12,123 research outputs found
Nonlinear Propagation of Light in One Dimensional Periodic Structures
We consider the nonlinear propagation of light in an optical fiber waveguide
as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is
assumed to have an index of refraction which varies periodically along its
length. The wavelength of light is selected to be in resonance with the
periodic structure (Bragg resonance). The AMLE system considered incorporates
the effects non-instantaneous response of the medium to the electromagnetic
field (chromatic or material dispersion), the periodic structure (photonic band
dispersion) and nonlinearity. We present a detailed discussion of the role of
these effects individually and in concert. We derive the nonlinear coupled mode
equations (NLCME) which govern the envelope of the coupled backward and forward
components of the electromagnetic field. We prove the validity of the NLCME
description and give explicit estimates for the deviation of the approximation
given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known
to have gap soliton states. A consequence of our results is the existence of
very long-lived {\it gap soliton} states of AMLE. We present numerical
simulations which validate as well as illustrate the limits of the theory.
Finally, we verify that the assumptions of our model apply to the parameter
regimes explored in recent physical experiments in which gap solitons were
observed.Comment: To appear in The Journal of Nonlinear Science; 55 pages, 13 figure
Localization of Electromagnetic Fields in Disordered Fano Metamaterials
We present the first study of disorder in planar metamaterials consisting of
strongly interacting metamolecules, where coupled electric dipole and magnetic
dipole modes give rise to a Fano-type resonant response and show that
positional disorder leads to light localization inherently linked to collective
magnetic dipole excitations. We demonstrate that the magnetic excitation
persists in disordered arrays and results in the formation of "magnetic
hot-spots"
Linear and non-linear theory of a parametric instability of hydrodynamic warps in Keplerian discs
We consider the stability of warping modes in Keplerian discs. We find them
to be parametrically unstable using two lines of attack, one based on
three-mode couplings and the other on Floquet theory. We confirm the existence
of the instability, and investigate its nonlinear development in three
dimensions, via numerical experiment. The most rapidly growing non-axisymmetric
disturbances are the most nearly axisymmetric (low m) ones. Finally, we offer a
simple, somewhat speculative model for the interaction of the parametric
instability with the warp. We apply this model to the masing disc in NGC 4258
and show that, provided the warp is not forced too strongly, parametric
instability can fix the amplitude of the warp.Comment: 14 pages, 6 figures, revised version with appendix added, to be
published in MNRA
Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow
Hollerbach and Rudiger have reported a new type of magnetorotational
instability (MRI) in magnetized Taylor-Couette flow in the presence of combined
axial and azimuthal magnetic fields. The salient advantage of this "helical''
MRI (HMRI) is that marginal instability occurs at arbitrarily low magnetic
Reynolds and Lundquist numbers, suggesting that HMRI might be easier to realize
than standard MRI (axial field only). We confirm their results, calculate HMRI
growth rates, and show that in the resistive limit, HMRI is a weakly
destabilized inertial oscillation propagating in a unique direction along the
axis. But we report other features of HMRI that make it less attractive for
experiments and for resistive astrophysical disks. Growth rates are small and
require large axial currents. More fundamentally, instability of highly
resistive flow is peculiar to infinitely long or periodic cylinders: finite
cylinders with insulating endcaps are shown to be stable in this limit. Also,
keplerian rotation profiles are stable in the resistive limit regardless of
axial boundary conditions. Nevertheless, the addition of toroidal field lowers
thresholds for instability even in finite cylinders.Comment: 16 pages, 2 figures, 1 table, submitted to PR
Quasirational models of sentencing
Cognitive continuum theory points to the middle-ground between the intuitive and analytic modes of cognition, called quasirationality. In the context of sentencing, we discuss how legal models prescribe the use of different modes of cognition. These models aim to help judges perform the cognitive balancing act required between factors indicating a more or less severe penalty for an offender. We compare sentencing in three common law jurisdictions (i.e., Australia, the US, and England and Wales). Each places a different emphasis on the use of intuition and analysis; but all are quasirational. We conclude that the most appropriate mode of cognition will likely be that which corresponds best with properties of the sentencingtask. Finally, we discuss the implications of this cognition-task correspondence approach for researchers and legal policy-makers
Density of states in an optical speckle potential
We study the single particle density of states of a one-dimensional speckle
potential, which is correlated and non-Gaussian. We consider both the repulsive
and the attractive cases. The system is controlled by a single dimensionless
parameter determined by the mass of the particle, the correlation length and
the average intensity of the field. Depending on the value of this parameter,
the system exhibits different regimes, characterized by the localization
properties of the eigenfunctions. We calculate the corresponding density of
states using the statistical properties of the speckle potential. We find good
agreement with the results of numerical simulations.Comment: 11 pages, 11 figures, revtex
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