We have numerically calculated the resonance curve and the region of existence of high-energy dissipative solitons in systems governed by the complex cubic-quintic Ginzburg-Landau equation. The calculations are carried out for negative reactive quintic nonlinearity. This choice allows the resonance curve to be continued into the region of positive net dispersion, thus showing that high-energy p...

We show that a class of negative index (n) materials has interesting anisotropic optical properties, manifest in the effective refraction index that can be positive, negative, or purely imaginary under different incidence conditions. With dispersion taken into account, reflection at a planar negative-index interface exhibits frequency selective total oblique transmission that is distinct from t...

In a previous paper we developed a matrix theory that applies to any cylindrically symmetric fiber surrounded by Bragg cladding. Using this formalism, along with Finite Difference Time Domain (FDTD) simulations, we study the waveguide dispersion for the m = 1 mode in an air-core Bragg fiber and showed it is possible to achieve very large negative dispersion values (~ -20,000 ps/(nm.km)) with si...

We investigated the dispersion characteristics of submicron sized AlGaAs waveguides. Numerical simulations shows that the tight confinement of the optical waves in such nanowires leads to strong variations of the dispersion characteristics compared to classic, weakly guided waveguides of the same material system. We found numerically that the investigated structure has negative GVD for the TE m...

The eigenvalues of the quartic anharmonic oscillator as functions of the anharmonicity constant satisfy a once-subtracted dispersion relation. In turn, this dispersion relation is driven by the purely imaginary discontinuity of the eigenvalues across the negative real axis. In this paper we calculate explicitly the asymptotic expansion of this discontinuity up to second-exponentially-small orde...

In this paper we consider a linear KdV equation with a transport term posed on a finite interval with the boundary conditions considered by Colin and Ghidaglia. The main results concern the behavior of the cost of null controllability with respect to the dispersion coefficient when the control acts on the left endpoint. In particular, for any final time we prove that this cost grows exponential...

A reanalysis of Budescu et al.’s (2009) data on numerical interpretations of the Intergovernmental Panel on Climate Change (IPCC 2007) fourth report’s verbal probability expressions (PE’s) revealed that negative wording has deleterious effects on lay judgements. Budescu et al. asked participants to interpret PE’s in IPCC report sentences, by asking them to provide lower, “best” and upper estima...

We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad-hoc pre-processing steps commonly required in existing algorithms. We propose to use the gamma (beta) negative binomial process, which takes into account different sequencing depths using sample-specific negative binomial probability (dispersio...