12,479 research outputs found
A uniform controllability result for the Keller-Segel system
In this paper we study the controllability of the Keller-Segel system
approximating its parabolic-elliptic version. We show that this parabolic
system is locally uniform controllable around a constant solution of the
parabolic-elliptic system when the control is acting on the component of the
chemical
-particle sigma model: Momentum-space quantization of a particle on the sphere
We perform the momentum-space quantization of a spin-less particle moving on
the group manifold, that is, the three-dimensional sphere , by
using a non-canonical method entirely based on symmetry grounds. To achieve
this task, non-standard (contact) symmetries are required as already shown in a
previous article where the configuration-space quantization was given. The
Hilbert space in the momentum space representation turns out to be made of a
subset of (oscillatory) solutions of the Helmholtz equation in four dimensions.
The most relevant result is the fact that both the scalar product and the
generalized Fourier transform between configuration and momentum spaces deviate
notably from the naively expected expressions, the former exhibiting now a
non-trivial kernel, under a double integral, traced back to the non-trivial
topology of the phase space, even though the momentum space as such is flat. In
addition, momentum space itself appears directly as the carrier space of an
irreducible representation of the symmetry group, and the Fourier transform as
the unitary equivalence between two unitary irreducible representations.Comment: 29 pages, 3 figure
A Non-Perturbative Chiral Approach for Meson-Meson Interactions
A non-perturbative method which combines constraints from chiral symmetry
breaking and coupled channel unitarity is used to describe meson-meson
interactions up to \sqrt{s}\lesssim 1.2 GeV, extending in this way the range of
applicability of the information contained in Chiral Perturbation Theory (\chi
PT), since this perturbative series is typically restricted to \sqrt{s}\lesssim
500 MeV. The approach uses the O(p^2) and O(p^4) \chiPT Lagrangians. The seven
free parameters resulting from the O(p^4) Lagrangian are fitted to the
experimental data. The approach makes use of the expansion of T^{-1} instead of
the amplitude itself as done in \chiPT. The former expansion is suggested by
analogy with the effective range approximation in Quantum Mechanics and it
appears to be very useful. The results, in fact, are in good agreement with a
vast amount of experimental analyses.Comment: 4 pages, 2 figures, LaTeX, Talk given at PANIC99, Uppsala (Sweden),
June 10-16, 199
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