13,553 research outputs found
Theory of emission from an active photonic lattice
The emission from a radiating source embedded in a photonic lattice is
calculated. The analysis considers the photonic lattice and free space as a
combined system. Furthermore, the radiating source and electromagnetic field
are quantized. Results show the deviation of the photonic lattice spectrum from
the blackbody distribution, with intracavity emission suppressed at certain
frequencies and enhanced at others. In the presence of rapid population
relaxation, where the photonic lattice and blackbody populations are described
by the same equilibrium distribution, it is found that the enhancement does not
result in output intensity exceeding that of the blackbody at the same
frequency. However, for slow population relaxation, the photonic lattice
population has a greater tendency to deviate from thermal equilibrium,
resulting in output intensities exceeding those of the blackbody, even for
identically pumped structures.Comment: 19 pages, 11 figure
Single-charge rotating black holes in four-dimensional gauged supergravity
We consider four-dimensional U(1)^4 gauged supergravity, and obtain
asymptotically AdS_4, non-extremal, charged, rotating black holes with one
non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a
generalization that includes a NUT parameter. The general solution has a
discrete symmetry involving inversion of the rotation parameter, and has a
string frame metric that admits a rank-2 Killing-Stackel tensor.Comment: 9 page
Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity
We introduce a system with one or two amplified nonlinear sites ("hot spots",
HSs) embedded into a two-dimensional linear lossy lattice. The system describes
an array of evanescently coupled optical or plasmonic waveguides, with gain
applied at selected HS cores. The subject of the analysis is discrete solitons
pinned to the HSs. The shape of the localized modes is found in
quasi-analytical and numerical forms, using a truncated lattice for the
analytical consideration. Stability eigenvalues are computed numerically, and
the results are supplemented by direct numerical simulations. In the case of
self-focusing nonlinearity, the modes pinned to a single HS are stable or
unstable when the nonlinearity includes the cubic loss or gain, respectively.
If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at
the HS supports stable modes in a small parametric area, while weak cubic loss
gives rise to a bistability of the discrete solitons. Symmetric and
antisymmetric modes pinned to a symmetric set of two HSs are considered too.Comment: Philosophical Transactions of the Royal Society A, in press (a
special issue on "Localized structures in dissipative media"
Local transient rheological behavior of concentrated suspensions
This paper reports experiments on the shear transient response of
concentrated non-Brownian suspensions. The shear viscosity of the suspensions
is measured using a wide-gap Couette rheometer equipped with a Particle Image
Velocimetry (PIV) device that allows measuring the velocity field. The
suspensions made of PMMA particles (31m in diameter) suspended in a
Newtonian index- and density-matched liquid are transparent enough to allow an
accurate measurement of the local velocity for particle concentrations as high
as 50%. In the wide-gap Couette cell, the shear induced particle migration is
evidenced by the measurement of the time evolution of the flow profile. A
peculiar radial zone in the gap is identified where the viscosity remains
constant. At this special location, the local particle volume fraction is taken
to be the mean particle concentration. The local shear transient response of
the suspensions when the shear flow is reversed is measured at this point where
the particle volume fraction is well defined. The local rheological
measurements presented here confirm the macroscopic measurements of
Gadala-Maria and Acrivos (1980). After shear reversal, the viscosity undergoes
a step-like reduction, decreases slower and passes through a minimum before
increasing again to reach a plateau. Upon varying the particle concentration,
we have been able to show that the minimum and the plateau viscosities do not
obey the same scaling law with respect to the particle volume fraction. These
experimental results are consistent with the scaling predicted by Mills and
Snabre (2009) and with the results of numerical simulation performed on random
suspensions [Sierou and Brady (2001)]. The minimum seems to be associated with
the viscosity of an isotropic suspension, or at least of a suspension whose
particles do not interact through non-hydrodynamic forces, while the plateau
value would correspond to the viscosity of a suspension structured by the shear
where the non-hydrodynamic forces play a crucial role
Installed performance of air-augmented nozzles based on analytical determination of internal ejector characteristics
Procedures for matching intake and ejector pumping characteristics of air-augmented nozzle
Pinned modes in lossy lattices with local gain and nonlinearity
We introduce a discrete linear lossy system with an embedded "hot spot" (HS),
i.e., a site carrying linear gain and complex cubic nonlinearity. The system
can be used to model an array of optical or plasmonic waveguides, where
selective excitation of particular cores is possible. Localized modes pinned to
the HS are constructed in an implicit analytical form, and their stability is
investigated numerically. Stability regions for the modes are obtained in the
parameter space of the linear gain and cubic gain/loss. An essential result is
that the interaction of the unsaturated cubic gain and self-defocusing
nonlinearity can produce stable modes, although they may be destabilized by
finite amplitude perturbations. On the other hand, the interplay of the cubic
loss and self-defocusing gives rise to a bistability.Comment: Phys. Rev. E (in press
Exact States in Waveguides With Periodically Modulated Nonlinearity
We introduce a one-dimensional model based on the nonlinear
Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject
to spatially periodic modulation in terms of the Jacobi dn function, with three
free parameters including the period, amplitude, and internal form-factor. An
exact periodic solution is found for each set of parameters and, which is more
important for physical realizations, we solve the inverse problem and predict
the period and amplitude of the modulation that yields a particular exact
spatially periodic state. Numerical stability analysis demonstrates that the
periodic states become modulationally unstable for large periods, and regain
stability in the limit of an infinite period, which corresponds to a bright
soliton pinned to a localized nonlinearity-modulation pattern. Exact
dark-bright soliton complex in a coupled system with a localized modulation
structure is also briefly considered . The system can be realized in planar
optical waveguides and cigar-shaped atomic Bose-Einstein condensates.Comment: EPL, in pres
Averaging approximation to singularly perturbed nonlinear stochastic wave equations
An averaging method is applied to derive effective approximation to the
following singularly perturbed nonlinear stochastic damped wave equation \nu
u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on an open bounded domain
\,, \,. Here is a small parameter
characterising the singular perturbation, and \,, \,, parametrises the strength of the noise. Some scaling transformations
and the martingale representation theorem yield the following effective
approximation for small , u_t=\D u+f(u)+\nu^\alpha\dot{W} to an error of
\ord{\nu^\alpha}\,.Comment: 16 pages. Submitte
- …