Asymptotic soliton train solutions of the defocusing nonlinear Schrodinger equation

Asymptotic behavior of initially large and smooth pulses is investigated at two typical stages of their evolution governed by the defocusing nonlinear Schrodinger equation. At first, wave breaking phenomenon is studied in the limit of small dispersion. A solution of the Whitham modulational equations is found for the case of dissipationless shock wave arising after the wave breaking point. Then, asymptotic soliton trains arising eventually from a large and smooth initial pulse are studied by means of a semiclassical method. The parameter varying along the soliton train is calculated from the generalized Bohr-Sommerfeld quantization rule, so that the distribution of eigenvalues depends on two functions-intensity rho(0)(x) of the initial pulse and its initial chirp v(0)(x). The influence of the initial chirp on the asymptotic state is investigated. Excellent agreement of the numerical solution of the defocusing NLS equation with predictions of the asymptotic theory is found.

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

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

NOISE and ULTRAVIOLET DIVERGENCES IN SIMULATIONS of GINZBURG-LANDAU-LANGEVIN TYPE of EQUATIONS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

Dehydration and volatilization non isothermic kinetic of the solid state aluminium 8-hydroxyquinolinate

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

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Environmental solutions of recovery of Amazonian forest mining operations

In order for the projects of recovery of degraded areas to be successful, it is necessary to have a perfect recovery of the soil where the revegetation will be implanted as an initial action in the recovery of the whole process. The use of native forest species fully adapted to these types of terrain is another aspect of great importance, once the non-selection of these species, even if abundant in the surrounding areas, as it is in our case, implies great mortality of individuals during the planting and their low fixation during the process. The establishment of a monitoring program that contemplates the advancements obtained in the soil, the vegetation and the return of wild animals also collaborate in the evaluation of the success of the process. And, finally, the effective participation of the mining company, accepting and applying the techniques tested and indicated by research, even if, initially, the return time is longer than expected, also guarantees the success of the process. The mining company not only implemented a partnership with important universities in Brazil to obtain solutions for the environmental problems but also applied the developed techniques and the monitoring program. In the present work, we have attempted to summarize important aspects to evaluate the advancements in the rehabilitation plan for those areas, being here presented some results of the monitoring of areas under different levels of recovery, in accordance with the techniques adopted. Biological parameters of the soil were used to verify the efficiency of these different techniques in the recovery process. This work is part of the monitoring program of areas in rehabilitation by the mining company, implemented as of 1999 and in partnership with universities. The microbial activity was determined through the quantification of the carbon and nitrogen microbial biomass (BMC and BMN) and the activity of the dehydrogenase evaluated in the mining floor and tailing areas in different levels of soil preparation and planting of native species. The analysis of the parameters studied revealed that the preparation of the soil, following the three years proposed by the methodology, was important for the success in establishing the rehabilitation process. Some of the areas analyzed already show some parameters with values close or superior to those found in the capoeira (secondary forest), the latter being the non-treated area. © 2010 WIT Press.

Salmonella enterica serovar typhimurium colonizing the lumen of the chicken intestine grows slowly and upregulates a unique set of virulence and metabolism genes

The pattern of global gene expression in Salmonella enterica serovar Typhimurium bacteria harvested from the chicken intestinal lumen (cecum) was compared with that of a late-log-phase LB broth culture using a whole-genome microarray. Levels of transcription, translation, and cell division in vivo were lower than those in vitro. S. Typhimurium appeared to be using carbon sources, such as propionate, 1,2-propanediol, and ethanolamine, in addition to melibiose and ascorbate, the latter possibly transformed to D-xylulose. Amino acid starvation appeared to be a factor during colonization. Bacteria in the lumen were non- or weakly motile and nonchemotactic but showed upregulation of a number of fimbrial and Salmonella pathogenicity island 3 (SPI-3) and 5 genes, suggesting a close physical association with the host during colonization. S. Typhimurium bacteria harvested from the cecal mucosa showed an expression profile similar to that of bacteria from the intestinal lumen, except that levels of transcription, translation, and cell division were higher and glucose may also have been used as a carbon source. © 2011, American Society for Microbiology.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.