31,820 research outputs found
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
Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries
An approximate strategy for studying the evolution of binary systems of
extended objects is introduced. The stars are assumed to be polytropic
ellipsoids. The surfaces of constant density maintain their ellipsoidal shape
during the time evolution. The equations of hydrodynamics then reduce to a
system of ordinary differential equations for the internal velocities, the
principal axes of the stars and the orbital parameters. The equations of motion
are given within Lagrangian and Hamiltonian formalism. The special case when
both stars are axially symmetric fluid configurations is considered. Leading
order gravitational radiation reaction is incorporated, where the quasi-static
approximation is applied to the internal degrees of freedom of the stars. The
influence of the stellar parameters, in particular the influence of the
polytropic index , on the leading order gravitational waveforms is studied.Comment: 31 pages, 7 figures, typos correcte
Cusp-scaling behavior in fractal dimension of chaotic scattering
A topological bifurcation in chaotic scattering is characterized by a sudden
change in the topology of the infinite set of unstable periodic orbits embedded
in the underlying chaotic invariant set. We uncover a scaling law for the
fractal dimension of the chaotic set for such a bifurcation. Our analysis and
numerical computations in both two- and three-degrees-of-freedom systems
suggest a striking feature associated with these subtle bifurcations: the
dimension typically exhibits a sharp, cusplike local minimum at the
bifurcation.Comment: 4 pages, 4 figures, Revte
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