Solitons in Ideal Optical Fibers - A Numerical Development

This work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers.Comment: Article accepted for publication in Semina: Ci\^encias Exatas e Tecnol\'ogica

Freedom of expression and the desecration of flags and religious books in Israeli law

SUMMARY: 1. Introduction - 2. Flag Protection. Legislation - 3. Flag Protection. Jurisprudence - 4. Foreign Flags - 5. Desecration of Religious Books - 6. Conclusions. ABSTRACT: Freedom of expression is axiomatic to liberal democracy. However, extremely divergent paradigms about when it must be curbed are manifest in the legal systems of different countries, especially concerning hate speech and speech offensive to religious or patriotic feelings. The United States is more protective of freedom of expression even at the cost of deliberately ignoring the need - especially in culturally diverse societies common in democratic countries nowadays - for dialogue rather than confrontation and for a pluralistic respect of the dignity and integrity of others and that which they cherish. In contrast, the European paradigm willingly sacrifices freedom of expression for the sake of protecting the sensibilities of the different segments of society. The theoretical question of the proper perimeters of such infringements upon freedom of expression aside, legislation prohibiting the desecration of national symbols on the one hand, and of religiously venerated objects on the other hand, can be seen as a measure of the emphasis ascribed in a jurisdiction to tolerance and pluralism as a justification for limiting democratic rights. This paper is a critical review of the legislation and case-law of flag burning statutes, and statutes outlawing the desecration of religious books, in Israel

A modeling of the carbon-nitrogen cycle transport at Igap\'o I Lake - Londrina, Paran\'a, Brazil

This work is a contribution to better understand the effect that domestic sewage discharges may cause in a water body, specifically Igap\'o I Lake, in Londrina, Paran\'a, Brazil. The simulation of the dynamics of pollutant concentrations all over the water body is conducted by means of structured discretization of the geometry of Igap\'o I Lake, together with the finite differences and the finite elements methods. Firstly, the hydrodynamic flow (without the pollutants), modeled by Navier-Stokes and pressure equations, is numerically resolved by the finite differences method, and associated with the fourth order Runge-Kutta procedure. After that, by using the hydrodynamic field velocity, the flow of the reactive species (pollutants) is described through a transport model, which considers advective and diffusive processes, as well as through a reactions model, restricted to the carbon-nitrogen cycle. The transport and reactions model is numerically resolved by the stabilized finite elements method, by means of a semidiscrete formulation. A qualitative analysis of the numerical simulations conducted in function of the diffusion coefficient provided better understanding of the dynamics of the processes involved in the flow of the reactive species, such as the dynamics of the nitrification process, of the biochemical requirement of oxygen and of the level of oxygen dissolved in the water body at Igap\'o I Lake

Lee Kingman Correspondence

Entries include typed and handwritten letters on personal stationery

Time-Dependent Variational Principle for ϕ4\phi^4 Field Theory: RPA Approximation and Renormalization (II)

The Gaussian-time-dependent variational equations are used to explored the physics of $(\phi^4)_{3+1}$ field theory. We have investigated the static solutions and discussed the conditions of renormalization. Using these results and stability analysis we show that there are two viable non-trivial versions of $(\phi^4)_{3+1}$. In the continuum limit the bare coupling constant can assume $b\to 0^{+}$ and $b\to 0^{-}$, which yield well defined asymmetric and symmetric solutions respectively. We have also considered small oscillations in the broken phase and shown that they give one and two meson modes of the theory. The resulting equation has a closed solution leading to a ``zero mode'' and vanished scattering amplitude in the limit of infinite cutoff.Comment: 29 pages, LaTex file, to appear in Annals of Physic