634 research outputs found
Nonlinear normal modes and spectral submanifolds: Existence, uniqueness and use in model reduction
We propose a unified approach to nonlinear modal analysis in dissipative
oscillatory systems. This approach eliminates conflicting definitions, covers
both autonomous and time-dependent systems, and provides exact mathematical
existence, uniqueness and robustness results. In this setting, a nonlinear
normal mode (NNM) is a set filled with small-amplitude recurrent motions: a
fixed point, a periodic orbit or the closure of a quasiperiodic orbit. In
contrast, a spectral submanifold (SSM) is an invariant manifold asymptotic to a
NNM, serving as the smoothest nonlinear continuation of a spectral subspace of
the linearized system along the NNM. The existence and uniqueness of SSMs turns
out to depend on a spectral quotient computed from the real part of the
spectrum of the linearized system. This quotient may well be large even for
small dissipation, thus the inclusion of damping is essential for firm
conclusions about NNMs, SSMs and the reduced-order models they yield.Comment: To appear in Nonlinear Dynamic
Proton polarizability contribution to the hyperfine splitting in muonic hydrogen
The contribution of the proton polarizability to the ground state hyperfine
splitting in muonic hydrogen is evaluated on the basis of modern experimental
and theoretical results on the proton polarized structure functions. The value
of this correction is equal to 4.6(8)\cdot 10^{-4} times the Fermi splitting
E_F.Comment: 10 pages (revtex), 5 figure
On the Existence of Localized Excitations in Nonlinear Hamiltonian Lattices
We consider time-periodic nonlinear localized excitations (NLEs) on
one-dimensional translationally invariant Hamiltonian lattices with arbitrary
finite interaction range and arbitrary finite number of degrees of freedom per
unit cell. We analyse a mapping of the Fourier coefficients of the NLE
solution. NLEs correspond to homoclinic points in the phase space of this map.
Using dimensionality properties of separatrix manifolds of the mapping we show
the persistence of NLE solutions under perturbations of the system, provided
NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam
chains we rigorously prove the existence of NLE solutions.Comment: 13 pages, LaTeX, 2 figures will be mailed upon request (Phys. Rev. E,
in press
Generalized Schr\"odinger-Newton system in dimension : critical case
In this paper we study a system which is equivalent to a nonlocal version of
the well known Brezis Nirenberg problem. The difficulties related with the lack
of compactness are here emphasized by the nonlocal nature of the critical
nonlinear term. We prove existence and nonexistence results of positive
solutions when and existence of solutions in both the resonance and the
nonresonance case for higher dimensions.Comment: 18 pages, typos fixed, some minor revision
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