Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

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

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Asymptotic soliton train solutions of Kaup-Boussinesq equations

Asymptotic soliton trains arising from a 'large and smooth' enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup-Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr-Sommerfeld quantization rule which generalizes the usual rule to the case of 'two potentials' h(0)(x) and u(0)(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u(0)(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup-Boussinesq equations with predictions of the asymptotic theory is found. (C) 2003 Elsevier B.V. All rights reserved.

On the asymptotic behavior of effective QED at finite temperature

The aim of this paper is to study finite temperature effects in effective quantum electrodynamics using Weisskopf's zero-point energy method in the context of thermo, field dynamics. After a general calculation for a weak magnetic field at fixed T, the asymptotic behavior of the Euler-Kockel-Heisenberg Lagrangian density is investigated focusing on the regularization requirements in the high temperature limit. In scalar QED the same problem is also discussed.

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.

Genetic trends in the expected progeny difference of the asymptotic weight of Nelore females

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

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

MODEL FOR ASYMPTOTIC D-STATE PARAMETERS OF LIGHT-NUCLEI - APPLICATION TO HE-4

A simple method for calculating the asymptotic D-state observables for light nuclei is suggested. The method exploits the dominant clusters of the light nuclei. The method is applied to calculate the He-4 asymptotic D to S normalization ratio rho(alpha) and the closely related D-state parameter D2alpha. The study predicts a correlation between D2alpha and B(alpha), and between rho(alpha) and B(alpha), where B(alpha) is the binding energy of He-4. The present study yields rho(alpha) congruent-to -0.14 and D2alpha congruent-to -0.12 fm2 consistent with the correct experimental eta(d) and the binding energies of the deuteron, triton, and the alpha particle, where eta(d) is the deuteron D-state to S-state normalization ratio.

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

NN scattering: Chiral predictions for asymptotic observables

We assume that the nuclear potential for distances larger than 2.5 fm is given just by the exchanges of one and two pions and, for the latter, we adopt a model based on chiral symmetry and subthreshold pion-nucleon amplitudes, which contains no free parameters. The predictions produced by this model for nucleon-nucleon observables are calculated and shown to agree well with both experiment and those due to phenomenological potentials.

Weak expansions: a distinctive feature of the business cycle in Latin America and the Caribbean

Using two standard cycle methodologies (Classical and Deviation Cycle) and a comprehensive sample of 83 countries worldwide, including all developing regions, we show that the Latin American and Caribbean cycle exhibits two distinctive features. First, and most importantly, its expansion performance is shorter and for the most par less imtense than that of the rest of the regions considered, and in particular than that of East Asia and the Pacific, East Asia and the Pacific's expansions last five years longer than those of LAC, and its output gain is 50% greater than that of LAC. Second, LAC tends to exhibit contractions that are not significantly different in terms of duration and amplitude than t those of other regions. Both these features imply that the complete Latin American and Caribbean cycle has, overall, the shortest duration and smallest amplitude in relation to other regions. The specificities of the Latin American and Caribbean cycle are not confined to the short run. These are also reflected in variables such as productivity and investment, which are linked to long-run growth. East Asia and the Pacific's cumulative gain in labor productivity during the expansionary phase is twice that of LAC. Moreover, the evidence also shows that the effects of the contraction in public investment surpass those of the expansion leading to a declining trend over the entire cycle. In this sense we suggest that policy analysis needs to increase its focus on the expansionary phase of the cycle. Improving our knowledge of the differences in the expansionary dynamics of countries and regions, can further our understanding of the differences in their rates of growth and levels of development. We also suggest that while, the management of the cycle affects the short-run fluctuations of economic activity and hence volatility, it is not trend neutral. Hence, the effects of aggregate demand management policies may be more persistent over time and less transitory than currently thought.

Asymptotic approach for the nonlinear equatorial long wave interactions

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are disccussed. In particular, we discuss the implications of the results for El Nĩo and the Madden-Julian in connection with other scales of time and spatial variability. © Published under licence by IOP Publishing Ltd.