Nikolai V. Brilliantov and Thorsten Pöschel
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter introduces the notation to describe particle collisions using the coefficient of restitution. It raises the question of whether the coefficient of restitution is adequate to describe ...
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This chapter introduces the notation to describe particle collisions using the coefficient of restitution. It raises the question of whether the coefficient of restitution is adequate to describe particle collisions in granular gas. It considers the motion of two colliding spheres.Less
This chapter introduces the notation to describe particle collisions using the coefficient of restitution. It raises the question of whether the coefficient of restitution is adequate to describe particle collisions in granular gas. It considers the motion of two colliding spheres.
Nikolai V. Brilliantov and Thorsten Pöschel
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book ...
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Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book is aimed at readers from the advanced undergraduate level upwards and leads on to the present state of research. Throughout, special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity-dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formation are studied. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for derivation of kinetic properties, which allows for the application of computer algebra. The text is self-contained, requiring no mathematical or physical knowledge beyond that of standard physics undergraduate level. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. The molecular dynamics and computer-algebra programs can be downloaded from a companion web page.Less
Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book is aimed at readers from the advanced undergraduate level upwards and leads on to the present state of research. Throughout, special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity-dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formation are studied. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for derivation of kinetic properties, which allows for the application of computer algebra. The text is self-contained, requiring no mathematical or physical knowledge beyond that of standard physics undergraduate level. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. The molecular dynamics and computer-algebra programs can be downloaded from a companion web page.
Nikolai V. Brilliantov and Thorsten Pöschel
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This introductory chapter discusses basic concepts of the kinetic theory of granular gases and mentions some of the exciting phenomena in gas dynamics. Topics covered include kinetic theory for ...
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This introductory chapter discusses basic concepts of the kinetic theory of granular gases and mentions some of the exciting phenomena in gas dynamics. Topics covered include kinetic theory for dissipative particles, atomic level of material deformation, continuum description of particles, pairwise collision of particles, many-particle systems, and hydrodynamics.Less
This introductory chapter discusses basic concepts of the kinetic theory of granular gases and mentions some of the exciting phenomena in gas dynamics. Topics covered include kinetic theory for dissipative particles, atomic level of material deformation, continuum description of particles, pairwise collision of particles, many-particle systems, and hydrodynamics.
Nikolai V. Brilliantov and Thorsten Pöschel
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter illustrates the concept of restitution via two examples of few-particle systems. It shows that the detailed mechanics of collisions is important to overall behaviour: even small systems ...
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This chapter illustrates the concept of restitution via two examples of few-particle systems. It shows that the detailed mechanics of collisions is important to overall behaviour: even small systems consisting of only viscoelastic particles behave qualitatively different from equivalent systems when a constant coefficient of restitution is assumed. Thus, it can be expected that details of pairwise particle collisions determine the properties of a granular many-body system, that is, a granular gas, qualitatively too.Less
This chapter illustrates the concept of restitution via two examples of few-particle systems. It shows that the detailed mechanics of collisions is important to overall behaviour: even small systems consisting of only viscoelastic particles behave qualitatively different from equivalent systems when a constant coefficient of restitution is assumed. Thus, it can be expected that details of pairwise particle collisions determine the properties of a granular many-body system, that is, a granular gas, qualitatively too.
Peter Jenni, Markus Nordberg, and Max Boisot
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199567928
- eISBN:
- 9780191728945
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199567928.003.0002
- Subject:
- Business and Management, Knowledge Management, Organization Studies
ATLAS is a new high-energy physics (HEP) detector built by an international community of researchers and located at CERN just outside Geneva. ATLAS is big, global, and exciting. Together with three ...
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ATLAS is a new high-energy physics (HEP) detector built by an international community of researchers and located at CERN just outside Geneva. ATLAS is big, global, and exciting. Together with three other detectors, it forms an integral part of the Large Hadron Collider (LHC), a project that, because of the much higher particle-collision energies and production rates it achieves compared to existing accelerators, opens up challenging new frontiers in particle physics. This chapter presents background material on the ATLAS Collaboration that will help to clarify the chapters that follow. It briefly describes the ATLAS detector and the role it will play in the LHC experiments. It also offers a jargon-free outline of some of the physics that underpins the experiments and the technical challenges that had to be overcome. The history and the organization of the ATLAS Collaboration are also presented, as are its relationships with the host laboratory, CERN, and with the many firms and institutions that helped to build the detector.Less
ATLAS is a new high-energy physics (HEP) detector built by an international community of researchers and located at CERN just outside Geneva. ATLAS is big, global, and exciting. Together with three other detectors, it forms an integral part of the Large Hadron Collider (LHC), a project that, because of the much higher particle-collision energies and production rates it achieves compared to existing accelerators, opens up challenging new frontiers in particle physics. This chapter presents background material on the ATLAS Collaboration that will help to clarify the chapters that follow. It briefly describes the ATLAS detector and the role it will play in the LHC experiments. It also offers a jargon-free outline of some of the physics that underpins the experiments and the technical challenges that had to be overcome. The history and the organization of the ATLAS Collaboration are also presented, as are its relationships with the host laboratory, CERN, and with the many firms and institutions that helped to build the detector.
Nikolai V. Brilliantov and Thorsten Pöschel
- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198530381
- eISBN:
- 9780191713057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530381.003.0020
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter generalizes the Chapman–Enskog approach for the case of granular gases whose particles collide inelastically. Under the assumption of constant coefficient of restitution, the kinetic ...
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This chapter generalizes the Chapman–Enskog approach for the case of granular gases whose particles collide inelastically. Under the assumption of constant coefficient of restitution, the kinetic coefficients and velocity distribution function are derived.Less
This chapter generalizes the Chapman–Enskog approach for the case of granular gases whose particles collide inelastically. Under the assumption of constant coefficient of restitution, the kinetic coefficients and velocity distribution function are derived.
Rodrigo Soto
- Published in print:
- 2016
- Published Online:
- June 2016
- ISBN:
- 9780198716051
- eISBN:
- 9780191824401
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198716051.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Kinetic equations become extremely complex when models become realistic for several effects taking place simultaneously. It is hopeless trying to find analytic solutions and numerical methods should ...
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Kinetic equations become extremely complex when models become realistic for several effects taking place simultaneously. It is hopeless trying to find analytic solutions and numerical methods should therefore be devised to solve them. This chapter presents numerical methods appropriate for kinetic theory. First, the moment method is described, where the kinetic equations are transformed into coupled partial differential equations, which can be solved using standard tools. The method is exemplified by the Grad method for the Boltzmann equation. Second, the stochastic methods are presented, where particles sample the distribution function and are advanced in time so as to reproduce the evolution of the distribution function. Special methods are given to reproduce the streaming motion, particle collisions (classical and quantum), Brownian motion, and long-range interactions.Less
Kinetic equations become extremely complex when models become realistic for several effects taking place simultaneously. It is hopeless trying to find analytic solutions and numerical methods should therefore be devised to solve them. This chapter presents numerical methods appropriate for kinetic theory. First, the moment method is described, where the kinetic equations are transformed into coupled partial differential equations, which can be solved using standard tools. The method is exemplified by the Grad method for the Boltzmann equation. Second, the stochastic methods are presented, where particles sample the distribution function and are advanced in time so as to reproduce the evolution of the distribution function. Special methods are given to reproduce the streaming motion, particle collisions (classical and quantum), Brownian motion, and long-range interactions.
Gabriele Veneziano
- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198727965
- eISBN:
- 9780191794278
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198727965.003.0017
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter summarizes some 25 years of work on the transplanckian-energy collisions of particles, strings, and branes, seen as a theoretical laboratory for understanding how gravity and quantum ...
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This chapter summarizes some 25 years of work on the transplanckian-energy collisions of particles, strings, and branes, seen as a theoretical laboratory for understanding how gravity and quantum mechanics can be consistently combined in string theory. The ultimate aim of the exercise is to understand whether and how a consistent quantization of gravity can solve some longstanding paradoxes, such as the apparent loss of information in the production and decay of black holes at a semiclassical level. Considerable progress has been made in understanding the emergence of General Relativity expectations and in evaluating several kinds of quantum string corrections to them in the weak-gravity regime while keeping unitarity manifest. While some progress has also been made in the strong-gravity/gravitational collapse domain, full control of how unitarity works in that regime is still lacking.Less
This chapter summarizes some 25 years of work on the transplanckian-energy collisions of particles, strings, and branes, seen as a theoretical laboratory for understanding how gravity and quantum mechanics can be consistently combined in string theory. The ultimate aim of the exercise is to understand whether and how a consistent quantization of gravity can solve some longstanding paradoxes, such as the apparent loss of information in the production and decay of black holes at a semiclassical level. Considerable progress has been made in understanding the emergence of General Relativity expectations and in evaluating several kinds of quantum string corrections to them in the weak-gravity regime while keeping unitarity manifest. While some progress has also been made in the strong-gravity/gravitational collapse domain, full control of how unitarity works in that regime is still lacking.
Pankaj S. Joshi
- Published in print:
- 2015
- Published Online:
- January 2015
- ISBN:
- 9780199686766
- eISBN:
- 9780191766817
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199686766.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
In this final chapter, several recent and frontier developments, together with possible observable consequences of naked singularities which may distinguish them from their black hole counterparts ...
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In this final chapter, several recent and frontier developments, together with possible observable consequences of naked singularities which may distinguish them from their black hole counterparts through astrophysical signatures are considered. This chapter discusses the current major black hole paradoxes, such as the information paradox and the teleology or causality issues created by the black hole event horizons. Their possible resolution and a way out is proposed using current gravitational collapse results. The descent in a black hole versus that for a naked singularity by an observer are discussed and contrasted. The chapter also points out what are the current available possibilities to test the cosmic censorship conjecture through astronomical observations. In particular, super-rotating models and objects could play an important part here. The accretion disks around black holes and naked singularities are discussed which imply important physical differences in the characteristic emission spectra for these objects. Very high energy particle collisions and gravitational lensing near black holes and naked singularities are then discussed.Less
In this final chapter, several recent and frontier developments, together with possible observable consequences of naked singularities which may distinguish them from their black hole counterparts through astrophysical signatures are considered. This chapter discusses the current major black hole paradoxes, such as the information paradox and the teleology or causality issues created by the black hole event horizons. Their possible resolution and a way out is proposed using current gravitational collapse results. The descent in a black hole versus that for a naked singularity by an observer are discussed and contrasted. The chapter also points out what are the current available possibilities to test the cosmic censorship conjecture through astronomical observations. In particular, super-rotating models and objects could play an important part here. The accretion disks around black holes and naked singularities are discussed which imply important physical differences in the characteristic emission spectra for these objects. Very high energy particle collisions and gravitational lensing near black holes and naked singularities are then discussed.
