عنوان

Physics of Gravitating Systems II Nonlinear Collective Processes:

(Number (ISBN

3642878334

(Number (ISBN

9783642878336

Number

b574899

Title Proper

Physics of Gravitating Systems II Nonlinear Collective Processes:

General Material Designation

[Book]

Other Title Information

Nonlinear Waves, Solitons, Collisionless Shocks, Turbulence. Astrophysical Applications.

First Statement of Responsibility

Fridman, A. M.

Place of Publication, Distribution, etc.

Springer Verlag

Date of Publication, Distribution, etc.

2013

Text of Note

(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- 4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a "Black Hole" at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- 5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- 1. Oort's Antievolutionary Hypothesis.- 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- 4. Lynden-Bell's Collisionless Relaxation.- 5. Estimates of "Collisionlessness" of Particles in Different Real Systems.- IX Spherical Systems.- 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- 2. Classification of Unstable Modes in Scales.- 3. Universal Criterion of the Instability.- 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System's Evolution.- 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- 6. Example of Strongly Unstable Model.- 7. Can Lynden-Bell's Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- 8. Is the "Unstable" Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a "Black Hole"?.- X Ellipsoidal Systems.- 1. Objects Under Study.- 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- 3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- 1. Different Points of View on the Nature of Spiral Structure.- 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The Spiral Galaxy as an Infinite System of Harmonic Oscillators.- 3.3. On "Two-Armness" of the Spiral Structure.- 3.4. The Main Difficulties of the Stationary Wave Theory of Lin and Shu.- 4. Linear Theory of Growing Density Waves.- 4.1. Spiral Structure as the Most Unstable Mode.- 4.2. Gravitational Instability at the Periphery of Galaxies.- 4.3. Waves of Negative Energy Generated Near the Corotation Circle and Absorbed at the Inner Lindblad Resonance-Lynden-BellKalnaj's Picture of Spiral Pattern Maintenance.- 4.4. Kelvin-Helmholz Instability and Flute-like Instability in the Near-Nucleus Region of the Galaxy as Possible Generators of Spiral Structure.- 4.5. The "Trailing" Character of Spiral Arms.- 5. Comparison of the Lin-Shu Theory with Observations.- 5. 1 The Galaxy.- 5.2. M33, M51, M81.- 6. Experimental Simulation of Spiral Structure Generation.- 6. 1 In a Rotating Laboratory Plasma.- 6.2. In Numerical Experiment.- 7. The Hypothesis of the Origin of Spirals in the SB-Galaxies.- XII Other Applications.- 1 On the Structure of Saturn's Rings.- l.1. Introduction.- 1.2. Model. Basic Equations.- 1.3. Jeans Instability.- 1.4. Dissipative Instabilities.- 1.5. Modulational Instability.- Appendix. Derivation of the Expression for the Perturbation Energy of Maclaurin's Ellipsoid.- 2. On the Law of Planetary Distances.- 3. Galactic Plane Bending.- 3.1. Quasistationary Tidal Deformation.- 3.2. Free Modes of Oscillations.- 3.3. Close Passage.- 4. Instabilities in Collisions of Elementary Particles.- 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. "Lagrange" Derivation of the Matrix Equation.- 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- 11. Derivation of the Kinetic Equation for Waves.- 12.

Text of Note

Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.

Class number

Book number

Fridman, A. M.

Aries, A. B.

Fridman, A. M.

Poliakoff, I. N.

Polyachenko, V. L.

Electronic name

[Book]

Y