scholarly journals Two-integral distribution functions for axisymmetric galaxies

1993 ◽  
pp. 357-358
Author(s):  
C. Hunter ◽  
E. Qian
Keyword(s):  
Distribution Functions ◽  
Integral Distribution

scholarly journals Anisotropic Distribution Functions for the Elliptical Galaxy NGC 1600

1996 ◽  
Vol 171 ◽  
pp. 413-413
Author(s):  
Michael Matthias ◽  
Ortwin Gerhard
Keyword(s):  
Perturbation Theory ◽  
Elliptical Galaxy ◽  
Major Axis ◽  
Distribution Functions ◽  
Minor Axis ◽  
Dynamical Models ◽  
Ccd Photometry ◽  
Radial Anisotropy ◽  
Best Fitting ◽  
Integral Distribution

Three-integral (3I) dynamical models for NGC 1600 were constructed as follows: (i) Lucy-inversion of CCD photometry and gravitational potential as in Binney, Davies, Illingworth (ApJ 361, 78, 1990), assuming axisymmetry. (ii) Third integral by perturbation theory as in Gerhard & Saha (MN 261, 311, 1991). (iii) Two- and three-integral distribution functions as in Dehnen & Gerhard (MN 261, 311, 1993), assuming various anisotropy patterns. The kinematic results from these models are presented in Fig. 1. The best-fitting 3I model (solid line, right panels) has outward-increasing radial anisotropy on the major axis and is nearly isotropic on the minor axis. The M/L of the various 3I-models varies only slightly around M/L=6.2.

scholarly journals On the Dynamics of very Flattened Ellipticals

1996 ◽  
Vol 171 ◽  
pp. 360-360 ◽  
Author(s):  
H. Dejonghe ◽  
V. de Bruyne ◽  
P. Vauterin ◽  
W.W. Zeilinger
Keyword(s):  
Data Analysis ◽  
Phase Space ◽  
Space Structure ◽  
Distribution Functions ◽  
Kinematic Data ◽  
Dust Lane ◽  
Phase Space Structure ◽  
Nuclear Dust ◽  
Integral Distribution

Our aim is to study the generic phase-space structure of flattened ellipticals by investigating a few typical cases. Here we report on the E4 elliptical NGC 4697.The construction of 2-integral and 3-integral distribution functions asks for photometry and kinematic data. In the course of the data analysis, we additionally detected a nuclear dust lane at 3.4″ or 0.4 kpc from the centre, which could be confirmed with HST data. This was put to good use to constrain the inclination.

scholarly journals Two-integral distribution functions for axisymmetric galaxies

1993 ◽  
Vol 153 ◽  
pp. 357-358
Author(s):  
C. Hunter ◽  
E. Qian
Keyword(s):  
Distribution Function ◽  
Angular Momentum ◽  
Stellar System ◽  
Distribution Functions ◽  
New Method ◽  
Integral Distribution ◽  
Axis Of Symmetry

We present a new method for finding a distribution function f, which depends only on the two classical integrals of energy E and angular momentum J about the axis of symmetry, for a stellar system with a known axisymmetric potential and density.

Sedimentation Analysis of Styrene Butadiene Copolymer Rubber

1966 ◽  
Vol 39 (3) ◽  
pp. 622-630
Author(s):  
Terutake Homma ◽  
Hiroshi Fujita
Keyword(s):  
Molecular Weight ◽  
Distribution Function ◽  
Mass Distribution ◽  
Sedimentation Coefficient ◽  
Distribution Functions ◽  
Sedimentation Analysis ◽  
Molecular Weights ◽  
Integral Distribution ◽  
Styrene Butadiene ◽  
Theta Solvent

Abstract Methods are presented by which the limiting viscosity number [η]Θ and the limiting sedimentation coefficient s0 of a monodisperse linear polymer in its theta solvent as functions of the molecular weight M may be deduced from data taken with a series of polydisperse samples of the polymer. The necessary data are the limiting viscosity numbers and the distribution functions of s0 of the chosen samples in the theta solvent, plus their number-average molecular weights. The methods are applied to unfractionated and fractionated samples of a styrene-butadiene co-polymer rubber (SBR) having 24 weight per cent bound styrene in a theta solvent, 2-pentanone, at 21.0° C. The following relations are deduced for monodisperse unbranched SBR in this theta solvent: [η]Θ=1.73×10−3M21 and s0=0.83×10−15M21, where [η]Θ is expressed in deciliters/gram and s0 in seconds. Besides these, the viscosity—molecular weight relations for this cold rubber in toluene and in cyclohexane, both at 30° C, are established. The new relation for the toluene system does not accord with the French-Ewart relation for “hot” rubber in the same solvent. The integral distribution of molecular weight in an unfractionated SBR is calculated from its distribution function of s0 in 2-pentanone at 21.0° C by using the derived s0 versus M relationship, and is found to coincide well with the mass distribution obtained from fractionation data if the new viscosity—molecular weight relation is used for the molecular weight of each fraction.

scholarly journals The Determination of Affinity Distributions: A Numerical Algorithm and its Application for Estimating the Energetic Heterogeneity of Complexing Silicas and Humic Substances

2000 ◽  
Vol 18 (3) ◽  
pp. 267-294 ◽  
Author(s):  
Yu. Kholin ◽  
S. Myerniy ◽  
G. Varshal
Keyword(s):  
Electrostatic Interactions ◽  
Distribution Functions ◽  
Differential Distribution ◽  
Chemically Modified ◽  
Energetic Heterogeneity ◽  
Ill Posed ◽  
Integral Distribution ◽  
Methodological Difficulties

The characterization of energetic heterogeneity has been discussed in the investigation of ion-binding and chemisorption processes. Both the calculation and the interpretation of the distribution of affinity constants are ambiguous. Methodological difficulties arise connected to the fact that electrostatic effects are difficult to separate from energetic heterogeneity because of the chemical biography of a given material. Only a close similarity between the distribution functions calculated for different ionic strengths allows the electrostatic interactions to be neglected. The numerical estimation of the distribution functions is complicated by the ill-posed nature of the problem. Some computational methods are briefly compared and methods for providing robust and unbiased estimations outlined. In contrast to differential distribution functions, the computation of integral ones may be transformed into the conventionally correct problem. On this basis, a fast and robust method for calculating integral distribution functions is proposed. In addition, this ensures numerically stable estimations of differential distribution functions. The method has been applied to a study of the energetic heterogeneity of 20 silicas chemically modified with aliphatic amines. When H+ ions are chemisorbed, the energetic heterogeneity observed is dependent on the surface topography and its hydration state. In addition, the binding properties of ashless fulvic and humic acids relative to H+, Hg2+ and Pb2+ ions have been examined. The existence of functional groups with different acidities and complexing abilities has been established.

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