Research of the synthesis of radiant intensity indicatrix of multicomponent beam diode module

Widespread use of semiconductor radiation sources in optoelectronic devices for various purposes requires further study of the mechanisms of formation of photometric characteristics of the integrated device in the near illumination zone, where the law of inverted squares is violated. A mathematical model of the multicomponent beam-diode module is proposed. On its basis the analysis of influence of the parameters of separate beam sources on the deformation of the indicatrix of radiant intensity at transition from the far zone to the near one is carried out. It is shown that the determining parameter of the indicatrix change in longitude and polar distance is the distribution in the plane of the modulus of the product of the radiant intensity of a single diode on its polar radius vector. The displacement of the polar angle of the maximum of the vector of the diode radiant intensity is more significant for wide radiation patterns than for concentrated ones. For specific parameters of diodes and geometry of their location the suitability of the proposed model for a priori modeling of beam-diode modules is illustrated.

Waves in thin oceans on oblate neutron stars

ABSTRACT Waves in thin fluid layers are important in various stellar and planetary problems. Due to rapid rotation such systems will become oblate, with a latitudinal variation in the gravitational acceleration across the surface of the object. In the case of accreting neutron stars, rapid rotation could lead to a polar radius smaller than the equatorial radius by a factor ∼0.8. We investigate how the oblateness and a changing gravitational acceleration affect different hydrodynamic modes that exist in such fluid layers through analytic approximations and numerical calculations. The wave vectors of g modes and Yanai modes increase for more oblate systems compared to spherical counterparts, although the impact of variations in the changing gravitational acceleration is effectively negligible. We find that for increased oblateness, Kelvin modes show less equatorial confinement and little change in their wave vector. For r modes, we find that for more oblate systems the wave vector decreases. The exact manner of these changes for the r modes depends on the model for the gravitational acceleration across the surface.

An Analytical Study of the Diffraction of Light by a Circular Aperture Using Spherical Harmonics for n≤1

Based on the importance of spherical harmonics and their applicability in many physical problems, this research aimed to study the diffraction pattern of light by a circular aperture starting from the first Rayleigh–Sommerfeld diffraction equation and to expand the polar radius of a point on the surface of the circular aperture based on spherical harmonics. We depended on this theoretical framework in our paper. We calculated the optical intensity compounds C00,C10,C11,C1−1 for n=0,1,m=−1,0,1. We studied the intensity distributions in three special cases (along the optical axis, at the geometrical focal plane, and along the boundary of the geometrical shadow). We presented numerical comparative examples to illustrate the variation of the intensity versus a ratio (Z/A is the ratio of the distance between the circular aperture and the observation plane to a radius of the circular aperture), and we used Maple program to represent these results. We noticed that the expansion we made using spherical harmonic analysis led to an increase in the number of fringes bright enough to be visible to the naked eye. We then concluded with a brief discussion of the results.

The rotation of α Oph investigated using polarimetry

ABSTRACT Recently we have demonstrated that high-precision polarization observations can detect the polarization resulting from the rotational distortion of a rapidly rotating B-type star. Here, we investigate the extension of this approach to an A-type star. Linear-polarization observations of α Oph (A5IV) have been obtained over wavelengths from 400 to 750 nm. They show the wavelength dependence expected for a rapidly rotating star combined with a contribution from interstellar polarization. We model the observations by fitting rotating-star polarization models and adding additional constraints including a measured vesin i. However, we cannot fully separate the effects of rotation rate and inclination, leaving a range of possible solutions. We determine a rotation rate (ω = Ω/Ωc) between 0.83 and 0.98 and an axial inclination i > 60°. The rotation-axis position angle is found to be 142 ± 4°, differing by 16° from a value obtained by interferometry. This might be due to precession of the rotation axis due to interaction with the binary companion. Other parameters resulting from the analysis include a polar temperature Tp = 8725 ± 175 K, polar gravity log gp = 3.93 ± 0.08 (dex cgs), and polar radius Rp = 2.52 ± 0.06 R⊙. Comparison with rotating-star evolutionary models indicates that α Oph is in the later half of its main-sequence evolution and must have had an initial ω of 0.8 or greater. The interstellar polarization has a maximum value at a wavelength (λmax) of 440 ± 110 nm, consistent with values found for other nearby stars.

Maximally rotating supermassive stars at the onset of collapse: effects of gas pressure

ABSTRACT The ‘direct collapse’ scenario has emerged as a promising evolutionary track for the formation of supermassive black holes early in the Universe. In an idealized version of such a scenario, a uniformly rotating supermassive star spinning at the mass-shedding (Keplerian) limit collapses gravitationally after it reaches a critical configuration. Under the assumption that the gas is dominated by radiation pressure, this critical configuration is characterized by unique values of the dimensionless parameters J/M2 and Rp/M, where J is the angular momentum, Rp the polar radius, and M the mass. Motivated by a previous perturbative treatment, we adopt a fully non-linear approach to evaluate the effects of gas pressure on these dimensionless parameters for a large range of masses. We find that gas pressure has a significant effect on the critical configuration even for stellar masses as large as $M \simeq 10^6 \, \mathrm{M}_{\odot }$. We also calibrate two approximate treatments of the gas pressure perturbation in a comparison with the exact treatment, and find that one commonly used approximation in particular results in increasing deviations from the exact treatment as the mass decreases, and the effects of gas pressure increase. The other approximation, however, proves to be quite robust for all masses $M \gtrsim 10^4 \, \mathrm{M}_{\odot }$.

A NEW REALIZATION OF THE GLOBAL LUNAR REFERENCE FRAME BASED ON CO-REGISTERED LOLA TRACKS

We present a method that aligns lunar south and north pole LOLA DTMs using selected LOLA tracks and co-registration techniques. The selected LOLA tracks were then co-registered to the aligned polar DTMs with the aim to create a new LOLA frame of high relative accuracy. At the poles the relative accuracy of the resulting LOLA frame improved in comparison with the original LOLA frame, especially at the north pole. At lower latitudes on the lunar near side we could show that we achieve smaller residuals between our LOLA frame and a photogrammetrically derived reference DTM than with the original LOLA frame. On the far side we could not achieve better results which we believe is stemming from the generally less accurate orbit knowledge there. From the aligned polar DTMs we were able to derive a polar radius of 1738,049 km.

Polar radius integral transform for affine invariant feature extraction

Affine transform is to describe the same target at different viewpoints to obtain the relationship between images of approximate model. Affine invariant feature extraction plays an important role in object recognition and image registration. Firstly, the definition of polar radius integral transform (PRIT) is put forward by means of the characterization of affine transform mapping straight line into straight line, where PRIT computes the integral along the polar radius direction and converts images into closed curves which keep the same affine transform with original images. Secondly, in order to extract affine invariant feature, an affine invariant feature extraction algorithm is also given based on PRIT. The proposed algorithm can be used to combine contour-based methods with region-based methods. It has some advantages of fewer amounts of computations and feasibility of feature extraction for objects with several components. Finally, the capability of anti-noise (Gaussian noise, salt and pepper noise) of PRIT is discussed. The simulation experiment results show that PRIT can effectively extract the affine invariant features, but also the low order PRIT has very strong robustness to noise.