Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

We extend the Miles mechanism of wind-wave generation to finite depth. A beta-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of beta is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the beta-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrodinger equation is derived and the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions for weak wind inputs in finite depth h are obtained.

Mid-infrared supercontinuum generation in a suspended-core As2S3 chalcogenide microstructured optical fiber

We demonstrate the supercontinuum (SC) generation in a suspended-core As2S3 chalcogenide microstructured optical fiber (MOF). The variation of SC is investigated by changing the fiber length, pump peak power and pump wavelength. In the case of long fibers (20 and 40 cm), the SC ranges are discontinuous and stop at the wavelengths shorter than 3500 nm, due to the absorption of fiber. In the case of short fibers (1.3 and 2.4 cm), the SC ranges are continuous and can extend to the wavelengths longer than 4 μm. The SC broadening is observed when the pump peak power increases from 0.24 to 1.32 kW at 2500 nm. The SC range increases with the pump wavelength changing from 2200 to 2600 nm, corresponding to the dispersion of As2S3 MOF from the normal to anomalous region. The SC generation is simulated by the generalized nonlinear Schrödinger equation. The simulation includes the SC difference between 1.3 and 2.4 cm long fiber by 2500 nm pumping, the variation of SC with pump peak power in 2.4 cm long fiber, and the variation of SC with pump wavelength in 1.3 cm long fiber. The simulation agrees well with the experiment.

Um estudo sobre a equação de Schrödinger biharmônica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Equação de Schrödinger não linear com coeficientes modulados

Pós-graduação em Física - FEG

Allometric equations for estimating tree biomass in restored mixed-species Atlantic Forest stands

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

MULTI-BUMP SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON R

This paper is concerned with the existence of multi-bump solutions to a class of quasilinear Schrodinger equations in R. The proof relies on variational methods and combines some arguments given by del Pino and Felmer, Ding and Tanaka, and Sere.

On the radial expansion of tubular structures in a quark-gluon plasma

We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes. (C) 2012 Elsevier B.V. All rights reserved.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Analytical investigation of squeeze film dampers

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Starting from linear Reynolds equation which governs the fluid behavior coupled with structure domain which is modeled by Kirchhoff plate equation, the effects of nondimensional parameters on the damped natural frequencies are presented using boundary characteristic orthogonal functions. For this purpose, the nondimensional coupled partial differential equations are obtained using Rayleigh-Ritz method and the weak formulation, are solved using polynomial and sinusoidal boundary characteristic orthogonal functions for structure and fluid domain respectively. In order to implement present approach to the complex geometries, a two dimensional isoparametric coupled finite element is developed based on Reissner-Mindlin plate theory and linearized Reynolds equation. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. As the next logical step, an analytical method for solution of squeeze film damping based upon Green’s function to the nonlinear Reynolds equation considering elastic plate is studied. This allows calculating modal damping and stiffness force rapidly for various boundary conditions. The nonlinear Reynolds equation is divided into multiple linear non-homogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling calculation of damping ratio and frequency shift as well as complex resistant pressure. Moreover, the theoretical results are correlated and compared with experimental results both in the literature and in-house experimental procedures including comparison against viscoelastic dampers.

Milk production during the colostral period is not related to the later lactational performance in dairy cows

In dairy cows, milk yield increases rapidly after parturition until a peak at around wk 6 of lactation. However, the description of the shape of the lactation curve is commonly based on weekly average milk yields. For a more detailed analysis of the milk production curve from the very beginning of lactation including the colostral period and the effect of colostrum yield on further lactational performance, the first 10 milkings after parturition, daily milk yields from d 1 to 28 of lactation, and the cumulative milk production on d 100 to 305 of lactation were investigated in 17 primiparous and 39 multiparous cows milked twice daily. Milk yield at the first milking after parturition (colostrum) ranged from 1.3 to 20.7kg (Δ=19.4kg) in multiparous and from 1.8 to 10.9kg in primiparous animals (Δ=9.1kg). At the tenth milking, milk production ranged from 9.2 to 21.5kg (Δ=12.3kg) in multiparous and from 7.0 to 15.2kg (Δ=8.2kg) in primiparous animals. Immediately after parturition, daily milk production increased rapidly, but after approximately 1wk in lactation, the slope of the daily milk production curve flattened and continued more linear. A nonlinear regression equation was used to determine this timely change, which occurred earlier in primiparous (d 6.9±0.3) than in multiparous cows (d 8.2±0.2). The correlation between the amount of first colostrum and milk production during further lactation decreased already from 0.47 on d 5 to 0.32 on d 14. In multiparous cows, the correlation between total milk production of the previous 305d standard lactation and the amount of first colostrum was not significant (correlation=0.29), whereas the correlation with the daily production increased from 0.45 on d 5 to 0.69 on d 14. However, in primiparous animals, correlations between first-colostrum yield and daily milk yields up to d 28 of lactation were not significant, possibly due to the smaller sample size compared with multiparous animals. First-colostrum yield and cumulative milk production of 100, 200, and 305 lactation days were not significantly correlated in multiparous and primiparous cows. In conclusion, the milk production during the first few milkings is widely independent from the overall production level of a cow. Potentially, genetic selection toward lower milk yield during the very first days after parturition at a simultaneously high lactational performance may be a tool to ensure sufficient colostrum quality and to reduce the metabolic load around parturition.

Estudio y desarrollo de un preproceso basado en la difusión no lineal para la segmentación en imágenes

En esta Tesis Doctoral se aborda la utilización de filtros de difusión no lineal para obtener imágenes constantes a trozos como paso previo al proceso de segmentación. En una primera parte se propone un formulación intrínseca para la ecuación de difusión no lineal que proporcione las condiciones de diseño necesarias sobre los filtros de difusión. A partir del marco teórico propuesto, se proporciona una nueva familia de difusividades; éstas son obtenidas a partir de técnicas de difusión no lineal relacionadas con los procesos de difusión regresivos. El objetivo es descomponer la imagen en regiones cerradas que sean homogéneas en sus niveles de grises sin contornos difusos. Asimismo, se prueba que la función de difusividad propuesta satisface las condiciones de un correcto planteamiento semi-discreto. Esto muestra que mediante el esquema semi-implícito habitualmente utilizado, realmente se hace un proceso de difusión no lineal directa, en lugar de difusión inversa, conectando con proceso de preservación de bordes. Bajo estas condiciones establecidas, se plantea un criterio de parada para el proceso de difusión, para obtener imágenes constantes a trozos con un bajo coste computacional. Una vez aplicado todo el proceso al caso unidimensional, se extienden los resultados teóricos, al caso de imágenes en 2D y 3D. Para el caso en 3D, se detalla el esquema numérico para el problema evolutivo no lineal, con condiciones de contorno Neumann homogéneas. Finalmente, se prueba el filtro propuesto para imágenes reales en 2D y 3D y se ilustran los resultados de la difusividad propuesta como método para obtener imágenes constantes a trozos. En el caso de imágenes 3D, se aborda la problemática del proceso previo a la segmentación del hígado, mediante imágenes reales provenientes de Tomografías Axiales Computarizadas (TAC). En ese caso, se obtienen resultados sobre la estimación de los parámetros de la función de difusividad propuesta. This Ph.D. Thesis deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. I have first shown an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, I have proposed a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. It has also proved that the proposed filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edgepreserving process. Under the conditions established for the diffusivity and using a stopping criterion I for the diffusion time, I have obtained piecewise constant images with a low computational effort. The whole process in the one-dimensional case is extended to the case where 2D and 3D theoretical results are applied to real images. For 3D, develops in detail the numerical scheme for nonlinear evolutionary problem with homogeneous Neumann boundary conditions. Finally, I have tested the proposed filter with real images for 2D and 3D and I have illustrated the effects of the proposed diffusivity function as a method to get piecewise constant images. For 3D I have developed a preprocess for liver segmentation with real images from CT (Computerized Tomography). In this case, I have obtained results on the estimation of the parameters of the given diffusivity function.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Soliton generation from randomly modulated return-to-zero pulses

We consider return-to-zero (RZ) pulses with random phase modulation propagating in a nonlinear channel (modelled by the integrable nonlinear Schrödinger equation, NLSE). We suggest two different models for the phase fluctuations of the optical field: (i) Gaussian short-correlated fluctuations and (ii) generalized telegraph process. Using the rectangular-shaped pulse form we demonstrate that the presence of phase fluctuations of both types strongly influences the number of solitons generated in the channel. It is also shown that increasing the correlation time for the random phase fluctuations affects the coherent content of a pulse in a non-trivial way. The result obtained has potential consequences for all-optical processing and design of optical decision elements.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Numerical modelling of dispersion managed soliton transmission

This thesis presents the results of numerical modelling of the propagation of dispersion managed solitons. The theory of optical pulse propagation in single mode optical fibre is introduced specifically looking at the use of optical solitons for fibre communications. The numerical technique used to solve the nonlinear Schrödinger equation is also introduced. The recent developments in the use of dispersion managed solitons are reviewed before the numerical results are presented. The work in this thesis covers two main areas; (i) the use of a saturable absorber to control the propagation of dispersion managed solutions and (ii) the upgrade of the installed standard fibre network to higher data rates through the use of solitons and dispersion management. Saturable absorbe can be used to suppress the build up of noise and dispersive radiation in soliton transmission lines. The use of saturable absorbers in conjunction with dispersion management has been investigated both as a single pulse and for the transmission of a 10Gbit/s data pattern. It is found that this system supports a new regime of stable soliton pulses with significantly increased powers. The upgrade of the installed standard fibre network to higher data rates through the use of fibre amplifiers and dispersion management is of increasing interest. In this thesis the propagation of data at both 10Gbit/s and 40Gbit/s is studied. Propagation over transoceanic distances is shown to be possible for 10Gbit/s transmission and for more than 2000km at 40Gbit/s. The contribution of dispersion managed solitons in the future of optical communications is discussed in the thesis conclusions.