Energy Technology Data Exchange (ETDEWEB)
Omnes, Roland [Commissariat a l' energie atomique et aux energies alternatives - CEA (France)
1960-07-01
A modification of the dispersion relations demonstration for two-particle collisions in field theory is indicated. The direct study of the holomorphy domain of the reaction amplitude, without any reference to a particular coordinate system, allows to demonstrate the dispersion relations with fixed pulse transfer for any input and output particle mass. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 250, p. 1203-1205, sitting of 15 February 1960 [French] On indique une modification de la demonstration des relations de dispersion pour les collisions a deux particules en theorie des champs. En etudiant directement le domaine d'holomorphie de l'amplitude de reaction sans se referer a un systeme de coordonnees particulier, on demontre les relations de dispersion a transfert d'impulsion fixe dans le cas ou les masses des particules entrantes et sortantes sont quelconques. Reproduction d'un article publie dans les Comptes rendus des seances de l'Academie des Sciences, t. 250, p. 1203-1205, seance du 15 fevrier 1960.
General characteristics of relative dispersion in the ocean
Corrado, Raffaele; Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia; Zambianchi, Enrico
2017-04-01
The multi-scale and nonlinear nature of the ocean dynamics dramatically affects the spreading of matter, like pollutants, marine litter, etc., of physical and chemical seawater properties, and the biological connectivity inside and among different basins. Based on the Finite-Scale Lyapunov Exponent analysis of the largest available near-surface Lagrangian data set from the Global Drifter Program, our results show that, despite the large variety of flow features, relative dispersion can ultimately be described by a few parameters common to all ocean sub-basins, at least in terms of order of magnitude. This provides valuable information to undertake Lagrangian dispersion studies by means of models and/or of observational data. Moreover, our results show that the relative dispersion rates measured at submesoscale are significantly higher than for large-scale dynamics. Auxiliary analysis of high resolution GPS-tracked drifter hourly data as well as of the drogued/undrogued status of the buoys is provided in support of our conclusions. A possible application of our study, concerning reverse drifter motion and error growth analysis, is proposed relatively to the case of the missing Malaysia Airlines MH370 aircraft.
Energy Technology Data Exchange (ETDEWEB)
Logunov, A A; Medvedev, B V; Mestvirishvili, M A; Pavlov, V P; Polivanov, M K; Sukhanov, A D [Gosudarstvennyj Komitet po Ispol' zovaniyu Atomnoj Ehnergii SSSR, Serpukhov. Inst. Fiziki Vysokikh Ehnergij
1977-11-01
Investigation of analytical structure of the three-particle forward scattering amplitude with respect to energy variable of one of particles is performed. The results obtained make it possible to draw the conclusions on crossing properties of the amplitude and to derive the generalized optical theorem relating the discontinuity of the amplitude to the distribution function of an inclusive process. For a special case when two of three particles are of zero mass, a dispersion relation is proved.
International Nuclear Information System (INIS)
Deeba, F.; Ahmad, Zahoor; Murtaza, G.
2010-01-01
A generalized dielectric constant for the electron Bernstein waves using non-Maxwellian distribution functions is derived in a collisionless, uniform magnetized plasma. Using the Neumann series expansion for the products of Bessel functions, we can derive the dispersion relations for both kappa and the generalized (r,q) distributions in a straightforward manner. The dispersion relations now become dependent upon the spectral indices κ and (r,q) for the kappa and the generalized (r,q) distribution, respectively. Our results show how the non-Maxwellian dispersion curves deviate from the Maxwellian depending upon the values of the spectral indices chosen. It may be noted that the (r,q) dispersion relation is reduced to the kappa distribution for r=0 and q=κ+1, which, in turn, is further reducible to the Maxwellian distribution for κ→∞.
Numerical study on general dispersion relation of anisotropic and weakly relativistic plasma
International Nuclear Information System (INIS)
Ke Fujiu; Chen Yanping
1987-01-01
The key problem in heating and instability studies in plasma physics is to obtain dispersive equation and its solution. This paper presents the general dispersive equation and corresponding procedure for electromagnetic wave which nearly poloidally impinges on anisotropic, weakly relativistic Maxwellian plasma with inhomogeneous density in nonuniform magnetic field (such as plasma in TOKAMAK). The double index function F ij , significant in plasma physics, was expanded as single index function F 1 , and then the values were calculated by means of dispersive function. It was also pointed out that the severe error would be involved in the calculation of F ij from recurrence relation of F 11
The general dispersion relation of induced streaming instabilities in quantum outflow systems
Energy Technology Data Exchange (ETDEWEB)
Mehdian, H., E-mail: mehdian@khu.ac.ir; Hajisharifi, K.; Hasanbeigi, A. [Department of Physics and Institute for Plasma Research, Kharazmi University, 49 Dr Mofatteh Avenue, Tehran 15614 (Iran, Islamic Republic of)
2015-11-15
In this manuscript the dispersion relations of streaming instabilities, by using the unique property (neutralized in charge and current by default) of plasma shells colliding, have been generalized and studied. This interesting property for interpenetrating beams enables one to find the general dispersion relations without any restrictions used in the previous works in this area. In our previous work [H. Mehdian et al., ApJ. 801, 89 (2015)], employing the plasma shell concept and boost frame method, the general dispersion relation for filamentation instability has been derived in the relativistic classical regime. But in this paper, using the above mentioned concepts, the general dispersion relations (for each of streaming instabilities, filamentation, two-stream and multi-stream) in the non-relativistic quantum regime have been derived by employing the quantum fluid equations together with Maxwell equations. The derived dispersion relations enable to describe any arbitrary system of interacting two and three beams, justified neutralization condition, by choosing the inertial reference frame embedded on the one of the beams. Furthermore, by the numerical and analytical study of these dispersion relations, many new features of streaming instabilities (E.g. their cut-off wave numbers and growth rates) in terms of all involved parameters have been illustrated. The obtained results in this paper can be used to describe many astrophysical systems and laboratory astrophysics setting, such as collision of non-parallel plasma shells over a background plasma or the collision of three neutralized plasma slabs, and justifying the many plasma phenomena such as particle accelerations and induced fields.
Theory of pairwise coupling embedded in more general local dispersion relations
International Nuclear Information System (INIS)
Fuchs, V.; Bers, A.; Harten, L.
1985-01-01
Earlier work on the mode conversion theory by Fuchs, Ko, and Bers is detailed and expanded upon, and its relation to energy conservation is discussed. Given a local dispersion relation, D(ω; k, z) = 0, describing stable waves excited at an externally imposed frequency ω, a pairwise mode-coupling event embedded therein is extracted by expanding D(k, z) around a contour k = k/sub c/(z) given by partialD/partialk = 0. The branch points of D(k, z) = 0 are the turning points of a second-order differential-equation representation. In obtaining the fraction of mode-converted energy, the connection formula and conservation of energy must be used together. Also, proper attention must be given to distinguish cases for which the coupling disappears or persists upon confluence of the branches, a property which is shown to depend on the forward (v/sub g/v/sub ph/>0) or backward (v/sub g/v/sub ph/<0) nature of the waves. Examples occurring in ion-cyclotron and lower-hybrid heating are presented, illustrating the use of the theory
International Nuclear Information System (INIS)
Kenyon, I.R.
1990-01-01
General relativity is discussed in this book at a level appropriate to undergraduate students of physics and astronomy. It describes concepts and experimental results, and provides a succinct account of the formalism. A brief review of special relativity is followed by a discussion of the equivalence principle and its implications. Other topics covered include the concepts of curvature and the Schwarzschild metric, test of the general theory, black holes and their properties, gravitational radiation and methods for its detection, the impact of general relativity on cosmology, and the continuing search for a quantum theory of gravity. (author)
Straumann, Norbert
2013-01-01
This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars – our best laboratories for general relativity – are studied in considerable detail. An introduction to gravitational lensing theory is included as well, so as to make the current literature on the subject accessible to readers. Considerable attention is devoted to the study of compact objects, especially to black holes. This includes a detailed derivation of the Kerr solution, Israel’s proof of his uniqueness theorem, and a derivation of the basic laws of black hole physics. Part II ends with Witten’s proof of the positive energy theorem, which is presented in detail, together with the required tools on spin structures and spinor analysis. In Part III, all of the differential geomet...
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
International Nuclear Information System (INIS)
Gourgoulhon, Eric
2013-01-01
The author proposes a course on general relativity. He first presents a geometrical framework by addressing, presenting and discussion the following notions: the relativistic space-time, the metric tensor, Universe lines, observers, principle of equivalence and geodesics. In the next part, he addresses gravitational fields with spherical symmetry: presentation of the Schwarzschild metrics, radial light geodesics, gravitational spectral shift (Einstein effect), orbitals of material objects, photon trajectories. The next parts address the Einstein equation, black holes, gravitational waves, and cosmological solutions. Appendices propose a discussion of the relationship between relativity and GPS, some problems and their solutions, and Sage codes
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
Dispersion relations in loop calculations
International Nuclear Information System (INIS)
Kniehl, B.A.
1996-01-01
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its absorptive part along the branch cut. In perturbative calculations, the latter may be constructed by means of Cutkosky's rule, which is briefly discussed. For illustration, we apply this procedure at one loop to the photon vacuum-polarization function induced by leptons as well as to the γf anti-f vertex form factor generated by the exchange of a massive vector boson between the two fermion legs. We also show how the hadronic contribution to the photon vacuum polarization may be extracted from the total cross section of hadron production in e + e - annihilation measured as a function of energy. Finally, we outline the application of dispersive techniques at the two-loop level, considering as an example the bosonic decay width of a high-mass Higgs boson. (author)
Chaotic Lagrangian models for turbulent relative dispersion.
Lacorata, Guglielmo; Vulpiani, Angelo
2017-04-01
A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.
Redshift and lateshift from homogeneous and isotropic modified dispersion relations
Pfeifer, Christian
2018-05-01
Observables which would indicate a modified vacuum dispersion relations, possibly caused by quantum gravity effects, are a four momentum dependence of the cosmological redshift and the existence of a so called lateshift effect for massless or very light particles. Existence or non-existence of the latter is currently analyzed on the basis of the available observational data from gamma-ray bursts and compared to predictions of specific modified dispersion relation models. We consider the most general perturbation of the general relativistic dispersion relation of freely falling particles on homogeneous and isotropic spacetimes and derive the red- and lateshift to first order in the perturbation. Our result generalizes the existing formulae in the literature and we find that there exist modified dispersion relations causing both, one or none of the two effects to first order.
Ridgely, Charles T.
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced…
Dispersion relation and relative intensity for double-plasmon satellites
International Nuclear Information System (INIS)
Srivastava, K.S.; Shiv Singh; Harsh, O.K.
1981-01-01
An expression for the dispersion relation and the relative intensity of double-plasmon oscillations and satellites has been derived by extending the dispersion relation and the extended Bohm and Pines Hamiltonian to second order. The calculated value of the relative intensity of the double-plasmon satellite for Be agrees fairly well with the value observed experimentally by other workers. (orig.)
Phonon dispersion relations for caesium thiocyanate
International Nuclear Information System (INIS)
Irving, M.A.; Smith, T.F.; Elcombe, M.M.
1984-01-01
Room temperature phonon dispersion relations for frequencies below 2 THz have been measured, along the three orthorhombic axes and selected diagonal directions by neutron inelastic scattering, for caesium thiocyanate. These curves, which represent 13 acoustic modes and 11 optic modes of vibration, do not agree with the dispersion behaviour calculated from the rigid-ion model developed by Ti and Ra to describe their Raman scattering observations
Theoretical general relativity: 1979
International Nuclear Information System (INIS)
Bergmann, O.
1979-01-01
The metric and field equations of Einstein's general relativity theory are written down. Solutions to the equations are discussed. Connection is made between relativity theory and elementary particle theory. Possibilities for a unified field theory are considered
International Nuclear Information System (INIS)
Rosen, N.
1979-01-01
A modification of general relativity is proposed involving a second metric tensor describing a space-time of constant curvature and associated with the fundamental rest-frame of the universe. The theory generally agrees with the Einstein theory, but gives cosmological models without singularities which can account for present observation, including helium abundance
Jackson, A. T.
1973-01-01
Reviews theoretical and experimental fundamentals of Einstein's theory of general relativity. Indicates that recent development of the theory of the continually expanding universe may lead to revision of the space-time continuum of the finite and unbounded universe. (CC)
General relativity and experiment
Damour, T.
1994-01-01
The confrontation between Einstein's theory of gravitation and experiment is summarized. Although all current experimental data are compatible with general relativity, the importance of pursuing the quest for possible deviations from Einstein's theory is emphasized.
International Nuclear Information System (INIS)
Ridgely, Charles T
2010-01-01
Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress-energy-momentum tensor is used to derive a general expression of the force experienced by an observer in general coordinates. The general force is then applied to the local co-moving coordinate system of a uniformly accelerating observer, leading to an expression of the inertial force experienced by the observer. Next, applying the general force in Schwarzschild coordinates is shown to lead to familiar expressions of the gravitational force. As a more complex demonstration, the general force is applied to an observer in Boyer-Lindquist coordinates near a rotating, Kerr black hole. It is then shown that when the angular momentum of the black hole goes to zero, the force on the observer reduces to the force on an observer held stationary in Schwarzschild coordinates. As a final consideration, the force on an observer moving in rotating coordinates is derived. Expressing the force in terms of Christoffel symbols in rotating coordinates leads to familiar expressions of the centrifugal and Coriolis forces on the observer. It is envisioned that the techniques presented herein will be most useful to graduate level students, as well as those undergraduate students having experience with general relativity and tensor analysis.
Planck-scale-modified dispersion relations in FRW spacetime
Rosati, Giacomo; Amelino-Camelia, Giovanni; Marcianò, Antonino; Matassa, Marco
2015-12-01
In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferred-frame scenarios") and to the alternative possibility of "DSR-relativistic theories," theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.
Ray, J. R.
1982-01-01
Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.
International Nuclear Information System (INIS)
Hayashi, K.; Shirafuji, T.
1979-01-01
A gravitational theory is formulated on the Weitzenboeck space-time, characterized by the vanishing curvature tensor (absolute parallelism) and by the torsion tensor formed of four parallel vector fields. This theory is called new general relativity, since Einstein in 1928 first gave its original form. New general relativity has three parameters c 1 , c 2 , and lambda, besides the Einstein constant kappa. In this paper we choose c 1 = 0 = c 2 , leaving open lambda. We prove, among other things, that (i) a static, spherically symmetric gravitational field is given by the Schwarzschild metric, that (ii) in the weak-field approximation an antisymmetric field of zero mass and zero spin exists, besides gravitons, and that (iii) new general relativity agrees with all the experiments so far carried out
Lectures on general relativity
Papapetrou, Achille
1974-01-01
This book is an elaboration of lecture notes for the graduate course on General Rela tivity given by the author at Boston University in the spring semester of 1972. It is an introduction to the subject only, as the time available for the course was limited. The author of an introduction to General Relativity is faced from the beginning with the difficult task of choosing which material to include. A general criterion as sisting in this choice is provided by the didactic character of the book: Those chapters have to be included in priority, which will be most useful to the reader in enabling him to understand the methods used in General Relativity, the results obtained so far and possibly the problems still to be solved. This criterion is not sufficient to ensure a unique choice. General Relativity has developed to such a degree, that it is impossible to include in an introductory textbook of a reasonable length even a very condensed treatment of all important problems which have been discussed unt...
General Relativity and Gravitation
Ehlers, J.; Murdin, P.
2000-11-01
The General Theory of Relativity (GR), created by Albert Einstein between 1907 and 1915, is a theory both of gravitation and of spacetime structure. It is based on the assumption that matter, via its energy-momentum, interacts with the metric of spacetime, which is considered (in contrast to Newtonian physics and SPECIAL RELATIVITY) as a dynamical field having degrees of freedom of its own (GRAVI...
Modified dispersion relations, inflation, and scale invariance
Bianco, Stefano; Friedhoff, Victor Nicolai; Wilson-Ewing, Edward
2018-02-01
For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.
International Nuclear Information System (INIS)
Penrose, R.
1979-01-01
Much theoretical work in General Relativity has been concerned with finding explicit solutions of Einstein field equations. Exact solutions must involve simplifying procedures which in the case of strong gravitational fields may not be valid. Computers can help but complementary to these are the global qualitative mathematics that have been introduced into relativity over the past years. These have shown that Einstein's equations together with suitable inequalities on the energy-momentum tensor can lead inevitably to space-time singularities arising, provided that some qualitative geometric criterion is satisfied. It seems that in suitable situations of gravitational collapse this criterion will be satisfied. Similarly in a cosmological setting the criterion can be applied in the reverse direction in time. There is, however, the unsolved problem in general relativity of cosmic censorship and this is discussed as a consequence of Einstein's equations. (UK)
International Nuclear Information System (INIS)
Clarke, C.
1979-01-01
The plan of the book is as follows: Chapter 1 develops special relativity in a setting and notation that can immediately be transferred to general relativity. Most of the fundamental geometrical ideas are established here. Chapter 2 gives a more conventional account of some selected applications of special relativity. Chapter 3 is the heart of the book. A geometrical model of space-time is progressively built up, motivated by physical arguments stemming from the equivalence principle, leading to Einstein's field equations. Chapter 4 deals very quickly with the simplest form of weak-field theory with application to gravitational radiation. Chapter 5 concludes the book with a fairly detailed analysis of the Schwarzschild solution, plane fronted gravitational waves, and the Robertson-Walker cosmological solutions. Exercises at the end of each chapter extend the general theory into particular applications, giving a broader picture of the scope of the subject. (author)
Dispersion relations in real and virtual Compton scattering
International Nuclear Information System (INIS)
Drechsel, D.; Pasquini, B.; Vanderhaeghen, M.
2003-01-01
A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general case of real Compton scattering (RCS). Various types of dispersion relations for RCS are presented as tools for extracting nucleon polarizabilities from the RCS data. The information on nucleon polarizabilities gained in this way is reviewed and the nucleon structure information encoded in these quantities is discussed. The dispersion relation formalism is then extended to virtual Compton scattering (VCS). The information on generalized nucleon polarizabilities extracted from recent VCS experiments is described, along with its interpretation in nucleon structure models. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are presented
Modified dispersion relations and black hole physics
International Nuclear Information System (INIS)
Ling Yi; Li Xiang; Hu Bo
2006-01-01
A modified formulation of the energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such a modification will give corrections to both the temperature and the entropy of black holes. In particular, this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaches the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter
General Relativity and Gravitation
Ashtekar, Abhay; Berger, Beverly; Isenberg, James; MacCallum, Malcolm
2015-07-01
Part I. Einstein's Triumph: 1. 100 years of general relativity George F. R. Ellis; 2. Was Einstein right? Clifford M. Will; 3. Cosmology David Wands, Misao Sasaki, Eiichiro Komatsu, Roy Maartens and Malcolm A. H. MacCallum; 4. Relativistic astrophysics Peter Schneider, Ramesh Narayan, Jeffrey E. McClintock, Peter Mészáros and Martin J. Rees; Part II. New Window on the Universe: 5. Receiving gravitational waves Beverly K. Berger, Karsten Danzmann, Gabriela Gonzalez, Andrea Lommen, Guido Mueller, Albrecht Rüdiger and William Joseph Weber; 6. Sources of gravitational waves. Theory and observations Alessandra Buonanno and B. S. Sathyaprakash; Part III. Gravity is Geometry, After All: 7. Probing strong field gravity through numerical simulations Frans Pretorius, Matthew W. Choptuik and Luis Lehner; 8. The initial value problem of general relativity and its implications Gregory J. Galloway, Pengzi Miao and Richard Schoen; 9. Global behavior of solutions to Einstein's equations Stefanos Aretakis, James Isenberg, Vincent Moncrief and Igor Rodnianski; Part IV. Beyond Einstein: 10. Quantum fields in curved space-times Stefan Hollands and Robert M. Wald; 11. From general relativity to quantum gravity Abhay Ashtekar, Martin Reuter and Carlo Rovelli; 12. Quantum gravity via unification Henriette Elvang and Gary T. Horowitz.
Dispersion relations in three-particle systems
International Nuclear Information System (INIS)
Grach, I.L.; Harodetskij, I.M.; Shmatikov, M.Zh.
1979-01-01
Positions of all dynamical singularities of the triangular nonrelativistic diagram are calculated including the form factors. The jumps of the amplitude are written in an analitical form. The dispersion method predictions for bound states in the three-particle system are compared with the results of the Amado exactly solvable model. It is shown that the one-channel N/D method is equivalent to the pole approximation in the Amado model, and that the three-particle s channel unitarity should be taken into account calculating (in the dispersion method) the ground and excited states of the three-particle system. The relation of the three-particle unitary contribution to the Thomas theorem and Efimov effect is briefly discussed
International Nuclear Information System (INIS)
Bini, Donato; Felice, Fernando de; Geralico, Andrea
2006-01-01
The definition of relative accelerations and strains among a set of comoving particles is studied in connection with the geometric properties of the frame adapted to a 'fiducial observer'. We find that a relativistically complete and correct definition of strains must take into account the transport law of the chosen spatial triad along the observer's congruence. We use special congruences of (accelerated) test particles in some familiar spacetimes to elucidate such a point. The celebrated idea of Szekeres' compass of inertia, arising when studying geodesic deviation among a set of free-falling particles, is here generalized to the case of accelerated particles. In doing so we have naturally contributed to the theory of relativistic gravity gradiometer. Moreover, our analysis was made in an observer-dependent form, a fact that would be very useful when thinking about general relativistic tests on space stations orbiting compact objects like black holes and also in other interesting gravitational situations
Photon gas with hyperbolic dispersion relations
International Nuclear Information System (INIS)
Mohseni, Morteza
2013-01-01
We investigate the density of states for a photon gas confined in a nonmagnetic metamaterial medium in which some components of the permittivity tensor are negative. We study the effect of the resulting hyperbolic dispersion relations on the black body spectral density. We show that for both of the possible wavevector space topologies, the spectral density vanishes at a certain frequency. We obtain the partition function and derive some thermodynamical quantities of the system. To leading order, the results resemble those of a one- or two-dimensional photon gas with an enhanced density of states. (paper)
Introduction to general relativity
Parthasarthy, R
2016-01-01
INTRODUCTION TO GENERAL RELATIVITY begins with a description of the geometry of curved space, explaining geodesics, parallel transport, covariant differentiation, geodesic deviation and spacetime symmetry by killing vectors. It then introduces Einstein's theory of gravitation followed by Schwarzschild solution with its relevance to Positive Mass theorem. The three tests for Einstein's gravity are explained. Other exact solutions such as Vaidya, Kerr and Reisner - Nordstrom metric are included. In the Chapter on cosmological solutions, a detailed description of Godel metric is provided. It then introduces five dimensional spacetime of Kaluza showing the unification of gravity with electromagnetism. This is extended to include non-Abelian gauge theory by invoking compact extra dimensions. Explicit expressions in this case for Christoffel connections and ricci tensor are derived and the higher dimensional gravity action is shown to compactification are given.
Long wave dispersion relations for surface waves in a magnetically structured atmosphere
International Nuclear Information System (INIS)
Rae, I.C.; Roberts, B.
1983-01-01
A means of obtaining approximate dispersion relations for long wavelength magnetoacoustic surface waves propagating in a magnetically structured atmosphere is presented. A general dispersion relation applying to a wide range of magnetic profiles is obtained, and illustrated for the special cases of a single interface and a magnetic slab. In the slab geometry, for example, the dispersion relation contains both the even (sausage) and odd (kink) modes in one formalism
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Conformally Coupled General Relativity
Directory of Open Access Journals (Sweden)
Andrej Arbuzov
2018-02-01
Full Text Available The gravity model developed in the series of papers (Arbuzov et al. 2009; 2010, (Pervushin et al. 2012 is revisited. The model is based on the Ogievetsky theorem, which specifies the structure of the general coordinate transformation group. The theorem is implemented in the context of the Noether theorem with the use of the nonlinear representation technique. The canonical quantization is performed with the use of reparametrization-invariant time and Arnowitt– Deser–Misner foliation techniques. Basic quantum features of the models are discussed. Mistakes appearing in the previous papers are corrected.
International Nuclear Information System (INIS)
Cohen, B.I.
1987-01-01
The existence of compact dispersion relations for parametric instabilities of coherent electromagnetic waves in magnetized plasmas is addressed here. In general, comprehensive dispersion relations for parametric instabilities in unmagnetized plasmas become more complicated in the presence of an applied time-independent magnetic field. This is demonstrated with a fluid perturbation theory. A compact dispersion relation for parametric instabilities in unmagnetized plasma is heuristically extended here to the case of a magnetized plasma. This dispersion relation gives the correct results in a variety of circumstances of interest in considering electron cyclotron heating applications
Twistors in general relativity
International Nuclear Information System (INIS)
Penrose, R.
1987-01-01
The two most significant definitions of a twistor in (conformally) flat space-time are that given by solutions of the twistor equation and that given by α-planes in the complexification of the space-time. It is shown that these concepts are naturally dual to one another, and that they give rise to various different twistor concepts in curved space-time when referred to submanifolds of differing dimension. One of these concepts, that of 2-surface twistors, gives rise to a quasi-local definition of mass (and angular momentum). The status of this definition is explored in relation to various examples. (author)
Improvements in or relating to dispersions
International Nuclear Information System (INIS)
Woodhead, J.L.
1981-01-01
A process is described for the preparation of an aqueous dispersion of ceria which comprises forming a slurry of cerium IV hydroxide with water and an acid, the acid being capable of causing deaggregation of aggregated crystallites in the cerium IV hydroxide, heating the slurry for such a time and at such a temperature that the pH reaches a steady value, the quantity of acid in the slurry being such that the steady value of pH is below 5.4, thereby to produce a conditioned slurry, and admixing water with the conditioned slurry to produce an aqueous dispersion of ceria. (author)
Dispersion relations for 1D high-gain FELs
International Nuclear Information System (INIS)
Webb, S.D.; Litvinenko, V.N.
2010-01-01
We present analytical results for the one-dimensional dispersion relation for high-gain FELs. Using kappa-n distributions, we obtain analytical relations between the dispersion relations for various order kappa distributions. Since an exact solution exists for the kappa-1 (Lorentzian) distribution, this provides some insight into the number of modes on the way to the Gaussian distribution.
Observables and dispersion relations in κ-Minkowski spacetime
Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna
2017-10-01
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.
Dispersal patterns of red foxes relative to population density
Allen, Stephen H.; Sargeant, Alan B.
1993-01-01
Factors affecting red fox (Vulpes vulpes) dispersal patterns are poorly understood but warranted investigation because of the role of dispersal in rebuilding depleted populations and transmission of diseases. We examined dispersal patterns of red foxes in North Dakota based on recoveries of 363 of 854 foxes tagged as pups and relative to fox density. Foxes were recovered up to 8.6 years after tagging; 79% were trapped or shot. Straight-line distances between tagging and recovery locations ranged from 0 to 302 km. Mean recovery distances increased with age and were greater for males than females, but longest individual recovery distances were by females. Dispersal distances were not related to population density for males (P = 0.36) or females (P = 0.96). The proportion of males recovered that dispersed was inversely related to population density (r = -0.94; n = 5; P = 0.02), but not the proportion of females (r = -0.49; n = 5; P = 0.40). Dispersal directions were not uniform for either males (P = 0.003) or females (P = 0.006); littermates tended to disperse in similar directions (P = 0.09). A 4-lane interstate highway altered dispersal directions (P = 0.001). Dispersal is a strong innate behavior of red foxes (especially males) that results in many individuals of both sexes traveling far from natal areas. Because dispersal distance was unaffected by fox density, populations can be rebuilt and diseases transmitted long distances regardless of fox abundance.
General relativity basics and beyond
Date, Ghanashyam
2015-01-01
A Broad Perspective on the Theory of General Relativity and Its Observable Implications General Relativity: Basics and Beyond familiarizes students and beginning researchers with the basic features of the theory of general relativity as well as some of its more advanced aspects. Employing the pedagogical style of a textbook, it includes essential ideas and just enough background material needed for readers to appreciate the issues and current research. Basics The first five chapters form the core of an introductory course on general relativity. The author traces Einstein’s arguments and presents examples of space-times corresponding to different types of gravitational fields. He discusses the adaptation of dynamics in a Riemannian geometry framework, the Einstein equation and its elementary properties, and different phenomena predicted or influenced by general relativity. Beyond Moving on to more sophisticated features of general relativity, the book presents the physical requirements of a well-defined de...
Dispersion relations and sum rules for natural optical activity
International Nuclear Information System (INIS)
Thomaz, M.T.; Nussenzveig, H.M.
1981-06-01
Dispersion relations and sum rules are derived for the complex rotatory power of an arbitrary linear (nonmagnetic) isotropic medium showing natural optical activity. Both previously known dispersion relations and sum rules as well as new ones are obtained. It is shown that the Rosenfeld-Condon dispersion formula is inconsistent with the expected asymptotic behavior at high frequencies. A new dispersion formula based on quantum eletro-dynamics removes this inconsistency; however, it still requires modification in the low-frequency limit. (Author) [pt
Niemann, Brand Lee
A major field program to study beta-mesoscale transport and dispersion over complex mountainous terrain was conducted during 1969 with the cooperation of three government agencies at the White Sands Missile Range in central Utah. The purpose of the program was to measure simultaneously on a large number of days the synoptic and mesoscale wind fields, the relative dispersion between pairs of particle trajectories and the rate of small scale turbulence dissipation. The field program included measurements during more than 60 days in the months of March, June, and November. The large quantity of data generated from this program has been processed and analyzed to provide case studies and statistics to evaluate and refine Lagrangian variable trajectory models. The case studies selected to illustrate the complexities of mesoscale transport and dispersion over complex terrain include those with terrain blocking, lee waves, and stagnation, as well as those with large vertical wind shears and horizontal wind field deformation. The statistics of relative particle dispersion were computed and compared to the classical theories of Richardson and Batchelor and the more recent theories of Lin and Kao among others. The relative particle dispersion was generally found to increase with travel time in the alongwind and crosswind directions, but in a more oscillatory than sustained or even accelerated manner as predicted by most theories, unless substantial wind shears or finite vertical separations between particles were present. The relative particle dispersion in the vertical was generally found to be small and bounded even when substantial vertical motions due to lee waves were present because of the limiting effect of stable temperature stratification. The data show that velocity shears have a more significant effect than turbulence on relative particle dispersion and that sufficient turbulence may not always be present above the planetary boundary layer for "wind direction shear
Dispersal from deep ocean sources: physical and related scientific processes
International Nuclear Information System (INIS)
Robinson, A.R.; Kupferman, S.L.
1985-02-01
This report presents the results of the workshop ''Dispersal from Deep Ocean Sources: Physical and Related Scientific Processes,'' together with subsequent developments and syntheses of the material discussed there. The project was undertaken to develop usable predictive descriptions of dispersal from deep oceanic sources. Relatively simple theoretical models embodying modern ocean physics were applied, and observational and experimental data bases were exploited. All known physical processes relevant to the dispersal of passive, conservative tracers were discussed, and contact points for inclusion of nonconservative processes (biological and chemical) were identified. Numerical estimates of the amplitude, space, and time scales of dispersion were made for various mechanisms that control the evolution of the dispersal as the material spreads from a bottom point source to small-, meso-, and world-ocean scales. Recommendations for additional work are given. The volume is presented as a handbook of dispersion processes. It is intended to be updated as new results become available
On the relativistic theory of electromagnetic dispersion relations and Poynting's theorem
International Nuclear Information System (INIS)
Lerche, I.
1975-01-01
Constitutive relations, and general dispersion relations, are derived for an arbitrary, anisotropic, dispersive and dissipative medium which is moving relative to an inertial observer. The constitutive relations are expressed in terms of the ''local'' dielectric tensor, magnetic permeability, etc., where ''local'' refers to the instantaneous rest frame of the medium. We also give the generalization of Poynting's theorem for power flow including the expression for the rate at which the moving medium does work on the radiation. In view of the current interest in radiation generated in, and passing through, pulsar magnetospheres, we believe that the general results presented here are, perhaps, not without some astrophysical import
Factoring the dispersion relation in the presence of Lorentz violation
International Nuclear Information System (INIS)
Colladay, Don; McDonald, Patrick; Mullins, David
2010-01-01
We produce an explicit formula for the dispersion relation for the Dirac equation in the standard model extension in the presence of Lorentz violation. Our expression is obtained using novel techniques which exploit the algebra of quaternions. The dispersion relation is found to conveniently factor in two special cases that each involve a mutually exclusive set of nonvanishing Lorentz-violating parameters. This suggests that a useful approach to studies of Lorentz-violating models is to split the parameter space into two separate pieces, each of which yields a simple, tractable dispersion relation that can be used for analysis.
International Nuclear Information System (INIS)
Censor, Dan
2010-01-01
Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fourier-transform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred. Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept satisfies the relativistic velocity-addition formula. In this respect it is considered to be 'real', i.e., substantial, physically measurable, and not merely a mathematical artifact. Conversely, if we assume the group velocity to be substantial, it follows that the dispersion relation must be a relativistic invariant. (orig.)
Modern canonical quantum general relativity
Thiemann, Thomas
2007-01-01
This is an introduction to the by now fifteen years old research field of canonical quantum general relativity, sometimes called "loop quantum gravity". The term "modern" in the title refers to the fact that the quantum theory is based on formulating classical general relativity as a theory of connections rather than metrics as compared to in original version due to Arnowitt, Deser and Misner. Canonical quantum general relativity is an attempt to define a mathematically rigorous, non-perturbative, background independent theory of Lorentzian quantum gravity in four spacetime dimensions in the continuum. The approach is minimal in that one simply analyzes the logical consequences of combining the principles of general relativity with the principles of quantum mechanics. The requirement to preserve background independence has lead to new, fascinating mathematical structures which one does not see in perturbative approaches, e.g. a fundamental discreteness of spacetime seems to be a prediction of the theory provi...
Cosmological tests of general relativity
International Nuclear Information System (INIS)
Hut, P.
1977-01-01
It is stated that the general relativity theory could be tested on a cosmological scale by measuring the Hubble constant and the deceleration parameter, if, in addition, everything could be known about the matter filling the universe. If, on the other hand, nothing could be presupposed about the matter content of the universe general relativity could not be tested by measuring any number of time derivatives of the scale factor. But upon making the assumption of a universe filled with non-interacting mixture of non-relativistic matter and radiation general relativity can in principle be tested by measuring the first five derivatives of the scale factor. Some general relations are here presented using this assumption. (author)
Geometrical optics in general relativity
Loinger, A.
2006-01-01
General relativity includes geometrical optics. This basic fact has relevant consequences that concern the physical meaning of the discontinuity surfaces propagated in the gravitational field - as it was first emphasized by Levi-Civita.
Cosmic frontiers of general relativity
International Nuclear Information System (INIS)
Kaufmann, W.J. III.
1977-01-01
All relevant topics in general astronomy are covered including orientation in space--time, special relativity, gravitation and general relativity, stars and stellar evolution, white dwarfs, pulsars, neutron stars, the black hole, the geometry of the Schwarzschild solution, and electrically charged and rotating black holes. Also the geometry of the Kerr solution, observations of black holes, white holes and particle creation, gravitational waves and lenses, exploding galaxies and massive and primordial black holes are discussed
A general evaluation of the irradiation behaviour of dispersion fuels
International Nuclear Information System (INIS)
Hofman, G.L.
1995-01-01
The irradiation behaviour of aluminum-based dispersion fuels is evaluated with emphasis on metallurgical processes that control the dispersion behaviour. Phase transformations and microstructural changes resulting from fuel-matrix interactions and the effect of fissioning in fuel are discussed. (author)
Dispersion Relation for Skeletal Vibrations in Deuterated Polyethylene
Energy Technology Data Exchange (ETDEWEB)
Feldkamp, L. A.; Venkataraman, G.; King, J. S. [Department of Nuclear Engineering, University of Michigan, Ann Arbor, MI (United States)
1968-09-15
The low frequency vibrations in polyethylene have been studied previously, utilizing the incoherent scattering technique which yields an amplitude-weighted density of states. In the present work the dispersion relations have been obtained directly by observing the coherent scattering from a deuterated sample. This represents the first such measurement on a crystalline polymer. A target in which the molecular chain axes were approximately parallel was prepared by stretching polycrystalline material. The FWHM of the rocking curve for the (002) reflection was measured to be 9 Degree-Sign . Constant-Q and constant-E scans were made on the University of Michigan triple-axis spectrometer at room temperature to observe phonons propagating along the chain direction. The resulting dispersion curve for the v{sub 5} mode follows generally the calculated curve of Tasumi and Krimm with systematically lower frequencies. The maximum frequency of 1.36 x 10{sup 13} Hz agrees with the cut-off frequency determined previously from the incoherent scattering spectrum. (author)
A linearized dispersion relation for orthorhombic pseudo-acoustic modeling
Song, Xiaolei; Alkhalifah, Tariq Ali
2012-01-01
Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen's parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.
Dispersion relation of linearly polarized strong electromagnetic waves
Energy Technology Data Exchange (ETDEWEB)
Ferrari, A; Massaglia, S [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Dobrowolny, M [Comitato Nazionale per l' Energia Nucleaire, Frascati (Italy). Lab. Plasma Spazio
1975-12-15
A numerical study is presented of the dispersion relation of linearly polarized strong electromagnetic waves in a cold electron plasma. The nonlinear effects introduced by the relativistic motion of electrons are: (1) the dispersion relation depends explicitly on the field strength ..cap alpha..=eE/sub 0//mc..omega../sub 0/, and (2) the propagation of modes with frequencies below the formal electron plasma frequency is allowed.
The power of general relativity
International Nuclear Information System (INIS)
Clifton, Timothy; Barrow, John D.
2005-01-01
We study the cosmological and weak-field properties of theories of gravity derived by extending general relativity by means of a Lagrangian proportional to R 1+δ . This scale-free extension reduces to general relativity when δ→0. In order to constrain generalizations of general relativity of this power class, we analyze the behavior of the perfect-fluid Friedmann universes and isolate the physically relevant models of zero curvature. A stable matter-dominated period of evolution requires δ>0 or δ -19 assuming that Mercury follows a timelike geodesic. The combination of these observational constraints leads to the overall bound 0≤δ -19 on theories of this type
Advanced mechanics and general relativity an introduction to general relativity
Franklin, Joel
2010-01-01
Aimed at advanced undergraduates with background knowledge of classical mechanics and electricity and magnetism, this textbook presents both the particle dynamics relevant to general relativity, and the field dynamics necessary to understand the theory. Focusing on action extremization, the book develops the structure and predictions of general relativity by analogy with familiar physical systems. Topics ranging from classical field theory to minimal surfaces and relativistic strings are covered in a homogeneous manner. Nearly 150 exercises and numerous examples throughout the textbook enable students to test their understanding of the material covered.
Generalized Moshinsky bracket recurrence relations
International Nuclear Information System (INIS)
Bevelacqua, J.J.
1979-01-01
Recurrence relations for generalized Talmi-Moshinsky brackets are derived. These relations permit the generation of transformation brackets once appropriate starting brackets are determined. The savings in computer time, when compared with generating brackets individually, is at least a factor of 10 for brackets with radial quantum numbers as large as 9 and angular quantum numbers as large as 2. (author)
Spinning fluids in general relativity
Ray, J. R.; Smalley, L. L.
1982-01-01
General relativity field equations are employed to examine a continuous medium with internal spin. A variational principle formerly applied in the special relativity case is extended to the general relativity case, using a tetrad to express the spin density and the four-velocity of the fluid. An energy-momentum tensor is subsequently defined for a spinning fluid. The equations of motion of the fluid are suggested to be useful in analytical studies of galaxies, for anisotropic Bianchi universes, and for turbulent eddies.
Drift wave dispersion relation for arbitrarily collisional plasma
International Nuclear Information System (INIS)
Angus, Justin R.; Krasheninnikov, Sergei I.
2012-01-01
The standard local linear analysis of drift waves in a plasma slab is generalized to be valid for arbitrarily collisional electrons by considering the electrons to be governed by the drift-kinetic equation with a BGK-like (Bhatnagar-Gross-Krook) collision operator. The obtained dispersion relation reduces to that found from collisionless kinetic theory when the collision frequency is zero. Electron temperature fluctuations must be retained in the standard fluid analysis in order to obtain good quantitative agreement with our general solution in the highly collisional limit. Any discrepancies between the fluid solution and our general solution in this limit are attributed to the limitations of the BGK collision operator. The maximum growth rates in both the collisional and collisionless limits are comparable and are both on the order of the fundamental drift wave frequency. The main role of the destabilizing mechanism is found to be in determining the parallel wave number at which the maximum growth rate will occur. The parallel wave number corresponding to the maximum growth rate is set by the wave-particle resonance condition in the collisionless limit and transitions to being set by the real frequency being on the order of the rate for electrons to diffuse a parallel wavelength in the collisional limit.
Drift wave dispersion relation for arbitrarily collisional plasma
Energy Technology Data Exchange (ETDEWEB)
Angus, Justin R.; Krasheninnikov, Sergei I. [Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California 92093-0417 (United States)
2012-05-15
The standard local linear analysis of drift waves in a plasma slab is generalized to be valid for arbitrarily collisional electrons by considering the electrons to be governed by the drift-kinetic equation with a BGK-like (Bhatnagar-Gross-Krook) collision operator. The obtained dispersion relation reduces to that found from collisionless kinetic theory when the collision frequency is zero. Electron temperature fluctuations must be retained in the standard fluid analysis in order to obtain good quantitative agreement with our general solution in the highly collisional limit. Any discrepancies between the fluid solution and our general solution in this limit are attributed to the limitations of the BGK collision operator. The maximum growth rates in both the collisional and collisionless limits are comparable and are both on the order of the fundamental drift wave frequency. The main role of the destabilizing mechanism is found to be in determining the parallel wave number at which the maximum growth rate will occur. The parallel wave number corresponding to the maximum growth rate is set by the wave-particle resonance condition in the collisionless limit and transitions to being set by the real frequency being on the order of the rate for electrons to diffuse a parallel wavelength in the collisional limit.
Wave dispersion relations in two-dimensional Yukawa systems
International Nuclear Information System (INIS)
Liu Yanhong; Liu Bin; Chen Yanping; Yang Size; Wang Long; Wang Xiaogang
2003-01-01
Collective modes in a two-dimensional Yukawa system are investigated by molecular dynamics simulation in a wide range of coupling parameter Γ and screening strength κ. The dispersion relations and sound speeds of the transverse and longitudinal waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the longitudinal wave is demonstrated. Frequency gaps are found on the dispersion curves of the transverse wave due to scattering of the waves on lattice defects for proper values of Γ. The common frequency of transverse and longitudinal waves drops dramatically with the increasing screening strength κ
Pseudo-complex general relativity
Hess, Peter O; Greiner, Walter
2016-01-01
This volume presents an pseudo-complex extension of General Relativity which addresses these issues and presents proposals for experimental examinations in strong fields near a large mass. General Relativity is a beautiful and well tested theory of gravitation. Nevertheless, it implies conceptual problems like the creation of singularities (Black Holes) as a result of the collapse of large masses, or the appearance of event horizons which exclude parts of the space-time from the observation of external observers. The mathematical and geometrical foundations of this extension are displayed in detail, and applications including orbits and accretion disks around large central masses, neutron stars or cosmological models are introduced. Calculations both for classical and extended applications are often executed in the form of problems with extensive solutions, which makes this volume also a valuable resource for any student of General Relativity.
Bimetric general relativity and cosmology
International Nuclear Information System (INIS)
Rosen, N.
1980-01-01
A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensor gsub(μupsilon) describing the space-time geometry and gravitation, there exists also a background metric tensor γsub(μupsilon). The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k = 1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. Simple isotropic closed models of the universe can be set up which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order of c 5 -h -1 G -2 approximately 10 93 g/cm 3 . The expansion from such a high-density state is similar to that from the singular state ('big bang') of the general relativity models. In the case of the dust-filled model the parameters can be fitted to present cosmological data. Using the radiation-filled model to describe the early history of the universe, the cosmic abundance of helium and other light elements can be accounted for in the same way as in ordinary general relativity. (author)
Conformal covariance of general relativity
International Nuclear Information System (INIS)
Ionescu-Pallas, N.; Gottlieb, I.
1980-01-01
The Einstein's equations of General Relativity are written in a conformal metric, resulting as a consequence of geometrizing the pressure forces. Accordingly, the trajectory of a test body pursues a geodetic line even inside the source of gravitational field. Moreover, the pressure, entering the perfect fluid scheme, may be replaced by a certain scalar interaction. This new manner of interpreting General Relativity is then applied to Cosmology, in order to build up a model of Universe whose static limit should coincide with that of Einstein. At the same time, the cosmological constant is connected to the scalar interaction acquiring a plausible explanation. (author)
The gauge in general relativity
International Nuclear Information System (INIS)
Cohn, J.
1975-01-01
The view is taken that the field equations of General Relativity, without a definition of congruence of length and time intervals at different events, are without physical content. The possibility is explored that the customary Einstein field equations are to be used but with a different congruence definition than is customary. When these resulting equations are, in turn, expressed with the customary congruence, they comprise a new set of field equations physically not equivalent to either Einstein's or Brans-Dicke's formulations of general relativity. Similarities with Einstein's and Brans-Dicke's formulations are discussed, and the possibility of experimental confirmation of these new equations is also briefly considered. (author)
General relativity and gravitational waves
Weber, Johanna
1961-01-01
An internationally famous physicist and electrical engineer, the author of this text was a pioneer in the investigation of gravitational waves. Joseph Weber's General Relativity and Gravitational Waves offers a classic treatment of the subject. Appropriate for upper-level undergraduates and graduate students, this text remains ever relevant. Brief but thorough in its introduction to the foundations of general relativity, it also examines the elements of Riemannian geometry and tensor calculus applicable to this field.Approximately a quarter of the contents explores theoretical and experimenta
Tests of General Relativity with GW150914
Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Birnholtz, O.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; De Rosa, R.; DeRosa, R. T.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, Abhirup; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Healy, J.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Johnson-McDaniel, N. K.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Haris, M. K.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, Nam-Gyu; Kim, Namjun; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; London, L. T.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lousto, C. O.; Lovelace, G.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pan, Y.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Pfeiffer, H. P.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Popolizio, P.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prix, R.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Quetschke, V.; Quintero, E. 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S.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Setyawati, Y.; Sevigny, A.; Shaddock, D. A.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. 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L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, D.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; Boyle, M.; Campanelli, M.; Hemberger, D. A.; Kidder, L. E.; Ossokine, S.; Scheel, M. A.; Szilagyi, B.; Teukolsky, S.; Zlochower, Y.; LIGO Scientific; Virgo Collaborations
2016-06-01
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 1013 km . In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.
Tests of General Relativity with GW150914.
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Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Johnson-McDaniel, N K; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Haris, M K; Kalaghatgi, C V; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karki, S; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kaur, T; Kawabe, K; Kawazoe, F; Kéfélian, F; Kehl, M S; Keitel, D; Kelley, D B; Kells, W; Kennedy, R; Key, J S; Khalaidovski, A; Khalili, F Y; Khan, I; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, C; Kim, J; Kim, K; Kim, Nam-Gyu; Kim, Namjun; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Kleybolte, L; Klimenko, S; Koehlenbeck, S M; Kokeyama, K; Koley, S; Kondrashov, V; Kontos, A; Korobko, M; Korth, W Z; Kowalska, I; Kozak, D B; Kringel, V; Krishnan, B; Królak, A; Krueger, C; Kuehn, G; Kumar, P; Kuo, L; Kutynia, A; Lackey, B D; Landry, M; Lange, J; Lantz, B; Lasky, P D; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E O; Lee, C H; Lee, H K; Lee, H M; Lee, K; Lenon, A; Leonardi, M; Leong, J R; Leroy, N; Letendre, N; Levin, Y; Levine, B M; Li, T G F; Libson, A; Littenberg, T B; Lockerbie, N A; Logue, J; Lombardi, A L; London, L T; Lord, J E; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J D; Lousto, C O; Lovelace, G; Lück, H; Lundgren, A P; Luo, J; Lynch, R; Ma, Y; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magaña-Sandoval, F; Magee, R M; Mageswaran, M; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Mandel, I; Mandic, V; Mangano, V; Mansell, G L; Manske, M; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A S; Maros, E; Martelli, F; Martellini, L; Martin, I W; Martin, R M; Martynov, D V; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Masso-Reid, M; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McCormick, S; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McWilliams, S T; Meacher, D; Meadors, G D; Meidam, J; Melatos, A; Mendell, G; Mendoza-Gandara, D; Mercer, R A; Merilh, E; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Meyers, P M; Mezzani, F; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, J; Millhouse, M; Minenkov, Y; Ming, J; Mirshekari, S; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moggi, A; Mohan, M; Mohapatra, S R P; Montani, M; Moore, B C; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Murphy, D J; Murray, P G; Mytidis, A; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nedkova, K; Nelemans, G; Neri, M; Neunzert, A; Newton, G; Nguyen, T T; Nielsen, A B; Nissanke, S; Nitz, A; Nocera, F; Nolting, D; Normandin, M E; Nuttall, L K; Oberling, J; Ochsner, E; O'Dell, J; Oelker, E; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; O'Shaughnessy, R; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, H; Pan, Y; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Paris, H R; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patricelli, B; Patrick, Z; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Perreca, A; Pfeiffer, H P; Phelps, M; Piccinni, O; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pitkin, M; Poggiani, R; Popolizio, P; Post, A; Powell, J; Prasad, J; Predoi, V; Premachandra, S S; Prestegard, T; Price, L R; Prijatelj, M; Principe, M; Privitera, S; Prix, R; Prodi, G A; Prokhorov, L; Puncken, O; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Qin, J; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rakhmanov, M; Rapagnani, P; Raymond, V; Razzano, M; Re, V; Read, J; Reed, C M; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Rew, H; Reyes, S D; Ricci, F; Riles, K; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Salconi, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sanchez, E J; Sandberg, V; Sandeen, B; Sanders, J R; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Sauter, O; Savage, R L; Sawadsky, A; Schale, P; Schilling, R; Schmidt, J; Schmidt, P; Schnabel, R; Schofield, R M S; Schönbeck, A; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sengupta, A S; Sentenac, D; Sequino, V; Sergeev, A; Serna, G; Setyawati, Y; Sevigny, A; Shaddock, D A; Shah, S; Shahriar, M S; Shaltev, M; Shao, Z; Shapiro, B; Shawhan, P; Sheperd, A; Shoemaker, D H; Shoemaker, D M; Siellez, K; Siemens, X; Sigg, D; Silva, A D; Simakov, D; Singer, A; Singer, L P; Singh, A; Singh, R; Singhal, A; Sintes, A M; Slagmolen, B J J; Smith, J R; Smith, N D; Smith, R J E; Son, E J; Sorazu, B; Sorrentino, F; Souradeep, T; Srivastava, A K; Staley, A; Steinke, M; Steinlechner, J; Steinlechner, S; Steinmeyer, D; Stephens, B C; Stone, R; Strain, K A; Straniero, N; Stratta, G; Strauss, N A; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, L; Sutton, P J; Swinkels, B L; Szczepańczyk, M J; Tacca, M; Talukder, D; Tanner, D B; Tápai, M; Tarabrin, S P; Taracchini, A; Taylor, R; Theeg, T; Thirugnanasambandam, M P; Thomas, E G; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, S; Tiwari, V; Tokmakov, K V; Tomlinson, C; Tonelli, M; Torres, C V; Torrie, C I; Töyrä, D; Travasso, F; Traylor, G; Trifirò, D; Tringali, M C; Trozzo, L; Tse, M; Turconi, M; Tuyenbayev, D; Ugolini, D; Unnikrishnan, C S; Urban, A L; Usman, S A; Vahlbruch, H; Vajente, G; Valdes, G; Vallisneri, M; van Bakel, N; van Beuzekom, M; van den Brand, J F J; Van Den Broeck, C; Vander-Hyde, D C; van der Schaaf, L; van Heijningen, J V; van Veggel, A A; Vardaro, M; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Vetrano, F; Viceré, A; Vinciguerra, S; Vine, D J; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Voss, D; Vousden, W D; Vyatchanin, S P; Wade, A R; Wade, L E; Wade, M; Walker, M; Wallace, L; Walsh, S; Wang, G; Wang, H; Wang, M; Wang, X; Wang, Y; Ward, R L; Warner, J; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Weßels, P; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Williams, D; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Worden, J; Wright, J L; Wu, G; Yablon, J; Yam, W; Yamamoto, H; Yancey, C C; Yap, M J; Yu, H; Yvert, M; Zadrożny, A; Zangrando, L; Zanolin, M; Zendri, J-P; Zevin, M; Zhang, F; Zhang, L; Zhang, M; Zhang, Y; Zhao, C; Zhou, M; Zhou, Z; Zhu, X J; Zucker, M E; Zuraw, S E; Zweizig, J; Boyle, M; Campanelli, M; Hemberger, D A; Kidder, L E; Ossokine, S; Scheel, M A; Szilagyi, B; Teukolsky, S; Zlochower, Y
2016-06-03
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.
General relativity 50 years old
1966-01-01
In May 1916, 'The Foundations of General Relativity Theory' by Albert Einstein was published in 'Annalen der Physik'. Fifty years later, this major contribution to scientific thought still has a rather isolated position with respect to the main-stream of scientific theory. (In contrast, the Special Theory of Relativity is one of the cornerstones of sub-nuclear physics.) To mark the anniversary of the publication of Einstein's paper a theoretician from CERN discusses the theory and its present status.
Quantum mechanics from general relativity
International Nuclear Information System (INIS)
Sachs, M.
1986-01-01
A generalization of quantum mechanics is demonstrated in the context of general relativity, following from a generally covariant field theory of inertia. Nonrelativistically, the formalism corresponds with linear quantum mechanics. In the limit of special relativity, nonlinearity remains and several new features are derived: (1) Particle-antiparticle pairs do not annihilate; an exact bound state solution is derived corresponding with all experimental facts about annihilation/creation - which, in approximation, gives the blackbody radiation spectrum for a sea of such pairs. (2) A result is proven, without approximation, that is physically equivalent to the Pauli exclusion principle - which, in linear approximation, gives the totally antisymmetrised many-body wave function and Fermi-Dirac statistics. (3) The hydrogen spectrum is derived, including the Lamb shifts, in agreement with experiment; new results are found for high energy electron-proton scattering. (4) Finally, several applications to the elementary particle domain are demonstrated, in agreement with results from experimental high energy physics. (Auth.)
General Relativity: horizons for tests
Yatskiv, Ya. S.; Alexandrov, A. N.; Vavilova, I. B.; Zhdanov, V. I.; Zhuk, A. I.; Kudrya, Yu. N.; Parnovsky, S. L.; Fedorova, E. V.; Khmil, S. V.
2013-12-01
Theoretical basis of the General Relativity Theory (GRT), its experimental tests as well as GRT applications are briefly summarized taking into account the results of the last decade. The monograph addresses scientists, post-graduated students, and students specialized in the natural sciences as well as everyone who takes an interest in GRT.
General relativity and dark matter
International Nuclear Information System (INIS)
Pestov, A.B.
1993-01-01
It is shown that from the first principles of General Relativity it follows that there exists a new type of interactions which are tightly connected with the gravitational interactions. New particles representing a new form of interactions do not interact electromagnetically, strongly and weakly with the known elementary particles. Physics of the new particles is defined by the Planck scales. (author.). 9 refs
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Modified General Relativity and Cosmology
Abdel-Rahman, A.-M. M.
1997-10-01
Aspects of the modified general relativity theory of Rastall, Al-Rawaf and Taha are discussed in both the radiation- and matter-dominated flat cosmological models. A nucleosynthesis constraint on the theory's free parameter is obtained and the implication for the age of the Universe is discussed. The consistency of the modified matter- dominated model with the neoclassical cosmological tests is demonstrated.
Algebraic computing in general relativity
International Nuclear Information System (INIS)
D'Inverno, R.A.
1975-01-01
The purpose of this paper is to bring to the attention of potential users the existence of algebraic computing systems, and to illustrate their use by reviewing a number of problems for which such a system has been successfully used in General Relativity. In addition, some remarks are included which may be of help in the future design of these systems. (author)
Cosmological models in general relativity
Indian Academy of Sciences (India)
Cosmological models in general relativity. B B PAUL. Department of Physics, Nowgong College, Nagaon, Assam, India. MS received 4 October 2002; revised 6 March 2003; accepted 21 May 2003. Abstract. LRS Bianchi type-I space-time filled with perfect fluid is considered here with deceler- ation parameter as variable.
Dimensional Analysis and General Relativity
Lovatt, Ian
2009-01-01
Newton's law of gravitation is a central topic in the first-year physics curriculum. A lecturer can go beyond the physical details and use the history of gravitation to discuss the development of scientific ideas; unfortunately, the most recent chapter in this history, general relativity, is not covered in first-year courses. This paper discusses…
Dispersion relations for η '→ η π π
Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P.; Stoffer, Peter
2017-07-01
We present a dispersive analysis of the decay amplitude for η '→ η π π that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the {π π } and {π }η scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.
From field theory to phenomenology: the history of dispersion relations
International Nuclear Information System (INIS)
Pickering, A.
1989-01-01
The authors chart the history of quantum field theory (QFT) in the 1950s with reference to the ideas of dispersion relations. QFT failed to explain strong interaction physics and so was discarded. Connections are drawn between a central group of particle theorists working on applying Kramers-Kronig light scattering relations to high energy particle scattering and the way physics developed. The concepts of single and double dispersion relations and Regge poles, when connected with the large quantity of empirical data from the large particle accelerators of the 1950s, could not be embodied within QFT, which then fell into decline. (UK)
The genesis of general relativity
Norton, John; Renn, Jürgen; Sauer, Tilman; Stachel, John
2007-01-01
This four-volume work represents the most comprehensive documentation and study of the creation of general relativity; one of the fundamental physical theories of the 20th century. It comprises key sources from Einstein and others who from the late 19th to the early 20th century contributed to this monumental development. Some of these sources are presented here in translation for the first time. Einstein’s famous Zurich notebook, which documents the pivotal steps toward general relativity, is reproduced here for the first time and transcribed in its entirety. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity. All in all, the facets of this work, based on more than a decade of research, combine to constitute one of the most in-depth studies of a scientific revolution ever written.
Testing general relativity on accelerators
Directory of Open Access Journals (Sweden)
Tigran Kalaydzhyan
2015-11-01
Full Text Available Within the general theory of relativity, the curvature of spacetime is related to the energy and momentum of the present matter and radiation. One of the more specific predictions of general relativity is the deflection of light and particle trajectories in the gravitational field of massive objects. Bending angles for electromagnetic waves and light in particular were measured with a high precision. However, the effect of gravity on relativistic massive particles was never studied experimentally. Here we propose and analyze experiments devoted to that purpose. We demonstrate a high sensitivity of the laser Compton scattering at high energy accelerators to the effects of gravity. The main observable – maximal energy of the scattered photons – would experience a significant shift in the ambient gravitational field even for otherwise negligible violation of the equivalence principle. We confirm predictions of general relativity for ultrarelativistic electrons of energy of tens of GeV at a current level of resolution and expect our work to be a starting point of further high-precision studies on current and future accelerators, such as PETRA, European XFEL and ILC.
Relativistic energy-dispersion relations of 2D rectangular lattices
Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi
2017-04-01
An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.
Quantum information and general relativity
International Nuclear Information System (INIS)
Peres, A.
2004-01-01
The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as on-way membranes for the propagation of quantum information, in particular black holes which act like sinks. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Quantum information and general relativity
Energy Technology Data Exchange (ETDEWEB)
Peres, A. [Technion, Israel Institute of Technology, Haifa (Israel)
2004-12-01
The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as on-way membranes for the propagation of quantum information, in particular black holes which act like sinks. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Quantum information and general relativity
Peres, Asher
2004-01-01
The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as one-way membranes for the propagation of quantum information, in particular black holes which act like sinks.
Quantum information and general relativity
Peres, A.
2004-11-01
The Einstein-Podolsky-Rosen paradox (1935) is reexamined in the light of Shannon's information theory (1948). The EPR argument did not take into account that the observers' information was localized, like any other physical object. General relativity introduces new problems: there are horizons which act as on-way membranes for the propagation of quantum information, in particular black holes which act like sinks.
Bubble collisions in general relativity
International Nuclear Information System (INIS)
Siklos, S.T.C.; Wu, Z.C.; University of Science and Technology of China, Hofei, Anhwei)
1983-01-01
The collision of two bubbles of true vacuum in a background of false vacuum is considered in the context of General Relativity. It is found that in the thin wall approximation, the problem, can be solved exactly. The region to the future of the collision is described by the pseudo-Schwarzschild de Sitter metric. The parameters in this metric are found by solving the junction conditions at each collision. (author)
An exact linear dispersion relation for CRM instability
International Nuclear Information System (INIS)
Choyal, Y; Minami, K
2011-01-01
An exact self-consistent linear dispersion relation of a large orbit electron beam including two principles of cyclotron emission with oscillation frequencies above and below the relativistic electron frequency is derived and analyzed numerically for the first time in the literature. The two principles are cyclotron resonance maser (CRM) instability and Cherenkov instability in the azimuthal direction. Self-consistency in the formulation and inclusion of proper boundary conditions have removed the unphysical instability existing for infinitely large k z observed in conventional dispersion relations of CRM instability.
Langmuir wave dispersion relation in non-Maxwellian plasmas
International Nuclear Information System (INIS)
Ouazene, M.; Annou, R.
2010-01-01
The Langmuir wave dispersion relation is derived in partially ionized plasmas, where free electrons are confined to move in a nearest neighbor ions' potential well. The equilibrium velocity distribution function experiences then, a departure from Maxwell distribution function. The effect of the non-Maxwellian character of the distribution function on the Langmuir phase and group velocities as well as the phase matching conditions and the nonlinear growth rate of decay instability is investigated. The proposed Langmuir wave dispersion relation is relevant to dense and cryogenic plasmas.
Gravitation. [Book on general relativity
Misner, C. W.; Thorne, K. S.; Wheeler, J. A.
1973-01-01
This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.
Results from Numerical General Relativity
Baker, John G.
2011-01-01
For several years numerical simulations have been revealing the details of general relativity's predictions for the dynamical interactions of merging black holes. I will review what has been learned of the rich phenomenology of these mergers and the resulting gravitational wave signatures. These wave forms provide a potentially observable record of the powerful astronomical events, a central target of gravitational wave astronomy. Asymmetric radiation can produce a thrust on the system which may accelerate the single black hole resulting from the merger to high relative velocity.
A generalized Principle of Relativity
International Nuclear Information System (INIS)
Felice, Fernando de; Preti, Giovanni
2009-01-01
The Theory of Relativity stands as a firm groundstone on which modern physics is founded. In this paper we bring to light an hitherto undisclosed richness of this theory, namely its admitting a consistent reformulation which is able to provide a unified scenario for all kinds of particles, be they lightlike or not. This result hinges on a generalized Principle of Relativity which is intrinsic to Einstein's theory - a fact which went completely unnoticed before. The road leading to this generalization starts, in the very spirit of Relativity, from enhancing full equivalence between the four spacetime directions by requiring full equivalence between the motions along these four spacetime directions as well. So far, no measurable spatial velocity in the direction of the time axis has ever been defined, on the same footing of the usual velocities - the 'space-velocities' - in the local three-space of a given observer. In this paper, we show how Relativity allows such a 'time-velocity' to be defined in a very natural way, for any particle and in any reference frame. As a consequence of this natural definition, it also follows that the time- and space-velocity vectors sum up to define a spacelike 'world-velocity' vector, the modulus of which - the world-velocity - turns out to be equal to the Maxwell's constant c, irrespective of the observer who measures it. This measurable world-velocity (not to be confused with the space-velocities we are used to deal with) therefore represents the speed at which all kinds of particles move in spacetime, according to any observer. As remarked above, the unifying scenario thus emerging is intrinsic to Einstein's Theory; it extends the role traditionally assigned to Maxwell's constant c, and can therefore justly be referred to as 'a generalized Principle of Relativity'.
A linearized dispersion relation for orthorhombic pseudo-acoustic modeling
Song, Xiaolei
2012-11-04
Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen\\'s parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.
Modern Canonical Quantum General Relativity
Thiemann, Thomas
2008-11-01
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum-algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. Implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel'fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics; Bibliography; Index.
Approximate Dispersion Relations for Waves on Arbitrary Shear Flows
Ellingsen, S. À.; Li, Y.
2017-12-01
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.Plain Language SummaryIn order to answer key questions such as how the ocean surface affects the climate, erodes the coastline and transports nutrients, we must understand how waves move. This is not so easy when depth varying currents are present, as they often are in coastal waters. We have developed a modeling tool for accurately predicting wave properties in such situations, ready for use, for example, in the complex oceanographic computer models. Our
Getting super-excited with modified dispersion relations
Energy Technology Data Exchange (ETDEWEB)
Ashoorioon, Amjad; Casadio, Roberto [INFN—Sezione di Bologna, viale B. Pichat 6/2, I-40127 Bologna (Italy); Geshnizjani, Ghazal; Kim, Hyung J., E-mail: amjad.ashoorioon@bo.infn.it, E-mail: roberto.casadio@bo.infn.it, E-mail: ggeshniz@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo Waterloo, Ontario, N2L 3G1 (Canada)
2017-09-01
We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as 'super-excited' states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called 'calm excited states'. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.
Homothetic motions in general relativity
International Nuclear Information System (INIS)
McIntosh, C.B.G.
1976-01-01
Properties of homothetic or self-similar motions in general relativity are examined with particular reference to vacuum and perfect-fluid space-times. The role of the homothetic bivector with components Hsub((a;b)) formed from the homothetic vector H is discussed in some detail. It is proved that a vacuum space-time only admits a nontrivial homothetic motion if the homothetic vector field is non-null and is not hypersurface orthogonal. As a subcase of a more general result it is shown that a perfect-fluid space-time cannot admit a non-trivial homothetic vector which is orthogonal to the fluid velocity 4-vector. (author)
Einstein algebras and general relativity
International Nuclear Information System (INIS)
Heller, M.
1992-01-01
A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs
General relativity and gravitation, 1989
International Nuclear Information System (INIS)
Ashby, N.; Bartlett, D.F.; Wyss, W.
1990-01-01
This volume records the lectures and symposia of the 12th International Conference on General Relativity and Gravitation. Plenary lecturers reviewed the major advances since the previous conference in 1986. The reviews cover classical and quantum theory of gravity, colliding gravitational waves, gravitational lensing, relativistic effects on pulsars, tests of the inverse square law, numerical relativity, cosmic microwave background radiation, experimental tests of gravity theory, gravitational wave detectors, and cosmology. The plenary lectures are complemented by summaries of symposia, provided by the chairmen. Almost 700 contributed papers were presented at these and they cover an even wider range of topics than the plenary talks. The book provides a comprehensive guide to research activity in both experimental and theoretical gravitation and its applications in astrophysics and cosmology. It will be essential reading for research workers in these fields, as well as theoretical and experimental physicists, astronomers, and mathematicians who wish to be acquainted with modern developments in gravitational theory and general relativity. All the papers and summaries of the workshop sessions are indexed separately. (16 united talks, 20 workshop sessions). (author)
The dispersion relation of a gravitating spiral system
International Nuclear Information System (INIS)
Evangelidis, E.
1977-01-01
The dispersion relation has been found for a galaxy, without the assumption that the centrifugal force is balanced by the gravitational force. It has been shown that such a system (1) can be gravitationally unstable under appropriate conditions, and (2) that there is no resonance at ω=2Ω (Ω=angular velocity of the Galaxy). (Auth.)
Quasi-pions with temperature dependent dispersion relation
International Nuclear Information System (INIS)
Gorenstein, M.I.
1995-01-01
We construct the procedure to calculate thermodynamical functions for a system of quasi-particles with temperature dependent dispersion relation. Two models for the hot quasi-pion system are considered to illustrate the importance of thermodynamical self consistency requirements. 8 refs., 9 figs
Mord studies in IR region by new dispersion relation
International Nuclear Information System (INIS)
Murthy, V.R.; Kumar, R. Jeevan
1994-01-01
This is the continuation of the series reporting MORD studies to typical problem in Chemistry and Polymer Science. In our earlier papers the MORDsup1.2 studied only in visible region. In this present investigation we extended the application of the New Dispersion Relation in IR region to determine the MORD and tested to some simple systems
Nonlinear generalization of special relativity
International Nuclear Information System (INIS)
Winterberg, F.
1985-01-01
In Poincares axiomatic formulation special relativity is a derived consequence of a true Lorentz contraction, for a rod in absolute motion through a substratum. Furthermore, Lorentz had shown that the rod contraction can be understood by an inverse square law interaction and therefore special relativity derived from more fundamental principles. The derivation by Lorentz shows that the root of the divergence problems is the singular inverse square law. By replacing the inverse square law with a regular one through the introduction of a finite length, the author has succeeded in deriving a nonlinear generalization of special relativity which eliminates all infinities. Besides the relative velocities, these nonlinear transformation equations also contain absolute velocities against a substratum, but in the limit of small energies they go over into the linear Lorentz transformations. Depending on the smallness of the fundamental length, departures from special relativity can be observed only at very high energies. The theorem that the velocity of light is the same in all reference systems still holds and likewise the conservation laws for energy and momentum
International Nuclear Information System (INIS)
Frank, A.I.; Nosov, V.G.
1995-01-01
Modern theoretical concepts concerning the dispersion relation for slow neutrons in matter are considered. The generally accepted optical-potential model is apparently not quite accurate and should be supplemented with some small corrections in the energy range attainable in experiments. For ultracold neutrons, these corrections are related to the proximity of the applicability boundary of the theory; for cold neutrons, these corrections are due to correlations in the positions of scatters. The accuracy of existing experiments is insufficient for confirmation or refutation these conclusions. A precision experiment is proposed to verify the dispersion relation for long-wave neutrons. 30 refs., 3 figs
Relativity: Special, General, and Cosmological
International Nuclear Information System (INIS)
Ellis, G F R
2005-01-01
Wolfgang Rindler is known as a writer of exceptional clarity. This quality is evident in this book as it explores in depth first special relativity, then general relativity, and finally relativistic cosmology. He bases his writing in the fundamental underlying ideas and principles that so successfully guided Einstein in his work, clarifying their nature and implications in an illuminating way with many examples. The usual suspects are there: the relativity principle and equivalence principle, the abolishing of absolute space, invariance of the speed of light, analytic and geometric representations of the Lorentz transformation, its kinematic and dynamic consequences, relativistic optics, Minkowski spacetime, energy and momentum conservation, and the Compton effect. Particularly useful is the emphasis on the unity of the whole: for example (p 63) that the kinematic effect of length shortening must imply a corresponding detailed mechanical explanation of that shortening. The tensor formulation of Maxwell's equations leads to the transformation properties of the electromagnetic field and consequent elegant derivation of the field of an infinite straight current; in this case, relativity is important even for slowly moving charges because an ordinary current moves a very big charge (p 151). General relativity is systematically introduced in stages, starting with curved spaces and moving on through static and stationary spacetimes, geodesics, and tensor calculus to the field equations. A considerable strength of the book is the careful detailed examination of the local and global geometry of the major significant solutions of the equations: the Schwarzschild spacetime and its Kruskal extension, plane gravitational waves, de sitter and anti-de Sitter spacetimes, and Robertson-Walker cosmologies. The latter includes a clear presentation of the dust and radiation model dynamics for the variety of possible cases, a detailed examination of observational relations, and
The dispersion relation of charge and current compensated relativistic electron beam-plasma system
International Nuclear Information System (INIS)
Vrba, P.; Schroetter, J.; Jarosova, P.; Koerbel, S.
1978-01-01
The unstable regions of relativistic electron beam-plasma system were determined by analysing the general dispersion relation numerically. The external parameters were varied to ensure more effective instability excitations. The full charge- and current compensation presumptions lead to the new synchronism predictions. The slow space charge wave and slow cyclotron wave of the return current are synchronous with the plasma ion wave. (author)
Dispersion Relations for Electroweak Observables in Composite Higgs Models
Contino, Roberto
2015-12-14
We derive dispersion relations for the electroweak oblique observables measured at LEP in the context of $SO(5)/SO(4)$ composite Higgs models. It is shown how these relations can be used and must be modified when modeling the spectral functions through a low-energy effective description of the strong dynamics. The dispersion relation for the parameter $\\epsilon_3$ is then used to estimate the contribution from spin-1 resonances at the 1-loop level. Finally, it is shown that the sign of the contribution to the $\\hat S$ parameter from the lowest-lying spin-1 states is not necessarily positive definite, but depends on the energy scale at which the asymptotic behavior of current correlators is attained.
Age--velocity-dispersion relation in the solar neighborhood
International Nuclear Information System (INIS)
Carlberg, R.G.; Dawson, P.C.; Hsu, T.; VandenBerg, D.A.
1985-01-01
The age--velocity-dispersion relation for stars in the solar neighborhood is examined as an indicator of the dominant acceleration mechanism of the stars and the formation history of the local disk. Twarog's sample of F stars, for which ages and photometric distances can be determined, is combined with astrometric data to obtain tangential velocities of a set of stars with a large age range. The resulting age--velocity-dispersion relation rises fairly steeply for stars less than 6 Gyr old, thereafter becoming nearly constant with age. These data are consistent with a simple model in which no local disk is initially present, following which stars are born at a constant rate in time and heated by transient spiral waves. The corresponding age-metallicity relation complements this dynamical measure of the formation history of the disk. The use of new stellar models and a revised metallicity calibration leads to quantitative differences from previous work
Relation of wave energy and momentum with the plasma dispersion relation in an inhomogeneous plasma
International Nuclear Information System (INIS)
Berk, H.L.; Pfirsch, D.
1988-01-01
The expressions for wave energy and angular momentum commonly used in homogeneous and near-homogeneous media is generalized to inhomogeneous media governed by a nonlocal conductivity tensor. The expression for wave energy applies to linear excitations in an arbitrary three-dimensional equilibrium, while the expression for angular momentum applies to linear excitations of azimuthally symmetric equilibria. The wave energy E-script/sub wave/ is interpreted as the energy transferred from linear external sources to the plasma if there is no dissipation. With dissipation, such a simple interpretation is lacking as energy is also thermally absorbed. However, for azimuthally symmetric equilibria, the expression for the wave energy in a frame rotating with a frequency ω can be unambiguously separated from thermal energy. This expression is given by E-script/sub wave/ -ωL/sub wave/ l, where L/sub wave/ is the wave angular momentum defined in the text and l the azimuthal wavenumber and it is closely related to the real part of a dispersion relation for marginal stability. The imaginary part of the dispersion is closely related to the energy input into a system. Another useful quantity discussed is the impedance form, which can be used for three-dimensional equilibrium without an ignorable coordinate and the expression is closely related to the wave impedance used in antenna theory. Applications to stability theory are also discussed
The renaissance of general relativity
International Nuclear Information System (INIS)
Will, C.
1989-01-01
A historical evaluation of Einstein's theory of general relativity is presented, including the three classical tests of the theory. Gravitation is shown to be a ''curved spacetime'' phenomenon, particularly if the Einstein equivalence principle (EEP) is true. The article traces the success and failures of the theory over the years and up to the present. The concept of gravitation waves was, for example, strengthened by the discovery of a binary pulsar in 1974. The author describes the theory's relevance to neutron stars and black holes and its role in establishing the hot big bang model of cosmological evolution. The article concludes by considering the possibility of antigravity and how gravitational calculations can be done by computer because of the large number of variables in the calculations. (U.K.)
General relativity: An erfc metric
Plamondon, Réjean
2018-06-01
This paper proposes an erfc potential to incorporate in a symmetric metric. One key feature of this model is that it relies on the existence of an intrinsic physical constant σ, a star-specific proper length that scales all its surroundings. Based thereon, the new metric is used to study the space-time geometry of a static symmetric massive object, as seen from its interior. The analytical solutions to the Einstein equation are presented, highlighting the absence of singularities and discontinuities in such a model. The geodesics are derived in their second- and first-order differential formats. Recalling the slight impact of the new model on the classical general relativity tests in the solar system, a number of facts and open problems are briefly revisited on the basis of a heuristic definition of σ. A special attention is given to gravitational collapses and non-singular black holes.
Spacecraft Tests of General Relativity
Anderson, John D.
1997-01-01
Current spacecraft tests of general relativity depend on coherent radio tracking referred to atomic frequency standards at the ground stations. This paper addresses the possibility of improved tests using essentially the current system, but with the added possibility of a space-borne atomic clock. Outside of the obvious measurement of the gravitational frequency shift of the spacecraft clock, a successor to the suborbital flight of a Scout D rocket in 1976 (GP-A Project), other metric tests would benefit most directly by a possible improved sensitivity for the reduced coherent data. For purposes of illustration, two possible missions are discussed. The first is a highly eccentric Earth orbiter, and the second a solar-conjunction experiment to measure the Shapiro time delay using coherent Doppler data instead of the conventional ranging modulation.
A general polynomial solution to convection–dispersion equation ...
Indian Academy of Sciences (India)
Jiao Wang
concentration profiles and optimal solute transport parameters. Furthermore, the general .... requirement; in other words, if Is(t) is cumulated solute added in the column ..... National Natural Science Foundation of China. (Nos. 41530854 and ...
Dispersion and energy conservation relations of surface waves in semi-infinite plasma
International Nuclear Information System (INIS)
Atanassov, V.
1981-01-01
The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered. (author)
Machian effects in general relativity
International Nuclear Information System (INIS)
Embacher, F.
1988-01-01
As a consequence of Mach's principle, rotating matter should cause local inertial frames or gyroscopes in its vicinity to undergo a small rotation which is not present in the Newtonian picture. H. Thirring and J. Lense were the first to derive similar predictions from the field equations of general relativity. Since these early days of relativity, a lot of exact and approximate solutions to Einstein's equations have been examined under this point of view. The qualitative features of Machian effects are most easily demonstrated in the cylinder symmetric case, where some exact results are available. For example, space-time is flat inside a uniformly rotating matter shell, and the rotation of this interior with respect to 'infinity' (the distant stars) has a clear meaning. In the more realistic case of what happens near a massive rotating star, one is forced to perform certain approximations. In modern language, Machian effects are described in terms of the twist of timelike killing vector fields. In the linearized theory, the equations that determine the Machian structure generated by a given matter distribution, resemble to some extent those of classical electrodynamics. This correspondence provides a pedagogical approach how to compute the quantitative extent of inertial frame 'dragging'. 6 refs., 5 figs. (Author)
Angular momentum in general relativity
International Nuclear Information System (INIS)
Prior, C.R.
1977-01-01
The definition of angular momentum proposed in part I of this series (Prior. Proc. R. Soc. Lond.; A354:379 (1977)) is investigated when applied to rotating black holes. It is shown how to use the formula to evaluate the angular momentum of a stationary black hole. This acts as a description of a background space on which the effect of first matter and then gravitational perturbations is considered. The latter are of most interest and the rate of change of angular momentum, dJ/dt, is found as an expression in the shear induced in the event horizon by the perturbation and in its time integral. Teukolsky's solutions (Astrophys. J.; 185:635 (1973)) for the perturbed component of the Weyl tensor are then used to find this shear and hence to give an exact answer for dJ/dt. One of the implications of the result is a direct verification of Bekenstein's formula (Phys. Rev.; 7D:949 (1973)) relating in a simple way the rate of change of angular momentum to the rate of change of mass caused by a plane wave. A more general expression is also given for dM/dt. Considering only stationary perturbations, it is shown how to generalize the definition of angular momentum so as to include information about its direction as well. Three problems are particularly discussed - a single moon, two or more moons and a ring of matter causing the perturbation - since they provide illustrations of all the main features of the black hole's behaviour. In every case it is found that the black hole realigns its axis of rotation so that the final configuration is axisymmetric if possible; otherwise is slows down completely to reach a static state. (author)
Improved pion pion scattering amplitude from dispersion relation formalism
International Nuclear Information System (INIS)
Cavalcante, I.P.; Coutinho, Y.A.; Borges, J. Sa
2005-01-01
Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude. (author)
Analytical solution of dispersion relations for the nuclear optical model
Energy Technology Data Exchange (ETDEWEB)
VanderKam, J.M. [Center for Communications Research, Thanet Road, Princeton, NJ 08540 (United States); Weisel, G.J. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States); Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 (United States); Tornow, W. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States)
2000-12-01
Analytical solutions of dispersion integral relations, linking the real and imaginary parts of the nuclear optical model, have been derived. These are displayed for some widely used forms of the volume- and surface-absorptive nuclear potentials. When the analytical solutions are incorporated into the optical-model search code GENOA, replacing a numerical integration, the code runs three and a half to seven times faster, greatly aiding the analysis of direct-reaction, elastic scattering data. (author)
Geometric quantization and general relativity
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-01-01
The purpose of geometric quantization is to give a rigorous mathematical content to the 'correspondence principle' between classical and quantum mechanics. The main tools are borrowed on one hand from differential geometry and topology (differential manifolds, differential forms, fiber bundles, homology and cohomology, homotopy), on the other hand from analysis (functions of positive type, infinite dimensional group representations, pseudo-differential operators). Some satisfactory results have been obtained in the study of dynamical systems, but some fundamental questions are still waiting for an answer. The 'geometric quantization of fields', where some further well known difficulties arise, is still in a preliminary stage. In particular, the geometric quantization on the gravitational field is still a mere project. The situation is even more uncertain due to the fact that there is no experimental evidence of any quantum gravitational effect which could give us a hint towards what we are supposed to look for. The first level of both Quantum Theory, and General Relativity describes passive matter: influence by the field without being a source of it (first quantization and equivalence principle respectively). In both cases this is only an approximation (matter is always a source). But this approximation turns out to be the least uncertain part of the description, because on one hand the first quantization avoids the problems of renormalization and on the other hand the equivalence principle does not imply any choice of field equations (it is known that one can modify Einstein equations at short distances without changing their geometrical properties). (Auth.)
ICRH programmes for antennas and for plasma dispersion relation
International Nuclear Information System (INIS)
Soell, M.; Springmann, E.
1984-02-01
This report describes the computer programmes used for designing the ICRH antennas at IPP. In the first part of the report the underlying physical principles are discussed on which the programmes are based. 2-D (two-dimensional) and 3-D (three-dimensional) models are used. In the second part the input and output of the programmes is described, and in the third part some results on ICRH antennas built for existing machines at IPP and antennas for machines which are in the design and construction phase are presented. In Appendix I the formulae for the 2-D model including plasma density profiles are described and an investigation of this 2-D model on folded dipol antennae is given. In Appendix II the main formulae for a computer program for the complete hot dispersion relation is given; the application of the program for an ASDEX plasma (dispersion for the fast wave and Bernstein wave) is shown. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Marshall, Shaun [Worcester Polytechnic Inst., Worcester, MA (United States). Dept. of Physics; Potter, Charles [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Medich, David [Worcester Polytechnic Inst., Worcester, MA (United States). Dept. of Physics
2018-05-01
A recent analysis of historical radionuclide resuspension datasets con rmed the general applicability of the Anspaugh and modified Anspaugh models of resuspension factors following both controlled and disastrous releases. The observations appear to increase in variance earlier in time, however all points were equally weighted in statistical fit calculations, inducing a positive skewing of resuspension coeffcients. Such data are extracted from the available deposition experiments spanning 2900 days. Measurements within a 3-day window are grouped into singular sample sets to construct standard deviations. A refitting is performed using a relative instrumental weighting of the observations. The resulting best-fit equations produces tamer exponentials which give decreased integrated resuspension factor values relative to those reported by Anspaugh. As expected, the fits attenuate greater error amongst the data at earlier time. The reevaluation provides a sharper contrast between the empirical models, and reafirms their deficiencies in the short-lived timeframe wherein the dynamics of particulate dispersion dominate the resuspension process.
Marshall, Shaun; Potter, Charles; Medich, David
2018-05-01
A recent analysis of historical radionuclide resuspension datasets confirmed the general applicability of the Anspaugh and modified Anspaugh models of resuspension factors following both controlled and disastrous releases. While observations appear to have larger variance earlier in time, previous studies equally weighted the data for statistical fit calculations; this could induce a positive skewing of resuspension coefficients in the early time-period. A refitting is performed using a relative instrumental weighting of the observations. Measurements within a 3-d window are grouped into singular sample sets to construct standard deviations. The resulting best-fit equations produce tamer exponentials, which give decreased integrated resuspension factor values relative to those reported by Anspaugh. As expected, the fits attenuate greater error among the data at earlier time. The reevaluation provides a sharper contrast between the empirical models and reaffirms their deficiencies in the short-lived timeframe wherein the dynamics of particulate dispersion dominate the resuspension process.
Pion-pair formation and the pion dispersion relation in a hot pion gas
Energy Technology Data Exchange (ETDEWEB)
Chanfay, G. [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; Alm, T. [Rostock Univ. (Germany); Schuck, P. [Grenoble-1 Univ., 38 (France). Inst. des Sciences Nucleaires; Welke, G. [Wayne State Univ., Detroit, MI (United States). Dept. of Physics and Astronomy
1996-09-01
The possibility of pion-pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans-Rashind transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two-particle propagator. In Bose systems there exists a second, lower critical temperature, associated with the appearance of the single-particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usual quasiparticle dispersion to a Bogoliubov-like dispersion relation at low momenta. This generalizes the non-relativistic results for an attractive Bose gas by Evans et al. Possible consequences for the inclusive pion spectra measured in heavy-ion collisions at ultra-relativistic energies are discussed. 21 refs.
Modern Canonical Quantum General Relativity;
International Nuclear Information System (INIS)
Kiefer, Claus
2008-01-01
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly divided into two classes: either one seeks a unified quantum framework of all interactions or one starts with a direct quantization of general relativity. In the first class, string theory (M-theory) is the only known example. In the second class, one can make an additional methodological distinction: while covariant approaches such as path-integral quantization use the four-dimensional metric as an essential ingredient of their formalism, canonical approaches start with a foliation of spacetime into spacelike hypersurfaces in order to arrive at a Hamiltonian formulation. The present book is devoted to one of the canonical approaches-loop quantum gravity. It is named modern canonical quantum general relativity by the author because it uses connections and holonomies as central variables, which are analogous to the variables used in Yang-Mills theories. In fact, the canonically conjugate variables are a holonomy of a connection and the flux of a non-Abelian electric field. This has to be contrasted with the older geometrodynamical approach in which the metric of three-dimensional space and the second fundamental form are the fundamental entities, an approach which is still actively being pursued. It is the author's ambition to present loop quantum gravity in a way in which every step is formulated in a mathematically rigorous form. The formal Leitmotiv of loop quantum gravity is background independence. Non-gravitational theories are usually quantized on a given non-dynamical background. In contrast, due to the geometrical nature of gravity, no such background exists in quantum gravity. Instead, the notion of a background is supposed to emerge a posteriori as an approximate notion from quantum states of geometry. As a consequence, the standard ultraviolet divergences of
Action principle for the generalized harmonic formulation of general relativity
International Nuclear Information System (INIS)
Brown, J. David
2011-01-01
An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona-Casas, and Palenzuela. The relationship between the generalized harmonic action and the Bona, Bona-Casas, and Palenzuela action is discussed in detail.
International Nuclear Information System (INIS)
Deeba, F.; Ahmad, Zahoor; Murtaza, G.
2015-01-01
Sharifi and Parvazian have presented comments on our paper by questioning the validity of the results. The plots of different curves of kappa and (r, q) distributions produced by them are incorrect. They pretended as if we have made claim that our results are valid for large arguments of product of Bessel Function, whereas Neumann's series expansion is valid only for small arguments. In our paper, no claim is made that the results are valid for all values of b. Our results are valid only for b ≪ 1. The results plotted by the commenters are incorrect and in this response we are presenting correct plots of dispersion curves
Energy Technology Data Exchange (ETDEWEB)
Deeba, F.; Ahmad, Zahoor [National Tokamak Fusion Program, PAEC, P.O. Box 3329, Islamabad 44000 (Pakistan); Murtaza, G. [Quaid-i-Azam University, Islamabad 44000 (Pakistan)
2015-02-15
Sharifi and Parvazian have presented comments on our paper by questioning the validity of the results. The plots of different curves of kappa and (r, q) distributions produced by them are incorrect. They pretended as if we have made claim that our results are valid for large arguments of product of Bessel Function, whereas Neumann's series expansion is valid only for small arguments. In our paper, no claim is made that the results are valid for all values of b. Our results are valid only for b ≪ 1. The results plotted by the commenters are incorrect and in this response we are presenting correct plots of dispersion curves.
A Generalized turbulent dispersion model for bubbly flow numerical simulation in NEPTUNE-CFD
Energy Technology Data Exchange (ETDEWEB)
Laviéville, Jérôme, E-mail: Jerome-marcel.lavieville@edf.fr; Mérigoux, Nicolas, E-mail: nicolas.merigoux@edf.fr; Guingo, Mathieu, E-mail: mathieu.guingo@edf.fr; Baudry, Cyril, E-mail: Cyril.baudry@edf.fr; Mimouni, Stéphane, E-mail: stephane.mimouni@edf.fr
2017-02-15
The NEPTUNE-CFD code, based upon an Eulerian multi-fluid model, is developed within the framework of the NEPTUNE project, financially supported by EDF (Electricité de France), CEA (Commissariat à l’Energie Atomique et aux Energies Alternatives), IRSN (Institut de Radioprotection et de Sûreté Nucléaire) and AREVA-NP. NEPTUNE-CFD is mainly focused on Nuclear Safety applications involving two-phase water-steam flows, like two-phase Pressurized Shock (PTS) and Departure from Nucleate Boiling (DNB). Many of these applications involve bubbly flows, particularly, for application to flows in PWR fuel assemblies, including studies related to DNB. Considering a very usual model for interfacial forces acting on bubbles, including drag, virtual mass and lift forces, the turbulent dispersion force is often added to moderate the lift effect in orthogonal directions to the main flow and get the right dispersion shape. This paper presents a formal derivation of this force, considering on the one hand, the fluctuating part of drag and virtual mass, and on the other hand, Turbulent Pressure derivation obtained by comparison between Lagrangian and Eulerian description of bubbles motion. An extension of the Tchen’s theory is used to express the turbulent kinetic energy of bubbles and the two-fluid turbulent covariance tensor in terms of liquid turbulent velocities and time scale. The model obtained by this way, called Generalized Turbulent Dispersion Model (GTD), does not require any user parameter. The model is validated against Liu & Bankoff air-water experiment, Arizona State University (ASU) experiment, DEBORA experiment and Texas A&M University (TAMU) boiling flow experiments.
de Waal, C; Rodger, J G; Anderson, B; Ellis, A G
2014-05-01
Dispersal and breeding system traits are thought to affect colonization success. As species have attained their present distribution ranges through colonization, these traits may vary geographically. Although several theories predict associations between dispersal ability, selfing ability and the relative position of a population within its geographic range, there is little theoretical or empirical consensus on exactly how these three variables are related. We investigated relationships between dispersal ability, selfing ability and range position across 28 populations of 13 annual, wind-dispersed Asteraceae species from the Namaqualand region of South Africa. Controlling for phylogeny, relative dispersal ability--assessed from vertical fall time of fruits--was positively related to an index of autofertility--determined from hand-pollination experiments. These findings support the existence of two discrete syndromes: high selfing ability associated with good dispersal and obligate outcrossing associated with lower dispersal ability. This is consistent with the hypothesis that selection for colonization success drives the evolution of an association between these traits. However, no general effect of range position on dispersal or breeding system traits was evident. This suggests selection on both breeding system and dispersal traits acts consistently across distribution ranges. © 2014 The Authors. Journal of Evolutionary Biology © 2014 European Society For Evolutionary Biology.
Zorn algebra in general relativity
International Nuclear Information System (INIS)
Oliveira, C.G.; Maia, M.D.
The covariant differential properties of the split Cayley subalgebra of local real quaternion tetrads is considered. Referred to this local quaternion tetrad several geometrical objects are given in terms of Zorn-Weyl matrices. Associated to a pair of real null vectors we define two-component spinor fields over the curved space and the associated Zorn-Weyl matrices which satisfy the Dirac equation written in terms of the Zorn algebra. The formalism is generalized by considering a field of complex tetrads defining a Hermitian second rank tensor. The real part of this tensor describes the gravitational potentials and the imaginary part the electromagnetic potentials in the Lorentz gauge. The motion of a charged spin zero test body is considered. The Zorn-Weyl algebra associated to this generalized formalism has elements belonging to the full octonion algebra [pt
Isotropic stars in general relativity
International Nuclear Information System (INIS)
Mak, M.K.; Harko, T.
2013-01-01
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior space-time of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy condition, a second order ordinary differential equation, into a Riccati type first order differential equation, and using a general integrability condition for the Riccati equation. This allows us to obtain an exact non-singular solution of the interior field equations for a fluid sphere, expressed in the form of infinite power series. The physical features of the solution are studied in detail numerically by cutting the infinite series expansions, and restricting our numerical analysis by taking into account only n=21 terms in the power series representations of the relevant astrophysical parameters. In the present model all physical quantities (density, pressure, speed of sound etc.) are finite at the center of the sphere. The physical behavior of the solution essentially depends on the equation of state of the dense matter at the center of the star. The stability properties of the model are also analyzed in detail for a number of central equations of state, and it is shown that it is stable with respect to the radial adiabatic perturbations. The astrophysical analysis indicates that this solution can be used as a realistic model for static general relativistic high density objects, like neutron stars. (orig.)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Zahn, J.W.
2006-12-15
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
International Nuclear Information System (INIS)
Zahn, J.W.
2006-12-01
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation
Energy Technology Data Exchange (ETDEWEB)
Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir; Dareyni, H.
2017-05-15
Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.
Numerical Hydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2003-01-01
Full Text Available The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.
Directory of Open Access Journals (Sweden)
M. Arshad
Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method
Stochastic quantization of general relativity
International Nuclear Information System (INIS)
Rumpf, H.
1986-01-01
Following an elementary exposition of the basic mathematical concepts used in the theory of stochastic relaxation processes the stochastic quantization method of Parisi and Wu is briefly reviewed. The method is applied to Einstein's theory of gravitation using a formalism that is manifestly covariant with respect to field redefinitions. This requires the adoption of Ito's calculus and the introduction of a metric in field configuration space, for which there is a unique candidate. Due to the indefiniteness of the Euclidean Einstein-Hilbert action stochastic quantization is generalized to the pseudo-Riemannian case. It is formally shown to imply the DeWitt path integral measure. Finally a new type of perturbation theory is developed. (Author)
A logic road from special relativity to general relativity
Andréka, Hajnal; Madarász, Judit X.; Németi, István; Székely, Gergely
2010-01-01
We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
Conformal methods in general relativity
Valiente Kroon, Juan A
2016-01-01
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
Pulsar timing and general relativity
Backer, D. C.; Hellings, R. W.
1986-01-01
Techniques are described for accounting for relativistic effects in the analysis of pulsar signals. Design features of instrumentation used to achieve millisecond accuracy in the signal measurements are discussed. The accuracy of the data permits modeling the pulsar physical characteristics from the natural glitches in the emissions. Relativistic corrections are defined for adjusting for differences between the pulsar motion in its spacetime coordinate system relative to the terrestrial coordinate system, the earth's motion, and the gravitational potentials of solar system bodies. Modifications of the model to allow for a binary pulsar system are outlined, including treatment of the system as a point mass. Finally, a quadrupole model is presented for gravitational radiation and techniques are defined for using pulsars in the search for gravitational waves.
The use of generalized functions and distributions in general relativity
International Nuclear Information System (INIS)
Steinbauer, R; Vickers, J A
2006-01-01
We review the extent to which one can use classical distribution theory in describing solutions of Einstein's equations. We show that there are a number of physically interesting cases which cannot be treated using distribution theory but require a more general concept. We describe a mathematical theory of nonlinear generalized functions based on Colombeau algebras and show how this may be applied in general relativity. We end by discussing the concept of singularity in general relativity and show that certain solutions with weak singularities may be regarded as distributional solutions of Einstein's equations. (topical review)
International Nuclear Information System (INIS)
Biswas, Anjan
2009-01-01
In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.
From dispersion relations to spectral dimension - and back again
International Nuclear Information System (INIS)
Sotiriou, Thomas P.; Visser, Matt; Weinfurtner, Silke
2011-01-01
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely, though not exclusively, by investigations of causal dynamical triangulations and Horava gravity as possible candidates for quantum gravity. We advocate the use of the spectral dimension as a probe for the kinematics of these (and other) systems in the region where spacetime curvature is small, and the manifold is flat to a good approximation. In particular, we show how to assign a spectral dimension (as a function of so-called diffusion time) to any arbitrarily specified dispersion relation. We also analyze the fundamental properties of spectral dimension using extensions of the usual Seeley-DeWitt and Feynman expansions and by using saddle point techniques. The spectral dimension turns out to be a useful, robust, and powerful probe, not only of geometry, but also of kinematics.
General relativity and mathematics; Relatividad General y Matematicas
Energy Technology Data Exchange (ETDEWEB)
Mars, M.
2015-07-01
General relativity is more than a theory of gravity, since any physical process occupies space and lasts for a time, forcing to reconcile that physical theory that describes what the dynamic nature of space-time itself. (Author)
Rainbows without unicorns: metric structures in theories with modified dispersion relations
International Nuclear Information System (INIS)
Lobo, Iarley P.; Loret, Niccolo; Nettel, Francisco
2017-01-01
Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)
Rainbows without unicorns: metric structures in theories with modified dispersion relations
Lobo, Iarley P.; Loret, Niccoló; Nettel, Francisco
2017-07-01
Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.
Rainbows without unicorns: metric structures in theories with modified dispersion relations
Energy Technology Data Exchange (ETDEWEB)
Lobo, Iarley P. [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); ICRANet, Pescara (Italy); CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); INFN Sezione Roma 1 (Italy); Loret, Niccolo [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia); Nettel, Francisco [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico (Mexico); INFN Sezione Roma 1 (Italy)
2017-07-15
Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)
Centennial of general relativity a celebration
2017-01-01
It has been over 100 years since the presentation of the Theory of General Relativity by Albert Einstein, in its final formulation, to the Royal Prussian Academy of Sciences. To celebrate 100 years of general relativity, World Scientific publishes this volume with a dual goal: to assess the current status of the field of general relativity in broad terms, and discuss future directions. The volume thus consists of broad overviews summarizing major developments over the past decades and their perspective contributions.
Dispersion relation for localized magnetic polaritons propagating at ...
Indian Academy of Sciences (India)
Abstract. Localized magnetic polaritons are investigated in the systems consisting of two magnetic superlattices, coupled by a ferromagnetic contact layer. The general dis- persion relation for localized magnetic polaritons are derived in the framework of the electromagnetic wave theory in the Voigt geometry by the 'transfer' ...
General Relativity in (1 + 1) Dimensions
Boozer, A. D.
2008-01-01
We describe a theory of gravity in (1 + 1) dimensions that can be thought of as a toy model of general relativity. The theory should be a useful pedagogical tool, because it is mathematically much simpler than general relativity but shares much of the same conceptual structure; in particular, it gives a simple illustration of how gravity arises…
Al-Jabr, Ahmad Ali; Alsunaidi, Mohammad A.; Ng, Tien Khee; Ooi, Boon S.
2013-01-01
In this paper, an finite-difference time-domain (FDTD) algorithm for simulating propagation of EM waves in anisotropic material is presented. The algorithm is based on the auxiliary differential equation and the general polarization formulation. In anisotropic materials, electric fields are coupled and elements in the permittivity tensor are, in general, multiterm dispersive. The presented algorithm resolves the field coupling using a formulation based on electric polarizations. It also offers a simple procedure for the treatment of multiterm dispersion in the FDTD scheme. The algorithm is tested by simulating wave propagation in 1-D magnetized plasma showing excellent agreement with analytical solutions. Extension of the algorithm to multidimensional structures is straightforward. The presented algorithm is efficient and simple compared to other algorithms found in the literature. © 2012 IEEE.
Al-Jabr, Ahmad Ali
2013-03-01
In this paper, an finite-difference time-domain (FDTD) algorithm for simulating propagation of EM waves in anisotropic material is presented. The algorithm is based on the auxiliary differential equation and the general polarization formulation. In anisotropic materials, electric fields are coupled and elements in the permittivity tensor are, in general, multiterm dispersive. The presented algorithm resolves the field coupling using a formulation based on electric polarizations. It also offers a simple procedure for the treatment of multiterm dispersion in the FDTD scheme. The algorithm is tested by simulating wave propagation in 1-D magnetized plasma showing excellent agreement with analytical solutions. Extension of the algorithm to multidimensional structures is straightforward. The presented algorithm is efficient and simple compared to other algorithms found in the literature. © 2012 IEEE.
Wang, Yu-Zhu; Wei, Changhua
2018-04-01
In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.
Dynamics of relative motion of test particles in general relativity
International Nuclear Information System (INIS)
Bazanski, S.L.
1977-01-01
Several variational principles which lead to the first and the second geodesic deviation equations, recently formulated by the author and used for the description of the relative motion of test particles in general relativity are presented. Relations between these principles are investigated and exhibited. The Hamilton-Jacobi equation is also studied for these generalized deviations and the conservation laws appearing here are discussed
The Confrontation between General Relativity and Experiment
Directory of Open Access Journals (Sweden)
Will Clifford
2001-01-01
Full Text Available The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements.When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.
Particle field in bimetric general relativity
International Nuclear Information System (INIS)
Falik, D.; Rosen, N.
1980-01-01
The field equations of the bimetric general relativity theory proposed recently by one of the authors (N. Rosen) are put into a static form. The equations are solved near the Schwarzschild sphere, and it is found that the field differs from that of the Einstein general relativity theory: instead of a black hole, one has an impenetrable sphere. For larger distances the field is found to agree with that of ordinary general relativity, so that solar system observations cannot distinguish between the two theories. For very large distances one gets a cosmic contribution to the field which may affect the dynamics of clusters of galaxies
Compact objects in bimetric general relativity
International Nuclear Information System (INIS)
Harpaz, A.; Rosen, N.
1985-01-01
The field equations of the bimetric general relativity theory proposed by one of the authors (N. Rosen), in the static form, are solved in order to investigate the structure of a star. It is found that for an ordinary star the bimetric theory gives the same results as the Einstein general relativity theory. However, for a collapsed star the two theories give different results. In the bimetric theory a configuration in hydrostatic equilibrium exists for a collapsed star filling its Schwarzschild sphere. In general relativity no equilibrium configuration exists in this region, and the star shrinks to a point singularity to form a black hole
Directory of Open Access Journals (Sweden)
Benjamin M. Cowan
2013-04-01
Full Text Available We describe a modification to the finite-difference time-domain algorithm for electromagnetics on a Cartesian grid which eliminates numerical dispersion error in vacuum for waves propagating along a grid axis. We provide details of the algorithm, which generalizes previous work by allowing 3D operation with a wide choice of aspect ratio, and give conditions to eliminate dispersive errors along one or more of the coordinate axes. We discuss the algorithm in the context of laser-plasma acceleration simulation, showing significant reduction—up to a factor of 280, at a plasma density of 10^{23} m^{-3}—of the dispersion error of a linear laser pulse in a plasma channel. We then compare the new algorithm with the standard electromagnetic update for laser-plasma accelerator stage simulations, demonstrating that by controlling numerical dispersion, the new algorithm allows more accurate simulation than is otherwise obtained. We also show that the algorithm can be used to overcome the critical but difficult challenge of consistent initialization of a relativistic particle beam and its fields in an accelerator simulation.
Correa, Sandra Bibiana; Arujo, Joisiane K; Penha, Jerry; Nunes da Cunha, Catia; Bobier, Karen E; Anderson, Jill T
2016-08-31
When species within guilds perform similar ecological roles, functional redundancy can buffer ecosystems against species loss. Using data on the frequency of interactions between fish and fruit, we assessed whether co-occurring frugivores provide redundant seed dispersal services in three species-rich Neotropical wetlands. Our study revealed that frugivorous fishes have generalized diets; however, large-bodied fishes had greater seed dispersal breadth than small species, in some cases, providing seed dispersal services not achieved by smaller fish species. As overfishing disproportionately affects big fishes, the extirpation of these species could cause larger secondary extinctions of plant species than the loss of small specialist frugivores. To evaluate the consequences of frugivore specialization for network stability, we extracted data from 39 published seed dispersal networks of frugivorous birds, mammals and fish (our networks) across ecosystems. Our analysis of interaction frequencies revealed low frugivore specialization and lower nestedness than analyses based on binary data (presence-absence of interactions). In that case, ecosystems may be resilient to loss of any given frugivore. However, robustness to frugivore extinction declines with specialization, such that networks composed primarily of specialist frugivores are highly susceptible to the loss of generalists. In contrast with analyses of binary data, recently developed algorithms capable of modelling interaction strengths provide opportunities to enhance our understanding of complex ecological networks by accounting for heterogeneity of frugivore-fruit interactions. © 2016 The Author(s).
Further study of a new dispersion relation for electron-atom scattering
International Nuclear Information System (INIS)
Bhatia, A.K.; Temkin, A.
1988-01-01
A new recently proposed dispersion relation (DR) [Temkin, Bhatia, and Kim, J. Phys. B 19, L707 (1986)] is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore we start to investigate the analytic structure of the difference amplitude, previously assumed to be nonsingular, on the negative scattering energy axis. Even under severe approximations we find that the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering. We conclude with some brief general remarks on this problem
O(3)-invariant tunneling in general relativity
International Nuclear Information System (INIS)
Berezin, V.A.; Tkachev, I.I.; Kuzmin, V.A.; AN SSSR, Moscow. Inst. Yadernykh Issledovanij)
1987-12-01
We derived a general formula for the action for any O(3)-invariant tunneling processes in false vacuum decay in general relativity. The general classification of the bubble Euclidean trajectories is elaborated and explicit expressions for bounces for some processes like the vacuum creation of a double bubble, in particular in the vicinity of a black hole; the subbarrier creation of the Einstein-Rosen bridge, creation from nothing of two Minkowski worlds connected by a shell etc., are given. (orig.)
Acoustic modes of the phonon dispersion relation of NbD/sub x/ alloys
International Nuclear Information System (INIS)
Rowe, J.M.; Vagelatos, N.; Rush, J.J.; Flotow, H.E.
1975-01-01
The acoustic modes of the phonon dispersion relation in Nb, NbD 0 . 15 , and NbD 0 . 45 were measured at 473 0 K for phonons with wave vectors along the [100], [110], and [111] axes by coherent neutron scattering. The observed neutron groups for both alloys were well defined, with little or no apparent broadening. Results are compared to similar data for Nb--Mo alloys and with previous lattice-dynamics results for PdD 0 . 63 . This comparison shows that despite differences in detail, the general features of the dispersion relations of NbD/sub x/ and Nb--Mo are similar after allowing for the differences in lattice parameters for the two alloys. The measured dispersion curves and derived phonon frequency distributions for the Nb--D alloys are quite different from the analogous results for PdD 0 . 63 in that the average acoustic phonon frequencies increase with increasing deuterium concentration and lattice parameter
Directory of Open Access Journals (Sweden)
Robert SZABO
2011-12-01
Full Text Available The dispersion relations, appearing in the analysis of the stability of a gas flow in a straight acoustically-lined duct with respect to perturbations produced by a time harmonic source, beside the wave number and complex frequency contain the solution of a boundary value problem of the Pridmore-Brown equation depending on the wave number and frequency. For this reason, in practice the dispersion relations are rarely simple enough for carried out the zeros. The determination of zeros of these dispersion relations is crucial for the prediction of the perturbation attenuation or amplification. In this paper an approximation of the dispersion relations is given. Our approach preserves the general character of the mean flow, the general Pridmore-Brown equation and it’s only in the shear flow that we replace the exact solution of the boundary value problem with its Taylor polynomial approximate. In this way new approximate dispersion relations are obtained which zero’s can be found by computer.
Moenster, Mathias; Steinmeyer, Günter; Iliew, Rumen; Lederer, Falk; Petermann, Klaus
2006-11-15
For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.
Axisymmetric solution with charge in general relativity
International Nuclear Information System (INIS)
Arutyunyan, G.G.; Papoyan, V.V.
1989-01-01
The possibility of generating solutions to the equations of general relativity from known solutions of the generalized theory of gravitation and vice versa is proved. An electrovac solution to Einstein's equations that describes a static axisymmetric gravitational field is found. 14 refs
Three-particle physics and dispersion relation theory
Anisovich, A V; Matveev, M A; Nikonov, V A; Nyiri, J; Sarantsev, A V
2013-01-01
The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.
Einstein and General Relativity: Historical Perspectives.
Chandrasekhar, S.
1979-01-01
This paper presented in the 1978 Oppenheimer Memorial Lecture at Los Alamos Scientific Laboratories on August 17, 1978, discusses Einstein's contributions to physics, in particular, his discovery of the general theory of relativity. (HM)
Quantum theory and Einstein's general relativity
International Nuclear Information System (INIS)
Borzeszkowski, H.H.v.; Treder, H.J.
1984-01-01
The paper concerns Einstein's general relativity, wave mechanics and the quantization of Einstein's gravitation equations. The principle of equivalence and its association with both wave mechanics and quantum gravity, is discussed. (U.K.)
Black hole dynamics in general relativity
Indian Academy of Sciences (India)
Abstract. Basic features of dynamical black holes in full, non-linear general relativity are summarized in a pedagogical fashion. Qualitative properties of the evolution of various horizons follow directly from the celebrated Raychaudhuri equation.
International Nuclear Information System (INIS)
Shore, B.W.; Lowder, S.; Johnson, M.A.
1991-01-01
This note considers some of the properties of the Stokes pulse that grows from a specified seed pulse in the presence of a strong pump pulse as it propagates through a dispersive atomic vapor. We first present an generic dimensionless form for the coupled equations that govern the propagation of pump and Stokes fields or collinear plane-wave pulses. By treating the two fields we permit pump depletion. We include transient atomic response (as embodied in the Raman coherence), but neglect changes in atomic populations. (Thus our equations pertain to the regime in which atoms are more numerous than photons). The equations employ a gain length, a dispersion time τ dis , and a Raman coherence time (or memory time) τ R as basic parameters: these two times, together with a single-photon stationary-atom detuning Δ, subsume the details of a particular atomic Raman transition and particular operating conditions. (The effects of Doppler shifts enters the equations through the coherence time). We discuss some general properties of these generic Raman propagation equations, and present illustrations of their solutions in the absence of dispersion. We comment on departures from exponential growth. We than show examples of behavior when dispersion is present and the pump pulse has a bandwidth that exceeds the transform limit. The illustrations presented here do not pertain to any specific atom (i.e. specific wavelengths and oscillator strengths) or to specific experimental conditions (i.e. number densities and pulse intensities). To permit the connection between the present generic results and particular experiments we conclude by providing expressions for the gain length and dispersion time in terms of atomic number density, polarizabilities, oscillator strengths, statistical weights, transition frequencies, and polarization directions. 11 figs
Phonon dispersion relations in monoatomic superlattices: a transfer matrix theory
International Nuclear Information System (INIS)
Albuquerque, E.L. de; Fulco, P.
1986-01-01
We present a lattice dynamical theory for monoatomic superlattices consisting of alternating layers of two different materials. Using a transfer matrix method we obtain explicit the equation for dispersion of the phonon's bulk modes, including the well known result in the long wave-length limit which can be obtained by elasticity theory. An illustation is shown and its features discussed. (Author) [pt
A numerical three-dimensional ocean general circulation and radionuclides dispersion model
International Nuclear Information System (INIS)
Chartier, M.; Marti, O.
1988-01-01
The dispersion of radioactive waste disposed of in the deep-sea or transferred from the atmosphere is a complex hydrodynamic problem concerned by space scales as large as the world ocean. The recent development in the high-speed computers has led to significant progress in ocean modelling and now allows a thorough improvement in the accuracy of the simulations of the nuclides dispersion in the sea. A three-dimensional ocean general circulation model has been recently developed in France for research and engineering purposes. The model solves the primitive equation of the ocean hydrodynamics and the advection-diffusion equation for any dissolved tracer. The code has been fully vectorized and multitasked on 1 to 4 processors of the CRAY-2
Einstein and general relativity: historical perspectives
International Nuclear Information System (INIS)
Chandrasekhar, S.
1978-01-01
The place of Einstein in 20th-century physics is discussed. The basic ideas that led Einstein to his theory of gravitation by the sheer power of speculative thought are described in the most general terms. The prediction of the bending of starlight by the Sun and the eclipse expedition of 1919 are recounted. The author feels that ''the general theory of relativity is incredibly rich in its content;...one finds a glittering face at almost every turn.'' The prediction of black holes by general relativity is noted
Energy and Uncertainty in General Relativity
Cooperstock, F. I.; Dupre, M. J.
2018-03-01
The issue of energy and its potential localizability in general relativity has challenged physicists for more than a century. Many non-invariant measures were proposed over the years but an invariant measure was never found. We discovered the invariant localized energy measure by expanding the domain of investigation from space to spacetime. We note from relativity that the finiteness of the velocity of propagation of interactions necessarily induces indefiniteness in measurements. This is because the elements of actual physical systems being measured as well as their detectors are characterized by entire four-velocity fields, which necessarily leads to information from a measured system being processed by the detector in a spread of time. General relativity adds additional indefiniteness because of the variation in proper time between elements. The uncertainty is encapsulated in a generalized uncertainty principle, in parallel with that of Heisenberg, which incorporates the localized contribution of gravity to energy. This naturally leads to a generalized uncertainty principle for momentum as well. These generalized forms and the gravitational contribution to localized energy would be expected to be of particular importance in the regimes of ultra-strong gravitational fields. We contrast our invariant spacetime energy measure with the standard 3-space energy measure which is familiar from special relativity, appreciating why general relativity demands a measure in spacetime as opposed to 3-space. We illustrate the misconceptions by certain authors of our approach.
Supersymmetry, General Relativity and Unity of Nature
Shima, Kazunari; Tsuda, Motomu
2008-01-01
The basic idea and some physical implications of nonlinear supersymmetric general relativity (NLSUSY GR) are presented. NLSUSY GR may give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g. the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.
Teaching General Relativity to the Layperson
Egdall, Mark
2009-01-01
This paper describes a lay course on general relativity (GR) given at the Osher Lifelong Learning Institute at Florida International University. It is presented in six hour-and-a-half weekly sessions. Other courses offered by the author include special relativity (which precedes the course described here), quantum theory, and cosmology. Students…
Black hole based tests of general relativity
International Nuclear Information System (INIS)
Yagi, Kent; Stein, Leo C
2016-01-01
General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the Universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is four-dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar–tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory. (paper)
General very special relativity in Finsler cosmology
International Nuclear Information System (INIS)
Kouretsis, A. P.; Stathakopoulos, M.; Stavrinos, P. C.
2009-01-01
General very special relativity (GVSR) is the curved space-time of very special relativity (VSR) proposed by Cohen and Glashow. The geometry of general very special relativity possesses a line element of Finsler geometry introduced by Bogoslovsky. We calculate the Einstein field equations and derive a modified Friedmann-Robertson-Walker cosmology for an osculating Riemannian space. The Friedmann equation of motion leads to an explanation of the cosmological acceleration in terms of an alternative non-Lorentz invariant theory. A first order approach for a primordial-spurionic vector field introduced into the metric gives back an estimation of the energy evolution and inflation.
The Confrontation between General Relativity and Experiment.
Will, Clifford M
2014-01-01
The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.
Buhmann, Stefan Yoshi
2012-01-01
In this book, a modern unified theory of dispersion forces on atoms and bodies is presented which covers a broad range of advanced aspects and scenarios. Macroscopic quantum electrodynamics is shown to provide a powerful framework for dispersion forces which allows for discussing general properties like their non-additivity and the relation between microscopic and macroscopic interactions. It is demonstrated how the general results can be used to obtain dispersion forces on atoms in the presence of bodies of various shapes and materials. Starting with a brief recapitulation of volume I, this volume II deals especially with bodies of irregular shapes, universal scaling laws, dynamical forces on excited atoms, enhanced forces in cavity quantum electrodynamics, non-equilibrium forces in thermal environments and quantum friction. The book gives both the specialist and those new to the field a thorough overview over recent results in the field. It provides a toolbox for studying dispersion forces in various contex...
Dispersion relations of the acoustic modes in divalent liquid metals
Directory of Open Access Journals (Sweden)
Inui Masanori
2017-01-01
Full Text Available Collective dynamics in liquid Ca and liquid Cd was studied by inelastic x-ray scattering (IXS. Using our experimental technique to prepare proper sample cells and high performance of an IXS beamline (BL35XU at SPring-8 in Japan, the dynamic structure factor with reasonable statistics was obtained for these divalent liquid metals. For both liquids, the dynamic structure factor at low Q exhibits a central peak with a shoulder or small hump clearly visible on each side, and the inelastic excitation energy determined using the model function composed of Lorentzian and the damped harmonic oscillator function disperses with increasing Q. The dispersion curves of these liquids were compared with that of the longitudinal acoustic phonon in each crystalline phase. From these results, clear difference in the interatomic interaction be- tween liquid Ca and liquid Cd was inferred.
Surface Resonance Bands on (001)W: Experimental Dispersion Relations
DEFF Research Database (Denmark)
Willis, R. F.; Feuerbacher, B.; Christensen, N. Egede
1977-01-01
A band of unbound surface states (resonances), located in an energy region above the vacuum threshold corresponding to an energy band gap in the electron states of the bulk crystal, has been observed by angle-resolved secondary-electron-emission spectroscopy. The experimental dispersion behavior...... is in agreement with the two-dimensional band structure of a clean (001)W surface recently proposed by Smith and Mittheiss....
On generalization uniaxial stress-strain relation
International Nuclear Information System (INIS)
Sahay, C.; Dubey, R.N.
1980-01-01
Different forms of constitutive relations have been advanced for elastic, plastic and elastic-plastic behaviour of materials. It is shown that the various forms of the stress-strain relationship are specialized forms of generalization of a single stress-strain relation. For example, it is shown how the laws of elastic deformation, and the incremental and total deformation relationship for plastic behaviour are derivable from the Ramberg-Osgood relation. (orig.)
The use of dispersion relations to construct unified nucleon optical potentials
International Nuclear Information System (INIS)
Hodgson, P.E.
1991-01-01
The dispersion relations provide a simple and accurate way of parametrizing the optical potential for a particular nucleus over a range of energies. A method is proposed for obtaining a global nucleon optical potential incorporating the dispersion relations. (author). 9 refs, 3 figs
Generalized transformations and coordinates for static spherically symmetric general relativity
Hill, James M.; O'Leary, Joseph
2018-04-01
We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.
Generalized transformations and coordinates for static spherically symmetric general relativity.
Hill, James M; O'Leary, Joseph
2018-04-01
We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.
Generalized Disjunctions in (Infinitary) Structural Consequence Relations
Czech Academy of Sciences Publication Activity Database
Cintula, Petr; Noguera, C.
2012-01-01
Roč. 18, č. 3 (2012), s. 442-443 ISSN 1079-8986. [Logic Colloquium 2011. 11.07.2011-16.07.2011, Barcelona] R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : Abstract Algebraic Logic * Generalized disjunction * Proof by cases properties * Consequence relations Subject RIV: BA - General Mathematics http://www.math.ucla.edu/~asl/bsl/1803- toc .htm
Einstein and the history of general relativity
International Nuclear Information System (INIS)
Howard, D.; Stachel, J.
1989-01-01
This book is a collection of essays by the authors and other people that deal with scientific opinions that led Einstein and his contemporaries to their views of general relativity. Some of the essays explore Einstein's passage from the special theory through a sequence of gravitational theories to the discovery of the field equations of the grand theory in November 1915. Two other essays discuss Einstein's public and private exchanges with Max Abraham and Tullio Levi-Civita in 1913 and 1914. A sympathetic picture of H.A. Lorentz's reaction to the general theory of relativity is included, and a careful and insightful essay on the early understanding of the Schwarzschild-Droste solution to the field equations of general relativity is presented. One paper presents a discussion on the state of the enterprise of general relativity between 1925 and 1928, and a short essay details the history of steps toward quantum gravitational through canonical quantization. A discussion of the history of derivations of the geodesic equation of motion from the field equation and conservation laws of the general theory is presented. The early history of geometrical unified field theories is included
Generalized Landau-Pollak uncertainty relation
International Nuclear Information System (INIS)
Miyadera, Takayuki; Imai, Hideki
2007-01-01
The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented. A possible application to the problem of separability criterion is also suggested
The Confrontation between General Relativity and Experiment
Directory of Open Access Journals (Sweden)
Will Clifford M.
2006-03-01
Full Text Available The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein’s equivalence principle (EEP is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.
Relational Coordination in Danish General Practice
DEFF Research Database (Denmark)
Lundstrøm, Sanne Lykke
. The dissertation present the research study and a collection of three research papers prepared during the period from May 2010 to June 2014. Relational coordination and organisational social capital are measures of novel aspects of an organisation's performance. Relational coordination analyse the communication...... and relationship networks through which work is coordinated across functional and organisational boundaries. Previous studies have shown that relational coordination is positively associated with delivery of care for patients with chronic illness. Organisational social capital is used when analysing...... the psychosocial work environment in organisations, and is seen as a powerful resources for improving organisational performance. Relational coordination and organisational social capital may oer new insight and opportunities for general practice to learn. General practice provides cost-efficient, first...
Generating perfect fluid spheres in general relativity
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-06-01
Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star—a static spherically symmetric blob of fluid with position-independent density—the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.
Generating perfect fluid spheres in general relativity
International Nuclear Information System (INIS)
Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke
2005-01-01
Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star--a static spherically symmetric blob of fluid with position-independent density--the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres
Generalization of Gibbs Entropy and Thermodynamic Relation
Park, Jun Chul
2010-01-01
In this paper, we extend Gibbs's approach of quasi-equilibrium thermodynamic processes, and calculate the microscopic expression of entropy for general non-equilibrium thermodynamic processes. Also, we analyze the formal structure of thermodynamic relation in non-equilibrium thermodynamic processes.
Gravity: An Introduction to Einstein's General Relativity
International Nuclear Information System (INIS)
Fabris, Julio C
2004-01-01
General relativity is one of the cornerstones of modern physics. In spite of this, the teaching of general relativity at undergraduate level remains quite marginal. The reasons for this particular situation are quite well known. We can quote, for example, two of them: general relativity requires specific mathematical tools that are somehow outside the mainstream of undergraduate technical development; moreover, this is a branch of physics whose observational and experimental applications have remained rare until recent times, and even though this scenario has changed dramatically in the last few years, the new situation has not yet been absorbed into undergraduate teaching. In this new book, Hartle attempts to address the difficulties that must be faced by anyone who teaches general relativity at undergraduate level. In order to not scare the student with the hard technical preparation needed to obtain the basic equations of general relativity, Einstein's equations, he simply gives up the idea of introducing these equations at the very beginning. Instead, he chooses to present Einstein's equations, with most of the mathematics needed to do them, in the last part of the book. This delicate (and of course dangerous) choice has the advantage of introducing the reader first to the physical aspects of general relativity. This approach can be dangerous because the relevant solutions of the equations necessary to discuss the physical content of general relativity are presented first without a formal derivation. The book is divided into three parts. In the first, covering five chapters of the 24 in the whole book, Newtonian physics and special relativity are reviewed. This review is done in a manner that prepares the reader for the subsequent discussion of general relativity itself. The principle of relativity, the variational principle, the geometrical content of Newtonian theory and the main ideas behind special relativity are all presented. The heart of the book is, in
Summary of classical general relativity workshop
Indian Academy of Sciences (India)
In the classical general relativity workshop, ten lectures were presented on various topics. The topics included aspects of black-hole physics, gravitational collapse and the formation of black holes, specific stellar models like a superdense star, method of extracting solutions by exploiting Noether symmetry, brane world and.
The confrontation between general relativity and experiment
Indian Academy of Sciences (India)
... and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser Interferometric Gravitational Wave Observatories on Earth and in space may provide new tests of scalar–tensor gravity and graviton-mass theories via the properties of gravitational waves.
Evaluation of the real parts of fermion and boson propagators using dispersion relations
International Nuclear Information System (INIS)
Davies, K.T.R.; Davies, R.W.
1991-01-01
General methods are developed for efficiently evaluating principal-value integrals containing fermion and boson causal propagators. These methods are particularly applicable to integrals containing step functions which appear in the zero temperature limit of infinite nuclear matter. Examples are given for the Green functions that occur in the solution of Dyson's equations, with the inclusion of nucleon-delta-mesonic interactions. It is shown how to discretize in order to evaluate numerically the real parts of the propagators. If the real and purely imaginary self-energies of a propagator obey a dispersion relation, then the propagator itself satisfies such a relation. Finally, we discuss the two types of resonances occurring in the pion Green function. (orig.)
Surface-plasmon dispersion relation for the inhomogeneous charge-density medium
International Nuclear Information System (INIS)
Harsh, O.K.; Agarwal, B.K.
1989-01-01
The surface-plasmon dispersion relation is derived for the plane-bounded electron gas when there is an inhomogeneous charge-density distribution in the plasma. The hydrodynamical model is used. Both cphi and dcphi/dx are taken to be continuous at the surface of the slab, where cphi is the scalar potential. The dispersion relation is compared with the theoretical works of Stern and Ferrell and of Harsh and Agarwal. It is also compared with the observations of Kunz. A dispersion relation for the volume-plasmon oscillations is derived which resembles the well-known relation of Bohm and Pines
International Nuclear Information System (INIS)
Hasan, M. Khayrul; Ali, M. Hossain
2009-01-01
We formulate the general relativistic magnetohydrodynamic equations for isothermal plasma in spatially flat Reissner–Nordström–de Sitter metric by using 3+1 split of spacetime. Respective perturbed equations are linearized for rotating magnetized surroundings. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed both analytically and numerically in order to investigate the nature of waves with positive angular frequency around the horizon
General relativity and gravitation a centennial perspective
Berger, Beverly K; Isenberg, James; MacCallum, Malcolm
2015-01-01
Explore spectacular advances in cosmology, relativistic astrophysics, gravitational wave science, mathematics, computational science, and the interface of gravitation and quantum physics with this unique celebration of the centennial of Einstein's discovery of general relativity. Twelve comprehensive and in-depth reviews, written by a team of world-leading international experts, together present an up-to-date overview of key topics at the frontiers of these areas, with particular emphasis on the significant developments of the last three decades. Interconnections with other fields of research are also highlighted, making this an invaluable resource for both new and experienced researchers. Commissioned by the International Society on General Relativity and Gravitation, and including accessible introductions to cutting-edge topics, ample references to original research papers, and informative colour figures, this is a definitive reference for researchers and graduate students in cosmology, relativity, and grav...
General Relativity and John Archibald Wheeler
Ciufolini, Ignazio
2010-01-01
Observational and experimental data pertaining to gravity and cosmology are changing our view of the Universe. General relativity is a fundamental key for the understanding of these observations and its theory is undergoing a continuing enhancement of its intersection with observational and experimental data. These data include direct observations and experiments carried out in our solar system, among which there are direct gravitational wave astronomy, frame dragging and tests of gravitational theories from solar system and spacecraft observations. This book explores John Archibald Wheeler's seminal and enduring contributions in relativistic astrophysics and includes: the General Theory of Relativity and Wheeler's influence; recent developments in the confrontation of relativity with experiments; the theory describing gravitational radiation, and its detection in Earth-based and space-based interferometer detectors as well as in Earth-based bar detectors; the mathematical description of the initial value pro...
Development of Einstein's general theory of relativity
International Nuclear Information System (INIS)
Datta, B.K.
1980-01-01
Starting from Poincare's Lorentz-invariant theory of gravity formulated in 1906, development of Einstein's general theory of relativity during 1906-1916 is discussed. Three stages in this development are recognised. In the first stage during 1907-1914, Einstein tried to extend the relativity principle of uniform motion to the frames in non-uniform motion. For this purpose, he introduced the principle of equivalence which made it possible to calculate the effect of homogeneous gravitational field on arbitrary physical processes. During the second stage comprising years 1912-1914 overlapping the first stage, Einstein and Grossmann were struggling to translate physical postulates into the language of the absolute differential calculus. In the period 1915-1916, Einstein formulated the field equations of general relativity. While discussing these developmental stages, theories of gravitation formulated by Abraham, Nordstroem and Mie are also discussed. (M.G.B.)
Partial Differential Equations in General Relativity
International Nuclear Information System (INIS)
Choquet-Bruhat, Yvonne
2008-01-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Partial Differential Equations in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne
2008-09-07
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Wandering stars: age-related habitat use and dispersal of Javan Hawk-eagles (Spizaetus bartelsi)
Nijman, V.; Balen, van S.
2003-01-01
Natal dispersal and philopatry have rarely been studied in tropical forest raptors. Especially with respect to endangered species with fragmented distributions more knowledge of dispersal and age-related habitat preferences is needed for proper management. We conducted an island-wide study on
The complex dispersion relation of surface plasmon polaritons at gold/para-hexaphenylene interfaces
DEFF Research Database (Denmark)
Lemke, Christoph; Leißner, Till; Klick, Alwin
2014-01-01
Two-photon photoemission electron microscopy (2P-PEEM) is used to measure the real and imaginary part of the dispersion relation of surface plasmon polaritons at different interface systems. A comparison of calculated and measured dispersion data for a gold/vacuum interface demonstrates...
Comparison of Forward Dispersion Relations with Experiments around 10 GeV
DEFF Research Database (Denmark)
Lautrup, B.; Møller-Nielsen, Peter; Olesen, P.
1965-01-01
no assumptions whatsoever about the unknown cross sections above 20 GeV. On account of the large systematic errors in the measured real parts, no definite conclusion can be drawn as to the validity of forward dispersion relations. In estimating the standard deviations in the dispersion integrals, a Monte Carlo...
The Confrontation between General Relativity and Experiment
Directory of Open Access Journals (Sweden)
Clifford M. Will
2014-06-01
Full Text Available The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse–Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.
Dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals
International Nuclear Information System (INIS)
Hojo, Hitoshi; Mase, Atsushi
2004-01-01
The dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals is studied. The plasma photonic crystal is a periodic array composed of alternating thin plasma and dielectric material. The dispersion relation is obtained by solving a Maxwell wave equation using a method analogous to Kronig-Penny's problem in quantum mechanics, and it is found that the frequency gap and cut-off appear in the dispersion relation. The frequency gap is shown to become larger with the increase of the plasma density as well as plasma width. (author)
General relativity with applications to astrophysics
Straumann, Norbert
2004-01-01
This text provides a comprehensive and timely introduction to general relativity The foundations of the theory in Part I are thoroughly developed together with the required mathematical background from differential geometry in Part III The six chapters in Part II are devoted to tests of general relativity and to many of its applications Binary pulsars are studied in considerable detail Much space is devoted to the study of compact objects, especially to black holes This includes a detailed derivation of the Kerr solution, Israel's proof of his uniqueness theorem, and derivations of the basic laws of black hole physics The final chapter of this part contains Witten's proof of the positive energy theorem The book addresses undergraduate and graduate students in physics, astrophysics and mathematics It is very well structured and should become a standard text for a modern treatment of gravitational physics The clear presentation of differential geometry makes it also useful for string theory and other fields of ...
A precise extragalactic test of General Relativity.
Collett, Thomas E; Oldham, Lindsay J; Smith, Russell J; Auger, Matthew W; Westfall, Kyle B; Bacon, David; Nichol, Robert C; Masters, Karen L; Koyama, Kazuya; van den Bosch, Remco
2018-06-22
Einstein's theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, γ. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that γ = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
On the relative contributions of wind vs. animals to seed dispersal of four Sierra Nevada pines.
Vander Wall, Stephen B
2008-07-01
Selective pressures that influence the form of seed dispersal syndromes are poorly understood. Morphology of plant propagules is often used to infer the means of dispersal, but morphology can be misleading. Several species of pines, for example, have winged seeds adapted for wind dispersal but owe much of their establishment to scatter-hoarding animals. Here the relative importance of wind vs. animal dispersal is assessed for four species of pines of the eastern Sierra Nevada that have winged seeds but differed in seed size: lodgepole pine (Pinus contorta murrayana, 8 mg); ponderosa pine (Pinus ponderosa ponderosa, 56 mg); Jeffrey pine (Pinus jeffreyi, 160 mg); and sugar pine (Pinus lambertiana, 231 mg). Pre-dispersal seed mortality eliminated much of the ponderosa pine seed crop (66%), but had much less effect on Jeffrey pine (32% of seeds destroyed), lodgepole pine (29%), and sugar pine (7%). When cones opened most filled seeds were dispersed by wind. Animals removed > 99% of wind-dispersed Jeffrey and sugar pine seeds from the ground within 60 days, but animals gathered only 93% of lodgepole pine seeds and 38% of ponderosa pine seeds during the same period. Animals gathered and scatter hoarded radioactively labeled ponderosa, Jeffrey, and sugar pine seeds, making a total of 2103 caches over three years of study. Only three lodgepole pine caches were found. Caches typically contained 1-4 seeds buried 5-20 mm deep, depths suitable for seedling emergence. Although Jeffrey and sugar pine seeds are initially wind dispersed, nearly all seedlings arise from animal caches. Lodgepole pine is almost exclusively wind dispersed, with animals acting as seed predators. Animals treated ponderosa pine in an intermediate fashion. Two-phased dispersal of large, winged pine seeds appears adaptive; initial wind dispersal helps to minimize pre-dispersal seed mortality whereas scatter hoarding by animals places seeds in sites with a higher probability of seedling establishment.
Generalized Weierstrass Relations and Frobenius Reciprocity
International Nuclear Information System (INIS)
Matsutani, Shigeki
2006-01-01
This article investigates local properties of the further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M from the viewpoint of the study of submanifold quantum mechanics. We show that the kernel of a certain Dirac operator defined over S, which we call a submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras S and M plays an important role
Screening vector field modifications of general relativity
International Nuclear Information System (INIS)
Beltrán Jiménez, Jose; Delvas Fróes, André Luís; Mota, David F.
2013-01-01
A screening mechanism for conformal vector–tensor modifications of general relativity is proposed. The conformal factor depends on the norm of the vector field and makes the field to vanish in high dense regions, whereas drives it to a non-null value in low density environments. Such process occurs due to a spontaneous symmetry breaking mechanism and gives rise to both the screening of fifth forces as well as Lorentz violations. The cosmology and local constraints are also computed
Interacting electromagnetic waves in general relativity
International Nuclear Information System (INIS)
Griffiths, J.B.
1976-01-01
The problem is considered of finding exact solutions of the Einstein-Maxwell equations which describe the physical situation of two colliding and subsequently interacting electromagnetic waves. The general theory of relativity predicts a nonlinear interaction between electromagnetic waves. The situation is described using an approximate geometrical method, and a new exact solution describing two interacting electromagnetic waves is given. This describes waves emitted from two sources mutually focusing each other on the opposite source. (author)
Gravity, general relativity theory and alternative theories
International Nuclear Information System (INIS)
Zel'dovich, Ya.B.; Grishchuk, L.P.; Moskovskij Gosudarstvennyj Univ.
1986-01-01
The main steps in plotting the current gravitation theory and some prospects of its subsequent development are reviewed. The attention is concentrated on a comparison of the relativistic gravitational field with other physical fields. Two equivalent formulations of the general relativity (GR) - geometrical and field-theoretical - are considered in detail. It is shown that some theories of gravity constructed as the field theories at a flat background space-time are in fact just different formulations of GR and not alternative theories
Between general relativity and quantum theory
International Nuclear Information System (INIS)
Rayski, J.
1982-01-01
Some possibilities of reconciling general relativity with quantum theory are discussed. The procedure of quantization is certainly not unique, but depends upon the choice of the coordinate conditions. Most versions of quantization predict the existence of gravitons, but it is also possible to formulate a quantum theory with a classical gravity whereby the expectation values of Tsub(μν) constitute the sources of the classical metric field. (author)
Testing General Relativity with Pulsar Timing
Directory of Open Access Journals (Sweden)
Stairs Ingrid H.
2003-01-01
Full Text Available Pulsars of very different types, including isolated objects and binaries (with short- and long-period orbits, and white-dwarf and neutron-star companions provide the means to test both the predictions of general relativity and the viability of alternate theories of gravity. This article presents an overview of pulsars, then discusses the current status of and future prospects for tests of equivalence-principle violations and strong-field gravitational experiments.
Probing the Higgs vacuum with general relativity
Mannheim, Philip D.; Kazanas, Demosthenes
1991-01-01
It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.
Special relativity, electrodynamics, and general relativity from Newton to Einstein
Kogut, John B
2018-01-01
Special Relativity, Electrodynamics and General Relativity: From Newton to Einstein, Second Edition, is intended to teach (astro)physics, astronomy, and cosmology students how to think about special and general relativity in a fundamental, but accessible, way. Designed to render any reader a "master of relativity," everything on the subject is comprehensible and derivable from first principles. The book emphasizes problem solving, contains abundant problem sets, and is conveniently organized to meet the needs of both student and instructor. Fully revised, updated and expanded second edition Includes new chapters on magnetism as a consequence of relativity and electromagnetism Contains many improved and more engaging figures Uses less algebra resulting in more efficient derivations Enlarged discussion of dynamics and the relativistic version of Newton's second law
Quantum theory and Einstein's general relativity
International Nuclear Information System (INIS)
Borzeszkowski, H. von; Treder, H.
1982-01-01
We dicusss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Einstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a ''quantization of geometry.'' However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies
Relativity the special and the general theory
Einstein, Albert
2015-01-01
After completing the final version of his general theory of relativity in November 1915, Albert Einstein wrote a book about relativity for a popular audience. His intention was "to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics." The book remains one of the most lucid explanations of the special and general theories ever written. In the early 1920s alone, it was translated into ten languages, and fifteen editions in the original German appeared over the course of Einstein's lifetime. This new edition of Einstein's celebrated book features an authoritative English translation of the text along with an introduction and a reading companion by Hanoch Gutfreund and Jürgen Renn that examines the evolution of Einstein's thinking and casts his ideas in a broader present-day context. A special chapter explores the history...
Simple recursion relations for general field theories
International Nuclear Information System (INIS)
Cheung, Clifford; Shen, Chia-Hsien; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.
Existence of solution for a general fractional advection-dispersion equation
Torres Ledesma, César E.
2018-05-01
In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.
A Neutron Study for Phonon Dispersion Relations in HgTe
DEFF Research Database (Denmark)
Kepa, H.; Gebicki, W.; Giebultowicz, T.
1980-01-01
Dispersion relations for acoustic phonons in mercury telluride in three high symmetry directions [111], [110] and [001] are presented. The eleven-parameter rigid-ion model is fitted to the experimental data....
Numerical method for the dispersion relation of a hot and inhomogeneous plasma with an electron beam
International Nuclear Information System (INIS)
Devia, A.; Orrego, C.E.; Buitrago, G.
1990-01-01
A numerical method that is based in kinetic theory (Vlasov-Poison equations) was developed in order to calculate the dispersion relation for the interaction between a hot cylindrical and electron beam in any temperature and density. The plasma-beam system is located in a strong magnetic field. Many examples showing the effect of the temperatures and densities on the dispersion relation are given. (Author)
International Nuclear Information System (INIS)
Dean, N.W.
1978-01-01
New data showing that the photon-nucleon total cross section increases with energy for ν > or = 50 GeV invalidate earlier comparisons with dispersion relations. Parametrization of the data are presented and used in a new formulation of the dispersion relations, in which an assumed asymptotic behavior avoids the need for subtraction. With this form the fitted amplitude can be compared directly with the Thomson limit. The experimental uncertainties are shown to have a significant effect upon such a comparison
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
Directory of Open Access Journals (Sweden)
Font José A.
2008-09-01
Full Text Available This article presents a comprehensive overview of numerical hydrodynamics and magnetohydrodynamics (MHD in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003, most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable
An Introduction to General Relativity and Cosmology
International Nuclear Information System (INIS)
Wainwright, John
2007-01-01
The present volume is an introduction to general relativity and cosmology, at a level suitable for beginning graduate students or advanced undergraduates. The book consists of two main parts, the first entitled 'Elements of differential geometry', and the second 'The theory of gravitation'. Chapters 2-7, part I, introduce the basic ideas of differential geometry in a general setting, and are based on previously unpublished notes by one of the authors. On the one hand, the treatment is modern in that it uses a 'top-down' approach, i.e. starting with general differentiable manifolds, and deferring the introduction of a metric tensor until after the notions of affine connection and curvature have been introduced. On the other hand, the treatment is classical in that it relies heavily, though not exclusively, on index notation. The general material, chapters 1-7, is then followed by four more specialized chapters dealing with matters of specific interest for general relativity. Part II deals with general relativity and cosmology. The basic assumptions of the theory and its application to spherically symmetric gravitational fields are discussed in two chapters, and there is some historical material and motivation for the basic assumptions at the beginning of the book. The final chapter contains a detailed discussion of the Kerr solution. But the main emphasis in part II is on relativistic cosmology, in particular the analysis of cosmological models more general than the familiar Friedmann-Lemaitre (FL) models. The material on cosmology begins with a discussion of relativistic hydrodynamics and thermodynamics. The kinematical quantities (rate of expansion, shear, etc, of a timelike congruence) are introduced and their evolution equations are derived. There follows a description of the fluid model of the Universe and optical observations in such a model, within the framework of a general spacetime geometry. The discussion is subsequently specialized to the Robertson
Energy conditions and stability in general relativity
International Nuclear Information System (INIS)
Hall, G.S.
1982-01-01
The dominant energy condition in general relativity theory, which says that every observer measures a nonnegative local energy density and a nonspacelike local energy flow, is examined in connection with the types of energy-momentum tensor it permits. The condition that the energy-momentum tensor be ''stable'' in obeying the dominant energy conditions is then defined in terms of a suitable topology on the set of energy-momentum tensors on space-time and the consequences are evaluated and discussed. (author)
Weak field approximation of new general relativity
International Nuclear Information System (INIS)
Fukui, Masayasu; Masukawa, Junnichi
1985-01-01
In the weak field approximation, gravitational field equations of new general relativity with arbitrary parameters are examined. Assuming a conservation law delta sup(μ)T sub(μν) = 0 of the energy-momentum tensor T sub(μν) for matter fields in addition to the usual one delta sup(ν)T sub(μν) = 0, we show that the linearized gravitational field equations are decomposed into equations for a Lorentz scalar field and symmetric and antisymmetric Lorentz tensor fields. (author)
The mathematical theory of general relativity
Katkar, L N
2014-01-01
This book is prepared for M. Sc. Students of Mathematics and Physics. The aim of writing this book is to give the reader a feeling for the necessity and beauty of the laws of general relativity. The contents of the book will attract both mathematicians and physicists which provides motivation and applications of many ideas and powerful mathematical methods of modern analysis and differential geometry. An attempt has been made to make the presentation comprehensive, rigorous and yet simple. Most calculations and transformations have been carried out in great detail. KEY FEATURE: Numerous solved examples using the well known mathematical techniques viz., the tensors and the differential forms in each chapter.
Tests of General Relativity with GW150914
Abbott, B. P.; Abbott, R.; Abernathy, M. R.; Adhikari, R. X.; Anderson, S. B.; Arai, K.; Araya, M. C.; Barayoga, J. C.; Barish, B. C.; Berger, B. K.; Billingsley, G.; Blackburn, J. K.; Bork, R.; Brooks, A. F.; Cahillane, C.
2016-01-01
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant’s mass and spin, as determined fro...
New Area Law in General Relativity.
Bousso, Raphael; Engelhardt, Netta
2015-08-21
We report a new area law in general relativity. A future holographic screen is a hypersurface foliated by marginally trapped surfaces. We show that their area increases monotonically along the foliation. Future holographic screens can easily be found in collapsing stars and near a big crunch. Past holographic screens exist in any expanding universe and obey a similar theorem, yielding the first rigorous area law in big bang cosmology. Unlike event horizons, these objects can be identified at finite time and without reference to an asymptotic boundary. The Bousso bound is not used, but it naturally suggests a thermodynamic interpretation of our result.
International Nuclear Information System (INIS)
Hnat, B.; O’Connell, D.; Nakariakov, V. M.; Sundberg, T.
2016-01-01
We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 10 4 km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward.
Energy Technology Data Exchange (ETDEWEB)
Hnat, B.; O’Connell, D.; Nakariakov, V. M. [Centre for Fusion, Space and Astrophysics, University of Warwick (United Kingdom); Sundberg, T., E-mail: B.Hnat@warwick.ac.uk [School of Physics and Astronomy, Queen Mary University of London (United Kingdom)
2016-08-20
We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 10{sup 4} km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward.
Commutative deformations of general relativity: nonlocality, causality, and dark matter
Energy Technology Data Exchange (ETDEWEB)
De Vegvar, P.G.N. [SWK Research, Bellingham, WA (United States)
2017-01-15
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on commutative manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above ∝1-10 TeV, other possibilities are viable dark matter candidates or a right-handed neutrino. First order deformed Maxwell equations are derived and yield immeasurably small cosmological dispersion and produce a propagation horizon only for photons at or above Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, grand unified theories, mirror worlds, or modifications of Newtonian dynamics. (orig.)
Anholonomic Cauchy problem in general relativity
International Nuclear Information System (INIS)
Stachel, J.
1980-01-01
The Lie derivative approach to the Cauchy problem in general relativity is applied to the evolution along an arbitrary timelike vector field for the case where the dynamical degrees of freedom are chosen as the (generally anholonomic) metric of the hypersurface elements orthogonal to the vector field. Generalizations of the shear, rotation, and acceleration are given for a nonunit timelike vector field, and applied to the three-plus-one breakup of the Riemann tensor into components parallel and orthogonal to the vector field, resulting in the anholonomic Gauss--Codazzi equations. A similar breakup of the Einstein field equations results in the form of the constraint and evolution equations for the anholonomic case. The results are applied to the case of a space--time with a timelike Killing vector field (stationary field) to demonstrate their utility. Other possible applications, such as in the numerical integration of the field equations, are mentioned. Definitions are given of three-index shear, rotation, and acceleration tensors, and their use in a two-plus-two decomposition of the Riemann tensor and field equations is indicated
Introduction to general relativity and cosmology
Berger, Mitchell A
2018-01-01
The textbook aims to present general relativity and modern cosmology in a friendly form suitable for advanced undergraduates. The text begins with a self-contained introduction to the theory of manifolds and then develops the tools needed to understand curved spaces and curved spacetimes. Special relativity can then be understood in a geometrical context, bypassing some of the difficulties students have when encountering relativistic effects (e.g. time dilation and length contraction) for the first time. The theory of curvature and its effects leads to the Einstein field equations and its classic tests in the precession of Mercury and the deflection of starlight. The second part of the book covers modern cosmology, starting with the evolution equations for the expansion of the universe. The microwave background, evidence for dark matter, and the clustering of galaxies are examined in detail.
Mechanics of extended masses in general relativity
International Nuclear Information System (INIS)
Harte, Abraham I
2012-01-01
The 'external' or 'Right' motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain 'effective metric' that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the 'bare' multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background. (paper)
Optical drift effects in general relativity
Korzyński, Mikołaj; Kopiński, Jarosław
2018-03-01
We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the standard relativistic geometric optics formalism and extend it to include the time derivatives of the observables. In the process we obtain two general, non-perturbative relations: the first one between the gravitational lensing, represented by the Jacobi matrix, and the apparent position drift, also called the cosmic parallax, and the second one between the apparent position drift and the redshift drift. The applications of the results include the theoretical study of the drift effects of cosmological origin (so-called real-time cosmology) in numerical or exact Universe models.
Kinematics in special and general relativity
International Nuclear Information System (INIS)
Woodside, R.W.M.
1979-05-01
This thesis investigates the problem of motion for extended bodies from the viewpoint of classical field theory, where the classical field is the body's energy-momentum or matter tensor. In special relativity a symmetric and divergence-free matter tensor combined with inertial frames is used to generate a kinematics for extended bodies. In general relativity the author suggests an analogous kinematics and applies it to the simplest non-trivial example of static, spherical stars, looking for special sets of vector fields whose matter currents are conserved. Such a set of ten vector fields defines a special frame, and integrals of the conserved matter currents define ten momenta whcih give the kinematics. Application of de Rham cohomology theory shows that the conserved matter currents for isolated bodies will have mechanical potentials which enable the momenta to be found from flux integrals evaluated in the vacuum region surrounding the body. These potentials contain the full Riemann curvature, allowing a body's general relativistic momenta to be determined by its vacuum graviational field
Kinematics of relative motion of test particles in general relativity
International Nuclear Information System (INIS)
Bazanski, S.L.
1977-01-01
A detailed mathematical study of the concept of geodesic deviation in pseudo-riemannian geometry is presented. A generalization of this concept to geodesic deviations of a higher order is then introduced and the second geodesic deviation is investigated in some detail. A geometric interpretation of the set of generalized geodesic deviations is given and applied in general relativity to determine a covariant and local description (with a desired order of accuracy) of test motions which take place in a certain finite neighbourhood of a given world line of an observer. The proper time evolution of two other objects related to geodesic deviation is also discussed: the space separation vector and the telescopic vector. This last name is given here to a field of null vectors along observer's world line which always point towards the same adjacent world line. The telescopic equations allow to determine the evolution of the frequency shift of electromagnetic radiation sent from and received on neighbouring world lines. On the basis of these equations also certain relations have been derived which connect the frequencies or frequency shifts with the curvature of space-time
Dispersion relations for the self-energy in noncommutative field theories
International Nuclear Information System (INIS)
Brandt, F.T.; Das, Ashok; Frenkel, J.
2002-01-01
We study the IR-UV connection in noncommutative φ 3 theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed
'' Ideal Gas '' gluon plasma with medium dependent dispersion relation
International Nuclear Information System (INIS)
Gorenstein, M.I.
1995-01-01
An '' ideal gas '' model with temperature dependent particle mass is constructed for the gluon plasma equation of state. This simple model gives us an example of a system with temperature dependent effective Hamiltonian. To satisfy thermodynamical relations in these systems, standard statistical mechanics formulas have to be supplemented by special requirements which are considered in details. A self-consistent '' ideal gas '' formulation is used to describe Monte Carlo lattice data for the thermodynamical functions of SU(2) and SU(3) gluon plasma. 14 refs., 8 figs
An elementary course on general relativity
International Nuclear Information System (INIS)
Regge, T.
1983-01-01
This report gives an informal account of the theory of general relativity, for non-specialists. It does not contain any detailed technical expose of tensor calculus but relies instead on a number of intuitive arguments. After a brief historical introduction the notion of curvature is developed, first in two dimensions (as done originally by Gauss) and then in higher dimensions, following the ideas of Riemann. This curvature is then related to quantities of physical interest through the following steps: i) The equality of gravitational and inertial masses is discussed and presented as the ''weak equivalence principle''. ii) This is then extended to the ''strong equivalence principle'' according to the original programme of Einstein. iii) The ''strong equivalence principle'' implies the existence of a local inertial observer in any point of space-time. In a sufficiently small region of space-time this observer will not sense any gravitational field. iv) In a larger region the observer will, however, sense residual tidal forces. These forces are identified with the curvature of spacetime, to achieve a direct geometrical interpretation of gravity. v) Finally certain curvature components are related to the distribution of matter through Einstein's field equations. Section 4 contains a discussion of the classical tests of the theory and of the possibility of detecting gravitational waves. Sections 5 and 6 deal with cosmology and with the possible extension of the theory along the lines of the original ideas of Einstein, with emphasis on the dimensional reduction techniques of current interest. (orig.)
General Relativity solutions in modified gravity
Motohashi, Hayato; Minamitsuji, Masato
2018-06-01
Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.
Dynamical laws of superenergy in general relativity
International Nuclear Information System (INIS)
Gomez-Lobo, Alfonso GarcIa-Parrado
2008-01-01
The Bel and Bel-Robinson tensors were introduced nearly 50 years ago in an attempt to generalize to gravitation the energy-momentum tensor of electromagnetism. This generalization was successful from the mathematical point of view because these tensors share mathematical properties which are remarkably similar to those of the energy-momentum tensor of electromagnetism. However, the physical role of these tensors in general relativity has remained obscure and no interpretation has achieved wide acceptance. In principle, they cannot represent energy and the term superenergy has been coined for the hypothetical physical magnitude lying behind them. In this work, we try to shed light on the true physical meaning of superenergy by following the same procedure which enables us to give an interpretation of the electromagnetic energy. This procedure consists in performing an orthogonal splitting of the Bel and Bel-Robinson tensors and analyzing the different parts resulting from the splitting. In the electromagnetic case such splitting gives rise to the electromagnetic energy density, the Poynting vector and the electromagnetic stress tensor, each of them having a precise physical interpretation which is deduced from the dynamical laws of electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel and Bel-Robinson tensors is more complex but, as expected, similarities with electromagnetism are present. Also the covariant divergence of the Bel tensor is analogous to the covariant divergence of the electromagnetic energy-momentum tensor and the orthogonal splitting of the former is found. The ensuing equations are to the superenergy what the Poynting theorem is to electromagnetism. Some consequences of these dynamical laws of superenergy are explored, among them the possibility of defining superenergy radiative states for the gravitational field
On multipole moments in general relativity
International Nuclear Information System (INIS)
Hoenselaers, C.
1986-01-01
In general situations, involving gravitational waves the question of multiple moments in general relativity restricts the author to stationary axisymmetric situations. Here it has been shown that multipole moments, a set of numbers defined at spatial infinity as far away from the source as possible, determine a solution of Einstein's equations uniquely. With the rather powerful methods for generating solutions one might hope to get solutions with predefined multipole moments. Before doing so, however, one needs an efficient algorithm for calculating the moments of a given solution. Chapter 2 deals with a conjecture pertaining to such a calculational procedure and shows it to be not true. There is another context in which multipole moments are important. Consider a system composed of several objects. To separate, if possible, the various parts of their interaction, one needs a definition for multipole moments of individual members of a many body system. In spite of the fact that there is no definition for individual moments, with the exception of mass and angular momentum, Chapter 3 shows what can be done for the double Kerr solution. The authors can identify various terms in he interaction of two aligned Kerr objects and show that gravitational spin-spin interaction is indeed proportional to the product of the angular momenta
Victories and defeats in general relativity theory
International Nuclear Information System (INIS)
Moeller, C.
1977-01-01
Only within the last 20 years has it been possible to conduct far-reaching experimental tests of the validity of Einstein's General Relativity Theory. Experimental confirmation in some fields is embarrassed by considerable difficulties in applying the theory to cosmic systems, which indicate that such major systems lie at the limit of the theory's applicability. The lecture here reproduced discusses both the successes and the limitations of the theory, starting with its replacement of the absolute space-time theory of Newton and its historical replacement by the relativistic gravitational postulates of Einstein which, in spite of its more complicated postulates, nevertheless introduced a great simplicity and comprehensiveness into the overall conception of nature. This theoretical 'beauty', however, can only be trusted if vindicated experimentally, which has to a considerable extent proved to be the case. For weak fields Newtonian and Einsteinian concepts coincide, while for stronger fields, and velocities not far from that of light, Einstein's theory is superior, giving,for example, an excellent correspondence with the precession of the perehelion of Mercury. On a larger scale, however, the theory appears to lead to conclusions which would invalidate the very concepts of space and time, even within a finite time-interval. A more generalized theory seems to be required. (A.D.N.)
Dispersion relation for pure dust Bernstein waves in a non-Maxwellian magnetized dusty plasma
International Nuclear Information System (INIS)
Deeba, F.; Ahmad, Zahoor; Murtaza, G.
2011-01-01
Pure dust Bernstein waves are investigated using non-Maxwellian kappa and (r,q) distribution functions in a collisionless, uniform magnetized dusty plasma. Dispersion relations for both the distributions are derived by considering waves whose frequency is of the order of dust cyclotron frequency, and dispersion curves are plotted. It is observed that the propagation band for dust Bernstein waves is rather narrow as compared with that of the electron Bernstein waves. However, the band width increases for higher harmonics, for both kappa and (r,q) distributions. Effect of dust charge on dispersion curves is also studied, and one observes that with increasing dust charge, the dispersion curves shift toward the lower frequencies. Increasing the dust to ion density ratio ((n d0 /n i0 )) causes the dispersion curve to shift toward the higher frequencies. It is also found that for large values of spectral index kappa (κ), the dispersion curves approach to the Maxwellian curves. The (r,q) distribution approaches the kappa distribution for r = 0, whereas for r > 0, the dispersion curves show deviation from the Maxwellian curves as expected. Relevance of this work can be found in astrophysical plasmas, where non-Maxwellian velocity distributions as well as dust particles are commonly observed.
Dispersion relation for pure dust Bernstein waves in a non-Maxwellian magnetized dusty plasma
Energy Technology Data Exchange (ETDEWEB)
Deeba, F. [National Tokamak Fusion Program, PAEC, P.O. Box 3329, Islamabad 44000 (Pakistan); Department of Physics, G.C. University, Lahore 54000 (Pakistan); Ahmad, Zahoor [National Tokamak Fusion Program, PAEC, P.O. Box 3329, Islamabad 44000 (Pakistan); Murtaza, G. [Salam Chair in Physics, G.C. University, Lahore 54000 (Pakistan)
2011-07-15
Pure dust Bernstein waves are investigated using non-Maxwellian kappa and (r,q) distribution functions in a collisionless, uniform magnetized dusty plasma. Dispersion relations for both the distributions are derived by considering waves whose frequency is of the order of dust cyclotron frequency, and dispersion curves are plotted. It is observed that the propagation band for dust Bernstein waves is rather narrow as compared with that of the electron Bernstein waves. However, the band width increases for higher harmonics, for both kappa and (r,q) distributions. Effect of dust charge on dispersion curves is also studied, and one observes that with increasing dust charge, the dispersion curves shift toward the lower frequencies. Increasing the dust to ion density ratio ((n{sub d0}/n{sub i0})) causes the dispersion curve to shift toward the higher frequencies. It is also found that for large values of spectral index kappa ({kappa}), the dispersion curves approach to the Maxwellian curves. The (r,q) distribution approaches the kappa distribution for r = 0, whereas for r > 0, the dispersion curves show deviation from the Maxwellian curves as expected. Relevance of this work can be found in astrophysical plasmas, where non-Maxwellian velocity distributions as well as dust particles are commonly observed.
Rotating Quark Stars in General Relativity
Directory of Open Access Journals (Sweden)
Enping Zhou
2018-03-01
Full Text Available We have built quasi-equilibrium models for uniformly rotating quark stars in general relativity. The conformal flatness approximation is employed and the Compact Object CALculator (cocal code is extended to treat rotating stars with surface density discontinuity. In addition to the widely used MIT bag model, we have considered a strangeon star equation of state (EoS, suggested by Lai and Xu, that is based on quark clustering and results in a stiff EoS. We have investigated the maximum mass of uniformly rotating axisymmetric quark stars. We have also built triaxially deformed solutions for extremely fast rotating quark stars and studied the possible gravitational wave emission from such configurations.
Motivations for antigravity in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Chardin, G. [DSM/DAPNIA/SPP, CEN-Saclay (France)
1997-08-15
We present arguments showing that it is natural to interpret the negative mass part of the Kerr solution as representing the geometry experienced by antimatter. The C, P and T discrete transformations are considered for this geometry. The C and T properties of the proposed identification are found to be in agreement with the usual representation of antimatter. In addition, we conjecture a property of perfect stigmatism through Kerr wormholes which allows General Relativity to mimic antigravity. Kerr wormholes would then act as 'supermirrors' reversing the C, P and T images of an object seen through it. This interpretation is subject to several experimental tests and able to provide an explanation, without any free parameter, of the 'CP' violation observed in the neutral kaon system.
Motivations for antigravity in General Relativity
International Nuclear Information System (INIS)
Chardin, G.
1997-01-01
We present arguments showing that it is natural to interpret the negative mass part of the Kerr solution as representing the geometry experienced by antimatter. The C, P and T discrete transformations are considered for this geometry. The C and T properties of the proposed identification are found to be in agreement with the usual representation of antimatter. In addition, we conjecture a property of perfect stigmatism through Kerr wormholes which allows General Relativity to mimic antigravity. Kerr wormholes would then act as 'supermirrors' reversing the C, P and T images of an object seen through it. This interpretation is subject to several experimental tests and able to provide an explanation, without any free parameter, of the 'CP' violation observed in the neutral kaon system
On thick domain walls in general relativity
Goetz, Guenter; Noetzold, Dirk
1989-01-01
Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.
A general theory of quantum relativity
International Nuclear Information System (INIS)
Minic, Djordje; Tze, C.-H.
2004-01-01
The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics
Dispersion relations for η{sup '} → ηππ
Energy Technology Data Exchange (ETDEWEB)
Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Stoffer, Peter [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); University of California at San Diego, Department of Physics, La Jolla, CA (United States)
2017-07-15
We present a dispersive analysis of the decay amplitude for η{sup '} → ηππ that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the ππ and πη scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory. (orig.)
Singular Null Hypersurfaces in General Relativity
International Nuclear Information System (INIS)
Dray, T
2006-01-01
Null hypersurfaces are a mathematical consequence of the Lorentzian signature of general relativity; singularities in mathematical models usually indicate where the interesting physics takes place. This book discusses what happens when you combine these ideas. Right from the preface, this is a no-nonsense book. There are two principal approaches to singular shells, one distributional and the other 'cut and paste'; both are treated in detail. A working knowledge of GR is assumed, including familiarity with null tetrads, differential forms, and 3 + 1 decompositions. Despite my own reasonably extensive, closely related knowledge, there was material unfamiliar to me already in chapter 3, although I was reunited with some old friends in later chapters. The exposition is crisp, with a minimum of transition from chapter to chapter. In fact, my main criticism is that there is no clear statement of the organization of the book, nor is there an index. Everything is here, and the story is compelling if you know what to look for, although it is less easy to follow the story if you are not already familiar with it. But this is really a book for experts, and the authors certainly qualify, having played a significant role in developing and extending the results they describe. It is also entirely appropriate that the book is dedicated to Werner Israel, who pioneered the thin-shell approach to (non-null) singular surfaces and later championed the use of similar methods for analysing null shells. After an introductory chapter on impulsive signals, the authors show how the Bianchi identities can be used to classify spacetimes with singular null hypersurfaces. This approach, due to the authors, generalizes the framework originally proposed by Penrose. While astrophysical applications are discussed only briefly, the authors point out that detailed physical characteristics of signals from isolated sources can be determined in this manner. In particular, they describe the behaviour of
Axially symmetric Lorentzian wormholes in general relativity
International Nuclear Information System (INIS)
Schein, F.
1997-11-01
The field equations of Einstein's theory of general relativity, being local, do not fix the global structure of space-time. They admit topologically non-trivial solutions, including spatially closed universes and the amazing possibility of shortcuts for travel between distant regions in space and time - so-called Lorentzian wormholes. The aim of this thesis is to (mathematically) construct space-times which contain traversal wormholes connecting arbitrary distant regions of an asymptotically flat or asymptotically de Sitter universe. Since the wormhole mouths appear as two separate masses in the exterior space, space-time can at best be axially symmetric. We eliminate the non-staticity caused by the gravitational attraction of the mouths by anchoring them by strings held at infinity or, alternatively, by electric repulsion. The space-times are obtained by surgically grafting together well-known solutions of Einstein's equations along timelike hypersurfaces. This surgery naturally concentrates a non-zero stress-energy tensor on the boundary between the two space-times which can be investigated by using the standard thin shell formalism. It turns out that, when using charged black holes, the provided constructions are possible without violation of any of the energy conditions. In general, observers living in the axially symmetric, asymptotically flat (respectively asymptotically de Sitter) region axe able to send causal signals through the topologically non-trivial region. However, the wormhole space-times contain closed timelike curves. Because of this explicit violation of global hyperbolicity these models do not serve as counterexamples to known topological censorship theorems. (author)
Scaling relations for soliton compression and dispersive-wave generation in tapered optical fibers
DEFF Research Database (Denmark)
Lægsgaard, Jesper
2018-01-01
In this paper, scaling relations for soliton compression in tapered optical fibers are derived and discussed. The relations allow simple and semi-accurate estimates of the compression point and output noise level, which is useful, for example, for tunable dispersive-wave generation with an agile ...
Dispersion relation and Landau damping of waves in high-energy density plasmas
International Nuclear Information System (INIS)
Zhu Jun; Ji Peiyong
2012-01-01
We present a theoretical investigation on the propagation of electromagnetic waves and electron plasma waves in high energy density plasmas using the covariant Wigner function approach. Based on the covariant Wigner function and Dirac equation, a relativistic quantum kinetic model is established to describe the physical processes in high-energy density plasmas. With the zero-temperature Fermi–Dirac distribution, the dispersion relation and Landau damping of waves containing the relativistic quantum corrected terms are derived. The relativistic quantum corrections to the dispersion relation and Landau damping are analyzed by comparing our results with those obtained in classical and non-relativistic quantum plasmas. We provide a detailed discussion on the Landau damping obtained in classical plasmas, non-relativistic Fermi plasmas and relativistic Fermi plasmas. The contributions of the Bohm potential, the Fermi statistics pressure and relativistic effects to the dispersion relation and Landau damping of waves are quantitatively calculated with real plasma parameters. (paper)
On the ultrarelativistic limit of general relativity
International Nuclear Information System (INIS)
Dautcourt, G.
1998-01-01
As is well-known, Newton's gravitational theory can be formulated as a four-dimensional space-time theory and follows as singular limit from Einstein's theory, if the velocity of light tends to the infinity. Here 'singular' stands for the fact, that the limiting geometrical structure differs from a regular Riemannian space-time. Geometrically, the transition Einstein → Newton can be viewed as an 'opening' of the light cones. This picture suggests that there might be other singular limits of Einstein's theory: Let all light cones shrink and ultimately become part of a congruence of singular world lines. The limiting structure may be considered as a null hypersurface embedded in a five-dimensional spacetime. While the velocity of light tends to zero here, all other velocities tend to the velocity of light. Thus one may speak of an ultrarelativistic limit of General Relativity. The resulting theory is as simple as Newton's gravitational theory, with the basic difference, that Newton's elliptic differential equation is replaced by essentially ordinary differential equations, with derivatives tangent to the generators of the singular congruence. The Galilei group is replaced by the Carroll group introduced by Levy-Leblond. We suggest to study near ultrarelativistic situations with a perturbational approach starting from the singular structure, similar to post-Newtonian expansions in the c → ∞ case. (author)
Direction dependent structures in general relativity
International Nuclear Information System (INIS)
Herberthson, M.
1993-01-01
This thesis deals with, within the theory of general relativity, asymptotic properties of certain types of space-times. Using conformal transformations, it is possible to describe asymptotic properties of a physical space-time in terms of the local behaviour of the new, rescaled space-time. One then uses so called direction dependent structures. We present two such structures and applications to them. One structure is used in the study of spacelike (or spatial) infinity. We discuss the asymptotic conditions on the gravitational and the electromagnetic field, especially the conditions put on directions corresponding to future and past null infinity. It is shown that these fields have desired physical properties. The other structure is used in connection with timelike infinity. Using this structure, we suggest a new definition of timelike infinity. This definition differs significantly from earlier definitions, and leads to the concept of asymptotically stationary space-times. We also suggest a definition of asymptotic flatness at future null infinity, and a definition of a black hole which is, in a sense, local. Both of these definitions fit nicely into the structure. (24 refs.)
Possibility of estimation of bare coupling of grand unification via theory of dispersion relations
International Nuclear Information System (INIS)
Perel'manl, C.
2004-01-01
Full Text:All processes of point particle elastic scatterings on the fixed point-like force center of any nature of coupling can be kinematically subdivided onto two classes: (proper) processes, at which complete energy throughout is not lesser kinetical one: E > If, and (improper) processes, at some interval of which potential energy become bigger complete energy (tunneling, backward scattering, etc.). The projector of proper processes, expressed via the Heaviside unit operator, P = θ(E - f), extracts from the general response functions (scattering amplitudes F) parts that describe all these processes: f (E, p, ...) = 9(E - E)F(E, p, ...). Its Fourier transformation leads to the dispersion relations in (t,r)-representation, which can be infinitely iterated and is represented in form of the Neumann series for the integral Fredholm equation. At this calculation the unique numerical constant α 0 = 2(2π) -5/2 ∼1/50 for (3+1) metrics is appeared, which does not depend from nature of coupling and therefore can be considered as the constant of decomposition of complete amplitude over number of interactions. Precisely this value, independent from dynamics, can be considered as the universal bare coupling. Via the Gell-Mann - Low relations it results in the GUT energy A-f = 10 18 GeV with consistent magnitudes of all running couplings and reasonable values of electron and nucleon masses as dynamical fields objects. Moreover it allows the consideration of some problems of black holes also
Wave dispersion relation of two-dimensional plasma crystals in a magnetic field
International Nuclear Information System (INIS)
Uchida, G.; Konopka, U.; Morfill, G.
2004-01-01
The wave dispersion relation in a two-dimensional strongly coupled plasma crystal is studied by theoretical analysis and molecular dynamics simulation taking into account a constant magnetic field parallel to the crystal normal. The expression for the wave dispersion relation clearly shows that high-frequency and low-frequency branches exist as a result of the coupling of longitudinal and transverse modes due to the Lorenz force acting on the dust particles. The high-frequency and the low-frequency branches are found to belong to right-hand and left-hand polarized waves, respectively
International Nuclear Information System (INIS)
Barry, J.P.
1994-08-01
Analyses of ocean currents in the vicinity of McMurdo Station, Antarctica, are relevant to the transport and dispersal of wastewater from the McMurdo Station sewage outfall pipe. Observations of ocean currents during the initial phases of this study have been presented by Howington and McFeters. These studies, using coliform bacterial counts as an indicator of dispersion of the wastewater plume and current meters to measure flow patterns, indicated that dispersal of the plume by local currents does not effectively remove the plume from the vicinity of McMurdo Sound, under the present outfall pipe location. Moreover, these studies suggest that, although the flow pattern is generally consistent with transport of the plume away from McMurdo Station, episodes of current reversal are sufficient to transport the wastewater plume along the shore toward the southeast, eventually overlapping the seawater intake area near the McMurdo jetty. Several concerns included (a) impacts of wastewater inputs to nearshore benthic and pelagic habitats adjacent to McMurdo Station, (b) effects of wastewater input to the McMurdo Station fresh water intake source, and (c) reduction in human impacts on the McMurdo Sound ecosystem. These concerns motivated studies to characterize nearshore currents more extensively in relation to dispersal of the wastewater plume. This report discusses analysis results of current observations from November 1992 to November 1993
General relativity invariance and string field theory
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Volovich, I.V.
1987-04-01
The general covariance principle in the string field theory is considered. The algebraic properties of the string Lie derivative are discussed. The string vielbein and spin connection are introduced and an action invariant under general co-ordinate transformation is proposed. (author). 18 refs
Gravitational Wave in Linear General Relativity
Cubillos, D. J.
2017-07-01
General relativity is the best theory currently available to describe the interaction due to gravity. Within Albert Einstein's field equations this interaction is described by means of the spatiotemporal curvature generated by the matter-energy content in the universe. Weyl worked on the existence of perturbations of the curvature of space-time that propagate at the speed of light, which are known as Gravitational Waves, obtained to a first approximation through the linearization of the field equations of Einstein. Weyl's solution consists of taking the field equations in a vacuum and disturbing the metric, using the Minkowski metric slightly perturbed by a factor ɛ greater than zero but much smaller than one. If the feedback effect of the field is neglected, it can be considered as a weak field solution. After introducing the disturbed metric and ignoring ɛ terms of order greater than one, we can find the linearized field equations in terms of the perturbation, which can then be expressed in terms of the Dalambertian operator of the perturbation equalized to zero. This is analogous to the linear wave equation in classical mechanics, which can be interpreted by saying that gravitational effects propagate as waves at the speed of light. In addition to this, by studying the motion of a particle affected by this perturbation through the geodesic equation can show the transversal character of the gravitational wave and its two possible states of polarization. It can be shown that the energy carried by the wave is of the order of 1/c5 where c is the speed of light, which explains that its effects on matter are very small and very difficult to detect.
The Concept of General Relativity is not Related to Reality
Kotas, Ronald
2015-04-01
The concept of general relativity is not related to reality. It is not real or factual Science. GR cannot account for objects falling to earth or for the weight of objects sitting on the earth. The Cavendish demonstration showing the attraction between two masses at right angles to earth's gravity, is not explained by GR. No one can prove the existence of ``space fabric.'' The concept of ``space time'' effects causing gravitational attraction between masses is wrong. Conservation law of energy - momentum does not exist in GR. LIGO fails in detecting ``gravity waves'' because there is no ``space fabric'' to transmit them. The Gravity B Probe data manipulated to show some effects, is not proof of ``space fabric.'' It is Nuclear Quantum Gravitation that provides clear definitive explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and Scientific Logic. Nuclear Quantum Gravitation has 10 clear, Scientific proofs and 21 more good indications. With this theory the Physical Forces are Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli-foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics, by Paul Marmet http://www.newtonphysics.on.ca/einstein/
Determining the near-surface current profile from measurements of the wave dispersion relation
Smeltzer, Benjamin; Maxwell, Peter; Aesøy, Eirik; Ellingsen, Simen
2017-11-01
The current-induced Doppler shifts of waves can yield information about the background mean flow, providing an attractive method of inferring the current profile in the upper layer of the ocean. We present measurements of waves propagating on shear currents in a laboratory water channel, as well as theoretical investigations of inversion techniques for determining the vertical current structure. Spatial and temporal measurements of the free surface profile obtained using a synthetic Schlieren method are analyzed to determine the wave dispersion relation and Doppler shifts as a function of wavelength. The vertical current profile can then be inferred from the Doppler shifts using an inversion algorithm. Most existing algorithms rely on a priori assumptions of the shape of the current profile, and developing a method that uses less stringent assumptions is a focus of this study, allowing for measurement of more general current profiles. The accuracy of current inversion algorithms are evaluated by comparison to measurements of the mean flow profile from particle image velocimetry (PIV), and a discussion of the sensitivity to errors in the Doppler shifts is presented.
Dispersion relation for elastic electron-hydrogen atom forward scattering amplitude
International Nuclear Information System (INIS)
Kuchiev, M.Yu.; Amusia, M.Ya.
1978-01-01
The elastic e+H forward scattering amplitude is an analytical function in the complex energy E plane and has two cuts on the real axis: 0 < E < infinity and -infinity < E < -B, B being the hydrogen ionization potential. The e+H dispersion relation contains two integrals over the right and left cuts. (Auth.)
Dispersion relation analysis of the neutral kaon regeneration amplitude in carbon
Angelopoulos, Angelos; Locher, M P; Markushin, V E; Aslanides, Elie; Backenstoss, Gerhard; Bargassa, P; Behnke, O; Benelli, A; Bertin, V; Blanc, F; Bloch, P; Carlson, P J; Carroll, M; Cawley, E; Chertok, M B; Danielsson, M; Dejardin, M; Derré, J; Ealet, A; Eleftheriadis, C; Faravel, L; Festcher, W; Fidecaro, Maria; Filipcic, A; Francis, D; Fry, J; Gabathuler, Erwin; Gamet, R; Gerber, H J; Go, A; Haselden, A; Hayman, P J; Henry-Coüannier, F; Hollander, R W; Jon-And, K; Kettle, P R; Kokkas, P; Kreuger, R; Le Gac, R; Leimgruber, F; Mandic, I; Manthos, N; Marel, Gérard; Mikuz, M; Miller, J; Montanet, François; Müller, A; Nakada, Tatsuya; Pagels, B; Papadopoulos, I M; Pavlopoulos, P; Polivka, G; Rickenbach, R; Roberts, B L; Ruf, T; Schäfer, M; Schaller, L A; Schietinger, T; Schopper, A; Tauscher, Ludwig; Thibault, C; Touchard, F; Touramanis, C; van Eijk, C W E; Vlachos, S; Weber, P; Wigger, O; Wolter, M; Zavrtanik, D; Zimmerman, D
1999-01-01
We apply a forward dispersion relation to the regeneration amplitude for kaon scattering on /sup 12/C using all available data. The CPLEAR data at low energies allow the determination of the net contribution from the subthreshold $9 region which turns out to be much smaller than earlier evaluations, solving a long standing puzzle. (29 refs).
Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function
International Nuclear Information System (INIS)
Sato, Masumi
1985-01-01
Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)
Chiral symmetry and dispersion relations: from $\\pi \\pi$ scattering to hadronic light-by-light.
CERN. Geneva
2018-01-01
Chiral symmetry provides strong constraints on hadronic matrix elements at low energy, which are most efficiently derived with chiral perturbation theory. As an effective quantum field theory the latter also accounts for rescattering or unitarity effects, albeit only perturbatively, via the loop expansion. In cases where rescattering effects are important it becomes necessary to go beyond the perturbative expansion, e.g. by using dispersion relations. A matching between the chiral and the dispersive representation provides in several cases results of high precision. I will discuss this approach with the help of a few examples, like $\\pi \\pi$ scattering (which has been tested successfully by CERN experiments like NA48/2 and DIRAC), $\\eta \\to 3 \\pi$ and the hadronic light-by-light contribution to $(g-2)_\\mu$. For the latter quantity the implementation of the dispersive approach has opened up the way to a model-independent calculation and the concrete possibility to significantly reduce the theoretical uncertain...
Li, Yutian; Zhu, Jianxin
2015-05-04
In this paper we consider the problem of computing the eigen-modes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.
DEFF Research Database (Denmark)
Pugliese, Lorenzo; Poulsen, Tjalfe; Straface, Salvatore
2013-01-01
Measurements of solute dispersion in porous media is generally much more time consuming than gas dispersion measurements performed under equivalent conditions. Significant time savings may therefore, be achieved if solute dispersion coefficients can be estimated based on measured gas dispersion...... data. This paper evaluates the possibility for estimating solute dispersion based on gas dispersion measurements. Breakthrough measurements were carried out at different fluid velocities (covering the same range in Reynolds number), using O2 and NaCl as gas and solute tracers, respectively. Three...... different, granular porous materials were used: (1) crushed granite (very angular particles), (2) gravel (particles of intermediate roundness) and (3) Leca® (almost spherical particles). For each material, 21 different particle size fractions were used. Gas and solute dispersion coefficients were determined...
International Nuclear Information System (INIS)
Mittal, R.; Chaplot, S.L.; Parthasarathy, R.; Bull, M.J.; Harris, M.J.
2000-01-01
The coherent inelastic neutron scattering technique is used for the measurements of phonon dispersion relation in a geophysically important mineral zircon using PRISMA spectrometer as ISIS, UK. Lattice dynamical calculations of the phonon dispersion relation are carried out using a shell model. The one-phonon structure factors are calculated for selecting the Bragg points for the measurements and assignment of phonons to different branches. The calculations are in good agreement with the measured phonon dispersion relation. (author)
The tensorial conservation law in general relativity
International Nuclear Information System (INIS)
Zhao, M.G.
1984-01-01
A general tensorial conservation law is formulated by starting from the invariance of the gravitational Lagrangian density. Utilising this new formula, the author derives some reasonable results for the mass-energy distribution which are in accordance with the Newtonian formulae. (author)
DEFF Research Database (Denmark)
Marini, Lorenzo; Bruun, Hans Henrik; Heikkinen, Risto
2012-01-01
Aim Habitat fragmentation is a major driver of biodiversity loss but it is insufficiently known how much its effects vary among species with different life-history traits; especially in plant communities, the understanding of the role of traits related to species persistence and dispersal in dete...... rural landscapes in NW Europe, mitigating the spatial isolation of remaining grasslands should be accompanied by restoration measures aimed at improving habitat quality for low competitors, abiotically dispersed and perennial, clonal species.......Aim Habitat fragmentation is a major driver of biodiversity loss but it is insufficiently known how much its effects vary among species with different life-history traits; especially in plant communities, the understanding of the role of traits related to species persistence and dispersal...... in determining dynamics of species communities in fragmented landscapes is still limited. The primary aim of this study was to test how plant traits related to persistence and dispersal and their interactions modify plant species vulnerability to decreasing habitat area and increasing isolation. Location Five...
Directory of Open Access Journals (Sweden)
S.-D. Zhang
2000-10-01
Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides
The 'Falling Box' method in general relativity
International Nuclear Information System (INIS)
Gladush, V.D.
1998-01-01
The problems of justification, generalization, and applicability of the 'falling box' method to obtained some exact solutions of the vacuum Einstein equations are investigated. The 'physical' inference of the Reissner-Nordstrom-de Sitter and Kerr metrics is shown. Explanation is given for the well-known relativistic phenomenon which consists in that gravity is created by the double density of the electrical field energy
The formulations of the AMS/EPA Regulatory Model Improvement Committee's applied air dispersion model (AERMOD) as related to the characterization of the planetary boundary layer are described. This is the first in a series of three articles. Part II describes the formulation of...
Dispersion Models to Forecast Traffic-related Emissions in Urban Areas
Directory of Open Access Journals (Sweden)
Davide Scannapieco
2011-11-01
Full Text Available Down the centuries, a direct link had been developed between increase in mobility and increase in wealth. On the other hand, air emission of greenhouse gases (GHG due to vehicles equipped with internal combustion engines can be regarded as a negative pressure over the environment. In the coming decades, road transport is likely to remain a significant contributor to air pollution in cities. Many urban trips cover distances of less than 6 km. Since the effectiveness of catalytic converters in the initial minutes of engine operation is small, the average emission per distance driven is very high in urban areas. Also, poorly maintained vehicles that lack exhaust aftertreatment systems are responsible for a major part of pollutant emissions. Therefore in urban areas, where higher concentrations of vehicles can be easily found, air pollution represents a critical issue, being it related with both environment and human health protection: in truth, research in recent decades consistently indicates the adverse effects of outdoor air pollution on human health, and the evidence points to air pollution stemming from transport as an important contributor to these effects. Several institutions (EEA, USEPA, etc. focused their interest in dispersion models because of their potential effectiveness to forecast atmospheric pollution. Furthermore, air micropollutants such as Polycyclic Aromatic Compounds (PAH and Metallic Trace Elements (MTE are traffic-related and although very low concentrations their dispersion is a serious issue. However, dispersion models are usefully implemented to better manage this estimation problem. Nonetheless, policy makers and land managers have to deal with model selection, taking into account that several dispersion models are available, each one of them focused on specific goals (e.g., wind transport of pollutants, land morphology implementation, evaluation of micropollutants transport, etc.; a further aspect to be considered is
Gyro-viscosity and linear dispersion relations in pair-ion magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Kono, M. [Faculty of Policy Studies, Chuo University, Tokyo 192-0393 (Japan); Vranjes, J. [Instituto de Astrofisica de Canarias, Tenerife E38205 (Spain); Departamento de Astrofisica, Universidad de La Laguna, Tenerife E38205 (Spain)
2015-11-15
A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the experiment has been already explained by a kinetic theory by the present authors, the kinetic derivations are so involved because of exact particle orbits in phase space, finite Lamor radius effects, and higher order ion cyclotron resonances. The present fluid theory provides a simple and transparent structure to the dispersion relations since the gyro-viscosity is renormalized into the ion cyclotron frequency which itself indicates the backward nature of dispersion. The usual disadvantage of a fluid theory, which treats only fundamental modes of eigen-waves excited in a system and is not able to describe higher harmonics that a kinetic theory does, is compensated by simple derivations and clear picture based on the renormalization of the gyro-viscosity.
General Information about AIDS-Related Lymphoma
... and treatment options. AIDS-related lymphoma is a disease in which malignant (cancer) cells form in the ... cord. The sample may also be checked for Epstein-Barr virus . This procedure is also called an LP ...
On ``minimally curved spacetimes'' in general relativity
Dadhich, Naresh
1997-01-01
We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.
Grand Canonical Ensembles in General Relativity
International Nuclear Information System (INIS)
Klein, David; Yang, Wei-Shih
2012-01-01
We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using that, we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition, we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials in anti-de Sitter space.
On hypermomentum in general relativity. Pt.1
International Nuclear Information System (INIS)
Hehl, F.W.; Kerlick, G.D.; Heyde, P. von der
1976-01-01
In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor Δsup(ijk) of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws. (orig.) [de
International Nuclear Information System (INIS)
Buske, D.
2011-01-01
The present contribution focuses on the question of radioactive material dispersion after discharge from a nuclear power plant in the context of micro-meteorology, i.e. an atmospheric dispersion model. The advection-diffusion equation with Fickian closure for the turbulence is solved for the atmospheric boundary layer where the eddy diffusivity coefficients and the wind profile are assumed to be space dependent. The model is solved in closed form using integral transform and spectral theory. Convergence of the solution is discussed in terms of a convergence criterion using a new interpretation of the Cardinal Theorem of Interpolation theory and Parseval's theorem. The solution is compared to other methods and model adequacy is analyzed. Model validation is performed against experimental data from a controlled release of radioactive material at the Itaorna Beach (Angra dos Reis, Rio de Janeiro state, Brazil, 1985). (author)
Singularities in the general theory of relativity
International Nuclear Information System (INIS)
Treder, H.J.
1980-01-01
'Regular solutions of Einstein's equations' mean very different things. In the case of the empty-space equations, Rsub(ik) = o, such solutions must be metrics gsub(ik)(xsup(l)) without additionaly singular 'field sources' (Einstein's 'Particle problem'). However the 'phenomenological matter' is defined by the Einstein equations Rsub(ik) - 1/2gsub(ik)R = -kappaTsub(ik) itselves. Therefore if 10 regular functions gsub(ik)(xsup(l)) are given (which the inequalities of Lorentz-signature fulfil) then these gsub(ik) define 10 functions Tsub(ik)(xsup(l)) without singularities. But, the matter-tensor Tsub(ik) must fulfil the two inequalities T >= o, T 0 0 >= 1/2 T only and therefore the Einstein-equations with 'phenomenological matter' mean the two inequalities R >= o, R 0 0 <= o which are incompatible with a permanently regular metric with Lorentz-signature, generally. (author)
Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations
Directory of Open Access Journals (Sweden)
Hui Li
2014-01-01
of the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.
International Nuclear Information System (INIS)
Abd-alla, Abo-el-nour N.; Al-sheikh, Fatimah; Al-Hossain, Abdullah Y.
2009-01-01
Effect of initial stresses on dispersion relation for transverse surface waves circulating around a piezoelectric cylinder covered with perfectly conducting layers is investigated. Two overlay materials are considered: Gold and Aluminum. The piezoelectric substrate is considered to have the symmetry of a hexagonal crystal, and the layer is perfectly conducting. The dispersion equation has been given in the form of determinant involving Bessel functions. The roots of the dispersion equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots are numerically calculated by 'Bisection method iterations technique' and presented graphically for various thickness of the overlayer and for different values of the initial stress. The effects of the initial stress on the natural frequencies are illustrated on the figures. It is found that both the thickness of the overlayer and the initial stress have a substantial effect on the dispersion behavior. The results obtained in this paper may not only help us get insight into the electro-mechanical coupling behavior of the piezoelectric composites cylinders, but can also offer theoretical basis and meaningful suggestions for the design of piezoelectric probes and electro-acoustic devices in the nondestructive evaluation technology. Finally, the results are compared graphically when the overlay is Gold or Aluminum with some special cases which do not have initial stresses and electric field.
Study of Phonon Dispersion Relations in Cuprous Oxide by Inelastic Neutron Scattering
DEFF Research Database (Denmark)
Beg, M. M.; Shapiro, S. M.
1976-01-01
Phonon dispersion relations in Cu2O have been studied at 20°C using inelastic neutron scattering. Seven acoustic branches and twelve optical branches have been studied in detail in the three symmetry directions [00ζ], [ζζ0], and [ζζζ] of the cubic lattice. Four of the six zone-center phonons have...... been observed and the assignments and energies are confirmed as Γ25=87±2 cm-1, Γ12′=105±3 cm-1, Γ15=146±1 cm-1, and Γ2′≈347 cm-1. The dispersion relations agree only qualitatively with the rigid-ion-model calculations. It is suggested that more detailed calculations may be performed in the light...
Spin-wave dispersion relations in disordered Fe-V alloys
International Nuclear Information System (INIS)
Nakai, Y.; Schibuya, N.; Kunitomi, N.; Wakabayashi, N.; Cooke, J.F.
1982-01-01
The spin-wave dispersion relations of the ferromagnetic disordered alloys Fe/sub 1-x/V/sub x/(x = 0.076, 0.135, 0.160, and 0.187) were studied by means of the inelastic scattering of neutrons. The observed dispersion relations are adequately represented by the power law, E = Dq 2 (1-βq 2 ), in a wide energy range up to 80 meV. The concentration dependence of the exchange stiffness constant D shows good agreement with previous results obtained by means of the small-angle scattering of neutrons and by the analysis of the temperature dependence of the bulk magnetization. The observed results can be explained by the Heisenberg model and, to some extent, by the itinerant-electron model
On the Sensitivity of Neutrino Telescopes to a Modified Dispersion Relation
International Nuclear Information System (INIS)
Bustamante, M.; Gago, A. M.; Bazo, J. L.; Miranda, O. G.
2008-01-01
We consider a modified dispersion relation and its effect on the flavour ratios of high-energy neutrinos originated at distant astrophysical sources such as active galactic nuclei. This dispersion relation arise naturally in different new physics (NP) effects such as violation of CPT invariance, of the equivalence principle and of Lorentz invariance. It is a common notion in the literature that by using the flux of high-energy neutrinos expected from distant astrophysical sources, the sensitivity to possible NP effects may be improved beyond the current bounds. However, performing a realistic analysis that takes into account the expected number of events in future neutrino telescopes, we find that the average detected flavour ratios with and without the inclusion of new physics have essentially the same value, making difficult to obtain an improved bound for this type of new physics
Dispersion relation of test waves in an electron beam plasma system
International Nuclear Information System (INIS)
Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.
1994-01-01
Test waves are propagated in an electron beam plasma system and the dispersion relation is measured. At the center of the experimental region a beam mode is excited. Near the chamber wall an electron plasma wave is excited and propagates from the chamber wall to the center of the experimental region. It is also found that observed unstable waves are standing wave which is formed by superposing the beam modes propagating in the opposite directions each other. (author). 6 refs, 6 figs
$K^{\\pm}n$ forward dispersion relations and the KN$\\Sigma$ coupling constant
Baillon, Paul; Ferro-Luzzi, M; Jenni, Peter; Perreau, J M; Tripp, R D; Ypsilantis, Thomas; Déclais, Y; Séguinot, Jacques
1976-01-01
Recent measurements of the K/sup -/n forward scattering amplitude at 1.2, 1.4, 2.6 GeV/c are used in a once-subtracted dispersion relation to determine the value of the KN Sigma coupling constant. The result is g/sub Sigma //sup 2/=1.9+or-3.2, in agreement with the prediction of the SU(3) theory.
Dispersion relation of Raman FEL with helical Wiggler and ion channel
International Nuclear Information System (INIS)
Hosseinalinezhad, M.; Bahmani, M.; Hasanbeigi, A.; Salehkoutahi, M.
2012-01-01
In this paper the theory of free electron laser with helical wiggler and ion channel guiding has been presented. The equations of motion for an electron have been analyzed. A formula for the dispersion relation is then derived in the low-gain-per-pass limit. The results of a numerical study of the growth rate enhancement due to the ion channel are presented and discussed.
Dispersion relation approach to sub-barrier heavy ion fusion reactions
International Nuclear Information System (INIS)
Franzin, V.L.M.; Hussein, M.S.
1986-07-01
With the aid of an inverse dispersion relation, which gives the imaginary part of the fusion inclusive polarization potential (IPP) in terms of the principal part integral involving the real part of the IPP, the sub-barrier fusion of heavy ions is discussed. The system 16 O+ A Sm is taken as an example. The reactive content of the extracted IPP is analysed within the coupled channels theory. (Author) [pt
The dispersion relation for the forward elastic electron-atom scattering amplitude
International Nuclear Information System (INIS)
Amusia, M.Y.
1978-01-01
The analytical properties of forward elastic electron-atom scattering amplitude are discussed. It is noted that the occurrence of exchange between the incoming and atomic electrons leads to the appearance of a number of singularities on the negative real axis in the complex energy plane. The conclusion is drawn that the dispersion relation for the forward electron-atom scattering amplitude should also include an integration over the negative energy from - I to - infinity, where I is the ionization potential. (author)
Energy Technology Data Exchange (ETDEWEB)
Wang Ru [Quantitative Light Imaging Laboratory, Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Wang Zhuo; Leigh, Joe; Popescu, Gabriel [Quantitative Light Imaging Laboratory, Department of Electrical and Computer Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Sobh, Nahil [Beckman Institute for Advanced Science and Technology, Department of Civil and Environmental Engineering, and Department of Mechanical Engineering and Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Millet, Larry; Gillette, Martha U [Department of Cell and Developmental Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Levine, Alex J, E-mail: alevine@chem.ucla.edu, E-mail: gpopescu@illinois.edu [Department of Chemistry and Biochemistry and Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095 (United States)
2011-09-21
We studied the active transport of intracellular components along neuron processes using a new method developed in our laboratory: dispersion-relation phase spectroscopy. This method is able to quantitatively map spatially the heterogeneous dynamics of the concentration field of the cargos at submicron resolution without the need for tracking individual components. The results in terms of density correlation function reveal that the decay rate is linear in wavenumber, which is consistent with a narrow Lorentzian distribution of cargo velocity. (paper)
Calculation of the Green functions by the coupling constant dispersion relations
International Nuclear Information System (INIS)
Bogomalny, E.B.
1977-01-01
The discontinuities of the Green functions on the cut in the complex plane of the coupling constant are calculated by the steepest descent method. The saddle points are given by the solutions of the classical field equations at those values of the coupling constant for which the classical theory has no ground state. The Green functions at the physical values of the coupling constant are determined by dispersion relations. (Auth.)
International Nuclear Information System (INIS)
Chen, C.
1994-01-01
A Pierce-type dispersion relation is derived for the interaction of an intense relativistic electron beam with a cylindrical slow-wave structure of arbitrary corrugation depth. It is shown that near a resonance, the Pierce parameter can be expressed in terms of the vacuum dispersion function and the beam current. The dispersion relation is valid in both the low-current (Compton) regime and the high-current (Raman) regime. The dispersion characteristics of the interaction, such as the linear instability growth rate and bandwidth, are analyzed for both regimes
Subtracted Dispersion Relations for In-medium Meson Correlators in QCD Sum Rules
Energy Technology Data Exchange (ETDEWEB)
Florkowski, W; Broniowski, W [The H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)
1999-01-01
We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out that importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of the vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels of the Fermi gas of nucleons. (author)
Black hole radiation with modified dispersion relation in tunneling paradigm: Static frame
Directory of Open Access Journals (Sweden)
Jun Tao
2017-09-01
Full Text Available To study possible deviations from the Hawking's prediction, we assume that the dispersion relations of matter fields are modified at high energies and use the Hamilton–Jacobi method to investigate the corresponding effects on the Hawking radiation in this paper. The preferred frame is the static frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energies but is modified near the Planck mass mp. We calculate the corrections to the Hawking temperature for massive and charged particles to O(mp−2 and massless and neutral particles to all orders. Our results suggest that the thermal spectrum of radiations near horizon is robust, e.g. corrections to the Hawking temperature are suppressed by mp. After the spectrum of radiations near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole. We find that the subleading logarithmic term of the entropy does not depend on how the dispersion relations of matter fields are modified. Finally, the luminosities of black holes are computed by using the geometric optics approximation.
International Nuclear Information System (INIS)
Bhattacharya, Sayak; Shah, Kushal
2015-01-01
The analytical dispersion relation of spoof surface plasmon (SSP) is known only in the low-frequency limit and thus cannot be used to describe various practically important characteristics of SSP in the high-frequency limit (such as multimodal nature, anisotropic propagation, self-collimation). In this article, we consider a square lattice of holes made on a perfect electric conductor and derive a closed form expression of the SSP dispersion relation in the high-frequency limit using a tight binding model. Instead of using prior knowledge of the band diagram along the entire first Brillouin zone (BZ) edge, we analytically determine the hopping parameters by using the eigenfrequencies only at the three high-symmetry points of the square lattice. Using this dispersion relation, we derive an expression for the self-collimation frequency of SSP. We show that this analytical formulation is also applicable to dielectric photonic crystals and can be used to predict the frequencies corresponding to centimetre-scale supercollimation and second band self-collimation in these structures. Finally, we show that our analytical results are in agreement with the simulation results for both SSP and photonic crystals. (paper)
Large-scale tides in general relativity
Energy Technology Data Exchange (ETDEWEB)
Ip, Hiu Yan; Schmidt, Fabian, E-mail: iphys@mpa-garching.mpg.de, E-mail: fabians@mpa-garching.mpg.de [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany)
2017-02-01
Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is much larger than the sound horizon of all fluid components. This fact is known as the 'separate universe' paradigm. However, no such relation is known for anisotropic adiabatic perturbations, which correspond to an FLRW spacetime with large-scale tidal fields. Here, we provide a closed, fully relativistic set of evolutionary equations for the nonlinear evolution of such modes, based on the conformal Fermi (CFC) frame. We show explicitly that the tidal effects are encoded by the Weyl tensor, and are hence entirely different from an anisotropic Bianchi I spacetime, where the anisotropy is sourced by the Ricci tensor. In order to close the system, certain higher derivative terms have to be dropped. We show that this approximation is equivalent to the local tidal approximation of Hui and Bertschinger [1]. We also show that this very simple set of equations matches the exact evolution of the density field at second order, but fails at third and higher order. This provides a useful, easy-to-use framework for computing the fully relativistic growth of structure at second order.
1982-11-01
time of application. Such designs were probably influenced by the ready availabilit " 51 of fire-fighting hoses on ships and tugs; the water stream not...8217 I I1 ---- i . . .. . IIII . . . I I PREFACE The use of chemicals for the dispersal of oil spilled on water has been the subject of discussion (and of...20 Oil Type, Weathering and Emulsification.. 20 Slick Thickness .......................... 28 Water Temperature
BOOK REVIEW: Advanced Mechanics and General Relativity Advanced Mechanics and General Relativity
Louko, Jorma
2011-04-01
Joel Franklin's textbook `Advanced Mechanics and General Relativity' comprises two partially overlapping, partially complementary introductory paths into general relativity at advanced undergraduate level. Path I starts with the Lagrangian and Hamiltonian formulations of Newtonian point particle motion, emphasising the action principle and the connection between symmetries and conservation laws. The concepts are then adapted to point particle motion in Minkowski space, introducing Lorentz transformations as symmetries of the action. There follows a focused development of tensor calculus, parallel transport and curvature, using examples from Newtonian mechanics and special relativity, culminating in the field equations of general relativity. The Schwarzschild solution is analysed, including a detailed discussion of the tidal forces on a radially infalling observer. Basics of gravitational radiation are examined, highlighting the similarities to and differences from electromagnetic radiation. The final topics in Path I are equatorial geodesics in Kerr and the motion of a relativistic string in Minkowski space. Path II starts by introducing scalar field theory on Minkowski space as a limit of point masses connected by springs, emphasising the action principle, conservation laws and the energy-momentum tensor. The action principle for electromagnetism is introduced, and the coupling of electromagnetism to a complex scalar field is developed in a detailed and pedagogical fashion. A free symmetric second-rank tensor field on Minkowski space is introduced, and the action principle of general relativity is recovered from coupling the second-rank tensor to its own energy-momentum tensor. Path II then merges with Path I and, supplanted with judicious early selections from Path I, can proceed to the Schwarzschild solution. The choice of material in each path is logical and focused. A notable example in Path I is that Lorentz transformations in Minkowki space are introduced
A new numerical method to solve the dispersion relation in multispecies plasma
International Nuclear Information System (INIS)
Cereceda, C.; Puerta, J.
2000-01-01
In this paper a new accurate and fast method for solving the linear dispersion relation for multispecies plasma is introduced. The method uses a four poles fractional approximation for the Z dispersion function, transforming the dispersion relation into a polynomial form. Time and space growth rates are then calculated. Calculations for a single beam - plasma are carried out being in good agreement with several authors. This method is very effective to simplify the calculation of growth rates in multi-ion plasmas. For multispecies plasmas several new modes of propagation arise. For two ion beam - plasma system, two slow modes can propagate, both which are unstable. Two maxima in the growth rates corresponding to each of these modes can be excited. The instability of one of the slow modes is fed by the energy of the light ion beam and the other one is fed by heavy beam ions. Each one of these two maxima is increased when the concentration of the corresponding species increases. But even for a small concentration of the light beam, the growth rate of the mode fed by it is the largest one, because in the single ion beam-plasma system the lighter ion yields the largest growth rate. (orig.)
Measurement of average density and relative volumes in a dispersed two-phase fluid
Sreepada, Sastry R.; Rippel, Robert R.
1992-01-01
An apparatus and a method are disclosed for measuring the average density and relative volumes in an essentially transparent, dispersed two-phase fluid. A laser beam with a diameter no greater than 1% of the diameter of the bubbles, droplets, or particles of the dispersed phase is directed onto a diffraction grating. A single-order component of the diffracted beam is directed through the two-phase fluid and its refraction is measured. Preferably, the refracted beam exiting the fluid is incident upon a optical filter with linearly varing optical density and the intensity of the filtered beam is measured. The invention can be combined with other laser-based measurement systems, e.g., laser doppler anemometry.
EXPERIMENTAL DETERMINATION OF WHISTLER WAVE DISPERSION RELATION IN THE SOLAR WIND
Energy Technology Data Exchange (ETDEWEB)
Stansby, D.; Horbury, T. S.; Chen, C. H. K.; Matteini, L., E-mail: david.stansby14@imperial.ac.uk [Department of Physics, Imperial College London, London SW7 2AZ (United Kingdom)
2016-09-20
The origins and properties of large-amplitude whistler wavepackets in the solar wind are still unclear. In this Letter, we utilize single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wavepackets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarized, travel anti-sunward, and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.
General and special education teachers' relations within teamwork ...
African Journals Online (AJOL)
and instruction, assessment and evaluation, and classroom management and behavior. Typically, the ... teaching techniques and learning processes. ... general objective of this research is to establish the relations of general and special.
Relation between the behaviors of P-wave and QT dispersions in elderly patients with heart failure
Directory of Open Access Journals (Sweden)
Szlejf Cláudia
2002-01-01
Full Text Available OBJECTIVE: To assess the relation between P-wave and QT dispersions in elderly patients with heart failure. METHODS: Forty-seven elderly patients (75.6±6 years with stable heart failure in NYHA functional classes II or III and with ejection fractions of 37±6% underwent body surface mapping to analyze P-wave and QT dispersions. The degree of correlation between P-wave and QT dispersions was assessed, and P-wave dispersion values in patients with QT dispersion greater than and smaller than 100 ms were compared. RESULTS: The mean values of P-wave and QT dispersions were 54±14 ms and 68±27 ms, respectively. The correlation between the 2 variables was R=0.41 (p=0.04. In patients with QT dispersion values > 100 ms, P-wave dispersion was significantly greater than in those with QT dispersion values < 100 ms (58±16 vs 53±12 ms, p=0.04 . CONCLUSION: Our results suggest that, in elderly patients with heart failure, a correlation between the values of P-wave and QT dispersions exists. These findings may have etiopathogenic, pathophysiologic, prognostic, and therapeutic implications, which should be investigated in other studies.
Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport
Energy Technology Data Exchange (ETDEWEB)
Xu, Bruce S. [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Lollar, Barbara Sherwood [Earth Sciences Department, University of Toronto, 22 Russell Street, Toronto, ON M5S 3B1 (Canada); Passeport, Elodie [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Chemical Engineering and Applied Chemistry Department, University of Toronto, 200 College Street, Toronto, ON M5S 3E5 (Canada); Sleep, Brent E., E-mail: sleep@ecf.utoronto.ca [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada)
2016-04-15
Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C{sub 0}), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D{sub mech}/D{sub eff}). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C{sub 0}/MDL ratios of 50 or higher. Much larger C{sub 0}/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D{sub mech}/D{sub eff} is
Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport
International Nuclear Information System (INIS)
Xu, Bruce S.; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E.
2016-01-01
Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C_0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D_m_e_c_h/D_e_f_f). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C_0/MDL ratios of 50 or higher. Much larger C_0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D_m_e_c_h/D_e_f_f is larger than 10, DRIF
Morakinyo, Tobi Eniolu; Lam, Yun Fat
2016-11-01
Numerical experiments involving street canyons of varying aspect ratio with traffic-induced pollutants (PM 2.5 ) and implanted trees of varying aspect ratio, leaf area index, leaf area density distribution, trunk height, tree-covered area, and tree planting pattern under different wind conditions were conducted using a computational fluid dynamics (CFD) model, ENVI-met. Various aspects of dispersion and deposition were investigated, which include the influence of various tree configurations and wind condition on dispersion within the street canyon, pollutant mass at the free stream layer and street canyon, and comparison between mass removal by surface (leaf) deposition and mass enhancement due to the presence of trees. Results revealed that concentration level was enhanced especially within pedestrian level in street canyons with trees relative to their tree-free counterparts. Additionally, we found a dependence of the magnitude of concentration increase (within pedestrian level) and decrease (above pedestrian level) due to tree configuration and wind condition. Furthermore, we realized that only ∼0.1-3 % of PM 2.5 was dispersed to the free stream layer while a larger percentage (∼97 %) remained in the canyon, regardless of its aspect ratio, prevailing wind condition, and either tree-free or with tree (of various configuration). Lastly, results indicate that pollutant removal due to deposition on leaf surfaces is potentially sufficient to counterbalance the enhancement of PM 2.5 by such trees under some tree planting scenarios and wind conditions.
Black hole radiation with modified dispersion relation in tunneling paradigm: free-fall frame
Energy Technology Data Exchange (ETDEWEB)
Wang, Peng; Yang, Haitang; Ying, Shuxuan [Sichuan University, Center for Theoretical Physics, College of Physical Science and Technology, Chengdu (China)
2016-01-15
Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study the effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass m{sub p}. The corrections to the Hawking temperature are calculated for massive and charged particles to O(m{sub p}{sup -2}) and neutral and massless particles with λ = 0 to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation. (orig.)
Relative dispersion of clustered drifters in a small micro-tidal estuary
Suara, Kabir; Chanson, Hubert; Borgas, Michael; Brown, Richard J.
2017-07-01
Small tide-dominated estuaries are affected by large scale flow structures which combine with the underlying bed generated smaller scale turbulence to significantly increase the magnitude of horizontal diffusivity. Field estimates of horizontal diffusivity and its associated scales are however rare due to limitations in instrumentation. Data from multiple deployments of low and high resolution clusters of GPS-drifters are used to examine the dynamics of a surface flow in a small micro-tidal estuary through relative dispersion analyses. During the field study, cluster diffusivity, which combines both large- and small-scale processes ranged between, 0.01 and 3.01 m2/s for spreading clusters and, -0.06 and -4.2 m2/s for contracting clusters. Pair-particle dispersion, Dp2, was scale dependent and grew as Dp2 ∼ t1.83 in streamwise and Dp2 ∼ t0.8 in cross-stream directions. At small separation scale, pair-particle (d law and became weaker as separation scale increases. Pair-particle diffusivity was described as Kp ∼ d1.01 and Kp ∼ d0.85 in the streamwise and cross-stream directions, respectively for separation scales ranging from 0.1 to 10 m. Two methods were used to identify the mechanism responsible for dispersion within the channel. The results clearly revealed the importance of strain fields (stretching and shearing) in the spreading of particles within a small micro-tidal channel. The work provided input for modelling dispersion of passive particle in shallow micro-tidal estuaries where these were not previously experimentally studied.
International Nuclear Information System (INIS)
Shirakata, Hikari; Kawaguchi, Toshihiro; Okamoto, Takashi; Ishiyama, Tomoaki
2017-01-01
We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs) against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016). We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.
Energy Technology Data Exchange (ETDEWEB)
Shirakata, Hikari [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Kawaguchi, Toshihiro [Department of Economics, Management and Information Science, Onomichi City University, Onomichi, Hiroshima (Japan); Okamoto, Takashi [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Ishiyama, Tomoaki, E-mail: shirakata@astro1.sci.hokudai.ac.jp [Institute of Management and Information Technologies, Chiba University, Chiba (Japan)
2017-09-12
We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs) against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016). We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.
DSR Theories, Conformal Group and Generalized Commutation Relation
International Nuclear Information System (INIS)
Leiva, Carlos
2006-01-01
In this paper the relationship of DSR theories and Conformal Group is reviewed. On the other hand, the relation between DSR Magueijo Smolin generators and generalized commutation relations is also shown
An Analysis of the New LHC Data through the Dispersion Relations
Selyugin, O.V.
2017-01-01
We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the total cross section. In particular, the determination of the phase of the elastic scattering amplitude will play an important role, and we shall study it via dispersion relations. We shall also examine the origin of the dependence on momentum transfer of the slopes of the different parts of the scattering amplitude in different models. We shall also give the results of another similar analysis based on a Regge-trajectory approach for the hadron scattering amplitude.
Bounds on Cubic Lorentz-Violating Terms in the Fermionic Dispersion Relation
Bertolami, O.; Rosa, J. G.
2004-01-01
We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the non-relativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the ${}^9\\textrm Be^+$ ion to bound the values of the Lorentz-violating parameters $\\eta_1$ and $\\eta_2$ for neutrons. The resulting bounds depend on the value of the Lorenz-...
Generalized uncertainty relations and characteristic invariants for the multimode states
International Nuclear Information System (INIS)
Sudarshan, E.C.G.; Chiu, C.B.; Bhamathi, G.
1995-01-01
The close relationship between the zero-point energy, the uncertainty relation, coherent states, squeezed states, and correlated states for one mode is investigated. This group theoretic perspective of the problem enables the parametrization and identification of their multimode generalization. A simple and efficient method of determining the canonical structure of the generalized correlated states is presented. Implication of canonical commutation relations for correlations are not exhausted by the Heisenberg uncertainty relation, not even by the Schroedinger-Robertson uncertainty inequality, but there are relations in the multimode case that are the generalization of the Schroedinger-Robertson relation
Dispersion relations of density fluctuations observed by heavy ion beam probe in the TEXT tokamak
International Nuclear Information System (INIS)
Ross, D.W.
1990-09-01
Wave numbers as functions of frequency for density fluctuations in the core of the TEXT tokamak are measured in Heavy Ion Beam Probe experiments by analyzing the relative phases of signals originating from nearby points in the plasma. The adjacent points are typically 2 cm apart, with their relative orientation (δr, δθ) depending on position (r,θ). for angular frequencies ω ≤ 10 6 /s the signals are quite coherent, leading to reasonably well-defined ''dispersion relations.'' These do not correspond to known modes of the drift wave type, i.e., ballooning or slab-like electron drift waves or ion temperature gradient modes. The effect of finite sample volume size does not significantly alter this conclusion. 25 refs., 6 figs., 3 tabs
Differential forms and the geometry of general relativity
Dray, Tevian
2015-01-01
Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.The book contains two intertwined but distinct halves. Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes
Keefe, Laurence
2016-11-01
Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.
Dispersion relations in the noncommutative φ3 and Wess-Zumino model in the Yang-Feldman formalism
International Nuclear Information System (INIS)
Doescher, C.; Zahn, J.
2006-05-01
We study dispersion relations in the noncommutative φ 3 and Wess-Zumino model in the Yang-Feldman formalism at one-loop order. Non-planar graphs lead to a distortion of the dispersion relation. We find that this effect is small if the scale of noncommutativity is identified with the Planck scale and parameters typical for a Higgs field are employed. (Orig.)
Huang, N. E.; Tung, C.-C.
1977-01-01
The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.
The age-velocity dispersion relation of the Galactic discs from LAMOST-Gaia data
Yu, Jincheng; Liu, Chao
2018-03-01
We present the age-velocity dispersion relation (AVR) in three dimensions in the solar neighbourhood using 3564 commonly observed sub-giant/red giant branch stars selected from The Large Sky Area Multi-Object Fiber Spectroscopic Telescope, which gives the age and radial velocity, and Gaia, which measures the distance and proper motion. The stars are separated into metal-poor ([Fe/H] -0.2 dex) groups, so that the metal-rich stars are mostly α-poor, while the metal-poor group are mostly contributed by α-enhanced stars. Thus, the old and metal-poor stars likely belong to the chemically defined thick disc population, while the metal-rich sample is dominated by the thin disc. The AVR for the metal-poor sample shows an abrupt increase at ≳7 Gyr, which is contributed by the thick disc component. On the other hand, most of the thin disc stars with [Fe/H] > -0.2 dex display a power-law-like AVR with indices of about 0.3-0.4 and 0.5 for the in-plane and vertical dispersions, respectively. This is consistent with the scenario that the disc is gradually heated by the spiral arms and/or the giant molecular clouds. Moreover, the older thin disc stars (>7 Gyr) have a rounder velocity ellipsoid, i.e. σϕ/σz is close to 1.0, probably due to the more efficient heating in vertical direction. Particularly for the old metal-poor sample located with |z| > 270 pc, the vertical dispersion is even larger than its azimuthal counterpart. Finally, the vertex deviations and the tilt angles are plausibly around zero with large uncertainties.
Constraints on stress-energy perturbations in general relativity
International Nuclear Information System (INIS)
Traschen, J.
1985-01-01
Conditions are found for the existence of integral constraints on stress-energy perturbations in general relativity. The integral constraints can be thought of as a general-relativistic generalization of the conservation of energy and momentum of matter perturbations in special relativity. The constraints are stated in terms of a vector field V, and the Robertson-Walker spacetimes are shown to have such constraint vectors. Although in general V is not a Killing vector, in a vacuum spacetime the constraint vectors are precisely the Killing vectors
Directory of Open Access Journals (Sweden)
Sophie S. Shamailov, Joachim Brand
2018-03-01
Full Text Available Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.
Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David
2013-09-09
The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.
Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates
International Nuclear Information System (INIS)
Gruner, T.; Welsch, D.
1996-01-01
Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. copyright 1996 The American Physical Society
6th International Conference on the History of General Relativity
Eisenstaedt, Jean; The Universe of General Relativity; GR 6
2005-01-01
This volume from the Einstein Studies Series is based largely on papers presented at the Sixth International Conference on the History of General Relativity, held in Amsterdam on June 26-29, 2002. These contributions from notable experts offer both new and historical insights on gravitation, general relativity, cosmology, unified field theory, and the history of science. Topics discussed include the prehistory of special relativity, early attempts at a relativistic theory of gravitation, the beginnings of general relativity, the problem of motion in the context of relativity, conservation laws, the axiomatization of relativity, classical and contemporary cosmology, gravitation and electromagnetism, quantum gravity, and relativity as seen through the eyes of the public and renowned relativists. Contributors: K. Brading; G. Gale; H.F.M. Goenner; J. Goldberg; S. Katzir; D. Kennefick; H. Kragh; C. Lehner; U. Majer; J. Mattingly; E.T. Newman; J.D. Norton; J. Renn; R. Rynasiewicz; J.M. Sánchez-Ron; T. Sauer; C. Sm...
Magnon dispersion relation and exchange interactions in MnF2
DEFF Research Database (Denmark)
Nikotin, O.; Lindgård, Per-Anker; Dietrich, O. W.
1969-01-01
The magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone. Using an exact dipole model, the three nearest-neighbour exchange constants were found to be J1 = 0·028 ± 0......·001 mev, J2 = -0·152 ± 0·001 mev and J3 = -0·004 ± 0·001 mev. The second moment was also calculated with this model. The density of magnon states was evaluated by applying a six-parameter simulation of the dispersion surface. The critical points in the density of states agree well with those obtained...... by optical double-magnon experiments, whereas the detailed shape of the density of states differs significantly, indicating that the effect of magnon-magnon interactions rather than that of distant-neighbour exchange is of primary importance in the optical measurements....
The consistency assessment of topological relations in cartographic generalization
Zheng, Chunyan; Guo, Qingsheng; Du, Xiaochu
2006-10-01
The field of research in the generalization assessment has been less studied than the generalization process itself, and it is very important to keep topological relation consistency for meeting generalization quality. This paper proposes a methodology to assess the quality of generalized map from topological relations consistency. Taking roads (including railway) and residential areas for examples, from the viewpoint of the spatial cognition, some issues about topological consistency in different map scales are analyzed. The statistic information about the inconsistent topological relations can be obtained by comparing the two matrices: one is the matrix for the topological relations in the generalized map; the other is the theoretical matrix for the topological relations that should be maintained after generalization. Based on the fuzzy set theory and the classification of map object types, the consistency evaluation model of topological relations is established. The paper proves the feasibility of the method through the example about how to evaluate the local topological relations between simple roads and residential area finally.
Generalized string theory mapping relations between gravity and gauge theory
International Nuclear Information System (INIS)
Bjerrum-Bohr, N.E.J.
2003-01-01
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang-Mills theory, as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings
Can one tell Einstein's unimodular theory from Einstein's general relativity?
Alvarez, Enrique
2005-01-01
The so called unimodular theory of gravitation is compared with general relativity in the quadratic (Fierz-Pauli) regime, using a quite broad framework, and it is argued that quantum effects allow in principle to discriminate between both theories.
The role of Einstein's general relativity theory in today's physics
International Nuclear Information System (INIS)
Bicak, J.
The relationships are discussed of the general relativity theory to other fields of today's physics. Recent results are reported of studies into gravitational radiation, relativistic astrophysics, cosmology and the quantum theory. (Z.M.)
Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements
International Nuclear Information System (INIS)
Dong Shihai; Chen Changyuan; Lozada-Cassou, M
2005-01-01
Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied
Guo, Xiao; Wei, Peijun
2016-03-01
The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.
70 years of the general theory of relativity
International Nuclear Information System (INIS)
Castro Diaz-Balart, F.; Cabezas Solorzano, R.
1986-06-01
In view of the 70th anniversary of the discovery of the General Theory of Relativity, an analysis was made of the special and general theories. The basic postulates, their consequences in the formulation of the theories, the main results, some aspects related to the experimental verification and its applications are presented, as are some elements of the mathematical formalism of the theories, to facilitate the logical interrelationships between its results and consequences. (author)
Using CAMAL for algebraic computations in general relativity
International Nuclear Information System (INIS)
Fitch, J.P.
1979-01-01
CAMAL is a collection of computer algebra systems developed in Cambridge, England for use mainly in theoretical physics. One of these was designed originally for general relativity calculations, although it is often used in other fields. In a recent paper Cohen, Leringe, and Sundblad compared six systems for algebraic computations applied to general relativity available in Stockholm. Here similar information for CAMAL is given and by using the same tests CAMAL is added to the comparison. (author)
Fickian dispersion is anomalous
Cushman, John H.; O'Malley, Dan
2015-12-01
The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion we illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify non-Fickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finite-size Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are p-self-similar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized self-similar processes. Power-law clocks are introduced to examine multi-scaling behavior. Several examples of these ideas are presented and discussed.
Effects of weak nonlinearity on dispersion relations and frequency band-gaps of periodic structures
DEFF Research Database (Denmark)
Sorokin, Vladislav; Thomsen, Jon Juel
2015-01-01
of these for nonlinear problems is impossible or cumbersome, since Floquet theory is applicable for linear systems only. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applica-tions may demand effects of nonlinearity on structural response to be accounted for....... The present work deals with analytically predicting dynamic responses for nonlinear continuous elastic periodic structures. Specifically, the effects of weak nonlinearity on the dispersion re-lation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending os-cillations are analyzed......The analysis of the behaviour of linear periodic structures can be traced back over 300 years, to Sir Isaac Newton, and still attracts much attention. An essential feature of periodic struc-tures is the presence of frequency band-gaps, i.e. frequency ranges in which waves cannot propagate...
Guo, Xiaohao; Lu, Chunsong; Zhao, Tianliang; Liu, Yangang; Zhang, Guang Jun; Luo, Shi
2018-01-01
This study investigates the influence of entrainment rate (λ) on relative dispersion (ε) of cloud droplet size distributions (CDSD) in the 99 growing precipitating deep convective clouds during TOGA-COARE. The results show that entrainment suppresses ε, which is opposite to the traditional understanding that entrainment-mixing broadens CDSD. To examine how the relationship between ε and λ is affected by droplets with different sizes, CDSDs are divided into three portions with droplet radius processes is developed to illustrate the possible scenarios entailing different relationships between ε and λ. The number concentration of small droplets and the degree of evaporation of small droplets are found to be key factors that shift the sign (i.e., positive or negative) of the ε-λ relationship.
Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant
Garattini, Remo
2012-07-01
Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.
Heavy-ion optical potential for sub-barrier fusion deduced from a dispersion relation
International Nuclear Information System (INIS)
Kim, B.T.; Kim, H.C.; Park, K.E.
1988-01-01
The heavy-ion energy-dependent optical potentials for the 16 O+ 208 Pb system are deduced from a dispersion relation. These potentials are used to analyze the elastic scattering, fusion, and spin distributions of compound nuclei for the system in a unified way based on the direct reaction theory. It turns out that the energy dependence of the optical potential is essential in explaining the data at near- and sub-barrier energies. The real part of the energy-dependent optical potential deduced was also used in calculating the elastic and fusion cross sections by the conventional barrier penetration model using an incoming wave boundary condition. The predictions of the elastic scattering, fusion cross sections, and the spin distributions of compound nuclei are not satisfactory compared with those from the direct reaction approach. It seems to originate from the fact that this model neglects absorption around the Coulomb barrier region
Zirak, H.; Jafari, S.
2015-06-01
In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge-Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.
Dispersion relation and growth rate in a Cherenkov free electron laser: Finite axial magnetic field
International Nuclear Information System (INIS)
Kheiri, Golshad; Esmaeilzadeh, Mahdi
2013-01-01
A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread
Measurements of the power spectrum and dispersion relation of self-excited dust acoustic waves
Nosenko, V.; Zhdanov, S. K.; Kim, S.-H.; Heinrich, J.; Merlino, R. L.; Morfill, G. E.
2009-12-01
The spectrum of spontaneously excited dust acoustic waves was measured. The waves were observed with high temporal resolution using a fast video camera operating at 1000 frames per second. The experimental system was a suspension of micron-size kaolin particles in the anode region of a dc discharge in argon. Wave activity was found at frequencies as high as 450 Hz. At high wave numbers, the wave dispersion relation was acoustic-like (frequency proportional to wave number). At low wave numbers, the wave frequency did not tend to zero, but reached a cutoff frequency instead. The cutoff value declined with distance from the anode. We ascribe the observed cutoff to the particle confinement in this region.
Dispersion relation for hadronic light-by-light scattering: two-pion contributions
Energy Technology Data Exchange (ETDEWEB)
Colangelo, Gilberto [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern (Switzerland); Hoferichter, Martin [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 (United States); Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States); Procura, Massimiliano [Theoretical Physics Department, CERN, Geneva (Switzerland); Stoffer, Peter [Helmholtz-Institut für Strahlen- und Kernphysik (Theory)and Bethe Center for Theoretical Physics, University of Bonn, 53115 Bonn (Germany); Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)
2017-04-27
In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g−2){sub μ}, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ{sup ∗}γ{sup ∗}→ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a{sub μ}{sup π-box}=−15.9(2)×10{sup −11}. As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ{sup ∗}γ{sup ∗}→ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f{sub 0}(500) to HLbL scattering in (g−2){sub μ}. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a{sub μ}{sup π-box}+a{sub μ,J=0}{sup ππ,π-pole} {sup LHC}=−24(1)×10{sup −11}.
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
Spinor formalism and complex-vector formalism of general relativity
International Nuclear Information System (INIS)
Han-ying, G.; Yong-shi, W.; Gendao, L.
1974-01-01
In this paper, using E. Cartan's exterior calculus, we give the spinor form of the structure equations, which leads naturally to the Newman--Penrose equations. Furthermore, starting from the spinor spaces and the el (2C) algebra, we construct the general complex-vector formalism of general relativity. We find that both the Cahen--Debever--Defrise complex-vector formalism and that of Brans are its special cases. Thus, the spinor formalism and the complex-vector formalism of general relativity are unified on the basis of the uni-modular group SL(2C) and its Lie algebra
Implications of a positive cosmological constant for general relativity.
Ashtekar, Abhay
2017-10-01
Most of the literature on general relativity over the last century assumes that the cosmological constant [Formula: see text] is zero. However, by now independent observations have led to a consensus that the dynamics of the universe is best described by Einstein's equations with a small but positive [Formula: see text]. Interestingly, this requires a drastic revision of conceptual frameworks commonly used in general relativity, no matter how small [Formula: see text] is. We first explain why, and then summarize the current status of generalizations of these frameworks to include a positive [Formula: see text], focusing on gravitational waves.
Effect of magnetic field on the wave dispersion relation in three-dimensional dusty plasma crystals
International Nuclear Information System (INIS)
Yang Xuefeng; Wang Zhengxiong
2012-01-01
Three-dimensional plasma crystals under microgravity condition are investigated by taking into account an external magnetic field. The wave dispersion relations of dust lattice modes in the body centered cubic (bcc) and the face centered cubic (fcc) plasma crystals are obtained explicitly when the magnetic field is perpendicular to the wave motion. The wave dispersion relations of dust lattice modes in the bcc and fcc plasma crystals are calculated numerically when the magnetic field is in an arbitrary direction. The numerical results show that one longitudinal mode and two transverse modes are coupled due to the Lorentz force in the magnetic field. Moreover, three wave modes, i.e., the high frequency phonon mode, the low frequency phonon mode, and the optical mode, are obtained. The optical mode and at least one phonon mode are hybrid modes. When the magnetic field is neither parallel nor perpendicular to the primitive wave motion, all the three wave modes are hybrid modes and do not have any intersection points. It is also found that with increasing the magnetic field strength, the frequency of the optical mode increases and has a cutoff at the cyclotron frequency of the dust particles in the limit of long wavelength, and the mode mixings for both the optical mode and the high frequency phonon mode increase. The acoustic velocity of the low frequency phonon mode is zero. In addition, the acoustic velocity of the high frequency phonon mode depends on the angle of the magnetic field and the wave motion but does not depend on the magnetic field strength.
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...
The general class of the vacuum spherically symmetric equations of the general relativity theory
International Nuclear Information System (INIS)
Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-01-01
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.
Shirazi, Mohammadali; Lord, Dominique; Dhavala, Soma Sekhar; Geedipally, Srinivas Reddy
2016-06-01
Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion. Copyright © 2016 Elsevier Ltd. All rights reserved.
Nonlinear Supersymmetric General Relativity and Unity of Nature
Shima, Kazunari; Tsuda, Motomu
2008-01-01
The basic idea and some physical implications of nonlinear supersymmetric general relativity (NLSUSY GR) are discussed, which give new insights into the origin of mass and the mysterious relations between the cosmology and the low energy particle physics, e.g. the spontaneous SUSY breaking scale, the cosmological constant, the (dark) energy density of the universe and the neutrino mass.
Indefinite-metric quantum field theory of general relativity, 2
International Nuclear Information System (INIS)
Nakanishi, Noboru
1978-01-01
The canonical commutation relations are analyzed in detail in the manifestly covariant quantum field theory of general relativity proposed previously. It is explicitly proved that the BRS charge is indeed the generator of the BRS transformation both in the Landau gauge and in the non-Landau one. The equivalence between the field equations and the Heisenberg equations is confirmed. (author)
Experimental tests of general relativity: recent progress and future directions
International Nuclear Information System (INIS)
Turyshev, S G
2009-01-01
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology, and fundamental physics are concerned. As such, this theory is used for many practical purposes involving spacecraft navigation, geodesy, and time transfer. We review the foundations of general relativity, discuss recent progress in tests of relativistic gravity, and present motivations for the new generation of high-accuracy tests of new physics beyond general relativity. Space-based experiments in fundamental physics are presently capable of uniquely addressing important questions related to the fundamental laws of nature. We discuss the advances in our understanding of fundamental physics that are anticipated in the near future and evaluate the discovery potential of a number of recently proposed space-based gravitational experiments. (reviews of topical problems)
Influence of local parameters on the dispersion of traffic-related pollutants within street canyons
Karra, Styliani; Malki-Epshtein, Liora; Martin Hyde Collaboration
2011-11-01
Ventilation within urban cities and street canyons and the associated air quality is a problem of increasing interest in the last decades. It is important for to minimise exposure of the population to traffic-related pollutants at street level. The residence time of pollutants within the street canyons depends on the meteorological conditions such as wind speed and direction, geometry layout and local parameters (position of traffic lane within the street). An experimental study was carried out to investigate the influence of traffic lane position on the dispersion of traffic-related pollutants within different street canyons geometries: symmetrical (equal building heights on both sides of the street), non-symmetrical (uniform building heights but lower on one side of the street) and heterogeneous (non-uniform building heights on both sides of the street) under constant meteorological conditions. Laboratory experiments were carried out within a water channel and simultaneous measurements of velocity field and concentration scalar levels within and above the street canyons using PIV and PLIF techniques. Traffic -related emissions were simulated using a line emission source. Two positions were examined for all street geometries: line emission source was placed in the centre of the street canyon; line emission source was placed off the centre of the street. TSI Incorporated.
Vanel, Florence O.; Baysal, Oktay
1995-01-01
Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.
Dinh, Khuong Van; Janssens, Lizanne; Therry, Lieven; Bervoets, Lieven; Bonte, Dries; Stoks, Robby
2016-11-01
How exposure to contaminants may interfere with the widespread poleward range expansions under global warming is largely unknown. Pesticide exposure may negatively affect traits shaping the speed of range expansion, including traits related to population growth rate and dispersal-related traits. Moreover, rapid evolution of growth rates during poleward range expansions may come at a cost of a reduced investment in detoxification and repair thereby increasing the vulnerability to contaminants at expanding range fronts. We tested effects of a sublethal concentration of the widespread pesticide chlorpyrifos on traits related to range expansion in replicated edge and core populations of the poleward moving damselfly Coenagrion scitulum reared at low and high food levels in a common garden experiment. Food limitation in the larval stage had strong negative effects both in the larval stage and across metamorphosis in the adult stage. Exposure to chlorpyrifos during the larval stage did not affect larval traits but caused delayed effects across metamorphosis by increasing the incidence of wing malformations during metamorphosis and by reducing a key component of the adult immune response. There was some support for an evolutionary trade-off scenario as the faster growing edge larvae suffered a higher mortality during metamorphosis. Instead, there was no clear support for the faster growing edge larvae being more vulnerable to chlorpyrifos. Our data indicate that sublethal delayed effects of pesticide exposure, partly in association with the rapid evolution of faster growth rates, may slow down range expansions. Copyright © 2016 Elsevier Ltd. All rights reserved.
Proceedings of the fourth Marcel Grossmann meeting on general relativity
International Nuclear Information System (INIS)
Ruffini, R.
1986-01-01
The Marcel Grossmann meetings were conceived with the aim of reviewing recent advances in gravitation and general relativity with the major emphasis on their mathematical foundations and physical predictions. Their main objective is to elicit contributions which deepen our understanding of space-time structures as well as to review the status of experiments verifying Einstein's Theory of Gravitation. It has been demonstrated by the previous meetings that these sessions provide physicists from various countries who are involved in research on general relativity with a unique opportunity to exchange experiences and enhance co-operation in fields of common interest. The meeting was essentially divided into 3 sub-areas; interplay between elementary particle physics and cosmology and relativistic astrophysics, classical relativity, and experimental relativity. Among the topics covered were supergravity and superstrings, bar gravitational wave detectors, black holes, classical relativity, computer relativity, cosmology and inos, early cosmology, exact solutions, Kaluza Klein theories, relativistic self-gravitating systems and quantum gravity. (Auth.)
The generalized Crewther relation in QCD and its experimental consequences
International Nuclear Information System (INIS)
Brodsky, S.J.; Gabadadze, G.T.; Kataev, A.L.; Lu, H.J.
1995-12-01
We use the BLM scale-fixing prescription to derive a renormalization-scheme invariant relation between the coefficient function for the Bjorken sum rule for polarized deep inelastic scattering and the R-ratio for the e + e - annihilation cross section. This relation provides a generalization of the Crewther relation to non-conformally invariant gauge theories. The derived relations allow one to calculate unambiguously without renormalization scale or scheme ambiguity the effective charges of the polarized Bjorken and the Gross-Llewellen Smith sum rules from the experimental value for the effective charge associated with R-ratio. Present data are consistent with the generalized Crewther relations, but measurements at higher precision and energies will be needed to decisively test these fundamental relations in QCD. (orig.)
Blum, Alexander; Lalli, Roberto; Renn, M Jürgen
2015-09-01
The history of the theory of general relativity presents unique features. After its discovery, the theory was immediately confirmed and rapidly changed established notions of space and time. The further implications of general relativity, however, remained largely unexplored until the mid 1950s, when it came into focus as a physical theory and gradually returned to the mainstream of physics. This essay presents a historiographical framework for assessing the history of general relativity by taking into account in an integrated narrative intellectual developments, epistemological problems, and technological advances; the characteristics of post-World War II and Cold War science; and newly emerging institutional settings. It argues that such a framework can help us understand this renaissance of general relativity as a result of two main factors: the recognition of the untapped potential of general relativity and an explicit effort at community building, which allowed this formerly disparate and dispersed field to benefit from the postwar changes in the scientific landscape.
Neutron optical potential of 28Si derived from the dispersion relation
International Nuclear Information System (INIS)
Kitazawa, H.; Igarasi, S.; Katsuragi, D.; Harima, Y.
1992-01-01
Based upon the dispersion theory, an optical potential of 28 Si was determined at the neutron energies from the Fermi energy to 20 MeV. In particular, discussion was given on a characteristic behavior of the optical potential for low-energy neutrons. Moreover, the validity of the dispersion theory was investigated for neutron single-particle bound states in 29 Si. (orig.)
Assessing the relative importance of dispersal in plant communities using an ecoinformatics approach
Ozinga, W.A.; Hennekens, S.M.; Schaminée, J.H.J.; Bekker, R.M.; Prinzing, A.; Bonn, S.; Poschlod, P.; Tackenberg, O.; Thompson, K.; Bakker, J.P.; Groenendael, van J.M.
2005-01-01
Increased insight into the factors that determine the importance of dispersal limitation on species richness and species composition is of paramount importance for conservation and restoration ecology. One way to explore the importance of dispersal limitation is to use seed-sowing experiments, but
On the rule of thumb for flipping the dispersion relation in BAW devices
Jose, Sumy; Hueting, Raymond Josephus Engelbart; Jansman, Andreas
2011-01-01
High-performance solidly mounted bulk acoustic wave resonators (SMRs) can be obtained by employing frame region, if these exhibit type I dispersion. The commonly used piezoelectric material Aluminum Nitride is a type II material, for which type I dispersion can be enforced by increasing the top
Relative toxicity of oil dispersants to Mytilus viridis and Macrobrachium idella
Digital Repository Service at National Institute of Oceanography (India)
DeSilva, C.; Row, A.
) was almost identical for both the species tested, although there was a significant shift in the range of LC sub(50) values, indicating that one species is less sensitive than the other. Oil dispersant mixtures were less toxic than the dispersants alone...
Dispersion bias, dispersion effect, and the aerosol-cloud conundrum
International Nuclear Information System (INIS)
Liu Yangang; Daum, Peter H; Guo Huan; Peng Yiran
2008-01-01
This work examines the influences of relative dispersion (the ratio of the standard deviation to the mean radius of the cloud droplet size distribution) on cloud albedo and cloud radiative forcing, derives an analytical formulation that accounts explicitly for the contribution from droplet concentration and relative dispersion, and presents a new approach to parameterize relative dispersion in climate models. It is shown that inadequate representation of relative dispersion in climate models leads to an overestimation of cloud albedo, resulting in a negative bias of global mean shortwave cloud radiative forcing that can be comparable to the warming caused by doubling CO 2 in magnitude, and that this dispersion bias is likely near its maximum for ambient clouds. Relative dispersion is empirically expressed as a function of the quotient between cloud liquid water content and droplet concentration (i.e., water per droplet), yielding an analytical formulation for the first aerosol indirect effect. Further analysis of the new expression reveals that the dispersion effect not only offsets the cooling from the Twomey effect, but is also proportional to the Twomey effect in magnitude. These results suggest that unrealistic representation of relative dispersion in cloud parameterization in general, and evaluation of aerosol indirect effects in particular, is at least in part responsible for several outstanding puzzles of the aerosol-cloud conundrum: for example, overestimation of cloud radiative cooling by climate models compared to satellite observations; large uncertainty and discrepancy in estimates of the aerosol indirect effect; and the lack of interhemispheric difference in cloud albedo.
Introduction to general relativity, black holes and cosmology
Choquet-Bruhat, Yvonne
2015-01-01
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the found...
Causality and dispersion relations and the role of the S-matrix in the ongoing research
International Nuclear Information System (INIS)
Schroer, Bert; Freie Univ. , Berlin
2011-01-01
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)
Causality and dispersion relations and the role of the S-matrix in the ongoing research
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert, E-mail: schroer@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Univ. , Berlin (Germany). Inst. fur Theoretische Physik
2011-07-01
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)
Zhou, Lulu; Forman, Henry Jay; Ge, Yi; Lunec, Joseph
2017-08-01
Chemical functionalization broadens carbon nanotube (CNT) applications, conferring new functions, but at the same time potentially altering toxicity. Although considerable experimental data related to CNT toxicity, at the molecular and cellular levels, have been reported, there is very limited information available for the corresponding mechanism involved (e.g. cell apoptosis and genotoxicity). The threshold dose for safe medical application in relation to both pristine and functionalized carbon nanotubes remains ambiguous. In this study, we evaluated the in vitro cytotoxicity of pristine and functionalized (OH, COOH) multi-walled carbon nanotubes (MWCNTs) for cell viability, oxidant detection, apoptosis and DNA mutations, to determine the non-toxic dose and influence of functional group in a human lung-cancer cell line exposed to 1-1000μg/ml MWCNTs for 24, 48 and 72h. The findings suggest that pristine MWCNTs induced more cell death than functionalized MWCNTs while functionalized MWCNTs are more genotoxic compared to their pristine form. The level of both dose and dispersion in the matrix used should be taken into consideration before applying further clinical applications of MWCNTs. Copyright © 2017 Elsevier Ltd. All rights reserved.
Operational evaluation of the RLINE dispersion model for studies of traffic-related air pollutants
Milando, Chad W.; Batterman, Stuart A.
2018-06-01
Exposure to traffic-related air pollutants (TRAP) remains a key public health issue, and improved exposure measures are needed to support health impact and epidemiologic studies and inform regulatory responses. The recently developed Research LINE source model (RLINE), a Gaussian line source dispersion model, has been used in several epidemiologic studies of TRAP exposure, but evaluations of RLINE's performance in such applications have been limited. This study provides an operational evaluation of RLINE in which predictions of NOx, CO and PM2.5 are compared to observations at air quality monitoring stations located near high traffic roads in Detroit, MI. For CO and NOx, model performance was best at sites close to major roads, during downwind conditions, during weekdays, and during certain seasons. For PM2.5, the ability to discern local and particularly the traffic-related portion was limited, a result of high background levels, the sparseness of the monitoring network, and large uncertainties for certain processes (e.g., formation of secondary aerosols) and non-mobile sources (e.g., area, fugitive). Overall, RLINE's performance in near-road environments suggests its usefulness for estimating spatially- and temporally-resolved exposures. The study highlights considerations relevant to health impact and epidemiologic applications, including the importance of selecting appropriate pollutants, using appropriate monitoring approaches, considering prevailing wind directions during study design, and accounting for uncertainty.
International Nuclear Information System (INIS)
Goel, P.
2001-01-01
This paper reports inelastic neutron scattering (INS) measurements of the phonon dispersion relations of the aluminum silicate minerals andalusite and sillimanite, Al 2 SiO 5 . The single crystal INS measurements were undertaken using the Triple-axis-spectrometer at the Dhruva reactor, Trombay for andalusite and at the Oak Ridge National Laboratory, USA for sillimanite. The phonon dispersion relations (upto 50 mev) along various high symmetry directions have been measured and have been analyzed on the basis of lattice dynamics shell model calculations. The calculated structure factors based on the model calculations were used as guides for planning these single crystal measurements and were used to identify regions in reciprocal space with large cross-sections. The calculated structure factors have been very useful in the planning, execution and analysis of the experimental data. The calculated phonon dispersion relations are found to be in good agreement with the measured data
The motion of a charged particle in general relativity
International Nuclear Information System (INIS)
Ludvigsen, M.
1979-01-01
A new approach to the problem of the motion of a self-interacting massive charged particle in general relativity is presented. A charged Robinson-Trautman solution is used as a general relativistic model of such a particle. Such a solution is shown to generate a unique world line in its own H space, which is interpreted as the world line of the particle. Using the R-T dynamical relations, the equation of motion of the particle is derived, which, in the limiting case of zero curvature, is shown to be the same as the classical Lorentz-Dirac equation of motion. (author)
Gravitational radiation and the validity of general relativity
International Nuclear Information System (INIS)
Will, C.M.
2001-01-01
The regular observation of gravitational radiation by a world-wide network of resonant and laser-interferometric detectors will usher in a new form of astronomy. At the same time, it will provide new and interesting tests of general relativity. We review the current empirical status of general relativity, and discuss three areas in which direct observation of gravitational radiation could test the theory further: polarization of the waves, speed of the waves, and back-reaction of the waves on the evolution of the source. (author)
On the mathematical theory of classical fields and general relativity
Klainerman, S
1993-01-01
From the perspective of an analyst, like myself, the General Theory of Relativity provides an extrordinary rich and vastly virgin territory. It is the aim of my lecture to provide, ﬁrst, an account of those aspects of the theory which attract me most and second a perspective of what has been accomplished so far in that respect. In trying to state our main objectives it helps to view General Relativity in the broader context of Classical Field Theory. EinsteiniVacuum equations, or shortly E—V, is already sufﬁciently complicated. I will thus restrict my attention to them.
Canonical quantization of general relativity in discrete space-times.
Gambini, Rodolfo; Pullin, Jorge
2003-01-17
It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.
Essays in general relativity a Festschrift for Abraham Taub
Tipler, Frank J
1981-01-01
Essays in General Relativity: A Festschrift for Abraham Taub is collection of essays to honor Professor Abraham H. Taub on the occasion of his retirement from the mathematics faculty of the University of California at Berkeley. Relativistic hydrodynamics has always been a subject dear to Taub's heart. In fact, many basic results on special relativistic fluid flows are due to him, and he has been a major contributor to the study of fluid flows near shocks. The book contains 16 chapters and begins with a discussion of a geometrical approach to general relativity. This is followed by separate cha
Directory of Open Access Journals (Sweden)
Hikari Shirakata
2017-09-01
Full Text Available We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016. We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.
Directory of Open Access Journals (Sweden)
Marwan Fahs
2018-02-01
Full Text Available The Henry problem (HP continues to play a useful role in theoretical and practical studies related to seawater intrusion (SWI into coastal aquifers. The popularity of this problem is attributed to its simplicity and precision to the existence of semi-analytical (SA solutions. The first SA solution has been developed for a high uniform diffusion coefficient. Several further studies have contributed more realistic solutions with lower diffusion coefficients or velocity-dependent dispersion. All the existing SA solutions are limited to homogenous and isotropic domains. This work attempts to improve the realism of the SA solution of the dispersive HP by extending it to heterogeneous and anisotropic coastal aquifers. The solution is obtained using the Fourier series method. A special hydraulic conductivity–depth model describing stratified heterogeneity is used for mathematical convenience. An efficient technique is developed to solve the flow and transport equations in the spectral space. With this technique, we show that the HP can be solved in the spectral space with the salt concentration as primary unknown. Several examples are generated, and the SA solutions are compared against an in-house finite element code. The results provide high-quality data assessed by quantitative indicators that can be effectively used for code verification in realistic configurations of heterogeneity and anisotropy. The SA solution is used to explain contradictory results stated in the previous works about the effect of anisotropy on the saltwater wedge. It is also used to investigate the combined influence of stratification and anisotropy on relevant metrics characterizing SWI. At a constant gravity number, anisotropy leads to landward migration of the saltwater wedge, more intense saltwater flux, a wider mixing zone and shallower groundwater discharge zone to the sea. The influence of stratified heterogeneity is more pronounced in highly anisotropic aquifers. The
Roe, Mark A; Collings, Rachel; Hoogewerff, Jurian; Fairweather-Tait, Susan J
2009-03-01
Food iron fortification is a sustainable and relatively simple strategy to reduce/prevent iron deficiency but is a challenge for the food industry because of possible adverse organoleptic changes caused by the added iron. A micronized dispersible ferric pyrophosphate, trademarked as SunActive Fe, has recently been developed. SunActive Fe has a small particle size, is water soluble and may be suitable for fortifying liquid products. To determine the relative bioavailability of SunActive Fe and its suitability for addition to pure apple juice. Iron absorption from SunActive Fe added to pure apple juice (Minute Maid) was compared with absorption from ferrous sulphate, a highly bioavailable form of iron, in 15 women with relatively low iron stores. Both forms of iron were enriched with an iron stable isotope and iron absorption from the apple juice drinks was calculated from the isotopic enrichment of red blood cells 14 days after the last test meal. Although mean absorption of iron from SunActive Fe was significantly lower than from ferrous sulphate (5.5% compared with 9.1%), the mean bioavailability of SunActive Fe iron relative to ferrous sulphate was 0.6, indicating that it is a good source of bioavailable iron. Iron Absorption from SunActive Fe was positively correlated (r = 0.97, P = 0.01) with absorption from ferrous sulphate, and negatively correlated with serum ferritin concentration (ferrous sulphate r = -0.81, P apple juice and is a potentially useful fortificant for liquid food products.
International Nuclear Information System (INIS)
Pepper, D.W.
1979-11-01
A three-dimensional numerical model is used to calculate ground-level air concentration and deposition (due to precipitation scavenging) after a hypothetical tornado strike at the General Electric Vallecitos Nuclear Center at Vallecitos, California. Plutonium particles less than 20 μm in diameter are assumed to be lifted into the tornadic storm cell by the vortex. The rotational characteristics of the tornadic storm are embedded within the larger mesoscale flow of the storm system. The design-basis translational wind values are based on probabilities associated with existing records of tornado strikes in the vicinity of the plant site. Turbulence exchange coefficients are based on empirical values deduced from experimental data in severe storms and from theoretical assumptions obtained from the literature. The method of moments is used to incorporate subgrid-scale resolution of the concentration within a grid cell volume. This method is a quasi-Lagrangian scheme which minimizes numerical error associated with advection. In all case studies, the effects of updrafts and downdrafts, coupled with scavenging of the particulates by precipitation, account for most of the material being deposited within 20 to 45 km downwind of the plant site. Ground-level isopleths in the x-y plane show that most of the material is deposited behind and slightly to the left of the centerline trajectory of the storm. Approximately 5% of the material is dispersed into the stratosphere and anvil section of the storm
Energy Technology Data Exchange (ETDEWEB)
Pepper, D.W.
1979-11-01
A three-dimensional numerical model is used to calculate ground-level air concentration and deposition (due to precipitation scavenging) after a hypothetical tornado strike at the General Electric Vallecitos Nuclear Center at Vallecitos, California. Plutonium particles less than 20 ..mu..m in diameter are assumed to be lifted into the tornadic storm cell by the vortex. The rotational characteristics of the tornadic storm are embedded within the larger mesoscale flow of the storm system. The design-basis translational wind values are based on probabilities associated with existing records of tornado strikes in the vicinity of the plant site. Turbulence exchange coefficients are based on empirical values deduced from experimental data in severe storms and from theoretical assumptions obtained from the literature. The method of moments is used to incorporate subgrid-scale resolution of the concentration within a grid cell volume. This method is a quasi-Lagrangian scheme which minimizes numerical error associated with advection. In all case studies, the effects of updrafts and downdrafts, coupled with scavenging of the particulates by precipitation, account for most of the material being deposited within 20 to 45 km downwind of the plant site. Ground-level isopleths in the x-y plane show that most of the material is deposited behind and slightly to the left of the centerline trajectory of the storm. Approximately 5% of the material is dispersed into the stratosphere and anvil section of the storm.
Doppler frequency in interplanetary radar and general relativity
Mcvittie, G. C.
1972-01-01
The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.
Cosmological perturbations in a family of deformations of general relativity
International Nuclear Information System (INIS)
Krasnov, Kirill; Shtanov, Yuri
2010-01-01
We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity
BOOK REVIEW: Partial Differential Equations in General Relativity
Halburd, Rodney G.
2008-11-01
Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed
Indefinite-metric quantum field theory of general relativity
International Nuclear Information System (INIS)
Nakanishi, Noboru
1978-01-01
Quantum field theory of Einstein's general relativity is formulated in the indefinitemetric Hilbert space in such a way that asymptotic fields are manifestly Lorentz covariant and the physical S-matrix is unitary. The general coordinate transformation is transcribed into a q-number transformation, called the BRS transformation. Its abstract definition is presented on the basis of the BRS transformation for the Yang-Mills theory. The BRS transformation for general relativity is then explicitly constructed. The gauge-fixing Lagrangian density and the Faddeev-Popov one are introduced in such a way that their sum behaves like a scalar density under the BRS transformation. One can then proceed in the same way as in the Kugo-Ojima formalism of the Yang-Mills theory to establish the unitarity of the physical S-matrix. (author)
General projective relativity and the vector-tensor gravitational field
International Nuclear Information System (INIS)
Arcidiacono, G.
1986-01-01
In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation
Test theories of special relativity: a general critique
International Nuclear Information System (INIS)
Maciel, A.K.A.; Tiomno, J.
1988-01-01
Absolute Spacetime Theories conceived for the purpose of testing Special Relativity (SR) are reviewed. It is found that most theories proposed were in fact SR in different coordinate systems, since in general no specific SR violations were introduced. Models based on possible SR violating mechanisms are considered. Misconceptions in recently published papers are examined. (author) [pt
Survey on Dirac equation in general relativity theory
International Nuclear Information System (INIS)
Paillere, P.
1984-10-01
Starting from an infinitesimal transformation expressed with a Killing vector and using systematically the formalism of the local tetrades, we show that, in the area of the general relativity, the Dirac equation may be formulated only versus the four local vectors which determine the gravitational potentials, their gradients and the 4-vector potential of the electromagnetic field [fr
An experiment designed to verify the general theory of relativity
International Nuclear Information System (INIS)
Surdin, Maurice
1960-01-01
The project for an experiment which uses the effect of gravitation on Maser-type clocks placed on the ground at two different heights and which is designed to verify the general theory of relativity. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 250, p. 299-301, sitting of 11 January 1960 [fr
Spinning fluids in general relativity: a variational formulation
International Nuclear Information System (INIS)
Oliveira, H.P. de; Salim, J.M.
1990-01-01
In this paper we present a variational formulation for spinning fluids in General Relativity. In our model each volume element of the fluid has rigid microstructure. We deduce a symmetrical energy-moment tensor where there is an explicit contribution of kinetic spin energy to the total energy. (author)
Albert Einstein's 1916 Review Article on General Relativity
Sauer, Tilman
2004-01-01
The first comprehensive overview of the final version of the general theory of relativity was published by Einstein in 1916 after several expositions of preliminary versions and latest revisions of the theory in November 1915. A historical account of this review paper is given, of its prehistory, including a discussion of Einstein's collaboration with Marcel Grossmann, and of its immediate reception.
Derivation of Einstein-Cartan theory from general relativity
Petti, Richard
2015-04-01
General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.
General relativity from a gauged Wess-Zumino-Witten term
International Nuclear Information System (INIS)
Anabalon, Andres; Willison, Steven; Zanelli, Jorge
2007-01-01
In this paper two things are done. First it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited
Einstein and Hilbert: The creation of general relativity
International Nuclear Information System (INIS)
Todorov, I.T.
1992-12-01
It took eight years after Einstein announced the basic physical ideas behind the relativistic gravity theory before the proper mathematical formulation of general-relativity was mastered. The efforts of the greatest physicist and of the greatest mathematician of the time was involved and reached a breathtaking concentration during the last month of the work. (author)
Proceedings of the third Marcel Grossmann meeting on general relativity
International Nuclear Information System (INIS)
Hu Ning
1983-01-01
This book contains 64 session papers presented at the 3rd Marcel Grossmann Meeting on General Relativity. The papers are divided into 10 sections including: classical problem in gravitation; alternative approaches to gravitational theory; supergravity; quantum gravity and quantum field theory in curved space; cosmology; early universe; physics of compact bodies; gravitational wave experiments; gravitational experiments; miscellaneous. (Auth.)
Generalized virial relations and the theory of subdynamics
International Nuclear Information System (INIS)
Obcemea, Ch.; Froelich, P.; Braandas, E.J.
1981-05-01
In this paper, we discuss the implication of the generalized virial relations in the spectral analysis of Liouville operators. In particular, we refer to the existence problem of the analytic continuation of these super-operators and their resolvents occurring in the reduced dynamics description of open systems. For completeness, we outline the main ideas of the subdynamics approach. (author)
Energy-momentum distribution: A crucial problem in general relativity
Sharif, M.; Fatima, T.
2005-01-01
This paper is aimed to elaborate the problem of energy–momentum in general relativity. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for two exact solutions of Einstein field equations. The space–times under
Statistical equilibrium and symplectic geometry in general relativity
International Nuclear Information System (INIS)
Iglesias, P.
1981-09-01
A geometrical construction is given of the statistical equilibrium states of a system of particles in the gravitational field in general relativity. By a method of localization variables, the expression of thermodynamic values is given and the compatibility of this description is shown with a macroscopic model of a relativistic continuous medium for a given value of the free-energy function [fr
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
The general theory of relativity, which is a field theory of gravitation, is described by the Einstein field equations. These equations whose fundamental constituent is the space-time metric gij, are highly non-linear partial differential equations and, therefore it is very difficult to obtain exact solutions. They become still more diffi-.
The general theory of relativity: the first thirty years
International Nuclear Information System (INIS)
Chandrasekhar, S.
1980-01-01
The principal landmarks in the development of general relativity (exclusive of cosmology) during the first 30 years after its founding are presented. The emergence of the new gravitational laws, their experimental consequences and the consequent growth of the present concern with gravitational collapse and black holes are traced. (U.K.)
Scalar fields and cosmic censorship hypothesis in general relativity
International Nuclear Information System (INIS)
Parnovs'kij, S.L.; Gajdamaka, O.Z.
2004-01-01
We discuss an influence of the presence of some nonstandard scalar fields in the vicinity of naked time-like singularity on the type and properties of this singularity. The main goal is to study the validity of the Penrose's Cosmic Censorship hypothesis in the General Relativity
Probing Students' Understanding of Some Conceptual Themes in General Relativity
Bandyopadhyay, Atanu; Kumar, Arvind
2010-01-01
This work is an attempt to see how physics undergraduates view the basic ideas of general relativity when they are exposed to the topic in a standard introductory course. Since the subject is conceptually and technically difficult, we adopted a "case studies" approach, focusing in depth on about six students who had just finished a one semester…
Galileons as the Scalar Analogue of General Relativity
Klein, Remko; Ozkan, Mehmet; Roest, Diederik
2016-01-01
We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial
Average and dispersion of the luminosity-redshift relation in the concordance model
Energy Technology Data Exchange (ETDEWEB)
Ben-Dayan, I. [DESY Hamburg (Germany). Theory Group; Gasperini, M. [Bari Univ. (Italy). Dipt. di Fisica; Istituto Nazionale di Fisica Nucleare, Bari (Italy); Marozzi, G. [College de France, 75 - Paris (France); Geneve Univ. (Switzerland). Dept. de Physique Theorique and CAP; Nugier, F. [Ecole Normale Superieure CNRS, Paris (France). Laboratoire de Physique Theorique; Veneziano, G. [College de France, 75 - Paris (France); CERN, Geneva (Switzerland). Physics Dept.; New York Univ., NY (United States). Dept. of Physics
2013-03-15
Starting from the luminosity-redshift relation recently given up to second order in the Poisson gauge, we calculate the effects of the realistic stochastic background of perturbations of the so-called concordance model on the combined light-cone and ensemble average of various functions of the luminosity distance, and on their variance, as functions of redshift. We apply a gauge-invariant light-cone averaging prescription which is free from infrared and ultraviolet divergences, making our results robust with respect to changes of the corresponding cutoffs. Our main conclusions, in part already anticipated in a recent letter for the case of a perturbation spectrum computed in the linear regime, are that such inhomogeneities not only cannot avoid the need for dark energy, but also cannot prevent, in principle, the determination of its parameters down to an accuracy of order 10{sup -3} - 10{sup -5}, depending on the averaged observable and on the regime considered for the power spectrum. However, taking into account the appropriate corrections arising in the non-linear regime, we predict an irreducible scatter of the data approaching the 10% level which, for limited statistics, will necessarily limit the attainable precision. The predicted dispersion appears to be in good agreement with current observational estimates of the distance-modulus variance due to Doppler and lensing effects (at low and high redshifts, respectively), and represents a challenge for future precision measurements.
Fast flavor conversions of supernova neutrinos: Classifying instabilities via dispersion relations
Capozzi, Francesco; Dasgupta, Basudeb; Lisi, Eligio; Marrone, Antonio; Mirizzi, Alessandro
2017-08-01
Supernova neutrinos can exhibit a rich variety of flavor conversion mechanisms. In particular, they can experience "fast" self-induced flavor conversions almost immediately above the core. Very recently, a novel method has been proposed to investigate these phenomena, in terms of the dispersion relation for the complex frequency and wave number (ω ,k ) of disturbances in the mean field of the νeνx flavor coherence. We discuss a systematic approach to such instabilities, originally developed in the context of plasma physics, and based of the time-asymptotic behavior of the Green's function of the system. Instabilities are typically seen to emerge for complex ω and can be further characterized as convective (moving away faster than they spread) and absolute (growing locally), depending on k -dependent features. Stable cases emerge when k (but not ω ) is complex, leading to disturbances damped in space, or when both ω and k are real, corresponding to complete stability. The analytical classification of both unstable and stable modes leads not only to qualitative insights about their features but also to quantitative predictions about the growth rates of instabilities. Representative numerical solutions are discussed in a simple two-beam model of interacting neutrinos. As an application, we argue that supernova and binary neutron star mergers exhibiting a "crossing" in the electron lepton number would lead to an absolute instability in the flavor content of the neutrino gas.
Xu, Yanlong
2015-08-01
The coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures\\' evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates. © 2015 Elsevier B.V.
The Riemann Surface of Static Limit Dispersion Relation and Projective Spaces
Majewski, M; Meshcheryakov, D V; Tran Quang Tuyet
2004-01-01
The rigorous Bogoliubov's prove of the dispersion relations (DR) for pion-nucleon scattering is a good foundation for the static models. DR contain the small parameter (ratio of the pion-nucleon masses). The static models arise when this parameter goes to zero. The S-matrix in the static models has a block structure. Each block of the S-matrix has a finite order N\\times N and is a matrix of meromorphic functions of the light particle energy \\omega in the complex plane with cuts (-\\inf,-1], [+1, +\\inf). In the elastic case, it reduces to N functions S_{i}(\\omega) connected by N\\times N the crossing-symmetry matrix A. The unitarity and the crossing symmetry are the base for the system of nonlinear boundary value problems. It defines the analytical continuation of S_{i}(\\omega) from the physical sheet to the unphysical ones and can be treated as a system of nonlinear difference equations. The problem is solvable for any 2\\times 2 crossing-symmetry matrix A that permits one to calculate the Regge trajectories for...
Plakhotnik, Taras; Reichardt, Jens
2018-03-01
A theoretical framework is presented that permits investigations of the relation between inelastic backscattering from microparticles and bulk samples of Raman-active materials. It is based on the Lorentz reciprocity theorem and no fundamental restrictions concerning the microparticle shape apply. The approach provides a simple and intuitive explanation for the enhancement of the differential backscattering cross-section in particles in comparison to bulk. The enhancement factor for scattering of water droplets in the diameter range from 0 to 60 μm (vitally important for the a priori measurement of liquid water content of warm clouds with spectroscopic Raman lidars) is about a factor of 1.2-1.6 larger (depending on the size of the sphere) than an earlier study has shown. The numerical calculations are extended to 1000 μm and demonstrate that dispersion of the refractive index of water becomes an important factor for spheres larger than 100 μm. The physics of the oscillatory phenomena predicted by the simulations is explained.
The Riemann surface of static limit dispersion relation and projective spaces
International Nuclear Information System (INIS)
Majewski, M.; Meshcheryakov, V.A.; Meshcheryakov, D.V.; Tran Quang Tuyet
2004-01-01
The rigorous Bogolyubov's proof of the dispersion relations (DR) for pion-nucleon scattering is a good foundation for the static models. DR contain a small parameter (ratio of the pion-nucleon masses). The static models arise when this parameter goes to zero. The S-matrix in the static models has a block structure. Each block of the S-matrix has a finite order NxN and is a matrix of meromorphic functions of the light particle energy ω in the complex plane with cuts (-∞, -1], [+1,+∞). In the elastic case, it reduces to N functions S i (ω) connected by the NxN crossing-symmetry matrix A. The unitarity and the crossing symmetry are the base for the system of nonlinear boundary value problems. It defines the analytical continuation of S i (ω) from the physical sheet to the unphysical ones and can be treated as a system of nonlinear difference equations. The problem is solvable for any 2x2 crossing-symmetry matrix A that permits one to calculate the Regge trajectories for the SU(2) static model. It is shown that global analyses of this system can be carried out effectively in projective spaces P N-1 and P N . The connection between the spaces P N-1 and P N is discussed. Some particular solutions of the system are found
Phonon dispersion relation of uranium nitrate above and below the Neel temperature
International Nuclear Information System (INIS)
Dolling, G.; Holden, T.M.; Evensson, E.C.; Buyers, W.J.L.; Lander, G.H.
1977-01-01
Neutron coherent inelastic scattering measurements have been made of the phonon dispersion relation of uranium nitride both above and below the Neel temperature T/sub N/ = 50 K. Within the precision of the measurements, about 1% in frequency and 10% in line width and in scattered neutron intensity, no significant changes in these phonon properties were observed as a function of temperature other than those arising from population factor changes and a small stiffening of the lattice as the temperature decreases. At 4.2 K, two acoustic and two optic branches have been determined for each of the [001], [110] and [111] directions. The optic mode measurements revealed (a) a 20% variation in frequency across the Brillouin zone and (b) an interesting disposition of the LO and TO modes, such that nu/sub LO/ > nu/sub TO/ along [001] and [110], while the reverse is true along the [111] directions. Within the experimental resolution, the LO and TO modes are degenerate near q = 0. We have been unable to obtain any satisfactory description of these results on the basis of conventional theoretical treatments (e.g. rigid-ion or shell models). Other possible interpretations of the results are discussed
Phonon dispersion relation of uranium nitride above and below the Neel temperature
International Nuclear Information System (INIS)
Dolling, G.; Holden, T.M.; Svensson, E.C.; Buyers, W.J.L.; Lander, G.H.
1977-01-01
Neutron coherent inelastic scattering measurements have been made of the phonon dispersion relation of uranium nitride both above and below the Neel temperature T N = 50 K. Within the precision of the measurements, about 1% in frequency and 10% in line width and in scattered neutron intensity, no significant changes in these phonon properties were observed as a function of temperature other than those arising from population factor changes and a small stiffening of the lattice as the temperature decreases. At 4.2 K, two acoustic and two optic branches have been determined for each of the [001], [110] and [111] directions. The optic mode measurements revealed (a) a 20% variation in frequency across the Brillouin zone and (b) and interesting disposition of the LO and TO modes, such that ν LO > ν TO along [001] and [11-], while the reverse is true along the [111] directions. Within the experimental resolution, the LO and TO modes are degenerate near q = 0. We have been unable to obtain any satisfactory description of these results on the basis of conventional theoretical treatments (e.g. rigid-ion or shell models). Other possible interpretations of the results are discussed. (author)
Statistical analysis of dispersion relations in turbulent solar wind fluctuations using Cluster data
Perschke, C.; Narita, Y.
2012-12-01
Multi-spacecraft measurements enable us to resolve three-dimensional spatial structures without assuming Taylor's frozen-in-flow hypothesis. This is very useful to study frequency-wave vector diagram in solar wind turbulence through direct determination of three-dimensional wave vectors. The existence and evolution of dispersion relation and its role in fully-developed plasma turbulence have been drawing attention of physicists, in particular, if solar wind turbulence represents kinetic Alfvén or whistler mode as the carrier of spectral energy among different scales through wave-wave interactions. We investigate solar wind intervals of Cluster data for various flow velocities with a high-resolution wave vector analysis method, Multi-point Signal Resonator technique, at the tetrahedral separation about 100 km. Magnetic field data and ion data are used to determine the frequency- wave vector diagrams in the co-moving frame of the solar wind. We find primarily perpendicular wave vectors in solar wind turbulence which justify the earlier discussions about kinetic Alfvén or whistler wave. The frequency- wave vector diagrams confirm (a) wave vector anisotropy and (b) scattering in frequencies.
On stability relative to vector elements of the orbit in general relativity motion
International Nuclear Information System (INIS)
Abdil'din, M.M.; Bejsenova, N.A.
2002-01-01
In this work a question of a new type of stability - stability relative to vector elements of the orbit is considered in general relativity mechanics in case of the Lenze-Thirring and two body rotation. (author)
Generalization of the test theory of relativity to noninertial frames
International Nuclear Information System (INIS)
Abolghasem, G.H.; Khajehpour, M.R.H.; Mansouri, R.
1988-08-01
We present a generalized test theory of special relativity, using a noninertial frame. Within the framework of the special theory of relativity the transport- and Einstein-synchronizations are equivalent on a rigidly rotating disk. But in any theory with a preferred frame such an equivalence does not hold. The time difference resulting from the two synchronization procedures is a measurable quantity within the reach of existing clock systems on the earth. The final result contains a term which depends on the angular velocity of the rotating system, and hence measures an absolute effect. This term is of crucial importance in our test theory of the special relativity. (author). 13 refs
Reformulation of the symmetries of first-order general relativity
Montesinos, Merced; González, Diego; Celada, Mariano; Díaz, Bogar
2017-10-01
We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n>3 ) that is the generalization of three-dimensional local translations. This symmetry is obtained through the direct application of the converse of Noether’s second theorem on the theory under consideration. We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action. As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity. Although their gauge algebra is open in general, it allows us to recover, without resorting to the equations of motion, the very well-known Lie algebra satisfied by translations and Lorentz transformations in three dimensions. We also report the analog of the new gauge symmetry for the Holst action with cosmological term, finding that it explicitly depends on the Immirzi parameter. The same result concerning its relation to diffeomorphisms and the open character of the gauge algebra also hold in this case. Finally, we consider the non-minimal coupling of a scalar field to gravity in n dimensions and establish that the new gauge symmetry is affected by this matter field. Our results indicate that general relativity in dimension greater than three can be thought of as a gauge theory.
Extent of the Immirzi ambiguity in quantum general relativity
International Nuclear Information System (INIS)
Marugan, Guillermo A Mena
2002-01-01
The Ashtekar-Barbero formulation of general relativity admits a one-parameter family of canonical transformations that preserves the expressions of the Gauss and diffeomorphism constraints. The loop quantization of the connection formalism based on each of these canonical sets leads to different predictions. This phenomenon is called the Immirzi ambiguity. It has been recently argued that this ambiguity could be generalized to the extent of a spatially dependent function instead of a parameter. This would ruin the predictability of loop quantum gravity. We prove that such expectations are not realized, so that the Immirzi ambiguity introduces exclusively a freedom in the choice of a real number. (letter to the editor)
Escape trajectories of solar sails and general relativity
Energy Technology Data Exchange (ETDEWEB)
Kezerashvili, Roman Ya. [Physics Department, New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States); Vazquez-Poritz, Justin F., E-mail: jvazquez-poritz@citytech.cuny.ed [Physics Department, New York City College of Technology, City University of New York, 300 Jay Street, Brooklyn, NY 11201 (United States); Graduate School and University Center, City University of New York, 365 Fifth Avenue, New York, NY 10016 (United States)
2009-11-16
General relativity can have a significant impact on the long-range escape trajectories of solar sails deployed near the sun. For example, spacetime curvature in the vicinity of the sun can cause a solar sail traveling from about 4 solar radii to 2550 AU to be deflected by on the order of a million kilometers, and should therefore be taken into account at the beginning of the mission. There are a number of smaller general relativistic effects, such as frame dragging due to the slow rotation of the sun which can cause a deflection of more than one thousand kilometers.
Escape trajectories of solar sails and general relativity
International Nuclear Information System (INIS)
Kezerashvili, Roman Ya.; Vazquez-Poritz, Justin F.
2009-01-01
General relativity can have a significant impact on the long-range escape trajectories of solar sails deployed near the sun. For example, spacetime curvature in the vicinity of the sun can cause a solar sail traveling from about 4 solar radii to 2550 AU to be deflected by on the order of a million kilometers, and should therefore be taken into account at the beginning of the mission. There are a number of smaller general relativistic effects, such as frame dragging due to the slow rotation of the sun which can cause a deflection of more than one thousand kilometers.
Phonon dispersion relations in PrBa2Cu3O6+x (x approximate to 0.2)
DEFF Research Database (Denmark)
Gardiner, C.H.; Boothroyd, A.T.; Larsen, B.H.
2004-01-01
We report measurements of the phonon dispersion relations in nonsuperconducting, oxygen-deficient PrBa2Cu3O6+x (xapproximate to0.2) by inelastic neutron scattering. The data are compared with a model of the lattice dynamics based on a common interatomic potential. Good agreement is achieved for all...
Gromke, C.B.; Blocken, B.J.E.
2013-01-01
The relative importance of vegetation terms was analysed for flow and dispersion in an urban street canyon with avenue-trees. To this end, simulations with three k-e turbulence models and different approaches to model vegetation were performed. The different approaches resulted in rather slight
International Nuclear Information System (INIS)
Amusia, M.Ya.; Kuchiev, M.Yu.
1979-01-01
The jump in the electron - atomic-hydrogen forward scattering amplitude at the cut extending to the left from E = -0.5 au is calculated as a function of the incident electron energy, E, by using the second Born approximation. The contribution from this singularity to the dispersion relation is determined. (Auth.)
Kanoun, Mohammed; Cavallo, Luigi
2014-01-01
an energy barrier close to 20 kcal/mol on Ag38, which decreases to slightly more than 10 kcal/mol on Au38. This behavior is analyzed to quantify the impact of relativity and of dispersion interactions through a comparison of nonrelativistic, scalar
Energy Technology Data Exchange (ETDEWEB)
Pippig, G
1975-01-01
Taking the Compton scattering of pions and deuterons as an example it is shown that low-energy theorems which are valid for the order e/sup 2/ are also valid for the next higher order of electromagnetic interactions. The imaginary component of the scattering amplitude was exactly calculated for the energy of incident photons in the order e/sup 4/ up to the desired one, whereas the real component was obtained from dispersion relations. It is proved that the results derived from the dispersion theory of strong interactions are equivalent to those obtained from quantum electrodynamics for spin 0 and spin 1, respectively.
Comparison of Einstein-Boltzmann solvers for testing general relativity
Bellini, E.; Barreira, A.; Frusciante, N.; Hu, B.; Peirone, S.; Raveri, M.; Zumalacárregui, M.; Avilez-Lopez, A.; Ballardini, M.; Battye, R. A.; Bolliet, B.; Calabrese, E.; Dirian, Y.; Ferreira, P. G.; Finelli, F.; Huang, Z.; Ivanov, M. M.; Lesgourgues, J.; Li, B.; Lima, N. A.; Pace, F.; Paoletti, D.; Sawicki, I.; Silvestri, A.; Skordis, C.; Umiltà, C.; Vernizzi, F.
2018-01-01
We compare Einstein-Boltzmann solvers that include modifications to general relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f (R ) gravity, a code that models covariant Galileons, a code that models Hořava-Lifschitz gravity, and two codes that model nonlocal models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the subpercent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.
New ghost-free extensions of general relativity
International Nuclear Information System (INIS)
Mann, R.B.
1989-01-01
The method of algebraic extension is shown to yield a large class of gravitational theories which are extensions of general relativity. Requiring positivity of energy in the flat-space limit of such theories provides some constraints, but a large set of theories of potential phenomenological interest survives this condition. Explicit examples of such theories include the non-symmetric gravitational theory, algebraically extended Hilbert gravity and a one-parameter family of theories with dynamical torsion. In general such theories do not alter general relativistic post-Newtonian predictions for time delay experiments; rather they alter the non-linearities of the post-Newtonian gravitational potential. Such effects may be probed by measuring periastron shifts, as in the eclipsing binary systems Di Her and As Cam, as well as in the binary pulsar PSR 1913 + 16 (author)
Isotropic extensions of the vacuum solutions in general relativity
Energy Technology Data Exchange (ETDEWEB)
Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)
2012-07-01
Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)
Noncommutative unification of general relativity and quantum mechanics
International Nuclear Information System (INIS)
Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw
2005-01-01
We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid Γ given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics
General Theory of Relativity: Will It Survive the Next Decade?
Bertolami, Orfeu; Paramos, Jorge; Turyshev, Slava G.
2006-01-01
The nature of gravity is fundamental to our understanding of our own solar system, the galaxy and the structure and evolution of the Universe. Einstein's general theory of relativity is the standard model that is used for almost ninety years to describe gravitational phenomena on these various scales. We review the foundations of general relativity, discuss the recent progress in the tests of relativistic gravity, and present motivations for high-accuracy gravitational experiments in space. We also summarize the science objectives and technology needs for the laboratory experiments in space with laboratory being the entire solar system. We discuss the advances in our understanding of fundamental physics anticipated in the near future and evaluate discovery potential for the recently proposed gravitational experiments.
Academic Training: Einstein and beyond: Introduction to General relativity
Françoise Benz
2005-01-01
2005-2006 ACADEMIC TRAINING PROGRAMME LECTURE SERIES 3, 4, 5, 6, 7 October from 11:00 to 12:00 - Main Auditorium, bldg. 500 Einstein and beyond: Introduction to General relativity by N. Straumann / Institut fur theoretische physics, Univ. Zürich We review the enduring achievements of Einstein's papers of 1905 and their impact on the further developments in physics. Program : Lectures I and II:Einstein's Contributions to Statistical Mechanics and Quantum Theory Lecture III:Einstein's Thesis at the University of Zürich Lecture IV: From Special to General Relativity Lecture V: The History and the Mystery of the Cosmological Constant ENSEIGNEMENT ACADEMIQUE ACADEMIC TRAINING Françoise Benz 73127 academic.training@cern.ch
Relations between task delegation and job satisfaction in general practice
DEFF Research Database (Denmark)
Riisgaard, Helle; Nexøe, Jørgen; Videbæk Le, Jette
2016-01-01
practitioners' and their staff's job satisfaction appears to be sparse even though job satisfaction is acknowledged as an important factor associated with both patient satisfaction and medical quality of care. Therefore, the overall aim of this study was 1) to review the current research on the relation between...... task delegation and general practitioners' and their staff's job satisfaction and, additionally, 2) to review the evidence of possible explanations for this relation. METHODS: A systematic literature review. We searched the four databases PubMed, Cinahl, Embase, and Scopus systematically. The immediate...... attitude towards task delegation was positive and led to increased job satisfaction, probably because task delegation comprised a high degree of work autonomy. CONCLUSIONS: The few studies included in our review suggest that task delegation within general practice may be seen by the staff as an overall...
Testing General Relativity with the Shadow Size of Sgr A(*).
Johannsen, Tim; Broderick, Avery E; Plewa, Philipp M; Chatzopoulos, Sotiris; Doeleman, Sheperd S; Eisenhauer, Frank; Fish, Vincent L; Genzel, Reinhard; Gerhard, Ortwin; Johnson, Michael D
2016-01-22
In general relativity, the angular radius of the shadow of a black hole is primarily determined by its mass-to-distance ratio and depends only weakly on its spin and inclination. If general relativity is violated, however, the shadow size may also depend strongly on parametric deviations from the Kerr metric. Based on a reconstructed image of Sagittarius A^{*} (Sgr A^{*}) from a simulated one-day observing run of a seven-station Event Horizon Telescope (EHT) array, we employ a Markov chain Monte Carlo algorithm to demonstrate that such an observation can measure the angular radius of the shadow of Sgr A^{*} with an uncertainty of ∼1.5 μas (6%). We show that existing mass and distance measurements can be improved significantly when combined with upcoming EHT measurements of the shadow size and that tight constraints on potential deviations from the Kerr metric can be obtained.
A century of general relativity: astrophysics and cosmology.
Blandford, R D
2015-03-06
One hundred years after its birth, general relativity has become a highly successful physical theory in the sense that it has passed a large number of experimental and observational tests and finds extensive application to a wide variety of cosmic phenomena. It remains an active area of research as new tests are on the way, epitomized by the exciting prospect of detecting gravitational waves from merging black holes. General relativity is the essential foundation of the standard model of cosmology and underlies our description of the black holes and neutron stars that are ultimately responsible for the most powerful and dramatic cosmic sources. Its interface with physics on the smallest and largest scales will continue to provide fertile areas of investigation in its next century. Copyright © 2015, American Association for the Advancement of Science.
A student's manual for A first course in general relativity
Scott, Robert B
2016-01-01
This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and in...
International Nuclear Information System (INIS)
Horst, Allison M.; Ji, Zhaoxia; Holden, Patricia A.
2012-01-01
Nanoparticle exposure in toxicity studies requires that nanoparticles are bioavailable by remaining highly dispersed in culture media. However, reported dispersion approaches are variable, mostly study-specific, and not transferable owing to their empirical basis. Furthermore, many published approaches employ proteinaceous dispersants in rich laboratory media, both of which represent end members in environmental scenarios. Here, a systematic approach was developed to disperse initially agglomerated TiO 2 nanoparticles (Aeroxide® TiO 2 P25, Evonik, NJ; primary particle size range 6.4–73.8 nm) in oligotrophic culture medium for environmentally relevant bacterial toxicity studies. Based on understanding particle–particle interactions in aqueous media and maintaining environmental relevance, the approach involves (1) quantifying the relationship between pH and zeta potential to determine the point of zero charge of select nanoparticles in water; (2) nominating, then testing and selecting, environmentally relevant stabilizing agents; and (3) dispersing via “condition and capture” whereby stock dry powder nanoparticles are sonicated in pre-conditioned (with base, or acid, plus stabilizing agent) water, then diluted into culture media. The “condition and capture” principle is transferable to other nanoparticle and media chemistries: simultaneously, mechanically and electrostatically, nanoparticles can be dispersed with surrounding stabilizers that coat and sterically hinder reagglomeration in the culture medium.
A theory of strong interactions ''from'' general relativity
International Nuclear Information System (INIS)
Caldirola, P.; Recami, E.
1979-01-01
In this paper a previous letter (where, among other things, a classical ''quark confinement'' was derived from general relativity plus dilatation-covariance), is completed by showing that the theory is compatible also with quarks ''asymptotic freedom''. Then -within a bi-scale theory of gravitational and strong interactions- a classical field theory is proposed for the (strong) interactions between hadrons. Various consequences are briefly analysed
On the geometry of null congruences in general relativity
International Nuclear Information System (INIS)
Ahsan, Zafar; Malik, N.P.
1977-01-01
Some theorems for the null congruences within the framework of general theory of relativity are given. These theorems are important in themselves as they illustrate the geometric meaning of the spin coefficients. The newly developed Geroch-Held-Penrose (GHP) formalism has been used throughout the investigations. The salient features of GHP formalism that are necessary for the present work are given and these techniques are applied to a pair of null congruences C(l) and C(n). (author)
Testing general relativity at cosmological scales: Implementation and parameter correlations
International Nuclear Information System (INIS)
Dossett, Jason N.; Ishak, Mustapha; Moldenhauer, Jacob
2011-01-01
The testing of general relativity at cosmological scales has become a possible and timely endeavor that is not only motivated by the pressing question of cosmic acceleration but also by the proposals of some extensions to general relativity that would manifest themselves at large scales of distance. We analyze here correlations between modified gravity growth parameters and some core cosmological parameters using the latest cosmological data sets including the refined Cosmic Evolution Survey 3D weak lensing. We provide the parametrized modified growth equations and their evolution. We implement known functional and binning approaches, and propose a new hybrid approach to evolve the modified gravity parameters in redshift (time) and scale. The hybrid parametrization combines a binned redshift dependence and a smooth evolution in scale avoiding a jump in the matter power spectrum. The formalism developed to test the consistency of current and future data with general relativity is implemented in a package that we make publicly available and call ISiTGR (Integrated Software in Testing General Relativity), an integrated set of modified modules for the publicly available packages CosmoMC and CAMB, including a modified version of the integrated Sachs-Wolfe-galaxy cross correlation module of Ho et al. and a new weak-lensing likelihood module for the refined Hubble Space Telescope Cosmic Evolution Survey weak gravitational lensing tomography data. We obtain parameter constraints and correlation coefficients finding that modified gravity parameters are significantly correlated with σ 8 and mildly correlated with Ω m , for all evolution methods. The degeneracies between σ 8 and modified gravity parameters are found to be substantial for the functional form and also for some specific bins in the hybrid and binned methods indicating that these degeneracies will need to be taken into consideration when using future high precision data.
Canonical perturbation theory in linearized general relativity theory
International Nuclear Information System (INIS)
Gonzales, R.; Pavlenko, Yu.G.
1986-01-01
Canonical perturbation theory in linearized general relativity theory is developed. It is shown that the evolution of arbitrary dynamic value, conditioned by the interaction of particles, gravitation and electromagnetic fields, can be presented in the form of a series, each member of it corresponding to the contribution of certain spontaneous or induced process. The main concepts of the approach are presented in the approximation of a weak gravitational field
The role of general relativity in the uncertainty principle
International Nuclear Information System (INIS)
Padmanabhan, T.
1986-01-01
The role played by general relativity in quantum mechanics (especially as regards the uncertainty principle) is investigated. It is confirmed that the validity of time-energy uncertainty does depend on gravitational time dilation. It is also shown that there exists an intrinsic lower bound to the accuracy with which acceleration due to gravity can be measured. The motion of equivalence principle in quantum mechanics is clarified. (author)
Introduction to General Relativity and Black Holes (5/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (3/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (1/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (2/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (4/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
New relativistic generalization of the Heisenberg commutation relations
International Nuclear Information System (INIS)
Bohm, A.; Loewe, M.; Magnollay, P.; Tarlini, M.; Aldinger, R.R.; Kielanowski, P.
1984-01-01
A relativistic generalization of the Heisenberg commutation relations is suggested which is different from the conventional ones used for the intrinsic coordinates and momenta in the relativistic oscillator model and the relativistic string. This new quantum relativistic oscillator model is determined by the requirement that it gives a unified description of relativistic vibrations and rotations and contracts in the nonrelativistic limit c -1 →0 into the usual nonrelativistic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
López, Rodrigo A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción (Chile); Moya, Pablo S. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, Maryland 20771 (United States); Department of Physics, Catholic University of America, Washington DC, DC 20064 (United States); Muñoz, Víctor [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Viñas, Adolfo F. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, Maryland 20771 (United States); Valdivia, J. Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Santiago (Chile)
2014-09-15
We use a kinetic treatment to study the linear transverse dispersion relation for a magnetized isotropic relativistic electron-positron plasma with finite relativistic temperature. The explicit linear dispersion relation for electromagnetic waves propagating along a constant background magnetic field is presented, including an analytical continuation to the whole complex frequency plane for the case of Maxwell-Jüttner velocity distribution functions. This dispersion relation is studied numerically for various temperatures. For left-handed solutions, the system presents two branches, the electromagnetic ordinary mode and the Alfvén mode. In the low frequency regime, the Alfvén branch has two dispersive zones, the normal zone (where ∂ω/∂k > 0) and an anomalous zone (where ∂ω/∂k < 0). We find that in the anomalous zone of the Alfvén branch, the electromagnetic waves are damped, and there is a maximum wave number for which the Alfvén branch is suppressed. We also study the dependence of the Alfvén velocity and effective plasma frequency with the temperature. We complemented the analytical and numerical approaches with relativistic full particle simulations, which consistently agree with the analytical results.
Generalization of uncertainty relation for quantum and stochastic systems
Koide, T.; Kodama, T.
2018-06-01
The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross-Pitaevskii equation and the Navier-Stokes-Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.
Tests of general relativity from timing the double pulsar.
Kramer, M; Stairs, I H; Manchester, R N; McLaughlin, M A; Lyne, A G; Ferdman, R D; Burgay, M; Lorimer, D R; Possenti, A; D'Amico, N; Sarkissian, J M; Hobbs, G B; Reynolds, J E; Freire, P C C; Camilo, F
2006-10-06
The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the "post-Keplerian" parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed.
Explanatory and illustrative visualization of special and general relativity.
Weiskopf, Daniel; Borchers, Marc; Ertl, Thomas; Falk, Martin; Fechtig, Oliver; Frank, Regine; Grave, Frank; King, Andreas; Kraus, Ute; Müller, Thomas; Nollert, Hans-Peter; Rica Mendez, Isabel; Ruder, Hanns; Schafhitzel, Tobias; Schär, Sonja; Zahn, Corvin; Zatloukal, Michael
2006-01-01
This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einstein's theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: The recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.
Hydrological dispersion of radioactive material in relation to nuclear power plant siting
International Nuclear Information System (INIS)
1985-01-01
This Guide discusses the dispersion of normal and accidental releases of radioactive materials from nuclear power plants into surface water, including the washout of airborne radionuclides, and gives recommendations on information to be collected during the various stages of the siting procedure, a minimum measurement programme and the selection and validation of appropriate mathematical models for predicting dispersion. Guidelines are also provided for the optimal use of models for a specific site situation and for defining the necessary input parameters. Results of existing validation studies are given
The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for MaxBCG Galaxy Clusters
Energy Technology Data Exchange (ETDEWEB)
Becker, M.R.; McKay, T.A.; /Michigan U.; Koester, B.; /Chicago U., Astron. Astrophys. Ctr.; Wechsler, R.H.; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.; Rozo, E.; /Ohio State U.; Evrard, A.; /Michigan U. /Michigan U., MCTP; Johnston, D.; /Caltech, JPL; Sheldon, E.; /New York U.; Annis, J.; /Fermilab; Lau, E.; /Chicago U., Astron. Astrophys. Ctr.; Nichol, R.; /Portsmouth U., ICG; Miller, C.; /Michigan U.
2007-06-05
The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG--galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202 {+-} 10 km s{sup -1} for small groups to more than 854 {+-} 102 km s{sup -1} for large clusters. We show the scatter to be at most 40.5{+-}3.5%, declining to 14.9{+-}9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass--observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.
Reilly, Christopher M; Morris, Rebecca; Dubielzig, Richard R
2005-01-01
To investigate the role of pigment dispersion and inflammation in the pathogenesis of goniodysgenesis-related glaucoma (GDRG). Cases of GDRG were selected when the duration of the disease was specified and there was not any confounding pathology. Cases were grouped into 7-day (chronic) durations, based on the time required to effect end-stage retinal damage. Acute cases were further divided into pigment dispersion: segmental loss of posterior iris pigment epithelium, clumping of posterior iris pigment epithelium, pigmented cells in the trabecular meshwork or anterior chamber and preferential settling of pigmented cells in the ventral aspect of the iridocorneal angle. Slides were also evaluated for the presence of neutrophils and/or lymphoplasmacytic cells in the trabecular meshwork (TM). Differences between groups were analyzed statistically. Of 100 cases evaluated, 34 were 7-days (chronic) in duration. Of all globes examined, 96% had at least one sign of pigment dispersion, with no significant difference between groups. Two or more signs of pigment dispersion were present in 76% of all globes. The 4-7-day group was significantly more likely than the 7-day groups. Neutrophils were present in the TM of 86% of 7-day cases to have neutrophils in the TM, with 65% and 17% [corrected] positive cases, respectively. Lymphoplasmacytic inflammation was present in 53% of all cases, with no significant difference between groups. Cases in the 7-day cases to have both types of inflammation. Our results indicate that both acute inflammation and pigment dispersion may be key factors in the pathogenesis of GDRG. Pigment dispersion is prevalent at all time points and increases during the first 7 days. The finding of iris pigment epithelial loss supports the theory that pupillary block associated with iris-lens touching may be important in the pathogenesis of GDRG.
Gauge stability of 3+1 formulations of general relativity
International Nuclear Information System (INIS)
Khokhlov, A M; Novikov, I D
2002-01-01
We present a general approach to the analysis of gauge stability of 3+1 formulations of general relativity (GR). Evolution of coordinate perturbations and the corresponding perturbations of lapse and shift can be described by a system of eight quasi-linear partial differential equations. Stability with respect to gauge perturbations depends on the choice of gauge and a background metric, but it does not depend on a particular form of a 3+1 system if its constrained solutions are equivalent to those of the Einstein equations. Stability of a number of known gauges is investigated in the limit of short-wavelength perturbations. All fixed gauges except a synchronous gauge are found to be ill posed. A maximal slicing gauge and its parabolic extension are shown to be ill posed as well. A necessary condition is derived for well-posedness of metric-dependent algebraic gauges. Well-posed metric-dependent gauges are found, however, to be generally unstable. Both instability and ill-posedness are associated with the existence of growing modes of coordinate perturbations related to perturbations of physical accelerations of reference frames
A database for extract solutions in general relativity
International Nuclear Information System (INIS)
Horvath, I.; Horvath, Zs.; Lukacs, B.
1993-07-01
The field of equations of General Relativity are coupled second order partial differential equations. Therefore no general method is known to generate solutions for prescribed initial and boundary conditions. In addition, the meaning of the particular coordinates cannot be known until the metric is not found. Therefore the result must permit arbitrary coordinate transformations, i.e. most kinds of approximating methods are improper. So exact solutions are necessary and each one is an individual product. For storage, retrieval and comparison database handling techniques are needed. A database of 1359 articles is shown (cross-referred at least once) published in 156 more important journals. It can be handled by dBase III plus on IBM PC's. (author) 5 refs.; 5 tabs
Solitons and action propagation according to general relativity (Part one)
International Nuclear Information System (INIS)
Stavroulakis, N.
1987-01-01
The current exposition of General Relativity involves two contradictory statements: at first it is asserted that every change in the distribution of matter brings about gravitational waves. Then it is asserted that, specifically, no gravitational effect is produced by the pulsations of a spherical source. By analysing the second statement, we conclude that it arises from a vicious circle tied up with mathematical errors which led to the Schwarzschild solution and the theory of black holes. In order to obtain the correct formulation of the problem, we establish rigorously the general form of the θ(4)-invariant space-time metrics on R x R 3 and bring out the principles allowing to associate gravitational effects with oscillating masses [fr
Charged point particles with magnetic moment in general relativity
International Nuclear Information System (INIS)
Amorim, R.; Tiomno, J.
1977-01-01
Halbwachs Lagrangean formalism for the theory of charged point particles with spin (g = 2) is generalized and formulated in General Relativity for particles of arbitrary charge and magnetic moment. Equations are obtained, both corresponding to Frenkel's condition Ssub(μν)Xsup(ν) = 0 and to Nakano's condition Ssub(μν)Psup(ν) = 0. With the later condition the exact equations are highly coupled and non linear. When linearized in the electromagnetic and gravitational fields they coincide with de Groot-Suttorp equations for vanishing gravitational fields and with Dixon-Wald equations in the absence of electromagnetic field. The equations corresponding to Frenkel's condition, when linearized in Ssub(μν), coincide with Papapetrou's and Frenkel's equations in the corresponding limits [pt
General relativity with spin and torsion: Foundations and prospects
International Nuclear Information System (INIS)
Hehl, F.W.; von der Heyde, P.; Kerlick, G.D.; Nester, J.M.
1976-01-01
A generalization of Einstein's gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan's torsion tensor. The theory which emerges from taking this coupling into account, the U 4 theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction mediated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the U 4 theory arises as a local gauge theory for the Poincare group in space-time. The deviations of the U 4 theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed
The revival of General Relativity at Princeton: Daring Conservatism
Brill, Dieter; Blum, Alexander
2018-01-01
After General Relativity was established in essentially its present form in 1915 it was celebrated as a great success of mathematical physics. But the initial hopes for this theory as a basis for all of physics began to fade in the next several decades, as General Relativity was relegated to the margins of theoretical physics. Its fate began to rise in the 1950's in a revival of interest and research that over time made gravitational physics one of the hottest research topics it is today. One center of this renaissance was Princeton, where two relative newcomers explored new and different approaches to gravitational physics. Robert Dicke showed that gravity is not as inaccessible to experiment as was thought, and John Wheeler propelled it into the mainstream by proposing highly original and imaginative consequences of Einstein's theory. We will concentrate on these ideas that, in his characteristically intriguing style, Wheeler called "Daring Conservatism" - a term well known to his associates, but one he never mentioned in print. With the aid of unpublished manuscripts and notes we will explore Daring Conservatism's origin and motivation, its successes and failures, and the legacy it left behind.
The revival of General Relativity at Princeton: Daring Conservatism
Directory of Open Access Journals (Sweden)
Brill Dieter
2018-01-01
Full Text Available After General Relativity was established in essentially its present form in 1915 it was celebrated as a great success of mathematical physics. But the initial hopes for this theory as a basis for all of physics began to fade in the next several decades, as General Relativity was relegated to the margins of theoretical physics. Its fate began to rise in the 1950's in a revival of interest and research that over time made gravitational physics one of the hottest research topics it is today. One center of this renaissance was Princeton, where two relative newcomers explored new and different approaches to gravitational physics. Robert Dicke showed that gravity is not as inaccessible to experiment as was thought, and John Wheeler propelled it into the mainstream by proposing highly original and imaginative consequences of Einstein's theory. We will concentrate on these ideas that, in his characteristically intriguing style, Wheeler called "Daring Conservatism" -- a term well known to his associates, but one he never mentioned in print. With the aid of unpublished manuscripts and notes we will explore Daring Conservatism's origin and motivation, its successes and failures, and the legacy it left behind.
On complicated continuum models in general relativity theory
International Nuclear Information System (INIS)
Tsypkin, A.G.
1987-01-01
A set of Euler's equations is obtained in the framework of the general relativity theory from the variational equation in the supposition that lagrangian of the material depends on additional (in comparison with classical theories) thermodynamic parameters and taking into account possible irreversible processes. Momentum equations for continuous medium of a thermodynamic closed set are shown to be the consequence of field equations. The problem about the type of energy-momentum material tensor in the presence of derivatives from additional thermodynamic parameters in the number of lagrangian arguments is considered
A superconducting gyroscope to test Einstein's general theory of relativity
Everitt, C. W. F.
1978-01-01
Schiff (1960) proposed a new test of general relativity based on measuring the precessions of the spin axes of gyroscopes in earth orbit. Since 1963 a Stanford research team has been developing an experiment to measure the two effects calculated by Schiff. The gyroscope consists of a uniform sphere of fused quartz 38 mm in diameter, coated with superconductor, electrically suspended and spinning at about 170 Hz in vacuum. The paper describes the proposed flight apparatus and the current state of development of the gyroscope, including techniques for manufacturing and measuring the gyro rotor and housing, generating ultralow magnetic fields, and mechanizing the readout.
Lectures on General Relativity, Cosmology and Quantum Black Holes
Ydri, Badis
2017-07-01
This book is a rigorous text for students in physics and mathematics requiring an introduction to the implications and interpretation of general relativity in areas of cosmology. Readers of this text will be well prepared to follow the theoretical developments in the field and undertake research projects as part of an MSc or PhD programme. This ebook contains interactive Q&A technology, allowing the reader to interact with the text and reveal answers to selected exercises posed by the author within the book. This feature may not function in all formats and on reading devices.
Hamiltonian Dynamics and Positive Energy in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Deser, S. [Physics Department, Brandeis University, Waltham, MA (United States)
1969-07-15
A review is first given of the Hamiltonian formulation of general relativity; the gravitational field is a self-interacting massless spin-two system within the framework of ordinary Lorentz covariant field theory. The recently solved problem of positive-definiteness of the field energy is then discussed. The latter, a conserved functional of the dynamical variables, is shown to have only one extremum, a local minimum, which is the vacuum state (flat space). This implies positive energy for the field, with the vacuum as ground-state. Similar results hold when minimally coupled matter is present. (author)
Indefinite-metric quantum field theory of general relativity, 5
International Nuclear Information System (INIS)
Nakanishi, Noboru
1979-01-01
The indefinite-metric quantum field theory of general relativity is extended to the coupled system of the gravitational field and a Dirac field on the basis of the vierbein formalism. The six extra degrees of freedom involved in vierbein are made unobservable by introducing an extra subsidiary condition Q sub(s) + phys> = 0, where Q sub(s) denotes a new BRS charge corresponding to the local Lorentz invariance. It is shown that a manifestly covariant, unitary, canonical theory can be constructed consistently on the basis of the vierbein formalism. (author)
Proposed new test of spin effects in general relativity.
O'Connell, R F
2004-08-20
The recent discovery of a double-pulsar PSR J0737-3039A/B provides an opportunity of unequivocally observing, for the first time, spin effects in general relativity. Existing efforts involve detection of the precession of the spinning body itself. However, for a close binary system, spin effects on the orbit may also be discernible. Not only do they add to the advance of the periastron (by an amount which is small compared to the conventional contribution) but they also give rise to a precession of the orbit about the spin direction. The measurement of such an effect would also give information on the moment of inertia of pulsars.
Conservation and non-conservation in general relativity
International Nuclear Information System (INIS)
Bondi, H.
1990-01-01
The difficulties of conservation laws in general relativity are discussed, with special reference to the non-tangible nature of gravitational energy and its transformation into tangible forms of energy. Inductive transfer of energy is marked out as wholly distinct from wave transfer. Slow (adiabatic) changes are utilized to make clear, in the axi-symmetric case, that the mass of an isolated body is conserved irrespective of any local changes (e.g. of shape) and that in inductive transfer the movement of energy between two bodies can readily be traced by the changes in their masses. (author)
Equivalence of the theories of reciprocity and general relativity
International Nuclear Information System (INIS)
Qadir, A.
1976-01-01
Khan's theory (Nuovo Cimento; 57B:321 (1968) and Int. J. Theor. Phys.; 6:383 (1972)) of reciprocity has been shown to be equivalent to the theory of general relativity (in a conformally flat space-time) in that the same predictions are made physically. It is is proved that, since 'centrifugal forces' are used by Khan, gravitational phenomena are being considered equal in status to electromagnetic phenomena, and hence the difference claimed to exist between Milne's theory and Khan's theory disappears. (author)
Dispersion-induced nonlinearities in semiconductors
DEFF Research Database (Denmark)
Mørk, Jesper; Mecozzi, A.
2002-01-01
A dispersive and saturable medium is shown, under very general conditions, to possess ultrafast dynamic behaviour due to non-adiabatic polarisation dynamics. Simple analytical expressions relating the effect to the refractive index dispersion of a semiconductor ire derived and the magnitude...... of the equivalent Kerr coefficient is shown to be in qualitative agreement with measurements on active semiconductor waveguides....
Gyroscope precession in special and general relativity from basic principles
Jonsson, Rickard M.
2007-05-01
In special relativity a gyroscope that is suspended in a torque-free manner will precess as it is moved along a curved path relative to an inertial frame S. We explain this effect, which is known as Thomas precession, by considering a real grid that moves along with the gyroscope, and that by definition is not rotating as observed from its own momentary inertial rest frame. From the basic properties of the Lorentz transformation we deduce how the form and rotation of the grid (and hence the gyroscope) will evolve relative to S. As an intermediate step we consider how the grid would appear if it were not length contracted along the direction of motion. We show that the uncontracted grid obeys a simple law of rotation. This law simplifies the analysis of spin precession compared to more traditional approaches based on Fermi transport. We also consider gyroscope precession relative to an accelerated reference frame and show that there are extra precession effects that can be explained in a way analogous to the Thomas precession. Although fully relativistically correct, the entire analysis is carried out using three-vectors. By using the equivalence principle the formalism can also be applied to static spacetimes in general relativity. As an example, we calculate the precession of a gyroscope orbiting a static black hole.
Kerr-Taub-NUT General Frame, Energy, and Momentum in Teleparallel Equivalent of General Relativity
Directory of Open Access Journals (Sweden)
Gamal G. L. Nashed
2012-01-01
Full Text Available A new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity (TEGR is derived. The solution is characterized by three parameters “the gravitational mass M, the rotation a, and the NUT L.” The vierbein field is axially symmetric, and the associated metric gives the Kerr-Taub-NUT spacetime. Calculation of the total energy using two different methods, the gravitational energy momentum and the Riemannian connection 1-form Γα̃β, is carried out. It is shown that the two methods give the same results of energy and momentum. The value of energy is shown to depend on the mass M and the NUT parameter L. If L is vanishing, then the total energy reduced to the energy of Kerr black hole.
Poisson, Eric
2010-05-01
A few years ago, in my review of Sean Carroll's book in Classical and Quantum Gravity [1], I wrote that while the 1970s was the decade of Weinberg [2] and Misner, Thorne and Wheeler [3], and while the eighties was the decade of Schutz [4] and Wald [5], the 2000s was clearly the decade of Hartle [6] and Carroll [7]. In my opinion, these books continue to stand out in the surprisingly dense crowd of introductory textbooks on general relativity. At the dawn of this new decade I look forward to see what fresh pedagogical insights will be produced next, and who will be revealed as the winners of the 2010s. It is, of course, much too early to tell, but Schutz is back, and he will set the standard just as he did back in 1985. This is the long-awaited second edition of his `First Course', a short, accessible, and very successful introduction to general relativity. The changes from the first edition are modest: Schutz wisely refrained from bloating the text with new topics, and limited himself to updating his discussion of gravitational-wave sources and detectors, neutron-star and black-hole astrophysics, and suggestions for further reading. Most importantly, he completely rewrote the chapter on cosmology, a topic that has evolved enormously since the first edition. The book begins in chapter 1 with a beautiful review of special relativity that emphasizes spacetime geometry and stays away from an algebraic approach based on the Lorentz transformation, which appears only later in the chapter. This is followed up in chapters 2 and 3 with an introduction to vector and tensor analysis in flat spacetime. The point of view is modern (tensors are defined as linear mapping of vectors and one-forms into real numbers) but the presentation is very accessible and avoids an overload of mathematical fine print. In chapter 4 the book introduces the spacetime description of fluids; it is here that the energy-momentum tensor makes its first appearance. The move to curved spacetime is
Theory of Nonlocal Point Transformations in General Relativity
Directory of Open Access Journals (Sweden)
Massimo Tessarotto
2016-01-01
Full Text Available A discussion of the functional setting customarily adopted in General Relativity (GR is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs. While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern (1 a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; (2 the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; (3 the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and (4 the diagonalization of nondiagonal metric tensors.
Geometrical determination of the constant of motion in General Relativity
International Nuclear Information System (INIS)
Catoni, F.; Cannata, R.; Zampetti, P.
2009-01-01
In recent time a theorem, due to E. Beltrami, through which the integration of the geodesic equations of a curved manifold is obtained by means of a merely geometric method, has been revisited. This way of dealing with the problem is well in accordance with the geometric spirit of the Theory of General Relativity. In this paper we show another relevant consequence of this method. Actually, the constants of the motion, introduced in this geometrical way that is completely independent of Newton theory, are related to the conservation laws for test particles in the Einstein theory. These conservation laws may be compared with the conservation laws of Newton. In particular, by the conservation of energy (E) and the L z component of angular momentum, the equivalence of the conservation laws for the Schwarzschild field is verified and the difference between Newton and Einstein theories for the rotating bodies (Kerr metric) is obtained in a straightforward way.
The problem of time quantum mechanics versus general relativity
Anderson, Edward
2017-01-01
This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon ...
Nonlinear generalization of special relativity at very high energies
International Nuclear Information System (INIS)
Winterberg, F.
1984-01-01
It is shown, that the introduction of a fundamental length constant into the operator representation of the quantum mechanical commutation relations, as suggested by Bagge, leads to a nonlinear generalization of the Lorentz transformations. The theory requires the introduction of a substratum (ether) and which can be identified as the zero point vacuum energy. At very high energies a non-Lorentz invariant behaviour for the cross sections between elementary particles is predicted. Using the Einstein clock synchronisation definition, the velocity of light is also constant and equal to c in the new theory, but the zero point vacuum energy becomes finite, as are all other quantities which are divergent in Lorentz invariant quantum field theories. In the limiting case where the length constant is set equal to zero, the zero point vacuum energy diverges and special relativity is recovered. (orig.) [de
Correlated quadratures of resonance fluorescence and the generalized uncertainty relation
Arnoldus, Henk F.; George, Thomas F.; Gross, Rolf W. F.
1994-01-01
Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.
Einstein and Beyond: A Critical Perspective on General Relativity
Directory of Open Access Journals (Sweden)
Ram Gopal Vishwakarma
2016-05-01
Full Text Available An alternative approach to Einstein’s theory of General Relativity (GR is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian solutions, problems related with the energy-stress tensor T i k and unphysical solutions. The new approach emanates from a critical analysis of these problems, providing a novel insight that the matter fields, together with the ensuing gravitational field, are already present inherently in the spacetime without taking recourse to T i k . Supported by lots of evidence, the new insight revolutionizes our views on the representation of the source of gravitation and establishes the spacetime itself as the source, which becomes crucial for understanding the unresolved issues in a unified manner. This leads to a new paradigm in GR by establishing equation R i k = 0 as the field equation of gravitation plus inertia in the very presence of matter.
DEFF Research Database (Denmark)
Lindgård, Per-Anker; Kowalska, A.; Laut, Peter
1967-01-01
curves are suggested. The magnon cross section for unpolarized neutrons is calculated and shown to be dependent on the anisotropy in the spin interaction. Thus in principle it allows the detection of anisotropy in the exchange interaction. Some remarks are made concerning antiferromagnetic and plane...... for the exchange interaction seem to be necessary for agreement with experimental dispersion curves be obtained. The effect of the anisotropy in the cross section is estimated and shown to be important for small magnon energies....
Directory of Open Access Journals (Sweden)
Liu Yongjun
2015-01-01
Full Text Available In this thesis, the influence of complete Coriolis force (the model includes both the vertical and horizontal components of Coriolis force on the dispersion relation of ocean internal-wave under background currents field are studied, it is important to the study of ocean internal waves in density-stratified ocean. We start from the control equation of sea water movement in the background of the non-traditional approximation, and the vertical velocity solution is derived where buoyancy frequency N(z gradually varies with the ocean depth z. The results show that the influence of complete Coriolis force on the dispersion relation of ocean internal-wave under background currents field is obvious, and these results provide strong evidence for the understanding of dynamic process of density stratified ocean internal waves.
Fixing extensions to general relativity in the nonlinear regime
Cayuso, Juan; Ortiz, Néstor; Lehner, Luis
2017-10-01
The question of what gravitational theory could supersede General Relativity has been central in theoretical physics for decades. Many disparate alternatives have been proposed motivated by cosmology, quantum gravity and phenomenological angles, and have been subjected to tests derived from cosmological, solar system and pulsar observations typically restricted to linearized regimes. Gravitational waves from compact binaries provide new opportunities to probe these theories in the strongly gravitating/highly dynamical regimes. To this end however, a reliable understanding of the dynamics in such a regime is required. Unfortunately, most of these theories fail to define well posed initial value problems, which prevents at face value from meeting such challenge. In this work, we introduce a consistent program able to remedy this situation. This program is inspired in the approach to "fixing" viscous relativistic hydrodynamics introduced by Israel and Stewart in the late 70's. We illustrate how to implement this approach to control undesirable effects of higher order derivatives in gravity theories and argue how the modified system still captures the true dynamics of the putative underlying theories in 3 +1 dimensions. We sketch the implementation of this idea in a couple of effective theories of gravity, one in the context of Noncommutative Geometry, and one in the context of Chern-Simons modified General Relativity.