FSBS resonances observed in a standard highly nonlinear fiber.

Forward stimulated Brillouin scattering (FSBS) is observed in a standard 2-km-long highly nonlinear fiber. The frequency of FSBS arising from multiple radially guided acoustic resonances is observed up to gigahertz frequencies. The tight confinement of the light and acoustic field enhances the interaction and results in a large gain coefficient of 34.7 W(-1) at a frequency of 933.8 MHz. We also find that the profile on the anti-Stokes side of the pump beam have lineshapes that are asymmetric, which we show is due to the interference between FSBS and the optical Kerr effect. The measured FSBS resonance linewidths are found to increase linearly with the acoustic frequency. Based on this scaling, we conclude that dominant contribution to the linewidth is from surface damping due to the fiber jacket and structural nonuniformities along the fiber.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Thermodynamic and dynamic contributions to future changes in regional precipitation variance: focus on the Southeastern United States

© 2014, Springer-Verlag Berlin Heidelberg.The frequency and severity of extreme events are tightly associated with the variance of precipitation. As climate warms, the acceleration in hydrological cycle is likely to enhance the variance of precipitation across the globe. However, due to the lack of an effective analysis method, the mechanisms responsible for the changes of precipitation variance are poorly understood, especially on regional scales. Our study fills this gap by formulating a variance partition algorithm, which explicitly quantifies the contributions of atmospheric thermodynamics (specific humidity) and dynamics (wind) to the changes in regional-scale precipitation variance. Taking Southeastern (SE) United States (US) summer precipitation as an example, the algorithm is applied to the simulations of current and future climate by phase 5 of Coupled Model Intercomparison Project (CMIP5) models. The analysis suggests that compared to observations, most CMIP5 models (~60 %) tend to underestimate the summer precipitation variance over the SE US during the 1950–1999, primarily due to the errors in the modeled dynamic processes (i.e. large-scale circulation). Among the 18 CMIP5 models analyzed in this study, six of them reasonably simulate SE US summer precipitation variance in the twentieth century and the underlying physical processes; these models are thus applied for mechanistic study of future changes in SE US summer precipitation variance. In the future, the six models collectively project an intensification of SE US summer precipitation variance, resulting from the combined effects of atmospheric thermodynamics and dynamics. Between them, the latter plays a more important role. Specifically, thermodynamics results in more frequent and intensified wet summers, but does not contribute to the projected increase in the frequency and intensity of dry summers. In contrast, atmospheric dynamics explains the projected enhancement in both wet and dry summers, indicating its importance in understanding future climate change over the SE US. The results suggest that the intensified SE US summer precipitation variance is not a purely thermodynamic response to greenhouse gases forcing, and cannot be explained without the contribution of atmospheric dynamics. Our analysis provides important insights to understand the mechanisms of SE US summer precipitation variance change. The algorithm formulated in this study can be easily applied to other regions and seasons to systematically explore the mechanisms responsible for the changes in precipitation extremes in a warming climate.

Photophysics of Re(I) and Ru(II) diimine complexes covalently linked to pyrene: Contributions from intra-ligand charge transfer states

The photophysical properties of Ru(II) and Re(I) polypyridyl complexes including a bis-bipyridyl pyrene ligand are presented. The complexes ([(bpy)(2)Ru](2)bpb)(4+) and [(CO)(3)ReCl(bpb)] (bpy = 2,2'-bipyridine, bpb = 1,6-bis-(4-(2,2'-bipyrid-yl)-pyrene) were designed with the intent of examining intramolecular energy migration between MLCT states localized on the metal complexes and pyrene-localized (3)(pi-pi) states. Absorption spectroscopy of both complexes containing the bpb ligand reveals that in addition to the MLCT and the pyrene-centered (1)(pi-pi) transitions, a new absorption band is observed near 400 nm for both complexes. Absorption spectral data for the Re(I) complex strongly suggest the presence of a pyrene(pi) to bpy(pi) intraligand charge transfer (ILCT) transition. Emission spectra at room temperature and at 77 K are almost identical for the Ru(II) and Re(I) complexes containing the bpb ligand. The (3)MLCT emission of related bipyridyl compounds lacking the pyrene is observed at higher energy than for the pyrene-containing complexes, ([(bpy)(2)Ru](2)bpb)(4+) and [(CO(3)ReCl(bpb)]. The Ru(II) complex emits at room temperature with a remarkably long lifetime (130 micros in degassed DMSO). This emission is also strongly sensitive to oxygen and is almost entirely quenched in an aerated solution. In addition, excited-state absorption spectra exhibit features not consistent with (3)MLCT or (3)(pi-pi) states of the parent chromophores. The combined characteristics suggest the emission arises from either (3)(pi-pi) or (3)ILCT states or a state with mixed parentage.

Evolution of soybean diseases in Argentina : past and present : contributions of FAUBA to the integrated management of plant diseases

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Evolution of soybean diseases in Argentina : past and present : contributions of FAUBA to the integrated management of plant diseases

p.37-52

Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.

On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.