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We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA–ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

We solve numerically in the complex plane all the differential equations involved in Hartle's perturbation method for computing general-relativistic polytropic models of rotating neutron stars. We give emphasis on computing quantities describing the geometry of models in rapid rotation. Compared to numerical results obtained by certain sophisticated iterative methods, we verify appreciable improvement of our results vs to those given by the classical Hartle's perturbative scheme.

We compute general-relativistic polytropic models of magnetized rotating neutron stars, assuming that magnetic field and rotation can be treated as decoupled perturbations acting on the nondistorted configuration. Concerning the magnetic field, we develop and apply a numerical method for solving the relativistic Grad–Shafranov equation as a nonhomogeneous Sturm–Liouville problem with nonstandard boundary conditions. We present significant geometrical and physical characteristics of six models, four of which are models of maximum mass. We find negative ellipticities owing to a magnetic field with both toroidal and poloidal components; thus the corresponding configurations have prolate shape. We also compute models of magnetized rotating neutron stars with almost spherical shape due to the counterbalancing of the rotational effect (tending to yield oblate configurations) and the magnetic effect (tending in turn to derive prolate configurations). In this work such models are simply called "equalizers." We emphasize on numerical results related to magnetars, i.e. ultramagnetized neutron stars with relatively long rotation periods.

The shapes of rotating drops of liquid bound by gravitation is a classical subject of study. Inspired by this classical theory, we have simulated numerically a related problem, the rotating rigid configurations of a finite number of point particles. Two particles at a distance $r$ have a long range attractive potential $-1∕r$ and a short range repulsive potential $1∕r^2$ preventing collapse. We take the angular momentum to be conserved, but not the energy.This system has a variable density, unlike the classical liquid drops. When the number of particles is small, it is more rigid than a liquid drop, implying that many different stable equilibrium configurations may exist with the same angular momentum but different energies. When the number of particles becomes large, our system should resemble a self-gravitating polytropic gas.We present here the results of a preliminary study with only 3, 4, and 5 particles. The methods used could be applied to the study of rotating molecules.

In order to simulate rigidly rotating polytropes, we have simulated systems of $N$ point particles, with $N$ up to 1800. Two particles at a distance $r$ interact by an attractive potential $-1∕r$ and a repulsive potential $1∕r^2$. The repulsion simulates the pressure in a polytropic gas of polytropic index $3∕2$. We take the total angular momentum $L$ to be conserved, but not the total energy $E$. The particles are stationary in the rotating coordinate system. The rotational energy is $L^2∕(2I)$ where $I$ is the moment of inertia. Configurations, where the energy $E$ has a local minimum, are stable. In the continuum limit $N\to \infty$, the particles become more and more tightly packed in a finite volume, with the interparticle distances decreasing as $N^{-1∕3}$. We argue that $N^{-1∕3}$ is a good parameter for describing the continuum limit. We argue further that the continuum limit is the polytropic gas of index $3∕2$. For example, the density profile of the nonrotating gas approaches that computed from the Lane–Emden equation describing the nonrotating polytropic gas. In the case of maximum rotation, the instability occurs by the loss of particles from the equator, which becomes a sharp edge, as predicted by Jeans in his study of rotating polytropes. We describe the minimum energy nonrotating configurations for a number of small values of $N$.

This paper focuses on studying thermal, elastic and coupled plasma waves, in the sense of a photo-thermal process transport within an infinite semiconductor medium. In order to study photo-thermal interactions in two-dimensional semiconducting materials, a new mathematical model based on the Moore–Gibson–Thompson equation (MGTE) is implemented. The MGTE model involving the Green–Naghdi model of type III as well as the heat transport equation proposed by Lord and Shulman. We consider the semi-conductor half-space is rotated at a uniform angular speed and magnetized. The analysis of the distribution of thermophysical fields has been extracted by a normal mode method, represented graphically and discussed. The results predicted by the new and improved model have been compared with the generalized and classic ones. In addition, all field quantities have been examined for effects of rotation, a lifetime of the photo-generated, and the applied magnetic field.