scholarly journals Instabilities of Uniformly Rotating Disks

1996 ◽  
Vol 169 ◽  
pp. 349-350 ◽  
Author(s):  
P. Vauterin ◽  
H. Dejonghe
Keyword(s):  
Distribution Function ◽  
Differential Rotation ◽  
Mass Concentration ◽  
Expansion Method ◽  
Rotating Disks ◽  
Central Mass ◽  
Reasonable Approximation ◽  
Central Regions ◽  
Series Expansion Method

We explore a series expansion method to calculate the instabilities and the structure of the perturbations for a variety of uniformly rotating finite stellar disks. This survey focuses on the role of the distribution function in stability analyses. Although the potential does not show differential rotation, it will in many cases be a reasonable approximation for the disk in the central regions of galaxies without massive central mass concentration.

scholarly journals 9.14. A simple mass estimate for central black holes in cuspy galaxies

1998 ◽  
Vol 184 ◽  
pp. 409-410
Author(s):  
S. de Rijcke ◽  
V. de Bruyne ◽  
H. Dejonghe ◽  
A. Mathieu
Keyword(s):  
Mass Concentration ◽  
Velocity Dispersion ◽  
Minor Axis ◽  
Minimum Mass ◽  
Central Mass ◽  
Central Regions ◽  
Monotonically Decreasing Function ◽  
Mass Estimate ◽  
Current Mass ◽  
Simple Mass

We argue that the velocity dispersion of the stars is likely a monotonically decreasing function of radius along the minor axis in the central regions of cuspy galaxies. We show that then a central mass concentration (a black hole) must be present and calculate its minimum mass, M⊙. This lower bound is relevant and entirely consistent with current mass estimates.

The iterative series-expansion method for quantitative texture analysis. II. Applications

1992 ◽  
Vol 25 (2) ◽  
pp. 259-267 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Distribution Function ◽  
Series Expansion ◽  
Expansion Method ◽  
Orientation Distribution ◽  
Polycrystalline Materials ◽  
Pole Density ◽  
General Outline ◽  
Positivity Condition ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) of the crystallites of polycrystalline materials can be calculated from experimentally measured pole density functions (pole figures). This procedure, called pole-figure inversion, can be achieved by the series-expansion method (harmonic method). As a consequence of the (hkl)-({\bar h}{\bar k}{\bar l}) superposition, the solution is mathematically not unique. There is a range of possible solutions (the kernel) that is only limited by the positivity condition of the distribution function. The complete distribution function f(g) can be split into two parts, \tilde {f}(g) and \tildes {f}(q), expressed by even- and odd-order terms of the series expansions. For the calculation of the even part \tilde {f}(g), the positivity condition for all pole figures contributes essentially to an `economic' calculation of this part, whereas, for the odd part, the positivity condition of the ODF is the essential basis. Both of these positivity conditions can be easily incorporated in the series-expansion method by using several iterative cycles. This method proves to be particularly versatile since it makes use of the orthogonality and positivity at the same time. In the previous paper in this series [Dahms & Bunge (1989) J. Appl. Cryst. 22, 439–447] a general outline of the method was given. This, the second part, gives details of the system of programs used as well as typical examples showing the versatility of the method.

scholarly journals The mass of the Milky Way out to 100 kpc using halo stars

2020 ◽  
Author(s):  
Alis J Deason ◽  
Denis Erkal ◽  
Vasily Belokurov ◽  
Azadeh Fattahi ◽  
Facundo A Gómez ◽  
...  
Keyword(s):  
Distribution Function ◽  
Mass Concentration ◽  
Milky Way ◽  
Function Analysis ◽  
Large Magellanic Cloud ◽  
Systematic Bias ◽  
Cosmological Simulations ◽  
Halo Stars ◽  
Systematic Effects ◽  
Mass Estimate

Abstract We use a distribution function analysis to estimate the mass of the Milky Way out to 100 kpc using a large sample of halo stars. These stars are compiled from the literature, and the vast majority ($\sim \! 98\%$) have 6D phase-space information. We pay particular attention to systematic effects, such as the dynamical influence of the Large Magellanic Cloud (LMC), and the effect of unrelaxed substructure. The LMC biases the (pre-LMC infall) halo mass estimates towards higher values, while realistic stellar halos from cosmological simulations tend to underestimate the true halo mass. After applying our method to the Milky Way data we find a mass within 100 kpc of M( < 100kpc) = 6.07 ± 0.29(stat.) ± 1.21(sys.) × 1011M⊙. For this estimate, we have approximately corrected for the reflex motion induced by the LMC using the Erkal et al. model, which assumes a rigid potential for the LMC and MW. Furthermore, stars that likely belong to the Sagittarius stream are removed, and we include a 5% systematic bias, and a 20% systematic uncertainty based on our tests with cosmological simulations. Assuming the mass-concentration relation for Navarro-Frenk-White haloes, our mass estimate favours a total (pre-LMC infall) Milky Way mass of M200c = 1.01 ± 0.24 × 1012M⊙, or (post-LMC infall) mass of M200c = 1.16 ± 0.24 × 1012 M⊙ when a 1.5 × 1011M⊙ mass of a rigid LMC is included.

HOLE–SPIN COUPLING AND SPIN DISTORTION IN HIGH Tc SUPERCONDUCTORS

1995 ◽  
Vol 09 (24) ◽  
pp. 1589-1594
Author(s):  
M. TIWARI ◽  
R. A. SINGH
Keyword(s):  
Correlation Function ◽  
Green Function ◽  
Low Temperature ◽  
Function Theory ◽  
Expansion Method ◽  
Temperature Series ◽  
Spin Coupling ◽  
High Tc Superconductors ◽  
High Tc ◽  
Series Expansion Method

The effect of hole–spin coupling together with spin distortion on the energy and hole correlation function have been studied in detail. Standard Green function theory and Low Temperature Series Expansion method have been utilised to get analytical results.

scholarly journals Approximation of the Orientation Distribution of Grains in Polycrystalline Samples by Means of Gaussians

1992 ◽  
Vol 19 (1-2) ◽  
pp. 9-27 ◽  
Author(s):  
D. I. Nikolayev ◽  
T. I. Savyolova ◽  
K. Feldmann
Keyword(s):  
Rolling Texture ◽  
Expansion Method ◽  
Operating Mode ◽  
Orientation Distribution ◽  
New Method ◽  
Gaussian Distributions ◽  
Positivity Condition ◽  
The Central Limit Theorem ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) obtained by classical spherical harmonics analysis may be falsified by ghost influences as well as series truncation effects. The ghosts are a consequence of the inversion symmetry of experimental pole figures which leads to the loss of information on the “odd” part of ODF.In the present paper a new method for ODF reproduction is proposed. It is based on the superposition of Gaussian distributions satisfying the central limit theorem in the SO(3)-space as well as the ODF positivity condition. The kind of ODF determination offered here is restricted to the fit of Gaussian parameters and weights with respect to the experimental pole figures. The operating mode of the new method is demonstrated for a rolling texture of copper. The results are compared with the corresponding ones obtained by the series expansion method.

scholarly journals Introduction of the Phone-Concept Into Pole Figure Inversion Using the Iterative Series Expansion Method

1992 ◽  
Vol 19 (3) ◽  
pp. 169-174 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Series Expansion ◽  
Expansion Method ◽  
Probabilistic Methods ◽  
Series Expansion Method

The phone-concept as it is used in the various kinds of probabilistic methods can easily be applied to the iterative series expansion method for quantitative texture analysis. Only slight modifications of the existing routines are necessary. The advantages of this concept are demonstrated by a mathematical and an experimental example.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

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