Atnaujinkite slapukų nuostatas

El. knyga: Relativistic Hydrodynamics [Oxford Scholarship Online E-books]

(Institute for Theoretical Physics, Frankfurt am Main), (Research Associate, University of Trento)
  • Formatas: 752 pages, 128 colour illustrations
  • Išleidimo metai: 26-Sep-2013
  • Leidėjas: Oxford University Press
  • ISBN-13: 9780198528906
Kitos knygos pagal šią temą:
  • Oxford Scholarship Online E-books
  • Kaina nežinoma
Relativistic HydrodynamicsDidesnis paveikslėlis
  • Formatas: 752 pages, 128 colour illustrations
  • Išleidimo metai: 26-Sep-2013
  • Leidėjas: Oxford University Press
  • ISBN-13: 9780198528906
Kitos knygos pagal šią temą:
Wiley OnlineMore info about Oxford Scholarship Online e-books
Partnerių interneto svetainė: http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198528906.001.0001/acprof-9780198528906
This book provides an up-to-date, lively and approachable introduction to the mathematical formalism, numerical techniques and applications of relativistic hydrodynamics. The topic is presented here in a form which will be appreciated both by students and researchers in the field.

Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field.

The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions).

It is often said that fluids are either seen as solutions of partial differential equations or as "wet". Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.
PART I THE PHYSICS OF RELATIVISTIC HYDRODYNAMICS
1 A Brief Review of General Relativity
3(65)
1.1 Why this chapter?
3(1)
1.2 The concept of spacetime
4(1)
1.3 Spacetime as a manifold
5(19)
1.3.1 Coordinates
6(3)
1.3.2 Curves and paths
9(1)
1.3.3 Tangent vectors
9(3)
1.3.4 Gradients of a function
12(1)
1.3.5 A geometrical view of vectors and covectors
13(2)
1.3.6 Tensors
15(2)
1.3.7 Tensor algebra
17(3)
1.3.8 The most important tensor: the metric
20(3)
1.3.9 Splitting a tensor through a vector
23(1)
1.4 Flat spacetime: special relativity
24(5)
1.5 Curved spacetimes: general relativity
29(17)
1.5.1 Lie derivative
31(3)
1.5.2 Covariant derivative and Christoffel symbols
34(3)
1.5.3 Symmetries and Killing vector fields
37(1)
1.5.4 Geodesic equation
38(3)
1.5.5 The Riemann tensor
41(5)
1.6 Einstein equations
46(2)
1.7 Spacetimes of astrophysical relevance
48(13)
1.7.1 Non-rotating black holes: the Schwarzschild solution
49(5)
1.7.2 Rotating black holes: the Kerr solution
54(5)
1.7.3 The Friedmann--Robertson--Walker metric
59(2)
1.8 Gravitational radiation
61(5)
1.9 Further reading
66(1)
1.10 Problems
67(1)
2 A Kinetic-Theory Description of Fluids
68(65)
2.1 On the fluid approximation
68(2)
2.2 Newtonian kinetic theory
70(19)
2.2.1 The Boltzmann equation
70(5)
2.2.2 The H-theorem
75(3)
2.2.3 The moment equations
78(3)
2.2.4 The Maxwell--Boltzmann equilibrium distribution
81(3)
2.2.5 The zero-order approximation: perfect fluids
84(3)
2.2.6 The first-order approximation: non-perfect fluids
87(2)
2.3 Relativistic kinetic theory
89(14)
2.3.1 The relativistic Boltzmann equation
90(1)
2.3.2 Relativistic transport fluxes
91(2)
2.3.3 The relativistic H-theorem
93(2)
2.3.4 The relativistic moment equations
95(1)
2.3.5 The general-relativistic hydrodynamic equations
96(1)
2.3.6 Relativistic equilibrium distributions
97(4)
2.3.7 The laws of thermodynamics
101(2)
2.4 Equations of state
103(28)
2.4.1 Degenerate relativistic fluid
109(1)
2.4.2 Non-degenerate relativistic fluid
110(1)
2.4.3 Non-degenerate non-relativistic fluid
111(1)
2.4.4 Ultrarelativistic fluid
112(2)
2.4.5 Degenerate Fermi fluid
114(1)
2.4.6 Ideal fluid
115(3)
2.4.7 Polytropic fluid
118(5)
2.4.8 Radiation fluid
123(3)
2.4.9 Dark-energy fluid
126(2)
2.4.10 Newtonian and relativistic barotropic fluids
128(3)
2.5 Further reading
131(1)
2.6 Problems
132(1)
3 Relativistic Perfect Fluids
133(57)
3.1 Kinematic properties of fluids
133(5)
3.1.1 Kinematic shear, expansion and vorticity
133(4)
3.1.2 Evolution laws of the kinematic quantities
137(1)
3.2 Mass current and energy--momentum of perfect fluids
138(5)
3.3 Hydrodynamics equations of perfect fluids
143(2)
3.4 Perfect fluids and symmetries
145(2)
3.5 The Newtonian limit of the hydrodynamic equations
147(3)
3.6 Stationary flows
150(2)
3.6.1 Bernoulli's theorem
150(2)
3.6.2 Relativistic Bernoulli theorem
152(1)
3.7 Irrotational flows
152(10)
3.7.1 Newtonian irrotational flows
152(2)
3.7.2 Kelvin--Helmholtz theorem
154(1)
3.7.3 Relativistic vorticity
155(2)
3.7.4 Relativistic irrotational flows
157(2)
3.7.5 Relativistic Kelvin--Helmholtz theorem
159(3)
3.8 Isentropic flows
162(2)
3.9 A velocity-potential approach to relativistic hydrodynamics
164(4)
3.10 A variational principle for relativistic hydrodynamics
168(7)
3.11 Perfect multifluids
175(12)
3.11.1 Coupled multifluids
175(4)
3.11.2 Interacting multifluids
179(8)
3.12 Further reading
187(1)
3.13 Problems
188(2)
4 Linear and Nonlinear Hydrodynamic Waves
190(68)
4.1 Hyperbolic systems of partial differential equations
190(8)
4.1.1 Quasi-linear formulation
190(5)
4.1.2 Conservative formulation
195(3)
4.2 Linear and nonlinear behaviour
198(10)
4.2.1 Characteristic equations for linear systems
198(2)
4.2.2 Riemann invariants
200(3)
4.2.3 Characteristic curves and caustics
203(3)
4.2.4 Domain of determinacy and region of influence
206(2)
4.3 Linear hydrodynamic waves
208(1)
4.3.1 Sound waves
208(1)
4.4 Nonlinear hydrodynamic waves
209(14)
4.4.1 Simple waves and discontinuous waves
209(2)
4.4.2 Rarefaction waves
211(3)
4.4.3 Shock waves
214(8)
4.4.4 Contact discontinuities
222(1)
4.5 The Riemann problem
223(4)
4.6 Solution of the one-dimensional Riemann problem
227(6)
4.6.1 Limiting relative velocities
228(5)
4.7 Solution of the multidimensional Riemann problem
233(12)
4.7.1 Jumps across a shock wave
235(1)
4.7.2 Jumps across a rarefaction wave
236(1)
4.7.3 Limiting relative velocities
237(2)
4.7.4 Relativistic effects in multidimensional Riemann problems
239(4)
4.7.5 Shock-detection techniques
243(2)
4.8 Stability of shock waves
245(4)
4.9 General-relativistic discontinuities
249(6)
4.10 Further reading
255(1)
4.11 Problems
256(2)
5 Reaction Fronts: Detonations and Deflagrations
258(27)
5.1 Basic properties of reaction fronts
258(1)
5.2 Reaction adiabat
259(3)
5.3 Relativistic detonations
262(4)
5.4 Relativistic deflagrations
266(2)
5.5 Stability of reaction fronts
268(15)
5.5.1 Stability of detonations
271(10)
5.5.2 Stability of deflagrations
281(2)
5.6 Further reading
283(1)
5.7 Problems
284(1)
6 Relativistic Non-Perfect Fluids
285(34)
6.1 On the four-velocity of a non-perfect fluid
285(2)
6.2 The energy--momentum tensor of non-perfect fluids
287(3)
6.3 Hydrodynamic equations of non-perfect fluids
290(1)
6.3.1 The general form of the momentum and energy equations
290(1)
6.3.2 The equilibrium state
291(1)
6.4 Classical Irreversible Thermodynamics (first-order theories)
291(5)
6.4.1 The constitutive equations
292(2)
6.4.2 The Newtonian limit: Navier--Stokes and heat conduction
294(2)
6.5 The importance of a causal theory
296(3)
6.5.1 Parabolic versus hyperbolic
296(2)
6.5.2 Non-causality of Classical Irreversible Thermodynamics
298(1)
6.6 Extended Irreversible Thermodynamics (second-order theories)
299(13)
6.6.1 The Israel--Stewart formulation
300(3)
6.6.2 Characteristic speeds of the Israel--Stewart formulation
303(3)
6.6.3 Divergence-type theories
306(6)
6.7 Concluding remarks
312(2)
6.8 Further reading
314(1)
6.9 Problems
315(4)
PART II NUMERICAL RELATIVISTIC HYDRODYNAMICS
7 Formulations of the Einstein--Euler Equations
319(67)
7.1 The 3+1 decomposition of spacetime
319(5)
7.2 Formulations of the Einstein equations
324(36)
7.2.1 Spherically symmetric Lagrangian formulations
325(4)
7.2.2 The ADM formulation
329(6)
7.2.3 Conformal traceless formulations
335(8)
7.2.4 Gauge conditions in 3+1 formulations
343(3)
7.2.5 The generalised harmonic formulation
346(4)
7.2.6 Constraint equations, initial data and constrained evolution
350(10)
7.3 Formulations of the hydrodynamic equations
360(23)
7.3.1 The Wilson formulation
360(2)
7.3.2 The importance of conservative formulations
362(2)
7.3.3 The 3+1 "Valencia" formulation
364(10)
7.3.4 The covariant formulation
374(1)
7.3.5 The light-cone formulation
375(2)
7.3.6 The discontinuous Galerkin formulation
377(6)
7.4 Further reading
383(1)
7.5 Problems
384(2)
8 Numerical Relativistic Hydrodynamics: Finite-Difference Methods
386(28)
8.1 The discretisation process
387(3)
8.2 Numerical errors
390(6)
8.2.1 Consistency, convergence and stability
394(2)
8.3 Finite-difference methods
396(13)
8.3.1 Analysis of the numerical stability
396(3)
8.3.2 The upwind scheme
399(2)
8.3.3 The FTCS scheme
401(1)
8.3.4 The Lax--Friedrichs scheme
402(2)
8.3.5 The leapfrog scheme
404(1)
8.3.6 The Lax--Wendroff scheme
405(2)
8.3.7 Kreiss--Oliger dissipation
407(2)
8.4 Artificial-viscosity approaches
409(3)
8.5 Further reading
412(1)
8.6 Problems
413(1)
9 Numerical Relativistic Hydrodynamics: HRSC Methods
414(45)
9.1 Conservative schemes
414(6)
9.1.1 Rankine--Hugoniot conditions
414(2)
9.1.2 Finite-volume conservative numerical schemes
416(2)
9.1.3 Finite-difference conservative numerical schemes
418(2)
9.2 Upwind methods
420(7)
9.2.1 Monotone methods
420(1)
9.2.2 Total variation diminishing methods
421(2)
9.2.3 Godunov methods
423(4)
9.3 Reconstruction techniques
427(9)
9.3.1 Slope-limiter methods
428(2)
9.3.2 The piecewise-parabolic method
430(4)
9.3.3 Reconstruction in characteristic variables
434(2)
9.4 Approximate Riemann solvers
436(11)
9.4.1 Incomplete Riemann solvers
436(3)
9.4.2 Complete Riemann solvers
439(8)
9.5 The method of lines
447(5)
9.5.1 Explicit Runge--Kutta methods
448(1)
9.5.2 Implicit-explicit Runge--Kutta methods
449(3)
9.6 Central numerical schemes
452(5)
9.6.1 Staggered central schemes
453(2)
9.6.2 Non-staggered central schemes
455(2)
9.7 Further reading
457(1)
9.8 Problems
458(1)
10 Numerical Relativistic Hydrodynamics: High-Order Methods
459(34)
10.1 Why high-order numerical methods?
459(1)
10.2 ENO and WENO methods for hyperbolic conservation laws
460(12)
10.2.1 Finite-volume ENO schemes
461(5)
10.2.2 Finite-volume WENO schemes
466(2)
10.2.3 Finite-difference ENO schemes
468(4)
10.2.4 Finite-difference WENO schemes
472(1)
10.3 Discontinuous Galerkin methods
472(7)
10.3.1 The essence of DG methods
472(3)
10.3.2 An example: a RKDG scheme in spherical symmetry
475(4)
10.4 The ADER approach
479(6)
10.4.1 The original formulation
479(3)
10.4.2 The local spacetime DG scheme
482(3)
10.5 Extension to multidimensional problems
485(4)
10.5.1 Finite-difference multidimensional schemes
486(1)
10.5.2 Finite-volume multidimensional schemes
487(2)
10.6 Further reading
489(1)
10.7 Problems
490(3)
PART III APPLICATIONS OF RELATIVISTIC HYDRODYNAMICS
11 Relativistic Hydrodynamics of Non-Selfgravitating Fluids
493(100)
11.1 Similar and self-similar flows
494(13)
11.1.1 One-dimensional self-similar flows
495(6)
11.1.2 Self-similar hydrodynamics of a bubble
501(3)
11.1.3 Self-similar hydrodynamics of a drop
504(3)
11.2 Relativistic blast waves
507(6)
11.3 Spherical flows onto and out of a compact object
513(3)
11.4 Spherical accretion onto a black hole
516(8)
11.5 Non-spherical accretion onto a moving black hole
524(13)
11.5.1 Accreting potential flows
525(4)
11.5.2 Bondi--Hoyle--Lyttleton flows
529(8)
11.6 Fluids in circular motion around a black hole
537(4)
11.6.1 Von Zeipel cylinders
537(4)
11.7 Geometrically thick tori
541(12)
11.7.1 The "runaway" instability
548(1)
11.7.2 On the sound speed in polytropic tori
549(2)
11.7.3 Thick tori in Schwarzschild--de Sitter spacetimes
551(2)
11.8 Relativistic accreting discs
553(12)
11.8.1 Rest-mass conservation
558(1)
11.8.2 Radial momentum conservation
559(1)
11.8.3 Angular momentum conservation
560(2)
11.8.4 Hydrostatic vertical equilibrium
562(1)
11.8.5 Energy conservation
563(2)
11.9 Relativistic jets
565(15)
11.9.1 Apparently superluminal jets
566(3)
11.9.2 Hydrodynamic acceleration mechanisms
569(8)
11.9.3 Numerical modelling of relativistic jets
577(3)
11.10 Relativistic heavy-ion collisions
580(9)
11.10.1 Basic concepts
580(4)
11.10.2 One-dimensional Bjorken flow
584(1)
11.10.3 Cylindrically symmetric flows
585(4)
11.11 Further reading
589(1)
11.12 Problems
590(3)
12 Relativistic Hydrodynamics of Selfgravitating Fluids
593(66)
12.1 Spherical stars
593(6)
12.2 Gravastars
599(5)
12.3 Rotating stars
604(8)
12.3.1 Uniformly rotating stars
604(4)
12.3.2 Differentially rotating stars
608(4)
12.4 Collapse of a compact star to a black hole
612(11)
12.4.1 Dust collapse: the Oppenheimer--Snyder solution
612(5)
12.4.2 Fluid collapse
617(6)
12.5 Dynamics of binary neutron stars
623(24)
12.5.1 Broadbrush picture
623(4)
12.5.2 Dynamics of equal-mass binaries
627(10)
12.5.3 Dynamics of unequal-mass binaries
637(10)
12.6 Dynamics of black-hole--neutron-star binaries
647(10)
12.6.1 Broadbrush picture
648(9)
12.7 Further reading
657(1)
12.8 Problems
658(1)
Appendix A Geometrised System of Units
659(2)
Appendix B Notable Thermodynamic Expressions
661(4)
B.1 Thermodynamic quantities and potentials
661(2)
B.2 Maxwell relations
663(2)
Appendix C Notable Tensors
665(3)
C.1 Relativistic expressions
665(2)
C.2 Newtonian expressions
667(1)
Appendix D Common Practices in Numerical Relativistic Hydrodynamics
668(10)
D.1 Conversion from conserved to primitive variables
668(5)
D.1.1 Analytic equations of state
668(3)
D.1.2 Tabulated equations of state
671(2)
D.2 Treatment of atmospheres
673(1)
D.3 Guaranteeing the positivity of pressure
674(1)
D.4 Domain excision
675(3)
Appendix E Numerical Building Blocks
678(4)
E.1 TVD slope limiters
678(1)
E.2 Basic Riemann solvers
679(1)
E.3 Reference one-dimensional pseudo-code
680(2)
References 682(39)
Index 721
Luciano Rezzolla received his PhD in Astrophysics in 1997 at International School for Advanced Studies (SISSA) in Trieste. After being a Research Associate at the University of Illinois at Urbana-Champaign, he returned to SISSA in 1999 as Associate Professor and Director of the Computing Centre. From 2006 to 2013 he joined the Albert Einstein Institute in Potsdam (Max-Planck Institute for gravitational physics) as the Head of the Numerical-Relativity Research. Since 2013 he is Chair of Theoretical Relativistic Astrophysics at the Institute of Theoretical Physics in Frankfurt. He has worked in several areas of relativistic hydrodynamics and relativistic astrophysics, ranging from the investigation of fundamental issues to the construction of advanced numerical codes for the simulation of sources of gravitational waves.

Olindo Zanotti received his PhD is Astrophysics in 2002 at the International School for Advanced Studies (SISSA) in Trieste. Since then he has worked as Research Associate at the University of Valencia (Spain), at the University of Florence (Italy), at the Notre Dame University (USA), and at the Albert Einstein Institute (Germany). His specific interests include accretion-disc physics, plasma physics, and numerical methods for the solution of hyperbolic equations. He is presently carrying out research at the University of Trento.
Pastovi nuoroda: https://www.kriso.lt/db/9780198528906_pe.html