We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.

Mixed finite elements in ℝ 3

There is a wide range of fundamental physical problems directly related to how pulsars function. Some of these are independent of the specific pulsar mechanism. Others relate directly to the physics of the pulsar and already shed some light on the properties of matter at high density (\ensuremath{\sim}${10}^{15}$ g/cc) and in strong magnetic fields (\ensuremath{\sim}${10}^{12}$ G). Pulsars are assumed to be rotating neutron stars surrounded by strong magnetic fields and energetic particles. It is somewhere within this "magnetosphere" that the pulsar action is expected to take place. Currently there has been considerable difficulty in formulating an entirely self-consistent theory of the magnetospheric behavior and there may be rapid revisions in the near future, which is all the more surprising since many of the issues involve "elementary" problems in electromagnetism. One interesting discovery is that charge-separated plasmas apparently can support stable static discontinuities.

Theory of pulsar magnetospheres

Since neural networks have universal approximation capabilities, therefore it is possible to postulate them as solutions for given differential equations that define unsupervised errors. In this paper, we present a wide survey and classification of different Multilayer Perceptron (MLP) and Radial Basis Function (RBF) neural network techniques, which are used for solving differential equations of various kinds. Our main purpose is to provide a synthesis of the published research works in this area and stimulate further research interest and effort in the identified topics. Here, we describe the crux of various research articles published by numerous researchers, mostly within the last 10 years to get a better knowledge about the present scenario.

Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: A survey

Neutron stars are fascinating astrophysical objects immersed in strong gravitational and electromagnetic fields, at the edge of our current theories. These stars manifest themselves mostly as pulsars, emitting a timely very stable and regular electromagnetic signal. Even though discovered almost fifty years ago, they still remain mysterious compact stellar objects. In this review, we summarize the most fundamental theoretical aspects of neutron star magnetospheres and winds. The main competing models susceptible to explain their radiative properties like multi-wavelength pulse shapes and spectra and the underlying physical processes such as pair creation and radiation mechanisms are scrutinized. A global but still rather qualitative picture emerges slowly thanks to recent advances in numerical simulations on the largest scales. However considerations about pulsar magnetospheres remain speculative. For instance the exact composition of the magnetospheric plasma is not yet known. Is it solely filled with a mixture of $e^\pm$~leptons, or does it contain a non negligible fraction of protons and/or ions? Actually, is it almost entirely filled or mostly empty except for some small anecdotal plasma filled regions? Answers to these questions will strongly direct the description of the magnetosphere to seemingly contradictory results leading sometimes to inconsistencies. Nevertheless, account are given to the latest developments in the theory of pulsar magnetospheres and winds, the existence of a possible electrosphere and physical insight obtained from related observational signatures of multi-wavelength pulsed emission.

/pdf/theory-of-pulsar-magnetosphere-and-wind-jtwil24ag9.pdf

Theory of pulsar magnetosphere and wind

This paper contains a survey of the past and current software developments in the field of partial differential equatmns. Software tools alined at reducing the task of solving partial differential equations are subdivided mto five classes Though attempting to give a broad overview of the field, the survey is biased toward general-purpose software, and the main emphasis is laid on two important classes of partial differentml equatmn software, that is, program packages with a high-level programmmg language interface and program packages with a special language interface.

A Survey of Software for Partial Differential Equations

Automatic production of programmes for solving partial differential equations by finite difference methods

Tranal — A program for the translation of symbolic algol I into symbolic algol II

Numerical modelling of pulsar magnetospheres

A numerical model based on the assumption that pulsars are spinning magnetized neutron stars is studied. A two-fluid model which includes inertial terms coupled self-consistently with Maxwell's equations is used. In this first paper of the series the case with aligned rotation and magnetic axes is examined with the assumption that the only source of charged particles is the star itself. It is found that under these conditions the magnetic field lines are closed everywhere and the particles in the equatorial region close to the light cylinder R/sub L/ reach sufficiently high energies to escape from the magnetosphere. With the Crab pulsar parameters, 1x10$sup 38$ ergs s$sup -1$ are carried away by relativistic particles and an equatorial region of high energy density is found near R/sub L/. A tentative conclusion is made that the described behavior is due to the assumption regarding the source of particles which results in 100 percent charge separation and a space-charge-limited emission from the star. In this space-charge-limited regime not enough current is available to open the field lines, but the electrostatic forces are large enough to force motion across the field lines. An artificially large particle rest mass has been used in this papermore » to ensure a smoother transition between the nonrelativistic and highly relativistic regions of space. Solutions which correspond to an essentially negligible rest mass in the nonrelativistic region will be discussed in subsequent papers. (AIP)« less

Numerical studies of the axisymmetric pulsar magnetosphere

Self-consistent solution for an axisymmetric pulsar model

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