Geometric Beam Research Articles

Erratum: Predicting ULX demographics from geometrical beaming

The ultraluminous X-ray source (ULX) population is known to contain neutron stars, but the relative number of these compared to black hole primaries is unknown. Assuming classical super-critical accretion and resultant geometrical beaming, we show that the observed population ratio can be predicted from the mean masses of each family of compact objects and the relative spatial density of neutron stars to black holes. Conversely - and perhaps more importantly - given even a crude estimate for the spatial densities, an estimate of the fraction of the population containing neutron stars will begin to constrain the mean mass of black holes in ULXs.

The plastic behavior of sandwich beams with core gradation

The objective of this paper is to establish yielding criteria for a slender sandwich beam with two-layer metal foam cores under transverse loading. A unified yielding criterion for this geometrical or physical asymmetry four-layer metallic sandwich beam is established. Based on the yield criteria, an analytical solution for large deformation of fully clamped multilayer sandwich beams under transverse loading is presented. Comparisons of present solutions with numerical results are given and good agreements are obtained. Finally, the effects of core strength and thickness ratios on the large deflection responses of the sandwich beams with core gradation are discussed in detail. It is demonstrated that the present analytical model can reasonably predict the behavior of the plastic deformation of four layer sandwich beams.

Predicting ultraluminous X-ray source demographics from geometrical beaming

Abstract The ultraluminous X-ray source (ULX) population is known to contain neutron stars (NS), but the relative number of these compared to black hole (BH) primaries is unknown. Assuming classical supercritical accretion and resultant geometrical beaming, we show that the observed population ratio can be predicted from the mean masses of each family of compact objects and the relative spatial density of NSs to BHs. Conversely – and perhaps more importantly – given even a crude estimate for the spatial densities, an estimate of the fraction of the population containing NSs will begin to constrain the mean mass of BHs in ultraluminous X-ray sources.

Geometrically nonlinear analysis of composite beams using Wiener-Milenković parameters

This paper presents a geometrically nonlinear analysis of composite beams including static, dynamic, and eigenvalue analyses. With the increase in size and flexibility of engineering components such as wind turbine blades, geometric nonlinearity plays an increasingly significant role in structural analysis. The Geometric Exact Beam Theory (GEBT), pioneered by Reissner and extended by Hodges, is adopted as the foundation for this work. Special emphasis is placed on the vectorial parameterization of finite rotation, which is a fundamental aspect in the geometrically nonlinear formulation. This method is introduced based on Euler's rotation theorem and the property of rotation operation: the length preservation of the rotated vector. The GEBT is then implemented with the Wiener-Milenković parameters using a mixed formulation. Several numerical examples are studied based on the derived theory, and the results are compared with analytical solutions and those available in the literature. The analysis of a realistic composite wind turbine blade is provided to show the capability of the present model for generalized composite slender structures. It concludes that the proposed model can be used as a beam tool in a multibody framework whose valid range of rotation is up to 2π.

A physics-based solver to optimize the illumination of cylindrical targets in spherically distributed high power laser systems.

In recent years, our understanding of high energy density plasmas has played an important role in improving inertial fusion confinement and in emerging new fields of physics, such as laboratory astrophysics. Every new idea required developing innovative experimental platforms at high power laser facilities, such as OMEGA or NIF. These facilities, designed to focus all their beams onto spherical targets or hohlraum windows, are now required to shine them on more complex targets. While the pointing on planar geometries is relatively straightforward, it becomes problematic for cylindrical targets or target with more complex geometries. This publication describes how the distribution of laser beams on a cylindrical target can be done simply by using a set of physical laws as a pointing procedure. The advantage of the method is threefold. First, it is straightforward, requiring no mathematical enterprise besides solving ordinary differential equations. Second, it will converge if a local optimum exists. Finally, it is computationally inexpensive. Experimental results show that this approach produces a geometrical beam distribution that yields cylindrically symmetric implosions.

Spectra of black hole accretion models of ultraluminous X-ray sources

We present general relativistic radiation MHD simulations of super-Eddington accretion on a $10M_\odot$ black hole. We consider a range of mass accretion rates, black hole spins, and magnetic field configurations. We compute the spectra and images of the models as a function of viewing angle, and compare them with the observed properties of ultraluminous X-ray sources (ULXs). The models easily produce apparent luminosities in excess of $10^{40}~{\rm erg\,s^{-1}}$ for pole-on observers. However, the angle-integrated radiative luminosities rarely exceed $2.5\times10^{39}~{\rm erg\,s^{-1}}$ even for mass accretion rates of tens of Eddington. The systems are thus radiatively inefficient, though they are energetically efficient when the energy output in winds and jets is also counted. The simulated models reproduce the main empirical types of spectra --- disk-like, supersoft, soft, hard --- observed in ULXs. The magnetic field configuration, whether MAD ("magnetically arrested disk") or SANE ("standard and normal evolution"), has a strong effect on the results. In SANE models, the X-ray spectral hardness is almost independent of accretion rate, but decreases steeply with increasing inclination. MAD models with non-spinning black holes produce significantly softer spectra at higher values of $\dot{M}$, even at low inclinations. MAD models with rapidly spinning black holes are quite different from all other models. They are radiatively efficient (efficiency factor $\sim10-20\%$), super-efficient when the mechanical energy output is also included ($70\%$), and produce hard blazar-like spectra. In all models, the emission shows strong geometrical beaming, which disagrees with the more isotropic illumination favored by observations of ULX bubbles.

Modelling the light curves of ultraluminous X-ray sources as precession

We present a freely available xspec model for the modulations seen in the long-term light curves of multiple ultraluminous X-ray sources (ULXs). By incorporating the physics of multiple electron scatterings (ray traced with a Monte-Carlo routine), we go beyond analytical predictions and show that the geometrical beaming of radiation in the conical outflow can be more than a factor of 100 for opening angles smaller than $10^\circ$. We apply our new model to the long-term, well sampled Swift light curve of the recently confirmed ULX pulsar NGC 5907 X-1 with an established period of 78 days. Our results suggest that geometrical beaming together with a slight precession of the conical wind can describe the light curve with a consistent set of parameters for the wind. The small opening angle of roughly $10\mathrm{-}13^\circ$ implies a highly super-critical flow and boosting factors at the order of $\mathcal{B}=60\mathrm{-}90$ that would yield a fairly low surface magnetic field strength of $2\times 10^{10}\,$Gauss.

DETECTION OF POLARIZED QUASI-PERIODIC MICROSTRUCTURE EMISSION IN MILLISECOND PULSARS

ABSTRACT Microstructure emission, involving short timescale, often quasi-periodic, intensity fluctuations in subpulse emission, is well known in normal period pulsars. In this Letter, we present the first detections of quasi-periodic microstructure emission from millisecond pulsars (MSPs), from Giant Metrewave Radio Telescope observations of two MSPs at 325 and 610 MHz. Similar to the characteristics of microstructure observed in normal period pulsars, we find that these features are often highly polarized and exhibit quasi-periodic behavior on top of broader subpulse emission, with periods of the order of a few μs. By measuring their widths and periodicities from single pulse intensity profiles and their autocorrelation functions, we extend the microstructure timescale–rotation period relationship by more than an order of magnitude down to rotation periods ∼5 ms, and find it to be consistent with the relationship derived earlier for normal pulsars. The similarity of behavior is remarkable, given the significantly different physical properties of MSPs and normal period pulsars, and rules out several previous speculations about the possible different characteristics of microstructure in MSP radio emission. We discuss the possible reasons for the non-detection of these features in previous high time resolution MSP studies along with the physical implications of our results, both in terms of a geometric beam sweeping model and temporal modulation model for micropulse production.

Geometrical beaming of stellar mass ULXs

Abstract The presence or lack of eclipses in the X-ray light curves of ultraluminous X-ray sources (ULXs) can be directly linked to the accreting system geometry. In the case where the compact object is stellar mass and radiates isotropically, we should expect eclipses by a main-sequence to sub-giant secondary star on the recurrence time-scale of hours to days. X-ray light curves are now available for large numbers of ULXs as a result of the latest XMM–Newton catalogue. We determine the amount of fractional variability that should be injected into an otherwise featureless light curve for a given set of system parameters as a result of eclipses and compare this to the available data. We find that the vast majority of sources for which the variability has been measured to be non-zero and for which available observations meet the criteria for eclipse searches, have fractional variabilities which are too low to derive from eclipses and so must be viewed such that θ ≤ cos− 1(R*/a). This would require that the disc subtends a larger angle than that of the secondary star and is therefore consistent with a conical outflow formed from super-critical accretion rates and implies some level of geometrical beaming in ULXs.

The X-ray spectral evolution of the ultraluminous X-ray source Holmberg IX X-1

We present a new analysis of X-ray spectra of the archetypal ultraluminous X-ray source (ULX) Holmberg IX X-1 obtained by the Swift, XMM-Newton and NuSTAR observatories. This ULX is a persistent source, with a typical luminosity of ~10^40 erg s^-1, that varied by a factor of 4 - 5 over eight years. We find that its spectra tend to evolve from relatively flat or two-component spectra in the medium energy band (1-6 keV), at lower luminosities, to a spectrum that is distinctly curved and disc-like at the highest luminosities, with the peak energy in the curved spectrum tending to decrease with increased luminosity. We argue that the spectral evolution of the ULX can be explained by super-Eddington accretion models, where in this case we view the ULX down the evacuated funnel along its rotation axis, bounded by its massive radiatively driven wind. The spectral changes then originate in enhanced geometric beaming as the accretion rate increases and wind funnel narrows, causing the scattered flux from the central regions of the supercritical flow to brighten faster than the isotropic thermal emission from the wind, and so the curved hard spectral component to dominate at the highest luminosities. The wind also Compton down-scatters photons at the edge of the funnel, resulting in the peak energy of the spectrum decreasing. We also confirm that Holmberg IX X-1 displays spectral degeneracy with luminosity, and suggest that the observed differences are naturally explained by precession of the black hole rotation axis for the suggested wind geometry.

A theoretical study of low-velocity impact of geometrically asymmetric sandwich beams

This paper uses the quasi-static method to investigate plastic behavior of fully clamped geometrical asymmetric sandwich beams with a metal foam core subjected to low-velocity impact. An analytical model is developed to predict the dynamic response of the geometrically asymmetric sandwich beams. Effects of local denting and core strength on the overall bending are considered. Good agreement is achieved between the analytical predictions and numerical results. It is demonstrated that the asymmetric sandwich beams with asymmetric factor α > 1 have the larger energy absorption than those with asymmetric factor 0 < α < 1.

The technique for solving the problem of light backscattering by ice crystals of cirrus clouds by the physical optics method for a lidar with zenith scanning

The technique for solving the problem of light backscattering by the physical optics method is considered. Recommendations on carrying out a preliminary estimation of the contribution of geometrical optics beams are given to reduce the list of beams that are necessary for the calculation by a factor of hundreds. The presented empirical estimating formulas and recommendations on choosing the optimum step of numerical integration make it possible to considerably reduce the resource intensity of the physical optics method for specified microphysical models of hexagonal crystalline particles. The obtained results of solving the light scattering problem are freely available in the form of a databank of Mueller matrices.

Modelling of soil–structure interaction behaviour: geometric nonlinearity of buried structures combined to spatial variability of soil

In the analysis of non-linear behaviour of buried structures, the soil–structure interaction is the most important cause of buried pipeline failure, especially when the soil is modelled as a random elastic medium. In order to design safe and economical means of transporting energy and fluid, it is necessary to predict realistic behaviour of buried pipeline. In this work, the influence of spatially random soil properties on the geometric non-linear behaviour of pipeline is investigated. However, a numerical model has been developed, by modelling the pipeline as a geometric non-linear long beam resting on linear elastic random soil. Due to large deflections and moderate rotations of pipeline, the von Kàrmàn-type non-linearity based on the finite element formulation of non-linear pipeline response is adopted and then combined with random field theory of soil based on Monte Carlo simulations. The equation of motion is obtained using the principal of virtual works and solved using the Newton–Raphson incremental iterative method. A MATLAB program has been developed to implement the numerical method applied to the non-linear analysis of the buried structure. When the pipeline undergoes large deflection, the spatial variability of soil properties significantly affect the pipeline’s response and in this case, the obtained results allow a more reliable design of pipeline.

Model of the Geometrical Computer for Carrying Out Exact Calculations in Applied Tasks

In article possibility of creation of mathematical model of the geometrical computer on the example of the classical task consisting in finding of the cube having volume is considered it is twice more than a volume of an initial cube. The geometrical computer,manipulating points and beams, allows to receive result with an absolute accuracy, without use of usual operations (multiplication, division, exponentiation, extraction of a root, addition and subtraction) with numbers. Opportunity to experts of the widest profile, without algebra opens, to solve applied problems in various areas of science and equipment where usual methods are unacceptable.

A Hybrid Interpolation Method for Geometric Nonlinear Spatial Beam Elements with Explicit Nodal Force

Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.

Geometric beam coupling impedance of LHC secondary collimators

The High Luminosity LHC project is aimed at increasing the LHC luminosity by an order of magnitude. One of the key ingredients to achieve the luminosity goal is the beam intensity increase. In order to keep beam instabilities under control and to avoid excessive power losses a careful design of new vacuum chamber components and an improvement of the present LHC impedance model are required. Collimators are among the major impedance contributors. Measurements with beam have revealed that the betatron coherent tune shifts were higher by about a factor of 2 with respect to the theoretical predictions based on the LHC impedance model up to 2012. In that model the resistive wall impedance has been considered as the dominating impedance contribution for collimators. By carefully simulating also their geometric impedance we have contributed to the update of the LHC impedance model, reaching also a better agreement between the measured and simulated betatron tune shifts. During the just ended LHC Long Shutdown I (LSI), TCS/TCT collimators were replaced by new devices embedding BPMs and TT2-111R ferrite blocks. We present here preliminary estimations of their broad-band impedance, showing that an increase of about 20% is expected in the kick factors with respect to previous collimators without BPMs.

음선 모델에 적용된 이층 해저 바닥 모델의 유효성

음선 모델링에서 다층 해저 바닥을 고려하는 경험적 방법 중 하나는 단일층 가정으로써, 다층 구조에 대한 평면파 반사계수를 사용하는 것이다. 본 연구자는 이층 해저 바닥에 대해 단일 층 가정의 유효성을 조사하고, 음속비, 송수신 거리 당 층 두께, 1차 반사파의 스침각의 함수로 표현되는 간단한 부등식 조건을 얻었다. 부등식 조건으로부터, 단일 층 가정이 실제 해양 환경의 중주파수 음선 모델링에 적용될 수 있음을 보였다. 마지막으로 한국 동해와 유사한 해양환경에 대해 수치실험을 수행하였다. 다층 해저 바닥에 대한 평면파 반사계수를 적용한 기하학적 빔 모델을 이용하여 비상관 전달손실을 계산하고, 서울대학교에서 개발한 포물선 방정식 패키지인 SNUPE 2.0의 결과와 비교하였다. A heuristic method treating a layered ocean bottom in a ray modeling is to use the plane wave reflection coefficient for multiple-layered structure, named an one-layer assumption in this paper. We examine the validity of one-layer assumption in the case of two-layered ocean bottom, and obtain a simple inequality condition depending on the sound speed ratio, the ratio of layer thickness to source-receiver range, and the grazing angle of first reflected ray. From this inequality condition, it is shown that an one-layer assumption can be applicable to ray propagation problems at mid frequencies. Finally, numerical experiments are performed in the ocean environment similar to the East Sea in Korea. Incoherent transmission loss is calculated by the geometrical beam model with the plane wave reflection coefficient for multiple-layered ocean bottom and compared with the result of SNUPE 2.0, which is a parabolic equation package developed in Seoul National University.

The initial plastic failure of fully clamped geometrical asymmetric metal foam core sandwich beams

The initial plastic failure of fully clamped geometrical asymmetric metal foam core sandwich beams is analytically and experimentally investigated. Initial failure modes of the clamped asymmetric sandwich beams are observed, i.e. face yield, core shear and indentation. The analytical formulae for the initial failure loads are developed and used to construct the initial failure mechanism maps for the fully clamped geometrical asymmetric sandwich beams. It is shown that the initial failure modes of the sandwich beams depend on geometry and material properties of the sandwich beams. The predicted failure mechanisms of fully clamped asymmetrical sandwich beams are consistent with the experimental results and obviously different from those of simply supported ones. Finally, the minimum weight designs are presented by using the analytical formulae.

Low energy, high power hydrogen neutral beam for plasma heating.

A high power, relatively low energy neutral beam injector was developed to upgrade of the neutral beam system of the gas dynamic trap device and C2-U experiment. The ion source of the injector produces a proton beam with the particle energy of 15 keV, current of up to 175 A, and pulse duration of a few milliseconds. The plasma emitter of the ion source is produced by superimposing highly ionized plasma jets from an array of four arc-discharge plasma generators. A multipole magnetic field produced with permanent magnets at the periphery of the plasma box is used to increase the efficiency and improve the uniformity of the plasma emitter. Multi-slit grids with 48% transparency are fabricated from bronze plates, which are spherically shaped to provide geometrical beam focusing. The focal length of the Ion Optical System (IOS) is 3.5 m and the initial beam diameter is 34 cm. The IOS geometry and grid potentials were optimized numerically to ensure accurate beam formation. The measured angular divergences of the beam are ±0.01 rad parallel to the slits and ±0.03 rad in the transverse direction.

High-Brightness Incoherent Combination of Fiber Lasers in 7 × 1 Fiber Couplers at Average Powers &gt; 5 kW

We report on the experimental realization of two different low-loss single- to multimode fiber coupler designs, each combining more than 5 kW of output power. The adiabatic mode evolution in the seven-fiber input bundle provides a brightness close to its theoretical maximum. The all-glass structures exhibit very low heat loads mainly due to small avoidable contamination, indicating room for improvement. To the best of our knowledge, regarding all-fiber geometrical combined power generation, beam quality and heat stability, the presented results had never been reported before.