The Effect of low Momentum Quantum Fluctuations on a Coherent Field Structure

In the present work the evolution of a coherent field structure of the Sine-Gordon equation under quantum fluctuations is studied. The basic equations are derived from the coherent state approximation to the functional Schr\"odinger equation for the field. These equations are solved asymptotically and numerically for three physical situations. The first is the study of the nonlinear mechanism responsible for the quantum stability of the soliton in the presence of low momentum fluctuations. The second considers the scattering of a wave by the Soliton. Finally the third problem considered is the collision of Solitons and the stability of a breather. It is shown that the complete integrability of the Sine-Gordon equation precludes fusion and splitting processes in this simplified model. The approximate results obtained are non-perturbative in nature, and are valid for the full nonlinear interaction in the limit of low momentum fluctuations. It is also found that these approximate results are in good agreement with full numerical solutions of the governing equations. This suggests that a similar approach could be used for the baby Skyrme model, which is not completely integrable. In this case the higher space dimensionality and the internal degrees of freedom which prevent the integrability will be responsable for fusion and splitting processes. This work provides a starting point in the numerical solution of the full quantum problem of the interaction of the field with a fluctuation.Comment: 15 pages, 9 (ps) figures, Revtex file. Some discussion expanded but conclusions unchanged. Final version to appear in PR

Multisymplectic Geometry and Multisymplectic Preissman Scheme for the KP Equation

The multisymplectic structure of the KP equation is obtained directly from the variational principal. Using the covariant De Donder-Weyl Hamilton function theories, we reformulate the KP equation to the multisymplectic form which proposed by Bridges. From the multisymplectic equation, we can derive a multisymplectic numerical scheme of the KP equation which can be simplified to multisymplectic forty-five points scheme.Comment: 17 papges, 8 figure

Elliptical optical solitary waves in a finite nematic liquid crystal cell

2015 Elsevier B.V. The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the chirp variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation

Fijación de fosforo en sedimientos de fondo de los Ríos Paraná, Paraguay y Bermejo

Phosphorus sorption'from Solutions containing 0-5 mgP/l was studied in bottom sediments from Paraná, Paraguay and Bermejo rivers. Sorptidh frtted a Langmuir isotherm with phosphate sorption capacities of 96, 87 and 52 MgP/g (dry weight) sediment. Hieltjesand Lijklema (1980) phosphorus fractionation showed that the iron bound phosphate is the mainfraction in the Paraná and Paraguay sediments while the calcium bound phosphorus is the main fraction in the Bermejo sediments. Caleiuhi content was high (32 mg/g) in the Bermejo sediments and low (5.5 and 5;3 mg/g) in the Paraná and Paraguay sediments, respectively, The organic matter composition is also dlfferent in the three rivers being the Paraná and the l^íraguay ríchér in huihic ^ibstánces. Low phosphorus content and sorption capacity in the three sediments are thought to be related with a granulometry dominated by the coarse fractions. Clay size partióles only accounted for 13-23 % of the total sediment weight.Phosphorus sorption'from Solutions containing 0-5 mgP/l was studied in bottom sediments from Paraná, Paraguay and Bermejo rivers. Sorptidh frtted a Langmuir isotherm with phosphate sorption capacities of 96, 87 and 52 MgP/g (dry weight) sediment. Hieltjesand Lijklema (1980) phosphorus fractionation showed that the iron bound phosphate is the mainfraction in the Paraná and Paraguay sediments while the calcium bound phosphorus is the main fraction in the Bermejo sediments. Caleiuhi content was high (32 mg/g) in the Bermejo sediments and low (5.5 and 5;3 mg/g) in the Paraná and Paraguay sediments, respectively, The organic matter composition is also dlfferent in the three rivers being the Paraná and the l^íraguay ríchér in huihic ^ibstánces. Low phosphorus content and sorption capacity in the three sediments are thought to be related with a granulometry dominated by the coarse fractions. Clay size partióles only accounted for 13-23 % of the total sediment weight

The Role of Carbonate Factories and Sea Water Chemistry on Basin-Wide Ramp to High-Relief Carbonate Platform Evolution: Triassic, Nanpanjiang Basin, South China

The end-Permian extinction and its aftermath altered carbonate factories globally for millions of years, but its impact on platform geometries remains poorly understood. Here, the evolution in architecture and composition of two exceptionally exposed platforms in the Nanpanjiang Basin are constrained and compared with geochemical proxies to evaluate controls on platform geometries. Geochemical proxies indicate elevated siliciclastic and nutrient fluxes in the basal Triassic, at the Induan—Olenekian boundary and in the uppermost Olenekian. Cerium/Ce* shifts from high Ce/Ce* values and a lack of Ce anomaly indicating anoxia during the Lower Triassic to a negative Ce anomaly indicating oxygenation in the latest Olenekian and Anisian. Uranium and Mo depletion represents widespread anoxia in the world\u27s oceans in the Early Triassic with progressive oxygenation in the Anisian. Carbonate factories shifted from skeletal in the Late Permian to abiotic and microbial in the Early Triassic before returning to skeletal systems in the Middle Triassic, Anisian coincident with declining anoxia. Margin facies shifted to oolitic grainstone in the Early Triassic with development of giant ooids and extensive marine cements. Anisian margins, in contrast, are boundstone with a diverse skeletal component. The shift in platform architecture from ramp to steep, high-relief, flat-topped profiles is decoupled from carbonate compositions having occurred in the Olenekian prior to the onset of basin oxygenation and biotic stabilisation of the margins. A basin-wide synchronous shift from ramp to high-relief platforms points to a combination of high subsidence rate and basin starvation coupled with high rates of abiotic and microbial carbonate accumulation and marine cement stabilisation of oolitic margins as the primary causes for margin up-building. High sea water carbonate saturation resulting from a lack of skeletal sinks for precipitation, and basin anoxia promoting an expanded depth of carbonate supersaturation, probably contributed to marine cement stabilisation of margins that stimulated the shift from ramp to high-relief platform architecture

Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals

The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions

Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells

The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal—a nematicon—is mathematically modelled. In order to overcome the Freédricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the (2+1)-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page

Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays

We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely

Bose-Einstein correlations of same-sign charged pions in the forward region in pp collisions at √s=7 TeV

Bose-Einstein correlations of same-sign charged pions, produced in protonproton collisions at a 7 TeV centre-of-mass energy, are studied using a data sample collected by the LHCb experiment. The signature for Bose-Einstein correlations is observed in the form of an enhancement of pairs of like-sign charged pions with small four-momentum difference squared. The charged-particle multiplicity dependence of the Bose-Einstein correlation parameters describing the correlation strength and the size of the emitting source is investigated, determining both the correlation radius and the chaoticity parameter. The measured correlation radius is found to increase as a function of increasing charged-particle multiplicity, while the chaoticity parameter is seen to decreas