scholarly journals A new set of analytical formulae for the computation of the bootstrap current and the neoclassical conductivity in tokamaks

2021 ◽  
Vol 28 (2) ◽  
pp. 022502
Author(s):  
A. Redl ◽  
C. Angioni ◽  
E. Belli ◽  
O. Sauter ◽  
◽  
...  
Keyword(s):  
Analytical Formulae ◽  
Bootstrap Current

scholarly journals Two-component galaxy models with a central BH – II. The ellipsoidal case

2020 ◽  
Vol 500 (1) ◽  
pp. 1054-1070
Author(s):  
Luca Ciotti ◽  
Antonio Mancino ◽  
Silvia Pellegrini ◽  
Azadeh Ziaee Lorzad
Keyword(s):  
Dark Matter ◽  
Stellar Dynamics ◽  
Azimuthal Velocity ◽  
Dark Matter Halo ◽  
Gas Flows ◽  
Total Density ◽  
Density Distributions ◽  
Stellar Component ◽  
Two Component ◽  
Analytical Formulae

ABSTRACT Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

scholarly journals Fluctuation of magnitude of wave loads for a long array of bottom-mounted cylinders

2019 ◽  
Vol 868 ◽  
pp. 244-285 ◽  
Author(s):  
Xiaohui Zeng ◽  
Fajun Yu ◽  
Min Shi ◽  
Qi Wang
Keyword(s):  
Incidence Angle ◽  
Local Maximum ◽  
Destructive Interference ◽  
Horizontal Distance ◽  
Wave Loads ◽  
Wave Load ◽  
Intrinsic Mechanism ◽  
Fluctuation Phenomenon ◽  
Analytical Formulae ◽  
Incident Waves

For wave loads on cylinders constituting a long but finite array in the presence of incident waves, variations in the magnitude of the load with the non-dimensional wavenumber exhibit interesting features. Towering spikes and nearby secondary peaks (troughs) associated with trapped modes have been studied extensively. Larger non-trapped regions other than these two are termed Region III in this study. Studies of Region III are rare. We find that fluctuations in Region III are regular; the horizontal distance between two adjacent local maximum/minimum points, termed fluctuation spacing, is constant and does not change with non-dimensional wavenumbers. Fluctuation spacing is related only to the total number of cylinders in the array, identification serial number of the cylinder concerned and wave incidence angle. Based on the interaction theory and constructive/destructive interference, we demonstrate that the fluctuation characteristics can be predicted using simple analytical formulae. The formulae for predicting fluctuation spacing and the abscissae of every peak and trough in Region III are proposed. We reveal the intrinsic mechanism of the fluctuation phenomenon. When the diffraction waves emitted from the cylinders at the ends of the array and the cylinder concerned interfere constructively/destructively, peaks/troughs are formed. The fluctuation phenomenon in Region III is related to solutions of inhomogeneous equations. By contrast, spikes and secondary peaks are associated with solutions of the eigenvalue problem. This study of Region III complements existing understanding of the characteristics of the magnitude of wave load. The engineering significances of the results are discussed as well.

scholarly journals Accumulation of mutations in sexual and asexual populations

1987 ◽  
Vol 49 (2) ◽  
pp. 135-146 ◽  
Author(s):  
Pekka Pamilo ◽  
Masatoshi Nei ◽  
Wen-Hsiung Li
Keyword(s):  
Weak Selection ◽  
Population Variance ◽  
Asexual Population ◽  
Term Evolution ◽  
A Genome ◽  
Analytical Formulae ◽  
The Mean ◽  
Asexual Populations ◽  
Mutant Genes

SummaryThe accumulation of beneficial and harmful mutations in a genome is studied by using analytical methods as well as computer simulation for different modes of reproduction. The modes of reproduction examined are biparental (bisexual, hermaphroditic), uniparental (selfing, automictic, asexual) and mixed (partial selfing, mixture of hermaphroditism and parthenogenesis). It is shown that the rates of accumulation of both beneficial and harmful mutations with weak selection depend on the within-population variance of the number of mutant genes per genome. Analytical formulae for this variance are derived for neutral mutant genes for hermaphroditic, selfing and asexual populations; the neutral variance is largest in a selfing population and smallest in an asexual population. Directional selection reduces the population variance in most cases, whereas recombination partially restores the reduced variance. Therefore, biparental organisms accumulate beneficial mutations at the highest rate and harmful mutations at the lowest rate. Selfing organisms are intermediate between biparental and asexual organisms. Even a limited amount of outcrossing in largely selfing and parthenogenetic organisms markedly affects the accumulation rates. The accumulation of mutations is likely to affect the mean population fitness only in long-term evolution.

scholarly journals Performance and optimization of X-ray grating interferometry

2014 ◽  
Vol 372 (2010) ◽  
pp. 20130027 ◽  
Author(s):  
T. Thuering ◽  
M. Stampanoni
Keyword(s):  
Interference Fringe ◽  
Refraction Angle ◽  
Fringe Visibility ◽  
X Ray ◽  
Analytical Formulae ◽  
Grating Interferometer ◽  
Differential Phase Contrast ◽  
Energy Dependent ◽  
Application Specific ◽  
Contrast Image

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot–Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energy-dependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

Vibration of Nonuniform Beams Under Moving Point Loads: An Approximate Analytical Solution in Time Domain

2017 ◽  
Vol 17 (03) ◽  
pp. 1750035 ◽  
Author(s):  
C. P. Sudheesh Kumar ◽  
C. Sujatha ◽  
K. Shankar
Keyword(s):  
Approximate Analytical Solution ◽  
Time Integration ◽  
Single Mode ◽  
Mode Analysis ◽  
Moving Loads ◽  
The Finite Element Method ◽  
Require Time ◽  
Analytical Formulae ◽  
Clamped Beams ◽  
Forced Responses

The forced-free responses of nonuniform beams under moving point loads are analyzed in this paper. Simple approximate analytical formulae for the forced responses of undamped nonuniform beams, derived using the fundamental mode by the Rayleigh–Ritz (R–R) method, are presented. The responses of both simply supported and clamped–clamped beams are analyzed. The responses are also determined by the finite element method (FEM) in which nonuniform elements are used for fast convergence. It is found that the present method yields results that are very close to those obtained by the FEM. As this method does not require time integration, it is faster and computationally more efficient. Though the single-mode analysis of forced vibration of uniform beams under moving loads has been done by several researchers, its application to nonuniform beams has not been reported.

scholarly journals Temperature Measurement at Curved Surfaces Using 3D Printed Planar Resistance Temperature Detectors

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1100
Author(s):  
Adam Steckiewicz ◽  
Kornelia Konopka ◽  
Agnieszka Choroszucho ◽  
Jacek Maciej Stankiewicz
Keyword(s):  
Temperature Measurement ◽  
Fused Deposition Modeling ◽  
Numerical Models ◽  
Elastic Base ◽  
Measuring Device ◽  
Fused Deposition ◽  
Influence Of Temperature On ◽  
Printed Sensors ◽  
Analytical Formulae ◽  
3D Printed

In this article, novel 3D printed sensors for temperature measurement are presented. A planar structure of the resistive element is made, utilizing paths of a conductive filament embedded in an elastic base. Both electrically conductive and flexible filaments are used simultaneously during the 3D printing procedure, to form a ready–to–use measuring device. Due to the achieved flexibility, the detectors may be used on curved and irregular surfaces, with no concern for their possible damage. The geometry and properties of the proposed resistance detectors are discussed, along with a printing procedure. Numerical models of considered sensors are characterized, and the calculated current distributions as well as equivalent resistances of the different structures are compared. Then, a nonlinear influence of temperature on the resistance is experimentally determined for the exemplary planar sensors. Based on these results, using first–order and hybrid linear–exponential approximations, the analytical formulae are derived. Additionally, the device to measure an average temperature from several measuring surfaces is considered. Since geometry of the sensor can be designed utilizing presented approach and printed by applying fused deposition modeling, the functional device can be customized to individual needs.

Radiation Configuration Factors Between Disks and a Class of Axisymmetric Bodies

1982 ◽  
Vol 104 (3) ◽  
pp. 426-431 ◽  
Author(s):  
M. H. N. Naraghi ◽  
B. T. F. Chung
Keyword(s):  
Numerical Integration ◽  
Analytical Solutions ◽  
Coaxial Cylinder ◽  
Present Approach ◽  
Shape Factors ◽  
Present Technique ◽  
Analytical Formulae ◽  
View Factors ◽  
Axisymmetric Bodies

A general formulation is developed for the radiation shape factors between a disk and a class of coaxial axisymmetric bodies such as cylinder, cone, ellipsoid, and paraboloid. In certain cases, the view factors can be derived analytically directly from the present technique, while in others, they can be generated from a single numerical integration. The analytical solutions for view factors from a disk to a coaxial cylinder based on the present approach are found to agree with those published earlier. The analytical formulae of view factors from disks or annular rings to circular cones, truncated cones, ellipsoid, paraboloids, and truncated praboloid are herein presented.

Prediction of Springback in Straight Flanging Operation

1999 ◽  
Author(s):  
Jian Cao ◽  
Zhihong Liu ◽  
Wing Kam Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Mechanism ◽  
The Finite Element Method ◽  
Moment Distribution ◽  
Analytical Formulae ◽  
Typical Distribution ◽  
Number Of Segments ◽  
Springback Angle ◽  
Energy Element

Abstract A straight flange problem is investigated with the expectation that this will lead to a better understanding of the deformation mechanism and to more complicated flanging problems. The “in-die” shape of the part is subdivided into a number of segments and individual springback of each segment is investigated, by releasing the elastic energy element by element, using the Finite Element Method (FEM). Typical distribution of the springback angle along the blank is obtained and found to be quite different from the widely used constant springback assumption for the curved part of the flange. A new model incorporating a non-uniform moment distribution at the curved part is proposed which reflects the above observation. Explicit analytical formulae are derived and the analytical predictions match with the experimental results very well.

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