Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the net field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value u(0) of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L, u(0)), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

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

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

On an Optimal Linear Control Applied to a Non-Ideal Load Transportation System, Modeled with Periodic Coefficients

In this paper, a load transportation system in platforms or suspended by cables is considered. It is a monorail device and is modelled as an inverted pendulum built on a car driven by a DC motor. The governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the DC motor and the dynamical system, that is, we have a so-called non-ideal periodic problem. The problem is analysed and we also developed an optimal linear control design to stabilize the problem.

Comments on energy confinement in non-periodic structures

In this study, we investigate the possibility of mode localization occurrence in a non-periodic Pfluger's column model of a rocket with an intermediate concentrated mass at its middle point. We discuss the effects of varying the intermediate mass magnitude and its position and the resulting energy confinement for two cases. Free vibration analysis and the severity of mode localization are appraised, without decoupling the system, by considering as a solution basis the fundamental free response or dynamical solution. This allows for the reduction of the dimension of the algebraic modal equation that arises from satisfying the boundary and continuity conditions. By using the same methodology, we also consider the case of a cantilevered Pluger's column with rotational stiffness at the middle support instead of an intermediate concentrated mass. (c) 2008 Elsevier Ltd. All rights reserved.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Gene expression modulation by chalcopyrite and bornite in Acidithiobacillus ferrooxidans

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chemical modulation on heterogeneous growth in Prochilodus lineatus (Valenciennes, 1847) (Pisces; Characiformes)

No presente trabalho, testou-se o efeito de fatores químicos liberados por coespecíficos sobre o crescimento e sua variabilidade no grupo (crescimento heterogêneo, CHet), numa espécie gregária, o curimbatá, Prochilodus lineatus. O CHet foi avaliado pelo coeficiente de variação do peso dos animais, em dois períodos consecutivos de 21 dias. Os peixes foram agrupados em aquários (4 peixes cada) que receberam água corrente, com vazão constante, de tanques contendo (C) ou não (N) coespecíficos. Quatro condições foram delineadas de acordo com a água que abastecia os aquários: a) água com contato prévio com coespecíficos durante todo o experimento (CC); b) água sem contato prévio com coespecíficos durante todo o experimento (NN); c) água com contato prévio com coespecíficos apenas no primeiro período, 0 a 21 dias (CN); e d) apenas no período de 21 a 42 dias (NC). Ao término dos experimentos, verificou-se que ocorre modulação química sobre a variabilidade de crescimento em P. lineatus: os peixes que receberam água com contato prévio com coespecífico (C) apresentaram exacerbação do CHet. Fato que corrobora a idéia de que o mecanismo predominante da determinação da variação intra-específica do crescimento, em espécies gregárias, está associado à ação de fatores químicos liberados por coespecíficos.

Modulation of parasitemia and antibody responce to Trypanosoma cruzy by cyclophosphamide in Calomys callosus (Rodentia, Cricetidae)

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

Competition between local potentials and attractive particle-particle interactions in superlattices

Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and as particular examples of emerging spatial inhomogeneity in interacting many-electron systems. Here we investigate the effect different types of modulation of the system parameters have on the ground-state energy and the charge-density distribution of the system. The superlattices are described by the inhomogeneous attractive Hubbard model, and the calculations are performed by density-functional and density-matrix renormalization group techniques. We find that modulations in local electric potentials are much more effective in shaping the system's properties than modulations in the attractive on-site interaction. This is the same conclusion we previously [M.F. Silva, N.A. Lima, A.L. Malvezzi, K. Capelle, Phys. Rev. B 71 (2005) 125130.] obtained for repulsive interactions, suggesting that it is not an artifact of a specific state, but a general property of modulated structures. (c) 2007 Elsevier Ltd. All rights reserved.

Modulation of coronary flow and cardiomyocyte size by sensory fibers

Cardiac tissue is densely innervated by sensory neurons that an believed to play important modulatory roles in cardiac functions. In this study, pretreatment of neonate mts with capsaicin was performed. In adult rats, cardiomyocyte size and amount of fibrous tissue in left ventricles as well as in vitro coronary flow were evaluated, the chronotropic and inotropic responses to beta-adrenoceptor agonists (norepinephrine and isoproterenol), muscarinic agonists (carbachol and pilocarpine), and calcitonin gene-related peptide (CGRP) were also investigated with the use of the isolated right atria preparation. Capsaicin pretreatment significantly (P<0.05) reduced both basal coronary flow (18% reduction) and cardiomyocyte size (34% reduction) without affecting the amount of fibrous tissues in the left ventricles. The positive inotropic and chronotropic effects in response to norepinephrine in the isolated rat heart did not significantly differ between control and capsaicin-treated rats, Similarly, the positive chronotropic effects in response to norepinephrine, isoproterenol, and CGRP as well as the negative chronotropic responses to carbachol and pilocarpine in the isolated light atria were not affected by capsaicin pretreatment, Our data are consistent with the suggestion that reductions of both basal coronary flow and cardiomyocyte size seen in hearts from capsaicin-pretreated rats may be consequences of CGRP depletion. The cardiomyocyte size reduction produced by capsaicin treatment may be related to a modulatory role of CGRP as a growth factor.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

ALLOSTERIC MODULATION BY ATP, CALCIUM AND MAGNESIUM-IONS OF RAT OSSEOUS PLATE ALKALINE-PHOSPHATASE

Alkaline phosphatase from rat osseous plate is allosterically modulated by ATP, calcium and magnesium at pH 7.5. At pH 9.4, the hydrolysis of ATP and PNPP follows Michaelis-Menten kinetics with K0.5 values of 154 muM and 42 muM, respectively. However, at pH 7.5 both substrates exhibit more complex saturation curves, while only ATP exhibited site-site interactions. Ca2+-ATP and Mg2+-ATP were effective substrates for the enzyme, while the specific activity of the enzyme for the hydrolysis of ATP at pH 7.5 was 800-900 U/mg and was independent of the ion species. ATP, but not PNPP, was hydrolyzed slowly in the absence of metal ions with a specific activity of 140 U/mg. These data demonstrate that in vitro and at pH 7.5 rat osseous plate alkaline phosphatase is an active calcium or magnesium-activated ATPase.