtained.Comment: One formula added, one unit changed, small misprints corrected, final
version to be published in Brazilian Journal of Physics; 13 pages, 8 figures,
aps-revte
Application and flight test of linearizing transformations using measurement feedback to the nonlinear control problem
The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers were applied to vehicle flight path control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. An approach to the nonlinear trajectory control problem is presented. This approach uses linearizing transformations with measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. By applying this approach and separating the inner-loop and outer-loop functions two things were achieved: (1) the need for incorporating detailed aerodynamic models in the controller is obviated; and (2) the controller is more easily incorporated into existing aircraft flight control systems. An implementation of the controller is discussed, and this controller is tested on a six degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Simulation data are presented which validates this approach over a large portion of the F-15 flight envelope. Proof of this concept is provided by flight-test data that closely matches simulation results. Flight-test data are also presented
- …