Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean floor can generate random caustics and focus the energy of tsunami waves. Caustics share many similarities to rogue waves, as they both exhibit heavy-tailed distribution, i.e. an overpopulation of large events. Linear Schr\"odinger-type equations are usually used to explain the wave dynamics of caustics. However, in that the wave amplitude increases dramatically in caustics, nonlinearity is inevitable in many systems. In this Letter, we investigate the effect of nonlinearity on the formation of optical caustics. We show experimentally that, in contrast to linear systems, even small phase fluctuations can generate strong caustics upon nonlinear propagation. We simulated our experiment based on the nonlinear Schr\"odinger equation (NLSE) with Kerr-type nonlinearity, which describes the wave dynamics not only in optics, but also in some other physical systems such as oceans. Therefore, our results may also aid our understanding of ocean phenomena.Comment: 5 pages, 4 figure

Quantized form factor shift in the presence of free electron laser radiation

In electron scattering, the target form factors contribute significantly to the diffraction pattern and carry information on the target electromagnetic charge distribution. Here we show that the presence of electromagnetic radiation, as intense as currently available in Free Electron Lasers, shifts the dependence of the target form factors by a quantity that depends on the number of photons absorbed or emitted by the electron as well as on the parameters of the electromagnetic radiation. As example, we show the impact of intense ultraviolet and soft X-ray radiation on elastic electron scattering by Ne-like Argon ion and by Xenon atom. We find that the shift brought by the radiation to the form factor is in the order of some percent. Our results may open up a new avenue to explore matter with the assistance of laser

Interatomic van der Waals potential in the presence of a magneto-electric sphere

On the basis of a general formula obtained earlier via fourth-order erturbation theory within the framework of macroscopic quantum electrodynamics, the van der Waals potential between two neutral, unpolarized, ground-state atoms in the presence of a homogeneous, dispersing and absorbing magnetoelectric sphere is studied. When the radius of the sphere becomes sufficiently large, the result asymptotically agrees with that for two atoms near a planar interface. In the opposite limit of a very small sphere, the sphere can effectively be regarded as being a third ground-state atom, and the nonadditive three-atom van der Waals potential is recovered. To illustrate the effect of a sphere of arbitrary radius, numerical results are presented for the triangular arrangement where the atoms are at equidistance from the sphere, and for the linear arrangement where the atoms and the sphere are aligned along a straight line. As demonstrated, the enhancement or reduction of the interaction potential in the presence of purely electric or magnetic spheres can be physically understood in terms of image charges.Comment: 13 pages, 7 figure

A Fabry-Perot interferometer with quantum mirrors: nonlinear light transport and rectification

Optical transport represents a natural route towards fast communications, and it is currently used in large scale data transfer. The progressive miniaturization of devices for information processing calls for the microscopic tailoring of light transport and confinement at length scales appropriate for the upcoming technologies. With this goal in mind, we present a theoretical analysis of a one-dimensional Fabry-Perot interferometer built with two highly saturable nonlinear mirrors: a pair of two-level systems. Our approach captures non-linear and non-reciprocal effects of light transport that were not reported previously. Remarkably, we show that such an elementary device can operate as a microscopic integrated optical rectifier

Preconcentration and extraction of copper(II) on activated carbon using ethyl-2-quinolyl-β (p-carboxyphenyl hydrazone)dioxo propionate

Activated carbon modified method was used for the preconcentration and determination of copper content in real samples such as tap water, wastewater and a synthetic water sample by flame atomic absorption spectrometry. The copper(II) was adsorbed quantitatively on activated carbon due to its complexation with ethyl-2-quinolyl-β(p-carboxyphenyl hydrazone)dioxo propionate (EQCPDP). The adsorbed copper(II) ion on solid phase was eluted quantitatively by using nitric acid. The important parameters such as pH, amount of carrier, flow rate, amount of activated carbon and type and concentration of eluting agent for obtaining maximum recovery were optimized. The method at optimum conditions gives linear concentration range of 0.05-1.0 μg mL-1 of copper(II) with correlation coefficient of 0.9994 and the detection limit of 0.99 ng mL-1. The preconcentration leads to enrichment factor of 175 and break through volume of 1750 mL. The method has good tolerance limit of interfering ions and selectivity and it has been successfully applied for determination of copper content in real sample such as blood, wastewater and river sample. KEY WORDS: Copper(II), Solid phase extraction, Activated carbon, Flame atomic absorption spectrometry  Bull. Chem. Soc. Ethiop. 2008, 22(3), 331-338

Controlling the isothermal crystallization of isodimorphic PBS-ran-PCL random copolymers by varying composition and supercooling

In this work, we study for the first time, the isothermal crystallization behavior of isodimorphic random poly(butylene succinate)-ran-poly(e-caprolactone) copolyesters, PBS-ran-PCL, previously synthesized by us. We perform nucleation and spherulitic growth kinetics by polarized light optical microscopy (PLOM) and overall isothermal crystallization kinetics by differential scanning calorimetry (DSC). Selected samples were also studied by real-time wide angle X-ray diffraction (WAXS). Under isothermal conditions, only the PBS-rich phase or the PCL-rich phase could crystallize as long as the composition was away from the pseudo-eutectic point. In comparison with the parent homopolymers, as comonomer content increased, both PBS-rich and PCL-rich phases nucleated much faster, but their spherulitic growth rates were much slower. Therefore, the overall crystallization kinetics was a strong function of composition and supercooling. The only copolymer with the eutectic composition exhibited a remarkable behavior. By tuning the crystallization temperature, this copolyester could form either a single crystalline phase or both phases, with remarkably different thermal propertiesPeer ReviewedPostprint (published version

Relativistic total cross section and angular distribution for Rayleigh scattering by atomic hydrogen

We study the total cross section and angular distribution in Rayleigh scattering by hydrogen atom in the ground state, within the framework of Dirac relativistic equation and second-order perturbation theory. The relativistic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of B-splines and B-polynomials. We pay particular attention to the effects that arise from higher (non-dipole) terms in the expansion of the electron-photon interaction. It is shown that the angular distribution of scattered photons, while it is symmetric with respect to the scattering angle $\theta$=90$^\circ$ within the electric dipole approximation, becomes asymmetric when higher multipoles are taken into account. The analytical expression of the angular distribution is parametrized in terms of Legendre polynomials. Detailed calculations are performed for photons in the energy range 0.5 to 10 keV. When possible, results are compared with previous calculations.Comment: 8 pages, 5 figure

Analytical evaluation of atomic form factors: application to Rayleigh scattering

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wavefunctions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.Comment: 7 pages, 1 figur

Using RAPD markers potential to identify heritability for growth in Fenneropenaeus indicus

Sampling was done using 90 post larvae which were produced by reproduction of some broodstocks of Fenneropenaeus indicus in one day and reared in the same situation for 4 months. Samples were divided into 3 groups: high, medium and low growth (based on weight and length). Genomic DNA was extracted from muscle tissue using the phenol-chloroform method. The polymerase chain reaction (PCR) was carried out using 21 RAPD loci and PCR products were separated on 3% Agarose gel. From 21 loci studied, 12 produced polymorphic bands. The most polymorphic produced bands using OPAQ 9 and the least by OPAQ 7. Search for specific markers in F. indicus one specific band was observed in the low growth group using OPAQ4. The highest genetic distance (0.457) was between the low growth group and the medium and the lowest (0.091) between high growth and medium groups, therefore the highest genetic identity (0.912) was between high growth and medium groups and the lowest (0.633) between low growth group and the medium. Neighbor-joining resulted in two groups, the first including high and medium growth groups and the second low growth group. It appears that low growth group depended on separated population. Considering the mean weight of F1 (mean weight of 90 specimens) (16.25±1.5 g), parental generation mean weight of 15 ±1.2 and mean weight of parent 31.6 g, response to selection (R) and heritability for growth in this species were estimated to be 1.2±0.2 and 0.07±0.01 respectively

Relativistic polarization analysis of Rayleigh scattering by atomic hydrogen

A relativistic analysis of the polarization properties of light elastically scattered by atomic hydrogen is performed, based on the Dirac equation and second order perturbation theory. The relativistic atomic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of $B$ splines and $B$ polynomials. We introduce two experimental scenarios in which the light is circularly and linearly polarized, respectively. For each of these scenarios, the polarization-dependent angular distribution and the degrees of circular and linear polarization of the scattered light are investigated as a function of scattering angle and photon energy. Analytical expressions are derived for the polarization-dependent angular distribution which can be used for scattering by both hydrogenic as well as many-electron systems. Detailed computations are performed for Rayleigh scattering by atomic hydrogen within the incident photon energy range 0.5 to 10 keV. Particular attention is paid to the effects that arise from higher (nondipole) terms in the expansion of the electron-photon interaction.Comment: 8 pages, 5 figure