There is evidence that trans-Planckian physics does not affect the Hawking radiation in four dimensions and, consequently, deviations from the linear dispersion relation (for massless particles) at very high energies cannot be revealed using four-dimensional black holes. We study this issue in the context of models with extra spatial dimensions and show that small black holes that could be prod...

This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated ...

It is well known that the Fisher scoring iteration for generalized linear models has the same form as the Gauss-Newton algorithm for normal regression. This note shows that exponential dispersion models are the most general families to preserve this form for the scoring iteration. Therefore exponential dispersion models are the most general extension of generalized linear models for which the a...

Traditionally the dispersion of particles in polymeric materials has proven difficult and frequently results in phase separation and agglomeration. We show that thermodynamically stable dispersion of nanoparticles into a polymeric liquid is enhanced for systems where the radius of gyration of the linear polymer is greater than the radius of the nanoparticle. Dispersed nanoparticles swell the li...

We have considered linear two point correlations of the form 1 xγ which are known to have a self-similar behaviour in a Ω = 1 universe. We investigate under what conditions the non-linear corrections, calculated using the Zel’dovich approximation, have the same self-similar behaviour. We find that the scaling properties of the non-linear corrections are decided by the spatial behaviour of the l...

We obtain optical vortices with classical orbital momentum = 1 and spin j = ±1/2 as exact solutions of a system of nonlinear Maxwell equations (NMEs). Two kinds of Kerr-type media, namely, those with and without linear dispersion of the electric and the magnet susceptibility, are investigated. The electric and magnetic fields are represented as sums of circular and linear components. This allow...

Conventionally, unitary transformations on optical modes have been implemented on a spatial basis set using a system of beamsplitters and phase shifters. We present methods which allow orders of magnitude increase in the number of modes in linear optics experiments by moving from spatial encoding to temporal encoding and using dispersion. This enables significant practical advantages for linear...

Four-wave mixing (FWM) in wavelength-division multiplexed systems with strong dispersion management and loss–amplification is comprehensively studied. The methods described apply to both soliton and quasilinear return-to-zero systems. A linear model is introduced that describes the resonant growth and saturation of the FWM products. The model yields a resonance condition between the channel sep...