Search results for "Nonlinear"
showing 10 items of 3684 documents
Long-range effects on the periodic deformable sine-Gordon chains
1999
The model of long-range interatomic interactions is found to reveal a number of new features, closely connected with the substrate potential shape parameter s. The phase trajectories, as well as an analytical analysis, provide information on a disintegration of solitons upon reaching some critical values of the lattice parameters. An implicit form for two classes of these topological solitons (kink) is calculated exactly.
Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation
2007
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…
Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk…
2019
A deformation of a disk D of radius r is described as follows: Let two disks D1 and D2 have the same radius r, and let the distance between the two disk centers be 2a, 0 ≤ a ≤ r. The deformation transforms D into the intersection D1 ∩ D2. This deformation is parametrized by e = a/r. For e = 0, there is no deformation, and the deformation starts when e, starting from 0, increases, transforming the disk into a lens. Analytic results are obtained for the eigenvalues of Helmholtz equation with zero Dirichlet boundary condition to the lowest order in e for this deformation. These analytic results are obtained via a Hamiltonian method for solving the Helmholtz equation with zero Dirichlet boundar…
Two frequency oscillation of a photorefractive oscillator as a perturbation of the mirrorless oscillation
2010
We consider the properties of the non-degenerate two frequency regime of oscillation of the semi-linear photorefractive oscillator and analyze its relation with the mirrorless oscillation. We consider the oscillator with or without a frequency shifted feedback by a vibrating mirror. This study shows that these two apparently different phenomena are closely related. We conclude from the obtained results that the two frequency oscillation can be considered as a perturbation of the mirrorless oscillation.
Modeling of photonic crystal fibers from the scalar wave equation with a purely transverse linearly polarized vector potential
2011
In this work, we propose a new technique for modeling light propagation in photonic crystal fibers where the electric field is evaluated from a purely transverse linearly polarized vector potential. The vector potential in a nonuniform dielectric obeys a wave equation coupled to the scalar potential, but it can be reduced to a scalar wave equation when the coupling term is ignored to the lowest order approximation. We show that this method gives reliable results for photonic crystal fibers when the scalar analysis is improved by a perturbational correction.
Relaxation, postponement, and features of the attractor in a driven varactor oscillator
1990
The driven varactor oscillator is investigated by numerical integration of its ODEs using the standard model of circuit theory. Attention is given to some properties of the basic relaxation mechanism. For time dependent amplitudes of the sinusoidal driving voltage the post-ponement of the bifurcations is characterized by transient Lyapunov numbers. The postponement of the first bifurcation shows the same dependence on the sweep velocity as in the case of the nonautonomous quadratic map. The shapes of the attractors are displayed in extended phase space. Generalized Renyi-dimensionsD 0 andD 1 have been determined in the chaotic region. A corresponding twodimensional Pioncare map indicates se…
Modulated magnetic structures of ErPb3, HoPb3, ErTl3 and HoTl3
1981
Neutron diffraction experiments have been carried out on the magnetically ordered phases of ErPb3, HoPb3, ErTl3 and HoTl3. The magnetic moments were found to be sinusoidally modulated with a propagation vector of (0, 0.2, 0.5) for the Pb-compounds and (0.38, 0.38, 0.16) for the Tl-compounds.
Cellular automaton for chimera states
2016
A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent struct…
Some Properties of Massless Particles in Arbitrary Dimensions
1998
Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group [Formula: see text] are investigated for n≥2. It is found that, for space-time dimensions n≥3, the situation is quite similar to the one of the n=4 case for Sn-massless representations of the n-De Sitter group [Formula: see text]. These representations are the restrictions of the singletons of [Formula: see text]. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representations. Finally some examples of Gupta–Bleuler triplets are given for arbitrary spin and…
MAGNETIC INTERACTIONS OF CHAINS FORMED BY FERROMAGNETIC SPHERES
2002
General properties of sphere-chain and chain-chain structures are analysed for homogeneously magnetized spheres. For field aligned structures the local maximum of the magnetic force is observed at H0/MS ≈ 0.5. The magnetic saturation effects are accounted by the Frölich-Kennelly law. Outlines of the approximate methodology of multi-chain interaction are given together with the test results.