scholarly journals On Gravothermal Instability of Anisotropic Self-Gravitating Gas Spheres: Singular Equilibrium Solution

1993 ◽  
Vol 132 ◽  
pp. 241-253
Author(s):  
R. Spurzem
Keyword(s):  
Equilibrium Solution ◽  
Stellar System ◽  
Hydrostatic Equilibrium ◽  
Linear Perturbation ◽  
Total Entropy ◽  
Boltzmann Entropy ◽  
First Order ◽  
Perturbation Functions ◽  
The Common ◽  
Linear Perturbation Theory

AbstractA reinvestigation of the linear perturbation theory is presented, which examines the hydrostatic readjustment of an isolated self-gravitating gas sphere to a redistribution of energy. The here presented model describes a stellar system by the common equations of gas in hydrostatic equilibrium but with the effect of the anisotropic velocity distribution on the pressure gradient. We take as equilibrium models the singular isothermal solution with and without anisotropy. The total variation of the Boltzmann entropy resulting from a perturbation of the system caused by a redistribution of heat (i.e. r.m.s. kinetic energy of the stars) is calculated for anisotropic solutions to first order as well as to second order for the isotropic equilibrium. The extremized eigenfunctions which represent the entropy and anisotropy perturbation functions, are determined analytically. They exhibit gravothermal behaviour in the central region where heat is removed. It is also found that the anisotropy readjusts non-thermally in the sense that the system departs from isotropy although the total entropy increases.

An Experiment on Compressible-Flow Perturbations

1959 ◽  
Vol 26 (1) ◽  
pp. 114-119
Author(s):  
T. A. d’Ews Thomson ◽  
R. E. Meyer
Keyword(s):  
Perturbation Theory ◽  
Order Theory ◽  
Linear Perturbation ◽  
Pressure Gradients ◽  
Local Pressure ◽  
Supersonic Wind Tunnel ◽  
First Order ◽  
First Order Theory ◽  
Mach Number Distribution ◽  
Linear Perturbation Theory

Abstract The effect which a slight tilting of the liners of a supersonic wind-tunnel nozzle has on the Mach-number distribution in the test-rhombus is determined on the basis of the linear-perturbation theory of reference [1]. Experiments are reported which (a) confirm that the first-order subsonic and transonic perturbations of the flow may be neglected compared with the supersonic perturbations, and (b) indicate that appreciable effects not accounted for by the first-order theory occur when the flow possesses high local pressure gradients.

Underlying Common Factors of Adolescent Problem Behaviors

2002 ◽  
Vol 29 (2) ◽  
pp. 161-182 ◽  
Author(s):  
Lening Zhang ◽  
John W. Welte ◽  
William F. Wieczorek
Keyword(s):  
Problem Behaviors ◽  
Latent Variable ◽  
Factor Model ◽  
Common Factor ◽  
Measurement Model ◽  
First Order ◽  
Adolescent Problem Behaviors ◽  
The Common ◽  
Order Factor ◽  
Second Order Factor Analysis

The Buffalo Longitudinal Study of Young Men was used to address the possibility of a common factor underlying adolescent problem behaviors. First, a measurement model with a single first-order factor was compared to a model with three separate correlated first-order factors. The three-factor model was better supported, making it logical to conduct a second-order factor analysis, which confirmed the logic. Second, a substantive model was estimated in each of two waves with psychopathic state as the common factor predicting drinking, drug use, and delinquency. Psychopathic state was stable across waves. The theory that a single latent variable accounts for large covariance among adolescent problem behaviors was supported.

Analytical linear perturbation theory for highly eccentric satellite orbits

1995 ◽  
Vol 61 (4) ◽  
pp. 369-387 ◽  
Author(s):  
Eugene Brumberg ◽  
Victor A. Brumberg ◽  
Thomas Konrad ◽  
Michael Soffel
Keyword(s):  
Perturbation Theory ◽  
Linear Perturbation ◽  
Satellite Orbits ◽  
Linear Perturbation Theory

Stability Features of the Saucer-Shaped Blend-Wing-Body Aircraft

2013 ◽  
Vol 712-715 ◽  
pp. 1307-1311
Author(s):  
Lin Lin Wang ◽  
Ge Gao
Keyword(s):  
Perturbation Theory ◽  
Longitudinal Mode ◽  
Flight Dynamics ◽  
Aerodynamic Characteristics ◽  
Linear Perturbation ◽  
Low Speed ◽  
Similarities And Differences ◽  
Linear Perturbation Theory ◽  
Dutch Roll ◽  
Directional Flight

The saucer-shaped aircraft is a novel aircraft adopting blend-wing-body configuration. The linear perturbation theory based on the classic flight dynamics was used to analyze the longitudinal, lateral and directional flight qualities of the saucer-shaped aircraft under low speed conditions. The flight qualities were given. Meanwhile the aerodynamic characteristics of the saucer-shaped aircraft, the conventional aircraft and the flying wing aircraft were also contrasted to discuss their similarities and differences. The results show that the saucer-shaped aircraft has stable longitudinal mode, rollover mode and Dutch roll mode. The spiral mode is unstable. The saucer-shaped aircraft exhibits superior flight qualities and excellent comprehensive performances.

A Simple Practical Criterion to Guarantee Second Order Smoothness of Blend Surfaces

1989 ◽  
Author(s):  
J. Pegna ◽  
F.-E. Wolter
Keyword(s):  
Second Order ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Common Boundary ◽  
First Order ◽  
Computer Aided ◽  
The Common ◽  
Blend Surfaces ◽  
Continuous Curves ◽  
Order Smoothness

Abstract Computer Aided Geometric Design of surfaces sometimes presents problems that were not envisioned by mathematicians in differential geometry. This paper presents mathematical results that pertain to the design of second order smooth blending surfaces. Second order smoothness normally requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve Theorem proved here shows that, for the blend to be second order smooth when it is already first order smooth, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. This property may be helpful to the designer since linkage curves can be constructed from low order piecewise continuous curves.

Principals and Agents: From the Convention’s Proposal to the Constitutional Treaty

2012 ◽  
Author(s):  
Thomas König ◽  
Daniel Finke
Keyword(s):  
Final Outcome ◽  
The Political ◽  
Principal Agent ◽  
Constitutional Treaty ◽  
Political Leaders ◽  
Voting Rules ◽  
Common View ◽  
Treaty Of Lisbon ◽  
First Order ◽  
The Common

This chapter examines the transformation of the Convention's proposal on the Treaty Establishing a Constitution for Europe to the Lisbon Treaty in the aftermath of the two negative referendums from a principal-agent perspective. It shows that the common view of unitary member states, in which principals and agents share interests in the revision of treaties, can only partially—if not wrongly—explain the Treaty of Lisbon. The principal-agent analysis reveals that the political leaders delegated power to negotiating agents who worked out compromise solutions by partially revising the initial interests of their first order principals, the political leaders. Governmental agents from smaller countries were able to focus the negotiations on a few central reform issues, such as the number of Commissioners and the voting rules of the Council, and they also successfully influenced the final outcome of these issues. A major reason for their success was their credibility, which they could increase by pointing to integration-skeptic voters—particularly in countries that had announced a referendum. Hence, governmental agents increased their bargaining efficiency by referring to voters as their second-order principals.

scholarly journals Contributions to the Local Gravitational Field from beyond the Local Supercluster

1987 ◽  
Vol 117 ◽  
pp. 435-443
Author(s):  
A. Yahil
Keyword(s):  
Gravitational Field ◽  
Background Radiation ◽  
Nonlinear Effects ◽  
Linear Perturbation ◽  
Density Parameter ◽  
Microwave Background ◽  
Dipole Component ◽  
Local Supercluster ◽  
Microwave Background Radiation ◽  
Linear Perturbation Theory

IRAS 60μ sources are used to map the local (≲200h−1 Mpc, Ho =100h km s−1 Mpc−1) gravitational field, and to determine its dipole component, on the assumption that the infrared radiation traces the matter. The dipole moment is found to point in the direction of the anisotropy of the microwave background radiation. Comparison of the two anisotropies, using linear perturbation theory, yields an estimate of the cosmological density parameter, Ω =0.85±0.16, with nonlinear effects increasing Ωo by ∼15%. The quadrupolar tidal field within the Local Supercluster, due presumably to the same density inhomogeneities, is detected in a kinematical study of the velocity field.

scholarly journals Spiral-arm instability – III. Fragmentation of primordial protostellar discs

2019 ◽  
Vol 491 (1) ◽  
pp. L24-L28 ◽  
Author(s):  
Shigeki Inoue ◽  
Naoki Yoshida
Keyword(s):  
Gravitational Instability ◽  
Finite Thickness ◽  
Linear Perturbation ◽  
Gas Cooling ◽  
Formation And Evolution ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Protostellar Discs ◽  
Self Gravity ◽  
Spiral Arm

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

Der Einfluß des Entladungsgefäßes auf die Bestimmung der Plasmaelektronendichte mit Hohlraumresonatoren / The Influence of the Discharge Tube on the Determination of the Plasma Electron Density by Means of Cavity Resonators

1972 ◽  
Vol 27 (3) ◽  
pp. 491-499 ◽  
Author(s):  
G Janzen
Keyword(s):  
Electron Density ◽  
Discharge Tube ◽  
Plasma Electron ◽  
Microwave Cavity ◽  
Linear Perturbation ◽  
Density Profiles ◽  
Cavity Resonators ◽  
Resonance Modes ◽  
Linear Perturbation Theory ◽  
Electron Density Profiles

AbstractThe eigenvalue equation of a plasma-discharge tube configuration in a cylindrical microwave cavity is derived and solved numerically by an exact theory for TMlm0 , TM0mn, and TE0mn resonance modes. The radial and axial electron density profiles are assumed to be homogeneous. The factors of proportionality between electron density and shift of the resonance frequency derived from the linear perturbation theory are compared with the exactly computed eigenvalues. Hence the range of validity of the linearly computed factors of proportionality (geometry factors) can be established. By considering the influence of the discharge tube the geometry factors are altered and consequently the sensitivity of the measurement. The influence of the discharge tube can be taken into account by means of suitable correction factors.

scholarly journals Re-examination of Large Scale Structure & Cosmic Flows

2014 ◽  
Vol 11 (S308) ◽  
pp. 310-317
Author(s):  
Marc Davis ◽  
Adi Nusser
Keyword(s):  
Perturbation Theory ◽  
Velocity Field ◽  
Gravity Field ◽  
Inverse Method ◽  
Large Scale ◽  
Linear Perturbation ◽  
Data Set ◽  
Galaxy Distribution ◽  
Standard Values ◽  
Linear Perturbation Theory

AbstractComparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

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