Initial data for the relativistic gravitational N-body problem
International Nuclear Information System (INIS)
Chrusciel, Piotr T; Corvino, Justin; Isenberg, James
2010-01-01
In general relativity, an initial data set for an isolated gravitational system takes the form of a solution of the Einstein constraint equations which is asymptotically Euclidean on a specified end. Given a collection of N such data sets with a subregion of interest (bounded away from the specified end) chosen in each, we show that there exists a family of new initial data sets, each of which contains exact copies of each of the N chosen subregions, positioned in a chosen array in a single asymptotic end. These composite initial data sets model isolated, relativistic gravitational systems containing N chosen bodies in specified initial configurations. (fast track communication)
Numerical integration of a relativistic two-body problem via a multiple scales method
Abouelmagd, Elbaz I.; Elshaboury, S. M.; Selim, H. H.
2016-01-01
We offer an analytical study on the dynamics of a two-body problem perturbed by small post-Newtonian relativistic term. We prove that, while the angular momentum is not conserved, the motion is planar. We also show that the energy is subject to small changes due to the relativistic effect. We also offer a periodic solution to this problem, obtained by a method based on the separation of time scales. We demonstrate that our solution is more general than the method developed in the book by Brumberg (Essential Relativistic Celestial Mechanics, Hilger, Bristol, 1991). The practical applicability of this model may be in studies of the long-term evolution of relativistic binaries (neutron stars or black holes).
Pion propagator in relativistic quantum field theories of the nuclear many-body problem
International Nuclear Information System (INIS)
Matsui, T.; Serot, B.D.
1982-01-01
Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored
Three-dimensional formulation of the relativistic two-body problem in terms of rapidities
International Nuclear Information System (INIS)
Amirkhanov, I.V.; Grusha, G.V.; Mir-Kasimov, R.M.
1976-01-01
The scheme, based on the three-dimensional relativistic equation of the quasi-potential type is developed. As a basic variable rapidity, canonically conjugated to the relativistic relative distance is adopted. The free Green function has a simple pole in the complex rapidity plane, ensuring the fulfillment of the elastic unitarity for real potentials. In the local potential case the corresponding partial wave equation in configurational r-representation is a differential second-order equation. The problem of boundary conditions, which is a non-trivial one in the relativistic r-space, is studied. The exact solutions of the equation in simple cases have been found
On the Coulomb sum rule in the relativistic nuclear many-body problem
International Nuclear Information System (INIS)
Matsui, T.
1983-01-01
It is shown that the relativistic many-body theory the Coulomb sum rule value is never exhausted in the space-like momentum transfer region. This implies that the Coulomb sum rule should be used with a particular caution to analyze deep inelastic electron scattering from nuclei. (orig.)
Memory function approach to retardation effects in the relativistic two-body problem
International Nuclear Information System (INIS)
Bilal, A.; Schuck, P.
1984-08-01
The memory function approach is applied to the relativistic two particle problem. We thus obtain integral equations similar to the Bethe-Salpeter equation, taking all retardation effects fully into account and eliminating the relative time variable. The formalism is studied for scalar Klein-Gordon fields as well as for spinorial Dirac fields. For both cases the memory function and the integral kernels are calculated for a given model explicitely. The scalar-scalar model of Cutkosky is treated in detail and numerical binding energies are obtained, very close to those of the original Bethe-Salpeter equation, thus showing the extreme importance of retardation effects. As an example for Dirac fields the memory function for a proton-antiproton pair interacting via exchange of a π 0 is established
High-energy gravitational scattering and the general relativistic two-body problem
Damour, Thibault
2018-02-01
A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys. Rev. D 94, 104015 (2016), 10.1103/PhysRevD.94.104015]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the two-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.
Some problems of relativistic electrodynamics
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1991-01-01
Some problems of electrodynamics are considered from the point of view of the radar formulation of relativity theory. This formulation is based on light or retarded distances, the increasing of longitudinal sizes of moving objects is its consequence ( e longation formula ) . Based of Lienard-Wiechert potentials it is shown that in terms of retarded distances equipotential surfaces take the form of rotation ellipsoids, stretched in the direction of electric charge motion. The difficulty connected with the appearance of charge in a moving (neutral) current-carrying conductor is overcome. 23 refs.; 4 figs
Relativistic Few-Body Hadronic Physics Calculations
Energy Technology Data Exchange (ETDEWEB)
Polyzou, Wayne [Univ. of Iowa, Iowa City, IA (United States)
2016-06-20
The goal of this research proposal was to use ``few-body'' methods to understand the structure and reactions of systems of interacting hadrons (neutrons, protons, mesons, quarks) over a broad range of energy scales. Realistic mathematical models of few-hadron systems have the advantage that they are sufficiently simple that they can be solved with mathematically controlled errors. These systems are also simple enough that it is possible to perform complete accurate experimental measurements on these systems. Comparison between theory and experiment puts strong constraints on the structure of the models. Even though these systems are ``simple'', both the experiments and computations push the limits of technology. The important property of ``few-body'' systems is that the ``cluster property'' implies that the interactions that appear in few-body systems are identical to the interactions that appear in complicated many-body systems. Of particular interest are models that correctly describe physics at distance scales that are sensitive to the internal structure of the individual nucleons. The Heisenberg uncertainty principle implies that in order to be sensitive to physics on distance scales that are a fraction of the proton or neutron radius, a relativistic treatment of quantum mechanics is necessary. The research supported by this grant involved 30 years of effort devoted to studying all aspects of interacting two and three-body systems. Realistic interactions were used to compute bound states of two- and three-nucleon, and two- and three-quark systems. Scattering observables for these systems were computed for a broad range of energies - from zero energy scattering to few GeV scattering, where experimental evidence of sub-nucleon degrees of freedom is beginning to appear. Benchmark calculations were produced, which when compared with calculations of other groups provided an essential check on these complicated calculations. In
Musielak, Z E; Quarles, B
2014-06-01
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more than 300 years. In this paper, we present a review of the three-body problem in the context of both historical and modern developments. We describe the general and restricted (circular and elliptic) three-body problems, different analytical and numerical methods of finding solutions, methods for performing stability analysis and searching for periodic orbits and resonances. We apply the results to some interesting problems of celestial mechanics. We also provide a brief presentation of the general and restricted relativistic three-body problems, and discuss their astronomical applications.
Dark matter: a problem in relativistic metrology?
International Nuclear Information System (INIS)
Lusanna, Luca
2017-01-01
Besides the tidal degrees of freedom of Einstein general relativity (GR) (namely the two polarizations of gravitational waves after linearization of the theory) there are the inertial gauge ones connected with the freedom in the choice of the 4-coordinates of the space-time, i.e. in the choice of the notions of time and 3-space (the 3+1 splitting of space-time) and in their use to define a non-inertial frame (the inertial ones being forbidden by the equivalence principle) by means of a set of conventions for the relativistic metrology of the space-time (like the GPS ones near the Earth). The canonical York basis of canonical ADM gravity allows us to identify the Hamiltonian inertial gauge variables in globally hyperbolic asymptotically Minkowskian space-times without super-translations and to define the family of non-harmonic Schwinger time gauges. In these 3+1 splittings of space-time the freedom in the choice of time (the problem of clock synchronization) is described by the inertial gauge variable York time (the trace of the extrinsic curvature of the instantaneous 3-spaces). This inertial gauge freedom and the non-Euclidean nature of the instantaneous 3-spaces required by the equivalence principle need to be incorporated as metrical conventions in a relativistic suitable extension of the existing (essentially Galilean) ICRS celestial reference system. In this paper I make a short review of the existing possibilities to explain the presence of dark matter (or at least of part of it) as a relativistic inertial effect induced by the non- Euclidean nature of the 3-spaces. After a Hamiltonian Post-Minkowskian (HPM) linearization of canonical ADM tetrad gravity with particles, having equal inertial and gravitational masses, as matter, followed by a Post-Newtonian (PN) expansion, we find that the Newtonian equality of inertial and gravitational masses breaks down and that the inertial gauge York time produces an increment of the inertial masses explaining at least
International Nuclear Information System (INIS)
Matsas, George E. A.
2003-01-01
We investigate and solve in the context of general relativity the apparent paradox which appears when bodies floating in a background fluid are set in relativistic motion. Suppose some macroscopic body, say, a submarine designed to lie just in equilibrium when it rests (totally) immersed in a certain background fluid. The puzzle arises when different observers are asked to describe what is expected to happen when the submarine is given some high velocity parallel to the direction of the fluid surface. On the one hand, according to observers at rest with the fluid, the submarine would contract and, thus, sink as a consequence of the density increase. On the other hand, mariners at rest with the submarine using an analogous reasoning for the fluid elements would reach the opposite conclusion. The general relativistic extension of the Archimedes law for moving bodies shows that the submarine sinks. As an extra bonus, this problem suggests a new gedankenexperiment for the generalized second law of thermodynamics
International Nuclear Information System (INIS)
Amado, R.D.
1975-01-01
An overview of the formal theory of the three-body problem as it has developed in the past twelve years is given. The formal structure of the theory, some of the techniques that have developed for handling the theory, and some results on how general quantum mechanical principles structure the results, are presented. The discussion is held entirely in the context of non-relativistic quantum mechanics with short-range forces. In this presentation the main outline of the theory is stressed, often at the expense of mathematical rigour [pt
Exact Solutions of Relativistic Bound State Problem for Spinless Bosons
Aslanzadeh, M.; Rajabi, A. A.
2017-01-01
We investigated in detail the relativistic bound states of spin-zero bosons under the influence of Coulomb-plus-linear potentials with an arbitrary combination of scalar and vector couplings. Through an exact analytical solution of three-dimensional Klein-Gordon equation, closed form expressions were derived for energy eigenvalues and wave functions and some correlations between potential parameters were found. We also presented the relativistic description of bound states and nonrelativistic limit of the problem in some special cases.
Relativistic predictive quantum potential: the N-body case
International Nuclear Information System (INIS)
Garuccio, A.; Kyprianidis, A.; Vigier, J.P.
1984-01-01
It is generalized to a system of N scalar particles the casual description with action at a distance already given for two-particle systems in EPR type of experiments. The many body quantum potential is shown to satisfy the predictivity constraints established by Droz-Vincent for relativistic mechanics
Analytical solution of relativistic three-body bound systems
Energy Technology Data Exchange (ETDEWEB)
Aslanzadeh, M.; Rajabi, A.A. [Shahrood University of Technology, Physics Department, Shahrood (Iran, Islamic Republic of)
2014-10-15
In this paper we have investigated in detail the relativistic three-body bound states. We carried out calculations in six-dimensional representation on the basis of the Jacobi coordinates. The obtained second-degree differential equation is solved by using the Nikiforov-Uvarov method and the energy eigenvalues are obtained. Consequently we obtained the binding energy of the three-nucleon bound system. Here we used the generalized Woods-Saxon spin-independent potential in our calculations. The dependence of the three-body binding energy on the potential parameters is also investigated. (orig.)
Relativistic three-body effects in black hole coalescence
International Nuclear Information System (INIS)
Campanelli, Manuela; Dettwyler, Miranda; Lousto, Carlos O.; Hannam, Mark
2006-01-01
Three-body interactions are expected to be common in globular clusters and in galactic cores hosting supermassive black holes. We consider an equal-mass binary black hole system in the presence of a third black hole. Using numerically generated binary black hole initial data sets, and first and second-order post-Newtonian (1PN and 2PN) techniques, we find that the presence of the third black hole has non-negligible relativistic effects on the location of the binary's innermost stable circular orbit (ISCO), and that these effects arise at 2PN order. For a stellar-mass black hole binary in orbit about a supermassive black hole, the massive black hole has stabilizing effects on the orbiting binary, leading to an increase in merger time and a decrease of the terminal orbital frequency, and an amplification of the gravitational radiation emitted from the binary system by up to 6%
Comparison of perturbative and variational procedures in a relativistic problem
International Nuclear Information System (INIS)
Moshinsky, M.; Benet, L.; Loyola, G.; Salinas, A.
1992-01-01
For bound states two of the most popular approximative procedures are the perturbative and variational ones. These procedures have been extensively used and compared in ordinary quantum mechanics. The sistuation is more delicate in the relativistic case where we need not only to develop the methods appropriately, but also to separate in them the contribution of positive energy states, as those from the negative ones are not allowed by Dirac's procedure, which assumes them occupied by particles satisfying an exclusion principle. To illustrate the problems that appear we discuss in this paper the particle-antiparticle system with a Dirac oscillator interaction in a one dimensional space for each particle. We then develop the appropriate perturbative and variational procedures, compare their results, and discuss their range of validity as function of the value of the frequency ω of the Dirac oscillator. (Author)
Code C# for chaos analysis of relativistic many-body systems
Grossu, I. V.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Felea, D.; Stan, E.; Esanu, T.
2010-08-01
This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the “fragmentation level” (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the “virial coefficient” to the stability analysis of chaotic systems is also discussed. Catalogue identifier: AEGH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 30 053 No. of bytes in distributed program, including test data, etc.: 801 258 Distribution format: tar.gz Programming language: Visual C# .NET 2005 Computer: PC Operating system: .Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread RAM: 128 Megabytes Classification: 6.2, 6.5 External routines: .Net Framework 2.0 Library Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, and energy conservation precision test. Additional comments: Easy copy/paste based deployment method. Running time: Quadratic complexity.
Hadjimichael, E
1986-01-01
This volume consists of two review articles. E Hadjimichael's contribution, 'The Nuclear Three-Body Systems', concentrates on recent experimental and theoretical progress achieved in the field. Together with a pedagogical survey of the theoretical framework extensive discussion on the 3N system in the continuum and reactions of electromagnetic probes with 3N systems are provided. 'Four-Nucleon Transfer Reactions' by W Oelert reviews many aspects of a-particle transfer studies. A careful and balanced presentation of both theory and experiment is given. Reasonable agreement between the two is ob
International Nuclear Information System (INIS)
Chernichenko, Yu.D.
2005-01-01
Within the relativistic quasipotential approach to quantum field theory, the relativistic inverse scattering problem is solved for the case where the total quasipotential describing the interaction of two relativistic spinless particles having different masses is a superposition of a nonlocal separable and a local quasipotential. It is assumed that the local component of the total quasipotential is known and that there exist bound states in this local component. It is shown that the nonlocal separable component of the total interaction can be reconstructed provided that the local component, an increment of the phase shift, and the energies of bound states are known
Marchal, Christian
1990-01-01
Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conje
Floerchinger, Stefan
2014-01-01
For non-relativistic quantum field theory in the few-body limit with instantaneous interactions it is shown within the functional renormalization group formalism that propagators are not renormalized and that the renormalization group equations of one-particle irreducible vertex functions are governed by a hierarchical structure. This hierarchy allows to solve the equations in the n-body sector without knowledge or assumptions about the m-body sectors where m>n.
Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential
Thylwe, K. E.
2018-02-01
A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed. Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.
Analytical Solution of Relativistic Few-Body Bound Systems with a Generalized Yukawa Potential
Aslanzadeh, M.; Rajabi, A. A.
2016-03-01
We have investigated in this paper the few-body bound systems in a simple semi-relativistic scheme. For this aim, we introduced a spin independent relativistic description for a few-identical body system by presenting the analytical solution of few-particle Klein-Gordon equation. Performing calculations in D-dimensional configuration on the basis of the hypercentral approach, we reduced the few-body Klein-Gordon equation to a Schrödinger-like form. This equation is solved by using the Nikiforov-Uvarov method, through which the energy equations and eigenfunctions for a few-body bound system are obtained. We used the spin- and isospin-independent generalized Yukawa potential in our calculations, and the dependence of the few-body binding energies on the potential parameters has been investigated.
Relativistic Many-Body Theory A New Field-Theoretical Approach
Lindgren, Ingvar
2011-01-01
Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...
Code C# for chaos analysis of relativistic many-body systems with reactions
Grossu, I. V.; Besliu, C.; Jipa, Al.; Stan, E.; Esanu, T.; Felea, D.; Bordeianu, C. C.
2012-04-01
In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular π distributions. Catalogue identifier: AEGH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 184 628 No. of bytes in distributed program, including test data, etc.: 7 905 425 Distribution format: tar.gz Programming language: Visual C#.NET 2005 Computer: PC Operating system: Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system. RAM: 128 Megabytes Classification: 6.2, 6.5 Catalogue identifier of previous version: AEGH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464 External routines: Net Framework 2.0 Library Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems with reactions
Relativistic three-body quark model of light baryons based on hypercentral approach
Aslanzadeh, M.; Rajabi, A. A.
2015-05-01
In this paper, we have treated the light baryons as a relativistic three-body bound system. Inspired by lattice QCD calculations, we treated baryons as a spin-independent three-quark system within a relativistic three-quark model based on the three-particle Klein-Gordon equation. We presented the analytical solution of three-body Klein-Gordon equation with employing the constituent quark model based on a hypercentral approach through which two- and three-body forces are taken into account. Herewith the average energy values of the up, down and strange quarks containing multiplets are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6)-multiplets are produced by the generalized Gürsey Radicati mass formula. The considered SU(6)-invariant potential is popular "Coulomb-plus-linear" potential and the strange and non-strange baryons spectra are in general well reproduced.
The relativistic Coulomb problem for particles with arbitrary half-integer spin
Czech Academy of Sciences Publication Activity Database
Niederle, Jiří; Nikitin, A. G.
2006-01-01
Roč. 39, - (2006), s. 10931-10944 ISSN 0305-4470 R&D Projects: GA MŠk 1P04LA211 Institutional research plan: CEZ:AV0Z10100502 Keywords : relativistic Coulomb problem * Kepler problem * integral particle with arbitrary half-integer spin Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 1.577, year: 2006
Relativistic effects due to gravimagnetic moment of a rotating body
Ramírez, Walberto Guzmán; Deriglazov, Alexei A.
2017-12-01
We compute the exact Hamiltonian (and corresponding Dirac brackets) for a spinning particle with gravimagnetic moment κ in an arbitrary gravitational background. The case κ =0 corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. κ =1 leads to modified MPTD equations with improved behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. The rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with the MPTD body: (A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. (B) For specific binary systems, gravimagnetic moment gives a contribution to the frame-dragging effect with the magnitude that turns out to be comparable with that of Schiff frame dragging.
The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
Jallouli, H.; Sazdjian, H.
1996-01-01
The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the scattering amplitude. The cases of scalar and vector interactions with massless photons are considered. The two-photon exchange contributions, calculated with covariant propagators,are globally free of spurious infra-red singularities and produce at leading order ...
Mücket-Treder's Two-Body Problem: Infinity Manifold
Mioc, Vasile
The two-body problem in the Mücket-Treder post-Newtonian classical field is revisited. Starting from the motion equations and first integrals in standard polar coordinates, we apply McGehee-type transformations of the first and second kind to suitably describe the escape/capture dynamics. To this end, the infinity manifold is defined, and the flow on it is depicted. The behaviour of orbits that neighbour infinity is wholly similar to the cases corresponding to some relativistic models.
Some problems of special theory of relativity. (Concept of relativistic length)
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1977-01-01
Two available definitions of the concept of length (distance) related (a) to moving the length standard and (b) to sending a light signal (similar to the radar method for measuring distances) are analyzed. Considerations in favour of the preferable use of the (b) definition are discussed. The extension of the (b) definition for fast moving bodies results in the introduction of the definition of relativistic length and volume. The increase of the longitudinal dimensions of fast moving objects is a consequence of the above definition. It should be noted that, e.g., for a rod, the definition corresponds to measurements on the lines orthogonal to the world strip of the given rod. It is shown that the known Michelson-Morley and Throuton-Noble experiments are naturally explained in the framework of the proposed concept of relativistic length. It is also shown that the definition introduced, unlike the conventional one, satisfies the principle of relativity
Relativistic many-body calculations of energies for n=3 states in aluminiumlike ions
Energy Technology Data Exchange (ETDEWEB)
Safronova, U.I.; Namba, C. [National Inst. for Fusion Science, Toki, Gifu (Japan); Johnson, W.R.; Safronova, M.S. [Department of Physics, Univ. of Notre Dame, Notre Dame, IN (United States)
2001-01-01
Energies of the 148 (3l3l'3l'') states for aluminiumlike ions with Z =14-100 are evaluated to second order in relativistic many-body perturbation theory. Second-order Coulomb and Breit-Coulomb interactions are included. Corrections are made to lowest order for the frequency-dependent Breit interaction and for the Lamb shift. A detailed discussion of the various contributions to the energy levels is given for aluminiumlike germanium (Z=32). Comparisons of the calculated energy levels with available experimental data are made for the entire sequence. (author)
Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle
International Nuclear Information System (INIS)
Krolikowski, W.
1983-01-01
A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)
Relativistic many-body theory a new field-theoretical approach
Lindgren, Ingvar
2016-01-01
This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...
Georgevic, R. M.; Anderson, J. D.
1973-01-01
The relationships between the osculating orbital elements for a family of solutions of the general relativistic Schwarzschild problems are developed. These relationships provide a method for evaluating orbital elements in different Schwarzschild coordinate systems without the necessity of fitting to real data every time the system of coordinates is changed. The objectivity of different coordinate systems is discussed. Considerations of orbital motions favor the standard Schwarzschild metric, but the propagation of light signals is more objective in the metric of Painleve. Because the orbital motions usually dominate the representation of data, the standard Schwarzschild coordinates are the best objective choice for most applications.
Stability of orbits around a spinning body in a pseudo-Newtonian Hill problem
International Nuclear Information System (INIS)
Steklain, A.F.; Letelier, P.S.
2009-01-01
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [I.A. Artemova, G. Bjoernsson, I.D. Novikov, Astrophys. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies, like the dragging of inertial frames. Poincare maps, Lyapunov exponents and fractal escape techniques are employed to study the stability of bounded and unbounded orbits for different spins of the central body
Three-body forces, relativistic effects, isobars, and pions in nuclear systems
International Nuclear Information System (INIS)
Wiringa, R.B.
1983-01-01
Conventional microscopic calculations in nuclear physics start from a nonrelativistic Hamiltonian. The many-body Schroedinger equation is then solved to obtain the ground state energy, wave function, and expectation values of other quantities of interest. Such a procedure gives a qualitative description of nuclear saturation properties, but it is now well established that the simple H is quantitatively inadequate. For example, the light nuclei are underbound with too large a charge radius, while nuclear matter is overbound at far too high a density. This note reviews recent studies that go beyond the simple H. These include 1) the introduction of three-nucleon potentials, 2) estimates of relativistic effects, 3) the introduction of isobar degrees of freedom in the two-body potential, and 4) probing the influence of pion degrees of freedom on nuclear systems
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Directory of Open Access Journals (Sweden)
Alexei A. Deriglazov
2017-01-01
Full Text Available We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B spin-induced noncommutativity and the problem of covariant formalism; (C three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.
Three-body problems with separable two-body interactions
International Nuclear Information System (INIS)
Osman, A.
1977-09-01
Faddeev equations for the three-body problem are reconsidered using separable two-body interactions. The separable potentials reduce the Faddeev equations to coupled integral equations in one continuous variable. Numerical calculations for the resulting integral equations are carried out using separable two-body interactions which include both attraction and repulsion potentials. Each of the separable attraction and repulsion potentials used is taken as a spin-dependent central force together with tensor forces. The potential functions of the different parts of the two body interactions are taken to be of the Yamaguchi, Gaussian, Tabakin, Mongan and Reid forms. Each of the nuclei 6 Li, 9 Be and 12 C is taken to be composed of three particles according to the cluster structure description of nuclei. The binding energies of the nuclei 6 Li, 9 Be and 12 C are calculated as a three-body problem and in the framework of the Faddeev formalism
Abdelsalhin, Tiziano; Maselli, Andrea; Ferrari, Valeria
2018-04-01
The LIGO/Virgo Collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e., to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.
International Nuclear Information System (INIS)
Johnson, W. R.; Safronova, U. I.; Derevianko, A.; Safronova, M. S.
2008-01-01
The excitation energies of ns, np, nd, and nf (n≤6) states in neutral lithium are evaluated within the framework of relativistic many-body theory. First-, second-, third-, and all-order Coulomb energies and first- and second-order Breit corrections to energies are calculated. All-order calculations of reduced matrix elements, oscillator strengths, transition rates, and lifetimes are given for levels up to n=4. Electric-dipole (2s-np), electric-quadrupole (2s-nd), and electric-octupole (2s-nf), matrix elements are evaluated to obtain the corresponding ground-state multipole polarizabilities using the sum-over-states approach. Scalar and tensor polarizabilities for the 2p 1/2 and 2p 3/2 states are also calculated. Magnetic-dipole hyperfine constants A are determined for low-lying levels up to n=4. The quadratic Stark shift for the (F=2 M=0)↔(F=1 M=0) ground-state hyperfine transition is found to be -0.0582 Hz/(kV/cm) 2 , in slight disagreement with the experimental value -0.061±0.002 Hz/(kV/cm) 2 . Matrix elements used in evaluating polarizabilities, hyperfine constants, and the quadratic Stark shift are obtained using the all-order method
Methods in relativistic nuclear physics
International Nuclear Information System (INIS)
Danos, M.; Gillet, V.; Cauvin, M.
1984-01-01
This book is intended to provide the methods and tools for performing actual calculations for finite many-body systems of bound relativistic constituent particles. The aim is to cover thoroughly the methodological aspects of the relativistic many-body problem for bound states while avoiding the presentation of specific models. The many examples contained in the later part of the work are meant to give concrete illustrations of how to actually apply the methods which are given in the first part. The basic framework of the approach is the lagrangian field theory solved in the time-independent Schroedinger picture. (Auth.)
Scattering in relativistic particle mechanics
International Nuclear Information System (INIS)
De Bievre, S.
1986-01-01
The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis the authors studied scattering in the relativistic two-body problem. He uses the results to analyze gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. A general geometric framework that underlies approaches to relativistic particle mechanics is presented and the kinematic properties of the scattering transformation, i.e., those properties that arise solely from the invariance of the theory under the Poincare group are studied. The second part of the analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Using general geometric arguments, gauge invariance of the scattering transformation in the Todorov-Komar Hamiltonian constraint model is proved. Finally, quantization of the models is discussed
A Hamilton-like vector for the special-relativistic Coulomb problem
International Nuclear Information System (INIS)
Munoz, Gerardo; Pavic, Ivana
2006-01-01
A relativistic point charge moving in a Coulomb potential does not admit a conserved Hamilton vector. Despite this fact, a Hamilton-like vector may be developed that proves useful in the derivation and analysis of the particle's orbit
Garofoli, Duilio; Haidle, Miriam Noël
2014-01-01
Cognitive archaeology (CA) has an inherent and major problem. The coupling between extinct minds, brains and behaviors cannot be investigated in a laboratory. Without direct testability, there is a risk that theories in CA will remain merely subjective opinions in which "anything goes". To counter this risk, opponents of relativism originally argued that CA should adopt a method of validation based on "indirectly" testing inferences from the archaeological record. In this paper, we will offer a two-part analysis. In the first part, we will discuss problems with the original anti-relativistic agenda. While we agree with the necessity of developing a rational methodology for this discipline, in our view previous analyses have significant weak points that need to be strengthened. In particular, we will propose that "indirect testability" should be superseded by a methodology based upon deductive mappings from networks of theories, followed by a plausibility-selection stage. This methodology will be implemented by adopting an extension of Barnard's (2010b) proposals for mapping hierarchical systems. In the second part, we will compare our methods with those currently adopted in the CA debate. From this analysis, it will emerge that some proposals in CA are inconsistent with our methodology and are incommensurable with those that are consistent with it. Furthermore, we will show that theories in CA can advance contradictory conclusions precisely because they have been developed using different methods. We conclude that a universal methodology, like that proposed here, is needed for CA to become more objective. It is also crucial for creating conditions for coherent and productive debate among different schools of thought in the field of cognitive evolution.
Cattaneo, Carlo
2011-01-01
This title includes: Pham Mau Quam: Problemes mathematiques en hydrodynamique relativiste; A. Lichnerowicz: Ondes de choc, ondes infinitesimales et rayons en hydrodynamique et magnetohydrodynamique relativistes; A.H. Taub: Variational principles in general relativity; J. Ehlers: General relativistic kinetic theory of gases; K. Marathe: Abstract Minkowski spaces as fibre bundles; and, G. Boillat: Sur la propagation de la chaleur en relativite.
Atomic structure calculations using the relativistic random phase approximation
International Nuclear Information System (INIS)
Cheng, K.T.; Johnson, W.R.
1981-01-01
A brief review is given for the relativistic random phase approximation (RRPA) applied to atomic transition problems. Selected examples of RRPA calculations on discrete excitations and photoionization are given to illustrate the need of relativistic many-body theories in dealing with atomic processes where both relativity and correlation are important
Pseudo-Newtonian planar circular restricted 3-body problem
Energy Technology Data Exchange (ETDEWEB)
Dubeibe, F.L., E-mail: fldubeibem@unal.edu.co [Facultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio (Colombia); Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Lora-Clavijo, F.D., E-mail: fadulora@uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); González, Guillermo A., E-mail: guillermo.gonzalez@saber.uis.edu.co [Grupo de Investigación en Relatividad y Gravitación, Escuela de Física, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia)
2017-02-12
We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor–Hoenselaers–Perjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ϵ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.
General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies
Kopeikin, Sergei
2003-01-01
The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.
Grossu, I. V.; Besliu, C.; Jipa, Al.; Felea, D.; Esanu, T.; Stan, E.; Bordeianu, C. C.
2013-04-01
In this paper we present a new version of the Chaos Many-Body Engine C# application (Grossu et al. 2012 [1]). In order to benefit from the latest technological advantages, we migrated the application from .Net Framework 2.0 to .Net Framework 4.0. New tools were implemented also. Trying to estimate the particle interactions dependence on initial conditions, we considered a new distance, which takes into account only the structural differences between two systems. We used this distance for implementing the “Structural Lyapunov” function. We propose also a new precision test based on temporal reversed simulations. New version program summaryProgram title: Chaos Many-Body Engine v03 Catalogue identifier: AEGH_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGH_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 214429 No. of bytes in distributed program, including test data, etc.: 9512380 Distribution format: tar.gz Programming language: Visual C# .Net 2010 Computer: PC Operating system: .Net Framework 4.0 running on MS Windows RAM: 128 MB Classification: 24.60.Lz, 05.45.a Catalogue identifier of previous version: AEGH_v2_0 Journal reference of previous version: Computer Physics Communications 183 (2012) 1055-1059 Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm. Implementation of temporal reversed simulation precision test, and “Structural Lyapunov” function. In order to benefit from the advantages involved in the latest technologies (e.g. LINQ Queries [2]), Chaos Many-Body Engine was migrated from .Net Framework 2.0 to .Net Framework 4.0. In addition to existing energy conservation
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Diego F.M., E-mail: diegofregolente@gmail.com [Institute for Multiscale Simulations, Friedrich-Alexander Universität, D-91052, Erlangen (Germany); Leonel, Edson D., E-mail: edleonel@rc.unesp.br [Departamento de Estatística, Matemática Aplicada e Computação, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Departamento de Física, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, 13506-900, Rio Claro, SP (Brazil)
2012-11-01
We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region.
Few body problems in nuclear and particle physics
International Nuclear Information System (INIS)
Slobodrian, R.J.; Cujec, B.; Ramavataram, K.
1975-01-01
Nucleon-nucleon interactions at all energies, meson-nucleon and meson-deuteron interactions, nuclear bremsstrahlung, on-shell and off-shell interactions, final-state interactions, bound and scattering states, few-body forces, polarization phenomena, short range correlations, quasi-free scattering, composite hadron models, subnucleon structure, multiparticle and coherent production processes, break-up reactions, electrodisintegration, relativistic effects and future resources in nuclear and particle physics are discussed in relation to the state of few-body physics in 1974. (B.F.G.)
Geilhufe, Matthias; Achilles, Steven; Köbis, Markus Arthur; Arnold, Martin; Mertig, Ingrid; Hergert, Wolfram; Ernst, Arthur
2015-11-01
For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related differential equations by means of standard methods for a direct solution and by means of integral equations. Our implementation is tested and exemplarily demonstrated for a spherically symmetric treatment of a Coulomb potential and for a Mathieu potential to cover the full-potential implementation. For the Coulomb potential we include an analytic discussion of the asymptotic behaviour of irregular scattering solutions close to the origin (r\\ll 1 ).
Haba, Z
2009-02-01
We discuss relativistic diffusion in proper time in the approach of Schay (Ph.D. thesis, Princeton University, Princeton, NJ, 1961) and Dudley [Ark. Mat. 6, 241 (1965)]. We derive (Langevin) stochastic differential equations in various coordinates. We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form. We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution. We discuss drag terms leading to an equilibrium distribution. The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Jüttner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.
Loop corrections and other many-body effects in relativistic field theories
International Nuclear Information System (INIS)
Ainsworth, T.L.; Brown, G.E.; Prakash, M.; Weise, W.
1988-01-01
Incorporation of effective masses into negative energy states (nucleon loop corrections) gives rise to repulsive many-body forces, as has been known for some time. Rather than renormalizing away the three- and four-body terms, we introduce medium corrections into the effective σ-exchange, which roughly cancel the nucleon loop terms for densities ρ ≅ ρ nm , where ρ nm is nuclear matter density. Going to higher densities, the repulsive contributions tend to saturate whereas the attractive ones keep on growing in magnitude. The latter is achieved through use of a density-dependent effective mass for the σ-particle, m σ = m σ (ρ), such that m σ (ρ) decreases with increasing density. Such a behavior is seen e.g. in the Nambu-Jona-Lasinio model. It is argued that a smooth transition to chiral restoration implies a similar behavior. The resulting nuclear equation of state is, because of the self-consistency in the problem, immensely insensitive to changes in the mass or coupling constant of the σ-particle. (orig.)
International Nuclear Information System (INIS)
Allen, M.A.; Azuma, O.; Callin, R.S.
1989-03-01
Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs
The infrared problem for the dressed non-relativistic electron in a magnetic field
International Nuclear Information System (INIS)
Amour, L.; Faupin, J.; Grebert, B.; Guillot, J.C.
2008-01-01
We consider a non-relativistic electron interacting with a classical magnetic field pointing along the x 3 -axis and with a quantized electromagnetic field. The system is translation invariant in the x 3 -direction and the corresponding Hamiltonian has a decomposition H ≅∫ R + H(P 3 )dP 3 . For a fixed momentum P 3 sufficiently small, we prove that H(P 3 ) has a ground state in the Fock representation if and only if E'(P 3 )=0, where P 3 →E'(P 3 ) is the derivative of the map P 3 →E(P 3 )=infσ(H(P 3 )). If E'(P 3 )≠0, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant. (authors)
Collinear Equilibrium Solutions of Four-body Problem Muhammad ...
Indian Academy of Sciences (India)
- eters in the four-body problems, very little analytical work has been carried out for greater than three bodies. In this paper we discuss collinear equilibrium configurations of four-body prob- lem. An equilibrium configuration of four-bodies is a ...
Few-Body Problem: Theory and Computer Simulations
Flynn, Chris
A conference held in honour of the 60th birthday of Professor Mauri Valtonen in Turku, Finland, 4th-9th July 2005. The conference's major themes were the few-body problem in celestial mechanics and its numerical study; the theory of few-body escape; dynamics of multiple stars; computer simulations versus observations; planetary systems and few-body dynamics, and chaos in the few-body problem.
International Nuclear Information System (INIS)
Mankiewicz, L.; Sawicki, M.
1989-01-01
Within a relativistically correct yet analytically solvable model of light-front quantum mechanics we construct the electromagnetic form factor of the two-body bound state and we study the validity of the static approximation to the full form factor. Upon comparison of full form factors calculated for different values of binding energy we observe an unexpected effect that for very strongly bound states further increase in binding leads to an increase in the size of the bound system. A similar effect is found for another quantum-mechanical model of relativistic dynamics
Algebraic treatment of three-body problems
International Nuclear Information System (INIS)
Bijker, R.; Leviatan, A.
1998-01-01
We discuss an algebraic treatment of three-body systems in terms of a U(7) spectrum-generating algebra. In particular, we develop the formalism for nonilnear configurations and present an algebraic description of vibrational and rotational excitations of, symmetric (X 3 ) and asymmetric tops (XY 2 and XYZ). The relevant point-group symmetry is incorporated exactly. (author)
Handbook of relativistic quantum chemistry
Energy Technology Data Exchange (ETDEWEB)
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Brevik, Iver
2012-09-01
The main part of this paper is to present an updated review of the Casimir energy at zero and finite temperature for the transverse oscillations of a piecewise uniform closed string. We make use of three different regularizations: the cutoff method, the complex contour integration method and the zeta-function method. The string model is relativistic, in the sense that the velocity of sound is for each string piece set equal to the velocity of light. In this sense the theory is analogous to the electromagnetic theory in a dielectric medium in which the product of permittivity and permeability is equal to unity (an isorefractive medium). We demonstrate how the formalism works for a two-piece string, and for a 2N-piece string, and show how in the latter case a compact recursion relation serves to facilitate the formalism considerably. The Casimir energy turns out to be negative, and the more so the larger the number of pieces in the string. The two-piece string is quantized in D-dimensional spacetime, in the limit when the ratio between the two tensions is very small. We calculate the free energy and other thermodynamic quantities, demonstrate scaling properties, and comment finally on the meaning of the Hagedorn critical temperature for the two-piece string. Thereafter, as a novel development we present a scalar field theory for a real field in three-dimensional space in a potential rising linearly with a longitudinal coordinate z in the interval 0 birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.
Collinear Equilibrium Solutions of Four-body Problem Muhammad ...
Indian Academy of Sciences (India)
Equilibrium solutions—celestial mechanics—four-body problem—few-body problem. 1. Introduction. The motion of systems of n-bodies under their mutual gravitational attraction has always fascinated mathematicians and astronomers which dates back to the times of. Isaac Newton. Because of the complicated nature of the ...
Relativistic quantum mechanics of leptons and fields
International Nuclear Information System (INIS)
Grandy, W.T. Jr.
1991-01-01
This book serves as an advanced text on the Dirac theory, and provides a monograph summarizing the description of relativistic quantum mechanics and quantum electrodynamics as classical field theories. It presents a broad, detailed, and up-to-date exposition of relativistic quantum mechanics, including the two-body problem. It also demonstrates the extent to which the behavior of stable particles and their interactions can be understood without introducing operator (second-quantized) fields. The subsequent difficulties are studied in detail and possible resolutions are presented through quantum field theory
Shao, Zhiqiang
2018-04-01
The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.
International Nuclear Information System (INIS)
Zhang, H; Luo, H J; Kolb, J; Kullie, O; Kolb, D
2005-01-01
In a recent paper (Zhang H et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 905), we showed that the minimax approach gives an optimal solution to the relativistic two-centre Coulomb problem for the light H + 2 and the super-heavy Th 179+ 2 systems, free of any artefacts. However, the non-linear energy dependence of the minimax functional makes the calculations very expensive, if completeness of the (needed) spectrum is to be guaranteed. Now we probe variational linear approximations to it, which lead to double-sized linear eigenvalue problems, the well-known kinetic balance being the simplest, but with a rather poor representation of the small spinor components. In the linear methods, one generates systematic basis sets for both the large and small spinor components and doubles the space of variational coefficients. The best linear scheme comes very close to Minimax LCAO, demonstrating its good projection property against negative continuum contributions in electronic states. Even though one loses the perfect projection properties of Minimax in LARM, the approximation error due to the chosen finite basis for the large components limits the accuracy of the energies very much the same as in Minimax LCAO. Detailed comparisons of different linear approximations together with the previously computed traditional 4-spinor LCAO, Minimax LCAO and 2-spinor finite-element method (FEM) values are given (Zhang H et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 905; Kullie O et al 2004 Chem. Phys. Lett. 383 215)
On regular solutions in the problem of two rigid bodies
Duboshin, G. N.
1982-07-01
The problem of the movement of two rigid bodies whose elementary particles are attracted to each other according to Newton's law is addressed. It is shown that for bodies possessing axial symmetry with respect to the equatorial plane, the problem admits of several exact particular solutions corresponding to movements, termed 'regular'. In these movements, the center of mass of a body describes a circular orbit with constant angular velocity about the center of mass of the other, which is equivalent to a rectilinear trajectory. The orientation of each body with respect to this orbit is invariable and each body rotates uniformly on its own axis of symmetry. It is possible to distinguish the different types of these regular movements according to the various possible mutual orientations of two bodies. Each type of movement is given and appropriate name, and all the results are based on developmental properties of the problem's force function and may be generalized.
An approach to the relativistic brachistochrone problem by sub-Riemannian geometry
Giannoni, Fabio; Piccione, Paolo; Verderesi, José A.
1997-12-01
We formulate a brachistochrone problem in Lorentzian geometry and we prove a variational principle valid for brachistochrones in stationary manifolds. This variational principle is stated in terms of geodesics in a suitable sub-Riemannian structure on M. Moreover, we prove the regularity of the solutions of our variational problem and we determine a differential equation satisfied by the brachistochrones. Some explicit examples are computed.
Report of seminar on relativistic approach to nuclear reaction and nuclear structure
International Nuclear Information System (INIS)
1986-05-01
A seminar on 'Relativistic Approach to Nuclear Reaction and Nuclear Structure' was held in 1985 at Osaka University. This booklet includes twenty-four reports given at the seminar, which deal with: Conventional Nonrelativistic Description of Nuclear Matter and Nuclear Spin-Orbit Interactions; Relativistic Approach to Nuclear Structure; Atomic and Molecular Structure Calculations; Electromagnetic Interaction in Nucleus and Relativistic Effect; Nuclear Magnetic Moment in the Relativistic Mean Field Theory, Effective Mass and Particle-Vibration Coupling in the Relativistic σ-ω Model; Gauge Invariance in Relativistic Many-Body Theory; Relativistic Description of Nucleon-Nucleon Interaction in Review; σ-Particle in NN Interaction; Nuclear Optical Potentials Based on the Brueckner-Hartree-Fock Approach; Elastic Backscattering and Optical Potential; Description of Intermediate-Energy Nuclear Reactions; Dirac Phenomenology at E(p) = 65 MeV; Relativistic Impulse Approximation; Reaction Studies with Intermediate Energy Deuterons at SATURNE; Folding Model for Intermediate-Energy Deutron Scattering; Folding Model for Polarized Deutron Scattering at 700 MeV; Dirac Approach Problems and a Different Viewpoint; Relativistic Approach and EMC Effect; Quasielastic Electron Scattering; Response Function of Quasielastic Electron Scattering; Relativistic Hartree Response Function for Quasielastic Electron Scattering on 12 C and 40 Ca; Backflow-, Retardation- and Relativistic Effects on the Longitudinal Response Function of Nuclear Matter; Pion-Photoproduction in the σ-ω Model. (Nogami, K.)
The Sharma-Parthasarathy stochastic two-body problem
Energy Technology Data Exchange (ETDEWEB)
Cresson, J. [LMAP/Université de Pau, 64013 Pau (France); SYRTE/Observatoire de Paris, 75014 Paris (France); Pierret, F. [SYRTE/Observatoire de Paris, 75014 Paris (France); Puig, B. [IPRA/Université de Pau, 64013 Pau (France)
2015-03-15
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.
The Sharma-Parthasarathy stochastic two-body problem
International Nuclear Information System (INIS)
Cresson, J.; Pierret, F.; Puig, B.
2015-01-01
We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case
Frontiers in Relativistic Celestial Mechanics, Vol. 1. Theory
Kopeikin, Sergei
2014-10-01
Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This first volume of a two-volume series is concerned with theoretical foundations such as post-Newtonian solutions to the two-body problem, light propagation through time-dependent gravitational fields, as well as cosmological effects on the movement of bodies in the solar systems. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: M. Soffel: On the DSX-framework T. Damour: The general relativistic two body problem G. Schaefer: Hamiltonian dynamics of spinning compact binaries through high post-Newtonian approximations A. Petrov and S. Kopeikin: Post-Newtonian approximations in cosmology T. Futamase: On the backreaction problem in cosmology Y. Xie and S. Kopeikin: Covariant theory of the post-Newtonian equations of motion of extended bodies S. Kopeikin and P. Korobkov: General relativistic theory of light propagation in multipolar gravitational fields
Numerical solutions of the N-body problem
International Nuclear Information System (INIS)
Marciniak, A.
1985-01-01
Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
Bernard, Julien
2018-02-01
I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.
The Link between Body Issues and Behavioral Problems.
Whitehead, James R.; Hoover, John H.
2000-01-01
This article highlights the myriad behavioral and adjustment problems that flow from negative self-perceptions about body image in children and adolescents. These negative beliefs are often exacerbated by peer harassment. (Author/MKA)
Relativistic many-body calculations of magnetic dipole transitions in Be-like ions
International Nuclear Information System (INIS)
Safronova, U.I.; Johnson, W.R.; Derevianko, A.
1999-01-01
Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l'-2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s) 2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed. (orig.)
The three-body problem from Pythagoras to Hawking
Valtonen, Mauri; Kholshevnikov, Konstantin; Mylläri, Aleksandr; Orlov, Victor; Tanikawa, Kiyotaka
2016-01-01
This book, written for a general readership, reviews and explains the three-body problem in historical context reaching to latest developments in computational physics and gravitation theory. The three-body problem is one of the oldest problems in science and it is most relevant even in today’s physics and astronomy. The long history of the problem from Pythagoras to Hawking parallels the evolution of ideas about our physical universe, with a particular emphasis on understanding gravity and how it operates between astronomical bodies. The oldest astronomical three-body problem is the question how and when the moon and the sun line up with the earth to produce eclipses. Once the universal gravitation was discovered by Newton, it became immediately a problem to understand why these three-bodies form a stable system, in spite of the pull exerted from one to the other. In fact, it was a big question whether this system is stable at all in the long run. Leading mathematicians attacked this problem over more than...
Health Behaviour and Body Mass Index Among Problem Gamblers
DEFF Research Database (Denmark)
Holst Algren, Maria; Ekholm, Ola; Davidsen, Michael
2015-01-01
Problem gambling is a serious public health issue. The objective of this study was to investigate whether past year problem gamblers differed from non-problem gamblers with regard to health behaviour and body mass index (BMI) among Danes aged 16 years or older. Data were derived from the Danish...... Health and Morbidity Surveys in 2005 and 2010. Past year problem gambling was defined using the lie/bet questionnaire. Logistic regression analyses were used to examine the association between past year problem gambling and health behaviour and BMI. Problem gambling was associated with unhealthy...... behaviour and obesity. The odds of smoking was significantly higher among problem gamblers than among non-problem gamblers. Further, the odds of high-risk alcohol drinking and illicit drug use were significantly higher among problem gamblers. The prevalence of sedentary leisure activity, unhealthy diet...
The stochastic mechanics of fields in a general relativistic context: Problems and perspectives
International Nuclear Information System (INIS)
De Falco, D.
1987-01-01
The problem of a formulation of Nelson's stochastic mechanics of scalar fields in the context of general relativity is considered. The simple example of the scalar field in the Wightman vacuum state on the Rindler wedge is examined, the stochastic counterpart of the Fulling ambiguity of canonical quantization is formulated, and the role of the stochastic quantization is formulated, and the role of the stochastic mechanics of thermal mixtures, as formulated by Guerra and Loffredo, is analyzed in the solution, in the spirit of Davies and Unruh, of the above ambiguity. An overall picture emerges which, both in the explicit example considered here and in its straightforward generalizations to static submanifolds of more general space-times, confirms Smolin's point of view that stochastic quantization is a very natural conceptual frame in which to study the general non covariance of the distinction between quantum and thermal fluctuations. (orig.)
Goldstein, Harris F.; Bender, Carl M.
1986-02-01
The trajectory joining two points a1 and a2, which minimizes the transit time for a particle, initially at rest, to fall in a uniform gravitational field from a1 to a2, is called the brachistochrone. Johann Bernoulli was the first to find an analytical form for the brachistochrone; in 1696, he discovered that the trajectory is a cycloid. In this paper the relativistic generalization of this classic problem is presented. Four separate curves are actually identified: a particle falling in both a uniform electric and uniform gravitational field is considered. The curves that minimize the times of flight measured by an observer in a laboratory in which a1 and a2 are fixed and also the curves that minimize the proper times of flight are found.
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Relativistic viscoelastic fluid mechanics
International Nuclear Information System (INIS)
Fukuma, Masafumi; Sakatani, Yuho
2011-01-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Symmetries of Mücket-Treder's two-body problem
Mioc, V.
The two-body problem associated to the classical potential field proposed by Mücket and Treder (1977) is considered from the only standpoint of symmetries. The corresponding vector field in Hamiltonian or standard polar coordinates presents nice symmetries that form eight-element symmetric Abelian groups endowed with an idempotent structure. Expressed in Levi-Civita coordinates, the problem exhibits a sixteen-element group of symmetries, also Abelian and presenting an idempotent structure.
THE MIND BODY PROBLEM: THE HERMENEUTICS OF AFRICAN ...
African Journals Online (AJOL)
principles in explaining the mind –body problem due to deep seated criticisms from the group of philosophers who held that the interaction is not liable to observation, many theories were advanced by philosophers ranging from Behaviorist doctrine which in order to solve the dichotomy caused by the dualists averred that.
Two-body quantum mechanical problem on spheres
Shchepetilov, Alexey V.
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
The three-body problem and equivariant Riemannian geometry
Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.
2017-08-01
We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.
Nuclear Astrophysics from View Point of Few-Body Problems
International Nuclear Information System (INIS)
Tumino, A.; Spitaleri, C.; Bertulani, C.; Mukhamedzhanov, A.M.
2013-01-01
Few-body systems provide very useful tools to solve different problems for nuclear astrophysics. This is the case of indirect techniques, developed to overcome some of the limits of direct measurements at astrophysical energies. Here the Coulomb dissociation, the asymptotic normalization coefficient and the Trojan Horse method are discussed. (author)
Key to good fit: body measurement problems specific to key ...
African Journals Online (AJOL)
The purpose of this research (as part of a broader research project) was to explore and describe the problems that the South African Clothing Industry currently experiences with regard to the key body measurements needed for the manufacturing of well-fitting clothes. A postal survey was conducted among South African ...
Qualitative analysis of the (N + 1)-body ring problem
Energy Technology Data Exchange (ETDEWEB)
Barrio, Roberto [GME, Depto. Matematica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: rbarrio@unizar.es; Blesa, Fernando [GME, Depto. Fisica Aplicada, Universidad de Zaragoza, E-50009 Zaragoza (Spain)], E-mail: fblesa@unizar.es; Serrano, Sergio [GME, Depto. Informatica e Ingenieria de Sistemas, Universidad de Zaragoza, E-50015 Zaragoza (Spain)], E-mail: sserrano@unizar.es
2008-05-15
In this paper we present a complete study of the (N + 1)-body ring problem. In particular, we review and describe the evolution of the equilibrium points, their stability, their bifurcations, the zero velocity curves and we provide new techniques that give new views to this classical problem. Some of these techniques are the OFLI2 (a Chaos Indicator given in [Barrio R. Sensitivity tools vs. Poincare sections. Chaos, Solitons and Fractals 2005;25(3):711-26; Barrio R. Painting chaos: a gallery of sensitivity plots of classical problems. Int J Bifur Chaos Appl Sci Eng [in press
Energy Technology Data Exchange (ETDEWEB)
Garcilazo, H., E-mail: humberto@esfm.ipn.mx [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Edificio 9, 07738 Mexico D.F. (Mexico); Gal, A., E-mail: avragal@savion.huji.ac.il [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
2013-01-02
The {pi}{Lambda}N-{pi}{Sigma}N coupled-channel system with quantum numbers (Y,I,J{sup P})=(1,3/2 ,2{sup +}) is studied in a relativistic three-body model, using two-body separable interactions in the dominant p-wave pion-baryon and {sup 3}S{sub 1}YN channels. Three-body equations are solved in the complex energy plane to search for quasibound state and resonance poles, producing a robust narrow {pi}{Lambda}N resonance about 10-20 MeV below the {pi}{Sigma}N threshold. Viewed as a dibaryon, it is a {sup 5}S{sub 2} quasibound state consisting of {Sigma}(1385)N and {Delta}(1232)Y components. Comparison is made between the present relativistic model calculation and a previous, outdated nonrelativistic calculation which resulted in a {pi}{Lambda}N bound state. Effects of adding a K{sup Macron }NN channel are studied and found insignificant. Possible production and decay reactions of this (Y,I,J{sup P})=(1,3/2 ,2{sup +}) dibaryon are discussed.
Non-integrability of the Anisotropic Stormer Problem and the Isosceles Three-Body Problem
Nomikos, D. G.; Papageorgiou, V. G.
2009-02-01
We study the Anisotropic Stormer Problem (ASP) and the Isosceles Three-Body Problem (IP), from the viewpoint of integrability, using Morales-Ramis theory and its generalization. The study of their integrability presents particular interest since they model important physical phenomena. Both problems can be reduced with respect to the S1 symmetry. Almeida and Stuchi [M.A. Almeida, T.J. Stuchi, Non-integrability of the anisotropic Stormer problem with angular momentum, Physica D 189 (2004) 219-233] proved that the reduced ASP is non-integrable for almost all values of the parameters. In this paper we establish the non-integrability (in the extended Liouville sense) of the remaining cases. The IP is a special case of the three-body problem and it can be considered as a generalization of the Sitnikov problem. Here we prove that the complexified reduced IP does not admit an additional independent meromorphic first integral.
The two-body problem of a pseudo-rigid body and a rigid sphere
DEFF Research Database (Denmark)
Kristiansen, Kristian Uldall; Vereshchagin, M.; Gózdziewski, K.
2012-01-01
n this paper we consider the two-body problem of a spherical pseudo-rigid body and a rigid sphere. Due to the rotational and "re-labelling" symmetries, the system is shown to possess conservation of angular momentum and circulation. We follow a reduction procedure similar to that undertaken...... in the study of the two-body problem of a rigid body and a sphere so that the computed reduced non-canonical Hamiltonian takes a similar form. We then consider relative equilibria and show that the notions of locally central and planar equilibria coincide. Finally, we show that Riemann's theorem on pseudo......-rigid bodies has an extension to this system for planar relative equilibria....
Biquaternions and relativistic kinematics
International Nuclear Information System (INIS)
Bogush, A.A.; Kurochkin, Yu.A.; Fedorov, F.I.
1979-01-01
The problems concerning the use of quaternion interpretation of the Lorentz group vector parametrization are considered for solving relativistic kinematics problems. A vector theory convenient for describing the characteristic features of the Lobachevsky space is suggested. The kinematics of elementary particle scattering is investigated on the basis of this theory. A synthesis of vector parametrization and of quaternion calculation has been shown to lead to natural formulation of the theory of vectors in the three-dimensional Lobachevsky space, realized on mass hyperboloids of relativistic particles
Relativistic approach to nuclear structure
International Nuclear Information System (INIS)
Nguyen Van Giai; Bouyssy, A.
1987-03-01
Some recent works related with relativistic models of nuclear structure are briefly reviewed. The Dirac-Hartree-Fock and Dirac-Brueckner-Hartree-Fock are recalled and illustrated by some examples. The problem of isoscalar current and magnetic moments of odd nuclei is discussed. The application of the relativistic model to the nuclear response function is examined
Non-relativistic supersymmetry
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1984-01-01
The most general one- and two-body hamiltonian invariant under galilean supersymmetry is constructed in superspace. The corresponding Feynman rules are given for the superfield Green functions. As demonstrated by a simple example, it is straightforward to construct models in which the supersymmetry is spontaneously broken by the non-relativistic vacuum. (orig.)
Computational Structure of the N-Body Problem
1988-04-01
14 I MONITORING AGENCY N4AME A AOORESS(II dhifeent Orson Conrolln Office) it. SECU ITY CLASS. tot #his report) Office of Naval Research UCASFE...is called the "many- body" or the "N-body" problem. Such studies are conducted in celestial mechanics, plasma physics, fluid mechanics as well as in...the source of the message). Since messages are function descriptions, all mes- sages are of equal length and the concept of message time is well
Problems of Municipal Service in Decisions of International Judicial Bodies
Directory of Open Access Journals (Sweden)
Milana R. Madojan
2017-03-01
Full Text Available Relevance of the chosen topic is due to the huge number of unresolved problems in the field of municipal service, exacerbated to date by the instability of the political and economic situation in the Russian Federation caused by the escalation of national conflicts in some regions of the world, imposed, in this regard, economic sanctions. Article examines main problems of the municipal service in the Russian Federation in the decisions of international judicial bodies, gives examples of judicial decisions made against municipal employees accused of bribery and fraud, lists main regulatory and legal acts that regulate the activities of the municipal service of the Russian Federation.
Parameter identification problems for thin inclusions in elastic bodies
Khludnev, A. M.; Popova, T. S.
2017-10-01
The paper concerns an identification of rigidity parameters for thin inclusions located inside elastic bodies. A delamination of the inclusions is assumed thus providing a crack between inclusions and the elastic matrix. Inequality type boundary conditions are imposed at the crack faces to exclude a mutual penetration. We consider elastic as well as rigid inclusions and solve an optimal control problem for finding a rigidity parameter minimizing a suitable cost functional. The cost functional characterizes a displacement of the inclusion, and a rigidity parameter serves as a control function. We prove a solution existence of the problems formulated.
Periodic solutions of the N-body problem
Meyer, Kenneth R
1999-01-01
The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic so...
Quantum N-body problem with a minimal length
International Nuclear Information System (INIS)
Buisseret, Fabien
2010-01-01
The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [x,p]=i(1+βp 2 ), leading to the existence of a minimal observable length √(β). For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of the N-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that in the harmonic oscillator case, the β-dependent term grows faster with increasing N than the β-independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for D-dimensional systems. Consequently, quantum N-body bound states might be interesting places to look at nontrivial manifestations of a minimal length, since the more particles that are present, the more the system deviates from standard quantum-mechanical predictions.
Antippa, Adel F.
2009-01-01
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…
The human body and weightlessness operational effects, problems and countermeasures
Thornton, William
2017-01-01
This book focuses on all of the major problems associated with the absence of body weight in space, by analyzing effects, adaption, and re-adaptation upon returning to Earth, using sound scientific principles embedded in a historical context. Serious problems for space travelers range from Space Motion Sickness (SMS) to recently discovered ocular effects that may permanently impair vision. Fluid loss and shifts, spinal changes, and bone and muscle loss are also all results of weightlessness. Starting with a brief definition and history of weightlessness, the authors then address in detail each problem as well as the countermeasures aimed at alleviating them. In some cases, alternative hypotheses regarding what can and should be attempted are also presented. As plans for long-term missions to the Moon and Mars develop, it will be essential to find countermeasures to weightlessness that are effective for missions that could span years.
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Geometrical themes inspired by the n-body problem
Herrera, Haydeé; Herrera, Rafael
2018-01-01
Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order t...
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
Polygonal rotopulsators of the curved n-body problem
Tibboel, Pieter
2018-02-01
We revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the n-body problem in H3 and S3 and prove the existence of these solutions and prove that the masses of these rotopulsators have to be equal if the rotopulsators are of nonconstant size and show that the number of negative elliptic relative equilibria of this type is finite, as is the number of positive elliptic relative equilibria if an upper bound on the size of the relative equilibrium is imposed. Additionally, we prove that a class of negative hyperbolic rotopulsators is in fact a subclass of the class of polygonal negative elliptic rotopulsators.
The three-body problem in quantum mechanics
International Nuclear Information System (INIS)
Antunes, A.C.B.
1973-01-01
Different methods used in the analysis of the scattering of an elementary particle by a system of two bound particles are compared. All particles are considered spinless and distinguishable from each other. Two approaches are used in the treatment of the problem. In the first method we build an effective - potential which accounts for the interaction of the incident particle with the bound system. The second approach consists in treating the target as a system of two particles, whose momentum distribution is given by the bound state wavefunction. The three body system is then treated by the techniques of the multiple scattering series and of Glauber theory. (author)
Relativistic nuclear physics with the spectator model
International Nuclear Information System (INIS)
Gross, F.
1988-01-01
The spectator model, a general approach to the relativistic treatment of nuclear physics problems in which spectators to nuclear interactions are put on their mass-shell, will be defined nd described. The approach grows out of the relativistic treatment of two and three body systems in which one particle is off-shell, and recent numerical results for the NN interaction will be presented. Two meson-exchange models, one with only 4 mesons (π, σ, /rho/, ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with 6 mesons (π, σ, /rho/, ω, δ, and /eta/) but a pure γ 5 γ/sup mu/ pion coupling, are shown to give very good quantitative fits to NN scattering phase shifts below 400 MeV, and also a good description of the /rho/ 40 Cα elastic scattering observables. 19 refs., 6 figs., 1 tab
Free time minimizers for the three-body problem
Moeckel, Richard; Montgomery, Richard; Sánchez Morgado, Héctor
2018-03-01
Free time minimizers of the action (called "semi-static" solutions by Mañe in International congress on dynamical systems in Montevideo (a tribute to Ricardo Mañé), vol 362, pp 120-131, 1996) play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi equation (Fathi in Weak KAM Theorem in Lagrangian Dynamics Preliminary Version Number 10, 2017). We prove that any solution to Newton's three-body problem which is asymptotic to Lagrange's parabolic homothetic solution is eventually a free time minimizer. Conversely, we prove that every free time minimizer tends to Lagrange's solution, provided the mass ratios lie in a certain large open set of mass ratios. We were inspired by the work of Da Luz and Maderna (Math Proc Camb Philos Soc 156:209-227, 1980) which showed that every free time minimizer for the N-body problem is parabolic and therefore must be asymptotic to the set of central configurations. We exclude being asymptotic to Euler's central configurations by a second variation argument. Central configurations correspond to rest points for the McGehee blown-up dynamics. The large open set of mass ratios are those for which the linearized dynamics at each Euler rest point has a complex eigenvalue.
Integrable Problems of the Dynamics of Coupled Rigid Bodies
Bogoyavlenskiĭ, O. I.
1993-06-01
Several classical problems of dynamics are shown to be integrable for the special systems of coupled rigid bodies introduced in this paper and called Ck-central configurations. It is proved that the dynamics of an arbitrary Ck-central configuration in the Newtonian gravitational field with an arbitrary quadratic potential is integrable in the Liouville sense and in theta-functions of Riemann surfaces. A hidden symmetry of the inertial dynamics of these configurations is found, and reductions of the corresponding Lagrange equations to the Euler equations on the direct sums of Lie coalgebras SO(3) are obtained. Reductions and integrable cases of the equations for the rotation of a heavy Ck-central configuration about a fixed point are indicated. Separation of rotations of a space station type orbiting system, which is a Ck-central configuration of rigid bodies, is proved. This result leads to the possibility of independent stabilization of rotations of the rigid bodies in such orbiting configurations. Integrability of the inertial dynamics of CRn-central configurations of coupled gyrostats is proved.
International Nuclear Information System (INIS)
Bastero-Gil, M.
2015-01-01
Relativistic cosmology is nothing but the study of the evolution of our universe expanding from the General Theory of Relativity, which describes the gravitational interaction at any scale and given its character far-reaching is the force that dominate the evolution of the universe. (Author)
Price, R H
1993-01-01
Work reported in the workshop on relativistic astrophysics spanned a wide varicy of topics. Two speciﬁc areas seemed of particular interest. Much attention was focussed on gravitational wave sources, especially on the waveforms they produce, and progress was reported in theoretical and observational aspects of accretion disks.
On the structure of 3-dimensional 2-body problem solutions in Wheeler-Feynman electrodynamics
International Nuclear Information System (INIS)
Klimenko, S.; Nikitin, I.
2001-01-01
The problem of the relativistic 3-dimensional motion of 2 oppositely charged equally massive particles in classical electrodynamics with half-retarded/half-advanced interactions is investigated. It is shown that at a certain critical energy value the topological structure of phase space is changed, leading to bifurcation (splitting) of solutions, appearance of extra non-Newtonian degrees of freedom and break of reflectional symmetries
Meson dynamics and the nuclear many-body problem. II. Finite density Hartree-Fock
International Nuclear Information System (INIS)
Wilets, L.; Puff, R.D.; Chiang, D.; Nutt, W.T.
1976-01-01
The field-theoretic many-nucleon problem is formulated, and an analysis which sums all ''uncrossed meson line'' diagrams is investigated in detail. The calculation of energy per nucleon, after proper identification of infinite mass renormalization terms, exhibits effects of nuclear recoil, relativistic kinematics, and retardation. Numerical results are presented for π and ω mesons, and the nucleon interaction energies obtained are compared with the traditional static limit of infinite nucleon mass
Energy Technology Data Exchange (ETDEWEB)
Amour, L. [Reims Univ., Lab. de Mathematiques EDPPM, FRE-CNRS 3111, 51 (France); Faupin, J. [Aarhus Univ., Institut for Matematiske Fag (Denmark); Grebert, B. [Nantes Univ, Lab. de Mathematiques Jean-Leray, UMR-CNRS 6629 (France); Guillot, J.C. [Ecole Polytechnique, Centre de Mathematiques Appliquees, UMR-CNRS 7641, 91 - Palaiseau (France)
2008-10-15
We consider a non-relativistic electron interacting with a classical magnetic field pointing along the x{sub 3}-axis and with a quantized electromagnetic field. The system is translation invariant in the x{sub 3}-direction and the corresponding Hamiltonian has a decomposition H {approx_equal}{integral}{sub R}{sup +}H(P{sub 3})dP{sub 3}. For a fixed momentum P{sub 3} sufficiently small, we prove that H(P{sub 3}) has a ground state in the Fock representation if and only if E'(P{sub 3})=0, where P{sub 3} {yields}E'(P{sub 3}) is the derivative of the map P{sub 3}{yields}E(P{sub 3})=inf{sigma}(H(P{sub 3})). If E'(P{sub 3}){ne}0, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant. (authors)
On the n-body problem on surfaces of revolution
Stoica, Cristina
2018-05-01
We explore the n-body problem, n ≥ 3, on a surface of revolution with a general interaction depending on the pairwise geodesic distance. Using the geometric methods of classical mechanics we determine a large set of properties. In particular, we show that Saari's conjecture fails on surfaces of revolution admitting a geodesic circle. We define homographic motions and, using the discrete symmetries, prove that when the masses are equal, they form an invariant manifold. On this manifold the dynamics are reducible to a one-degree of freedom system. We also find that for attractive interactions, regular n-gon shaped relative equilibria with trajectories located on geodesic circles typically experience a pitchfork bifurcation. Some applications are included.
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
Global regularization method for planar restricted three-body problem
Directory of Open Access Journals (Sweden)
Sharaf M.A.
2015-01-01
Full Text Available In this paper, global regularization method for planar restricted three-body problem is purposed by using the transformation z = x+iy = ν cos n(u+iv, where i = √−1, 0 < ν ≤ 1 and n is a positive integer. The method is developed analytically and computationally. For the analytical developments, analytical solutions in power series of the pseudotime τ are obtained for positions and velocities (u, v, u', v' and (x, y, x˙, y˙ in both regularized and physical planes respectively, the physical time t is also obtained as power series in τ. Moreover, relations between the coefficients of the power series are obtained for two consequent values of n. Also, we developed analytical solutions in power series form for the inverse problem of finding τ in terms of t. As typical examples, three symbolic expressions for the coefficients of the power series were developed in terms of initial values. As to the computational developments, the global regularized equations of motion are developed together with their initial values in forms suitable for digital computations using any differential equations solver. On the other hand, for numerical evolutions of power series, an efficient method depending on the continued fraction theory is provided.
Projection techniques to approach the nuclear many-body problem
International Nuclear Information System (INIS)
Sun, Yang
2016-01-01
Our understanding of angular–momentum-projection goes beyond quantum-number restoration for symmetry-violated states. The angular–momentum-projection method can be viewed as an efficient way of truncating the shell-model space which is otherwise too large to handle. It defines a transformation from the intrinsic system, where dominant excitation modes in the low-energy region are identified with the concept of spontaneous symmetry breaking, to the laboratory frame with well-organized configuration states according to excitations. An energy-dictated, physically-guided shell-model truncation can then be carried out within the projected space and the Hamiltonian is thereby diagonalized in a compact basis. The present article reviews the theory of angular–momentum-projection applied in the nuclear many-body problem. Angular momentum projection emerges naturally if a deformed state is treated quantum-mechanically. To demonstrate how different physical problems in heavy, deformed nuclei can be efficiently described with different truncation schemes, we introduce the projected shell model and show examples of calculation in a basis with axial symmetry, a basis with triaxiality, and a basis with both quasiparticle and phonon excitations. Technical details of how to calculate the projected matrix elements and how to build a workable model with the projection techniques are given in the appendix. (invited comment)
Global Regularization Method for Planar Restricted Three-body Problem
Sharaf, M. A.; Dwidar, H. R.
2015-12-01
In this paper, global regularization method for planar restricted three-body problem is purposed by using the transformation z=x+iy=ν cos n(u+iv), where i=√{-1}, 0 < ν ≤ 1 and n is a positive integer. The method is developed analytically and computationally. For the analytical developments, analytical solutions in power series of the pseudo-time τ are obtained for positions and velocities (u,v,u',v') and (x,y,dot{x},dot{y}) in both regularized and physical planes respectively, the physical time {t} is also obtained as power series in τ. Moreover, relations between the coefficients of the power series are obtained for two consequent values of {n}. Also, we developed analytical solutions in power series form for the inverse problem of finding τ in terms of {t}. As typical examples, three symbolic expressions for the coefficients of the power series were developed in terms of the initial values. As to the computational developments, the global regularized equations of motion are developed together with their initial values in forms suitable for digital computations using any differential equations solver. On the other hand, for the numerical evolutions of power series, an efficient method depending on the continued fraction theory is provided.
Relativistic studies in actinides
International Nuclear Information System (INIS)
Weinberger, P.; Gonis, A.
1987-01-01
In this review the theoretical background is given for a relativistic description for actinide systems. A short introduction is given of the density functional theory which forms the basis for a fully relativistic single-particle theory. A section on the Dirac Hamiltonian is followed by a brief summary on group theoretical concepts. Single site scattering is presented such that formal extensions to the case of the presence of an internal (external) magnetic field and/or anisotropic scattering are evident. Multiple scattering is discussed such that it can readily be applied also to the problem of dislocations. In connection with the problem of selfconsistency particular attention is drawn to the use of complex energies. Finally the various theoretical aspects discussed are illustrated through the results of numerical calculations. 101 refs.; 37 figs.; 5 tabs
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Relativistic two-body system in (1+1)-dimensional QED. 1. On the circle S1
International Nuclear Information System (INIS)
Barut, A.O.; Saradzhev, F.M.
1994-01-01
From the coupled Maxwell-Dirac equations for two fermion fields Ψ 1 , Ψ 2 the authors derive a covariant two-body equation for the composite field Φ(x 1 , x 2 ) in configuration space which includes radiative self-energy effects. Both Coulomb gauge and covariant gauge have been used and their equivalence is proved. For the space S 1 the authors solve the two-body equation with mutual interactions exactly and obtain the mass spectrum in the case of massless fermions. 7 refs., 5 figs
[The so-called body-mind problem].
Tress, Wolfgang
2011-01-01
Even psychosomatic researchers seem to want to avoid the so-called body-mind problem, which is actually a mind-brain problem. In line with Beckermann (2008), the first the four possible positions on the mind-brain problem are presented. The debate over the past 100 years has revolved around the question of whether mental events are ontologically independent of brain physiology or whether they are in fact entirely determined by it. Such a physicalism approach based on properties (i.e., mental characteristics or phenomena are physical or can be completely reduced to physical characteristics), however, is diametrically opposed to some of our strongest intuitions, e.g., that computers will never be able to develop qualities of human experience (qualia) and thus become subjects in the first person singular. Yet we are equally unable to prove the fundamental impossibility of such a development. In this stalemate situation, a differentiation was undertaken by Gottlob Frege (1892) which could be of help: Expressed in today's language, a distinction is made between the sense of an expression, its contextual presentation (e.g., where there is a difference between "the evening star" and "the morning star"), on the one hand, and its so-called reference (the object to which it refers, here the planet Venus in both cases) on the other. The school of Gestalt psychology that developed in Berlin at the start of the last century similarly posited a "psychophysical level of the CNS," a continuum in a pattern of electrical field forces which manifests itself first in cerebral physiological-neuronal processes as well as in other perspectives such as consciousness and experience. A subsequent speculative concept then extends this model to assume also an (as yet) unknown Alpha configuration as being a common reference of two sense contents: (1) the results of the neurophysiological third-person perspective and (2) of the emotional-cognitive first-person perspectives. Only through the
The relativistic gravity train
Seel, Max
2018-05-01
The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.
A simple coordinate space approach to three-body problems ...
Indian Academy of Sciences (India)
We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in a simple coordinate space variational approach. The method is constructive and gives an efﬁcient way of resolving a three-body system to an effective two-body system. It is illustrated by ...
Maximal lattice free bodies, test sets and the Frobenius problem
DEFF Research Database (Denmark)
Jensen, Anders Nedergaard; Lauritzen, Niels; Roune, Bjarke Hammersholt
Maximal lattice free bodies are maximal polytopes without interior integral points. Scarf initiated the study of maximal lattice free bodies relative to the facet normals in a fixed matrix. In this paper we give an efficient algorithm for computing the maximal lattice free bodies of an integral...... method is inspired by the novel algorithm by Einstein, Lichtblau, Strzebonski and Wagon and the Groebner basis approach by Roune....
Gerasimov, S. B.
2017-12-01
Within the non-relativistic approach to photo-absorption sum rules for the 3N(4N)-nuclei the new σ ‑1 sum rules proposed which are based on general charge-symmetry (CS) consequences for a pair of the “CS-conjugated” triton and 3 He nuclei and for the “self-conjugated” nucleus 4 He. The numerical deviations from the less general “charge-independent” approach leading to the long-known Foldy-Khokhlow sum rules are estimated. In the relativistic domain the functional inapplicability is demonstrated of the “charge independence” approximation in the derivation of the σ ‑1 - type sum rules in the case of nucleons. With application of the relevant “charge symmetry” approach, the general system of the sum rules is derived and the inevitable isospin-dependent dynamics of the constituent quarks is underlined.
Zhang, Bing; Li, Kunyang
2018-02-01
The “Breakthrough Starshot” aims at sending near-speed-of-light cameras to nearby stellar systems in the future. Due to the relativistic effects, a transrelativistic camera naturally serves as a spectrograph, a lens, and a wide-field camera. We demonstrate this through a simulation of the optical-band image of the nearby galaxy M51 in the rest frame of the transrelativistic camera. We suggest that observing celestial objects using a transrelativistic camera may allow one to study the astronomical objects in a special way, and to perform unique tests on the principles of special relativity. We outline several examples that suggest transrelativistic cameras may make important contributions to astrophysics and suggest that the Breakthrough Starshot cameras may be launched in any direction to serve as a unique astronomical observatory.
Gauge invariance and relativistic effects in X-ray absorption and scattering by solids
Bouldi, Nadejda; Brouder, Christian
2017-12-01
There is an incompatibility between gauge invariance and the semi-classical time-dependent perturbation theory commonly used to calculate light absorption and scattering cross-sections. There is an additional incompatibility between perturbation theory and the description of the electron dynamics by a semi-relativistic Hamiltonian. In this paper, the gauge-dependence problem of exact perturbation theory is described, the proposed solutions are reviewed and it is concluded that none of them seems fully satisfactory. The problem is finally solved by using the fully relativistic absorption and scattering cross-sections given by quantum electrodynamics. Then, a new general Foldy-Wouthuysen transformation is presented. It is applied to the many-body case to obtain correct semi-relativistic transition operators. This transformation considerably simplifies the calculation of relativistic corrections. In the process, a new light-matter interaction term emerges, called the spin-position interaction, that contributes significantly to the magnetic X-ray circular dichroism of transition metals. We compare our result with the ones obtained by using several semi-relativistic time-dependent Hamiltonians. In the case of absorption, the final formula agrees with the result obtained from one of them. However, the correct scattering cross-section is not given by any of the semi-relativistic Hamiltonians.
Relativistic models of nuclear structure
International Nuclear Information System (INIS)
Gillet, V.; Kim, E.J.; Cauvin, M.; Kohmura, T.; Ohnaka, S.
1991-01-01
The introduction of the relativistic field formalism for the description of nuclear structure has improved our understanding of fundamental nuclear mechanisms such as saturation or many body forces. We discuss some of these progresses, both in the semi-classical mean field approximation and in a quantized meson field approach. (author)
Body-modifying concepts and dermatologic problems: tattooing and piercing.
Kaatz, Martin; Elsner, Peter; Bauer, Andrea
2008-01-01
Recently, piercing and tattooing have gained increasing popularity worldwide, through all social classes and age groups. Besides pierced ear lobes, piercing of the tongue, nose, nipples, belly button, and even the genitals is quite common. The variety of tattoos range from temporary henna tattoos to permanent makeup and permanent tattoos, where the pigments are deposed in the dermis. These trends are supplemented by more invasive methods of body modification such as implanting, scarification, or branding. Parallel with the increasing popularity of piercing and tattoos, the knowledge about associated complications rose. Complications depend substantially on the circumstances in which body modifications are applied, the materials used, and the body region concerned. This article gives an overview of the most common complications of body modification methods, which mainly result from shortcomings in the application itself or in hygiene regimens. Consequences may be as severe as life-threatening events or permanent malfunction of different organs.
On the two-body problem in quantum mechanics
International Nuclear Information System (INIS)
Micu, L.
2008-01-01
Following the representation of a two-body system in classical mechanics, we build up a quantum picture which is free of spurious effects and retains the intrinsic features of the internal bodies. In the coordinate space the system is represented by the real particles, individually bound to a center of forces which in a certain limit coincides with the center of mass and the wave function writes as product of the individual wave functions with correlated arguments. (author)
Frontiers in relativistic celestial mechanics
2014-01-01
Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.
Few-Body Problems in Experimental Nuclear Astrophysics
DEFF Research Database (Denmark)
Fynbo, H.O.U.
2013-01-01
The 3α-reaction is one of the key reactions in nuclear astrophysics. Since it is a three-body reaction direct measurement is impossible, and therefore the reaction rate must be estimated theoretically. In this contribution I will discuss uncertainties in this reaction rate both at very low...
Fundamental length and relativistic length
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1988-01-01
It si noted that the introduction of fundamental length contradicts the conventional representations concerning the contraction of the longitudinal size of fast-moving objects. The use of the concept of relativistic length and the following ''elongation formula'' permits one to solve this problem
General-relativistic celestial mechanics
Energy Technology Data Exchange (ETDEWEB)
Treder, H.-J.
1980-01-01
The fundamental principles of general relativistic dynamics are deduced from Einstein's field equations and one- and two-particle problems in relativistic celestial mechanics are considered. Different opinions as to the physical meaning of calculations of gravitational radiation for double stars are discussed. It is shown that these different opinions are based on different interpretations of Einstein's gravitational equations as generally covariant determinations of the space-time metric and as gauge-invariant tensor field equations in a given space-time background.
Sitnikov cyclic configuration of N+1-body problem
Shahbaz Ullah, M.; Hassan, M. R.
2014-12-01
This manuscript deals with the generalisation of all previous works on series solutions and linear stability of equilibrium points of the Sitnikov problem. Following Giacaglia (1967), in Sect. 2 we have derived the equation of motion of the infinitesimal mass moving along the z-axis about which the plane of motion is rotating with unit angular velocity. In Sects. 3, 4 and 5 the series solutions of the Sitnikov problem have been developed by the method of MacMillan, Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the three series solutions have been compared graphically by putting N=2, 3, 4. In Sect. 7 the coordinates of equilibrium points have been calculated. In Sect. 8 the linear stability of equilibrium points has been examined by the method of Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) and it was found that the equilibrium points are stable in Sitnikov problem.
Gender differences dominate sleep disorder patients' body problem complaints
Directory of Open Access Journals (Sweden)
Ted L. Rosenthal
1994-12-01
Full Text Available We studied it age, gender, diagnostic status, and psychiatric features affected 291 consecutive sleep disorder patient's body complaints on a brief checklist. Gender had a strong impact on all four (tested dependent measures, with women reporting more distress than men. Age produced significant regressions on two measures, with younger patients complaining more than older. Presence of psychiatric features was associated with more complaints on one dependent measure - previously found to reflect internal medicine patients' emotional distress. The results of regression analyses were largely supported by follow-up ANOVAs. However, contrasting insomniac versus hypersomniac versus all other sleep disorder diagnoses did not affect body complaints on any dependent measure. The results caution against combining males and females to compare self-reported distress between sleep disorders.
Problem of Brief Interaction of Liquid and Amorphous Bodies
Simankov, D. S.
2016-01-01
The author has proposed a model of brief interaction of liquid and amorphous bodies with boundary conditions of the third kind in the amorphous body without a convective mass flux. Consideration has been given to the thermophysical aspect of formation of the temperature sensation of a biomedical object (BMO) on contact with the liquid body with a different temperature. The procedure of short measurements in the stage of irregular thermal regime (pulse method) was applied to investigation of thermal activity of various anatomical sections of the BMO skin as a function of its temperature. It has been shown experimentally that thermal activity grows with temperature and is within 640-1800 J/(m2·K·s0.5). The total relative error of the method of thermal-activity measurements amounted to ~5%. It has been proposed that analytical calculation of the surface temperature of the BMO on contact be modeled as a combination of the temperatures in liquid and solid media by using the criterion of moisture-content percentage in the BMO.
Screening and Absorption of Gravitation in Pre-Relativistic and Relativistic Theories
von Borzeszkowski, H.-H.; Chrobok, T.; Treder, H.-J.
After commenting on the early search for a mechanism explaining the Newtonian action-at-a-distance gravitational law we review non-Newtonian effects occurring in certain ansatzes for shielding, screening and absorption effects in pre-relativistic theories of gravity. Mainly under the aspect of absorption and suppression (or amplification), we then consider some implications of these ansatzes for relativistic theories of gravity and discuss successes and problems in establishing a general framework for a comparison of alternative relativistic theories of gravity. We examine relativistic representatives of theories with absorption and suppression (or amplification) effects, such as fourth-order theories, tetrad theories and the Einstein-Cartan-Kibble-Sciama theory.
Muonic helium atom as a classical three-body problem
Stuchi, T. J.; Antunes, A. C. B.; Andreu, M. A.
2000-12-01
We study the classical problem of the muonic helium atom, a helium atom with one of its electrons replaced by a muon. First, we establish the connection of the model with the one-dimensional frozen planetary approximation of the helium atom and find that there is classically stable motion for the configuration α-particle-electron-muon, and no stable motion for the α-particle-muon-electron configuration. After that, we introduce the restricted muonic helium problem, a model for the movement of an electron in the potential of the α particle/muon pair moving in a circular orbit. In this model, the equilibrium points, their associated Lyapunov families of periodic orbits, and their stability parameters were studied. The most interesting feature is the stability of the halo orbits, for a range of energy values. The vicinity of the α particle is also studied, examining Poincaré sections for increasing energy values showing an increase of the chaotic motion.
Non-relativistic and relativistic scattering by short-range potentials
DEFF Research Database (Denmark)
Arnbak, H.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2011-01-01
Relativistic and non-relativistic scattering by short-range potentials is investigated for selected problems. Scattering by the δ′ potential in the Schrödinger equation and δ potentials in the Dirac equation must be solved by regularization, efficiently carried out by a perturbation technique...
Analytical Treatment of the Two-Body Problem with Slowly Varying ...
Indian Academy of Sciences (India)
Abstract. The present work is concerned with the two-body problem with varying mass in case of isotropic mass loss from both components of the binary systems. The law of mass variation used gives rise to a perturbed. Keplerian problem depending on two small parameters. The problem is treated analytically in the ...
A frictional contact problem for an electro-viscoelastic body
Directory of Open Access Journals (Sweden)
Mircea Sofonea
2007-12-01
Full Text Available A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb's law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.
On a variational method in the many-body problem
International Nuclear Information System (INIS)
Bonch-Bruevich, V.L.; Stoyanova, I.S.
1975-01-01
A variational method for determining the single-particle energy spectrum of the Fermi-type elementary excitations is developed. The expression for the energy of Fermi quasi-particles is subjected to a variation. The problem of determining the single-particle spectrum of the Fermi excitations is reduced to solving a certain nonlinear integral equation. The interaction hamiltonian is taken in the statically screened form. The acse of a degenerate space-uniform and isotropic electron plasma with the simplest square-law of dispersion is discussed
A Digital Computer Approach to the Unsymmetric Rigid Body Problem.
1982-03-01
i A (1 2 I )1ii B (1 3 11)/12 C (1~ 1 1 2)/13 1412 I F, G, H Intermediate expression for computations of w 1 9 w 2 9 w3 d1, d 2, ei, e 2 trial...Staude problem. 6. Grammel (1948): Use of approximating functions in a recursive scheme. A brief description of Grammel’s work can be found in Section...HAMILTON’S EQUATIONS Hamilton’s equations are more general than the methods of Euler and Lagrange. The Hamiltonian, H , is related to the Lagrangian, L, by
Many-body problems in high temperature superconductivity
International Nuclear Information System (INIS)
Yu Lu.
1991-10-01
In this brief review the basic experimental facts about high T c superconductors are outlined. The superconducting properties of these superconductors are not very different from those of the ordinary superconductors. However, their normal state properties cannot be described by the standard Fermi liquid (FL) theory. Our current understanding of the strongly correlated models is summarized. In one dimension these systems behave like a ''Luttinger liquid'', very much distinct from the FL. In spite of the enormous efforts made in two-dimensional studies, the question of FL vs non-FL behaviour is still open. The numerical results as well as various approximation schemes are discussed. Both the single hole problem in a quantum antiferromagnet and finite doping regime are considered. (author). 104 refs, 9 figs
Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design
Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.
2001-01-01
The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.
Many-body problem in one-dimension
International Nuclear Information System (INIS)
Emery, V.J.
1979-11-01
This work attempts to give a qualitative feeling for the more important physical ideas involved with the study of many-body systems in one dimension, and considers a particular strong-coupling model. This model provides an excellent description of the chains of mercury ions in Hg/sub 3-delta/AsF 6 ; some of the predictions of the theory can be checked by x-ray and neutron diffraction. Much of the physics of nearly one-dimensional materials is concerned with understanding the possible types of phase transition that may take place, and establishing the conditions in which one or another will be predominant. The most significant feature of purely one-dimensional systems is the dominant effect of fluctuations. The paper is organized as follows: introduction; qualitative aspects of one-dimensional systems (general survey, mathematical model, qualitative discussion of strong coupling - strong attractive U, strong repulsive U, large V); strong coupling between parallel spins (independent spin systems, coupling between opposite spins); mercury chains; electrons with arbitrary coupling; boson representations of operators; and classical Coulomb gas
International Nuclear Information System (INIS)
Tan, Zhiqiang; Wilson, D.; Varghese, P.L.
1997-01-01
We consider an extension of the ordinary Riemann problem and present an efficient approximate solution that can be used to improve the calculations of aerodynamic forces on an accelerating body. The method is demonstrated with one-dimensional examples where the Euler equations and the body motion are solved in the non-inertial co-ordinate frame fixed to the accelerating body. 8 refs., 6 figs
Rotating relativistic neutron stars
Energy Technology Data Exchange (ETDEWEB)
Weber, F.; Glendenning, N.K.
1991-07-21
Models of rotating neutron stars are constructed in the framework of Einstein's theory of general relativity. For this purpose a refined version of Hartle's method is applied. The properties of these objects, e.g. gravitational mass, equatorial and polar radius, eccentricity, red- and blueshift, quadrupole moment, are investigated for Kepler frequencies of 4000 s{sup {minus}1} {le} {Omega}{sub K} {le} 9000 s{sup {minus}1}. Therefore a self-consistency problem inherent in the determination of {Omega}{sub K} must be solved. The investigation is based on neutron star matter equations of state derived from the relativistic Martin-Schwinger hierarch of coupled Green's functions. By means of introducing the Hartree, Hartree-Fock, and ladder ({Lambda}) approximations, models of the equation of state derived. A special feature of the latter approximation scheme is the inclusion of dynamical two-particle correlations. These have been calculated from the relativistic T-matrix applying both the HEA and Bonn meson-exchange potentials of the nucleon-nucleon force. The nuclear forces of the former two treatments are those of the standard scalar-vector-isovector model of quantum hadron dynamics, with parameters adjusted to the nuclear matter data. An important aspect of this work consists in testing the compatibility of different competing models of the nuclear equation of state with data on pulsar periods. By this the fundamental problem of nuclear physics concerning the behavior of the equation of state at supernuclear densities can be treated.
On the libration collinear points in the restricted three – body problem
Directory of Open Access Journals (Sweden)
Alzahrani F.
2017-03-01
Full Text Available In the restricted problem of three bodies when the primaries are triaxial rigid bodies, the necessary and sufficient conditions to find the locations of the three libration collinear points are stated. In addition, the Linear stability of these points is studied for the case of the Euler angles of rotational motion being θi = 0, ψi + φi = π/2, i = 1, 2 accordingly. We underline that the model studied in this paper has special importance in space dynamics when the third body moves in gravitational fields of planetary systems and particularly in a Jupiter model or a problem including an irregular asteroid.
Smit, Miranda; Van Stralen, Haike E; Van den Munckhof, Bart; Snijders, Tom J; Dijkerman, Hendrik Christiaan
2018-03-12
Reports on patients who lack ownership over their entire body are extremely rare. Here, we present patient SA who suffered from complete body disownership after a tumour resection in the right temporoparietal cortex. Neuropsychological assessment disclosed selective bilateral ownership problems, despite intact primary visual and somatosensory senses. SA's disownership seems to stem from a suboptimal multimodal integration, as shown by the rubber hand illusion and the beneficial effect during and after simple exercises aiming at multisensory recalibration. © 2018 The Authors. Journal of Neuropsychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.
Workshop on Quark-Gluon Plasma and Relativistic Heavy Ions
Lombardo, Maria Paola; Nardi, Marzia; GISELDA 2002; QGP 2002
2002-01-01
This book offers the unique possibility of tackling the problem of hadronic deconfinement from different perspectives. After general introductions to the physical issues, from both the theoretical and the experimental point of view, the book presents the most recent expertise on field theory approaches to the QCD phase diagram, many-body techniques and applications, the dynamics of phase transitions, and phenomenological analysis of relativistic heavy ion collisions. One of the major goals of this book is to promote interchange among those fields of research, which have traditionally been cult
The Kantian Attempt to Solve the Mind-Body Problem. A Critical Approach
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Pedro Jesús Teruel
2014-11-01
Full Text Available The mind-body problem is one of the perennial challenges in the history of ideas. Immanuel Kant (1724-1804 tried to solve it through an approach with several modulations –parallel to his intellectual evolution– that brought him into contact with both the later projection of the theoretical issue (the mind brain problem and its practical side (the immortality question. In this paper I face the Kantian approach to the mind-body problem from a triple perspective: descriptive, appraising and critical.
Solving few-body scattering problems in the momentum lattice basis
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Pomerantsev V.N.
2010-04-01
Full Text Available The brief description of a new approach based on the Wave-Packet Continuum Discretization method recently developed by the present authors towards solving few-body quantum scattering problems is given. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with non-singular matrix elements, averaged on energy over lattice cells.
Relativistic covariance of Ohm's law
Starke, R.; Schober, G. A. H.
2014-01-01
The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response l...
A relativistic, meson exchange model of pion-nucleon scattering
International Nuclear Information System (INIS)
Pearces, B.C.; Jennings, B.K.
1990-06-01
A relativistic meson exchange approach to the pion-nucleon interaction is developed using a three-dimensional relativistic two-body propagator, and the results using different propagators are compared. The relativistic approach is able to describe low energy scattering up to 400 MeV above threshold, while preserving the soft pion theorems. The different propagators give similar results, as the form factors necessary to get a fit suppress much of the multiple scattering. (Author) (24 refs., 4 tabs., 6 figs.)
Directory of Open Access Journals (Sweden)
Naumenko Mikhail
2018-01-01
Full Text Available Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman’s continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He and nuclei described as consisting of clusters and nucleons (e.g., 6He. The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.
Naumenko, Mikhail; Samarin, Viacheslav
2018-02-01
Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman's continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He) and nuclei described as consisting of clusters and nucleons (e.g., 6He). The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Relativistic Binaries in Globular Clusters
Directory of Open Access Journals (Sweden)
Matthew J. Benacquista
2013-03-01
Full Text Available Galactic globular clusters are old, dense star systems typically containing 10^4 – 10^6 stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution that leads to relativistic binaries, and current and possible future observational evidence for this population. Our discussion of globular cluster evolution will focus on the processes that boost the production of tight binary systems and the subsequent interaction of these binaries that can alter the properties of both bodies and can lead to exotic objects. Direct N-body integrations and Fokker–Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.
A unified treatment of the non-relativistic and relativistic hydrogen atom: Pt. 1
International Nuclear Information System (INIS)
Swainson, R.A.; Drake, G.W.F.
1991-01-01
In this and the following two papers in this series it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The angular part of such calculations, being well understood, is performed in the standard way. In this, the first paper, it is shown how a suitable linear transformation of the two relativistic radial wavefunctions allows the pair of relativistic coupled differential equations to be written as two uncoupled second-order equations which are simple generalizations of the corresponding non-relativistic equation. This transformation is presented in a manner which allows for a simple extension to the Green function problem. The transformed relativistic wavefunctions are explicitly derived and the normalization is presented in a novel and simple way. A new derivation is given for the recursion relations for both non-relativistic and relativistic radial wavefunctions, some of which are new. These relations are required in the subsequent papers. (author)
Three-body scattering problem in the fixed center approximation: The case of attraction
Energy Technology Data Exchange (ETDEWEB)
Kudryavtsev, Alexander E. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); Gani, Vakhid A. [National Research Center Kurchatov Institute, Institute for Theoretical and Experimental Physics, Moscow (Russian Federation); National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation); Romanov, Alexander I. [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)
2016-12-15
We study the scattering of a light particle on a bound pair of heavy particles (e.g., the deuteron) within the fixed center approximation in the case of light-heavy attraction, solving the integral equation for the three-body Green's function both in the coordinate and in the momentum space. The results for the three-body scattering amplitude appear to be ambiguous -they depend on a single real parameter. This parameter may be fixed by a three-body input, e.g., the three-body scattering length. We also solve the integral equation for the three-body Green function in the momentum space, introducing a finite cut-off. We show that all three approaches are equivalent. We also discuss how our approach to the problem matches with the introduction of three-body contact interaction as done by other authors. (orig.)
Properties of transit trajectory in the restricted three and four-body problem
Circi, Christian
2012-05-01
In the restricted three-body problem if the Jacobi constant is just below the value corresponding to Lagrangian point only a little neck exists around the equilibrium point and capture trajectories are indicated as low-energy. Capture properties depend on the dynamics around these critical points and qualitative results can be obtained using linearized systems. In this paper, to study transit trajectory properties in the restricted three and four-body problem, the Earth-Moon-Sun-Satellite system is considered as example and studied using different models. In the circular restricted three-body problem (Earth-Moon-Satellite), transit, non transit and asymptotic trajectories, are easily identified by using the principal reference frame. Dynamics around Lagrangian point are then studied introducing the Moon eccentricity into the elliptical restricted three-body model. A preferential region for transit orbit is individuated and studied as a function of eigenvalue properties. To introduce the Sun effect, the bi-circular four-body model is considered and dynamics around Lagrangian points studied as a function of angular distance between Earth-Sun and Earth-Moon line. Finally, results obtained in the elliptical three-body model and bi-circular four-body model, are compared with numerical simulations using real Sun-Moon-Earth ephemeris.
Lagrangian relative equilibria for a gyrostat in the three-body problem: bifurcations and stability
Energy Technology Data Exchange (ETDEWEB)
Guirao, Juan L G; Vera, Juan A, E-mail: juan.garcia@upct.e, E-mail: juanantonio.vera@upct.e [Departamento de Matematica Aplicada y EstadIstica, Universidad Politecnica de Cartagena, Hospital de Marina, 30203 Cartagena, Region de Murcia (Spain)
2010-05-14
In this paper we consider the non-canonical Hamiltonian dynamics of a gyrostat in the frame of the three-body problem. Using geometric/mechanic methods we study the approximate dynamics of the truncated Legendre series representation of the potential of an arbitrary order. Working in the reduced problem, we study the existence of relative equilibria that we refer to as Lagrange type following the analogy with the standard techniques. We provide necessary and sufficient conditions for the linear stability of Lagrangian relative equilibria if the gyrostat morphology form is close to a sphere. Thus, we generalize the classical results on equilibria of the three-body problem and many results on them obtained by the classic approach for the case of rigid bodies.
Hip-hop solutions of the 2N-body problem
Barrabés, Esther; Cors, Josep Maria; Pinyol, Conxita; Soler, Jaume
2006-05-01
Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.
Mass spectrum bound state systems with relativistic corrections
Energy Technology Data Exchange (ETDEWEB)
Dineykhan, M; Zhaugasheva, S A [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna (Russian Federation); Toinbaeva, N Sh; Jakhanshir, A [al-Farabi Kazak National University, 480012 Almaty (Kazakhstan)
2009-07-28
Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including relativistic corrections. The mass spectrum of the bound state is analytically derived. The mechanism for arising of the constituent mass of the relativistic bound-state forming particles is explained. The mass and the constituent mass of the two-, three- and n-body relativistic bound states are calculated taking into account relativistic corrections. The corrections arising due to the one- and two-loop electron polarization to the energy spectrum of muonic hydrogen with orbital and radial excitations are calculated.
Kinetic approach to relativistic dissipation
Gabbana, A.; Mendoza, M.; Succi, S.; Tripiccione, R.
2017-08-01
Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949), 10.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.
Diffraction radiation from relativistic particles
International Nuclear Information System (INIS)
Potylitsyn, Alexander Petrovich; Ryazanov, Mikhail Ivanovich; Strikhanov, Mikhail Nikolaevich; Tishchenko, Alexey Alexandrovich
2010-01-01
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results. (orig.)
Diffraction radiation from relativistic particles
Potylitsyn, Alexander Petrovich; Strikhanov, Mikhail Nikolaevich; Tishchenko, Alexey Alexandrovich
2010-01-01
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results.
Restricted three-body problem in effective-field-theory models of gravity
Battista, Emmanuele; Esposito, Giampiero
2014-04-01
One of the outstanding problems of classical celestial mechanics was the restricted three-body problem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for example, in the Sun-Earth-Moon system. On the other hand, over the last decades, a systematic investigation of quantum corrections to the Newtonian potential has been carried out in the literature on quantum gravity. The present paper studies the effect of these tiny quantum corrections on the evaluation of equilibrium points. It is shown that, despite the extreme smallness of the corrections, there exists no choice of sign of these corrections for which all qualitative features of the restricted three-body problem in Newtonian theory remain unaffected. Moreover, first-order stability of equilibrium points is characterized by solving a pair of algebraic equations of fifth degree, where some coefficients depend on the Planck length. The coordinates of stable equilibrium points are slightly changed with respect to Newtonian theory, because the planetoid is no longer at equal distance from the two bodies of large mass. The effect is conceptually interesting but too small to be observed, at least for the restricted three-body problems available in the solar system.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems
International Nuclear Information System (INIS)
Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.
2011-01-01
In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.
Chaos and maps in relativistic rynamical systems
Directory of Open Access Journals (Sweden)
L. P. Horwitz
2000-01-01
Full Text Available The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.
New integrable problems in a rigid body dynamics with cubic integral in velocities
Elmandouh, A. A.
2018-03-01
We introduce a new family of the 2D integrable mechanical system possessing an additional integral of the third degree in velocities. This system contains 20 arbitrary parameters. We also clarify that the majority of the previous systems with a cubic integral can be reconstructed from it as a special version for certain values of those parameters. The applications of this system are extended to include the problem of motion of a particle and rigid body about its fixed point. We announce new integrable problems describing the motion of a particle in the plane, pseudosphere, and surfaces of variable curvature. We also present a new integrable problem in a rigid body dynamics and this problem generalizes some of the previous results for Sokolov-Tsiganov, Yehia, Stretensky, and Goriachev.
Cloud Service Solving N-Body Problem Based on Windows Azure Platform
Augustyn, Dariusz Rafał; Warchał, Łukasz
This paper shows how to use cloud computing to solve N-body problem. It presents an idea and implementation of cloud service based on Windows Azure Platform. Clients can access cloud service via Internet over HTTP protocol. They create computation tasks supplying simulation parameters such as number of steps, time step and XML file with body definitions (initial position, mass and velocity). Presented solution uses Barnes-Hut Algorithm (based on adaptive oct tree) to reduce computation complexity form N ×N to N logN. All body interactions are computed in parallel, on worker nodes in cloud.
A General T-Matrix Approach Applied to Two-Body and Three-Body Problems in Cold Atomic Gases
International Nuclear Information System (INIS)
Cui, X.
2012-01-01
We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D-3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix. (author)
The effects of cosmetic surgery on body image, self-esteem, and psychological problems.
von Soest, T; Kvalem, I L; Roald, H E; Skolleborg, K C
2009-10-01
This study aims to investigate whether cosmetic surgery has an effect on an individual's body image, general self-esteem, and psychological problems. Further tests were conducted to assess whether the extent of psychological problems before surgery influenced improvements in postoperative psychological outcomes. Questionnaire data from 155 female cosmetic surgery patients from a plastic surgery clinic were obtained before and approximately 6 months after surgery. The questionnaire consisted of measures on body image, self-esteem, and psychological problems. Pre- and postoperative values were compared. Pre- and postoperative measures were also compared with the data compiled from a representative sample of 838 Norwegian women, aged 22-55, with no cosmetic surgery experience. No differences in psychological problems between the presurgery patient and comparison samples were found, whereas differences in body image and self-esteem between the sample groups were reported in an earlier publication. Analyses further revealed an improvement in body image (satisfaction with own appearance) after surgery. A significant but rather small effect on self-esteem was also found, whereas the level of psychological problems did not change after surgery. Postoperative measures of appearance satisfaction, self-esteem, and psychological problems did not differ from values derived from the comparison sample. Finally, few psychological problems before surgery predicted a greater improvement in appearance satisfaction and self-esteem after surgery. The study provides evidence of improvement in satisfaction with own appearance after cosmetic surgery, a variable that is thought to play a central role in understanding the psychology of cosmetic surgery patients. The study also points to the factors that surgeons should be aware of, particularly the role of psychological problems, which could inhibit the positive effects of cosmetic surgery.
Relativistic theory of gravity
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1985-01-01
This work presents an unambiguous construction of the relativistic theory of gravity (RTG) in the framework of relativity and the geometrization principle. The gauge principle has been formulated, and the Lagrangian density of the gravitational field has thus been constructed. This theory explains the totality of the available experimental data on the solar system and predicts the existence of gravitational waves of the Faraday-Maxwell type. According to the RTG, the Universe is infinite and ''flat'', hence it follows that its matter density should be equal to its critical density. Therefore, an appreciable ''hidden mass'' exceeding the presently observed mass of the matter almost 40-fold should exist in the Universe in some form of the matter or other. In accordance with the RTG, a massive body having a finite density ceases to contract under gravitational forces within a finite interval of proper time. From the viewpoint of an external reference frame, the brightness of the body decreases exponentially (it is getting darker), but nothing extraordinary happens in this case because its density always remains finite and, for example, for a body with the mass of about 10 8 M 0 it is equal to 2 g/cm 3 . That is why it follows from the RTG that there could be no object whatsoever (black holes) in which gravitational collapse of matter develops to an infinite density. As has been shown, the presence of a cosmological term necessarily requires the introduction of a term with an explicit dependence on the Minkowski metrics. For the long-range gravitational forces the cosmological constant vanishes
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neut...
International Nuclear Information System (INIS)
Kopeikin, Sergei; Vlasov, Igor
2004-01-01
Post-Newtonian relativistic theory of astronomical reference frames based on Einstein's general theory of relativity was adopted by General Assembly of the International Astronomical Union in 2000. This theory is extended in the present paper by taking into account all relativistic effects caused by the presumable existence of a scalar field and parametrized by two parameters, β and γ, of the parametrized post-Newtonian (PPN) formalism. We use a general class of the scalar-tensor (Brans-Dicke type) theories of gravitation to work out PPN concepts of global and local reference frames for an astronomical N-body system. The global reference frame is a standard PPN coordinate system. A local reference frame is constructed in the vicinity of a weakly self-gravitating body (a sub-system of the bodies) that is a member of the astronomical N-body system. Such local inertial frame is required for unambiguous derivation of the equations of motion of the body in the field of other members of the N-body system and for construction of adequate algorithms for data analysis of various gravitational experiments conducted in ground-based laboratories and/or on board of spacecrafts in the solar system.We assume that the bodies comprising the N-body system have weak gravitational field and move slowly. At the same time we do not impose any specific limitations on the distribution of density, velocity and the equation of state of the body's matter. Scalar-tensor equations of the gravitational field are solved by making use of the post-Newtonian approximations so that the metric tensor and the scalar field are obtained as functions of the global and local coordinates. A correspondence between the local and global coordinate frames is found by making use of asymptotic expansion matching technique. This technique allows us to find a class of the post-Newtonian coordinate transformations between the frames as well as equations of translational motion of the origin of the local frame
An existence proof of a symmetric periodic orbit in the octahedral six-body problem
Cavalcanti, Anete Soares
2016-01-01
We present a proof of the existence of a periodic orbit for the Newtonian six-body problem with equal masses. This orbit has three double collisions each period and no multiple collisions. Our proof is based on the minimization of the Lagrangian action functional on a well chosen class of symmetric loops.
Marigliano, Michelle L.; Russo, Michele J.
2011-01-01
Creative movement is an ideal way to help young children develop critical-thinking and problem-solving skills. Most young children are, by nature, extremely physical. They delight in exploring the world with their bodies and expressing their ideas and feelings through movement. During creative movement experiences, children learn to think before…
Stability of the Moons Orbits in Solar System in the Restricted Three-Body Problem
Directory of Open Access Journals (Sweden)
Sergey V. Ershkov
2015-01-01
Full Text Available We consider the equations of motion of three-body problem in a Lagrange form (which means a consideration of relative motions of 3 bodies in regard to each other. Analyzing such a system of equations, we consider in detail the case of moon’s motion of negligible mass m3 around the 2nd of two giant-bodies m1, m2 (which are rotating around their common centre of masses on Kepler’s trajectories, the mass of which is assumed to be less than the mass of central body. Under assumptions of R3BP, we obtain the equations of motion which describe the relative mutual motion of the centre of mass of 2nd giant-body m2 (planet and the centre of mass of 3rd body (moon with additional effective mass ξ·m2 placed in that centre of mass ξ·m2+m3, where ξ is the dimensionless dynamical parameter. They should be rotating around their common centre of masses on Kepler’s elliptic orbits. For negligible effective mass ξ·m2+m3 it gives the equations of motion which should describe a quasi-elliptic orbit of 3rd body (moon around the 2nd body m2 (planet for most of the moons of the planets in Solar System.
Relativistic covariance of Ohm's law
Starke, R.; Schober, G. A. H.
2016-04-01
The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμ ν relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμ ν and the microscopic conductivity tensor σkℓ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.
Perceived body weight, eating and exercise problems of different groups of women.
Coker, Elise; Telfer, James; Abraham, Suzanne
2012-10-01
To compare prevalence of problems with body weight, eating and exercise (past or present) of female psychiatric inpatients with routine care, gynaecological and obstetric female outpatients, and eating disorder inpatients. One thousand and thirty-eight females aged 18-55 years from routine care (n=99), gynaecological (n=263) and obstetric (n=271) outpatient clinics, and eating disorder (n=223) and general psychiatric units (n=182) participated. Participants self-reported past or current problems with weight, eating and exercise using a short survey. A sub-sample of women completed the Eating and Exercise Examination (EEE) which includes the Quality of Life for Eating Disorders (QOL ED). The prevalence of self-reported problems controlling weight (52%), disordered eating and eating disorders (43%) for the psychiatric patients was significantly greater than for the routine care and gynaecological and obstetrics outpatients. The psychiatric group had a significantly higher mean body mass index (BMI) of 27.3 kg/m(2) (standard deviation (SD)=6.7) and prevalence of self-reported obesity (28%) than the other groups. Treatment of women with psychiatric problems should include assessment and concurrent attention to body weight, eating disorder and exercise problems in association with appropriate medical, psychiatric, psychological and medication treatment of their presenting disorder.
Reply to C. M. Will on the axially symmetric two-body problem in general relativity
International Nuclear Information System (INIS)
Cooperstock, F.I.; Lim, P.H.
1985-01-01
The recent paper by Will (1983) is considered which purports to demonstrate that the gravitational radiation which the authors had computed from their model two-body free-fall system is consistent with the so-called quadrupole formula. It is shown that in fact the system presented by Will is different from the authors and that the illegitimate application of the quadrupole formula to the authors system leads to a smaller flux than that which is correctly deduced using general relativity and a proper consideration of nonlinearities. It is demonstrated that a judicious choice of stress release is propagated through the bodies as a superposition of plane and spherical waves leading to pressure fluctuations to the order in question. This underlines the essential distinction between the authors problem and the Will problem. Various aspects of the problem are also discussed. 25 references
Introduction to Hamiltonian dynamical systems and the N-body problem
Meyer, Kenneth R
2017-01-01
This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary exa...
Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field
Yang, C. J.; Grasso, M.; Moghrabi, K.; van Kolck, U.
2017-05-01
Phenomenological effective interactions like Skyrme forces are currently used in mean-field calculations in nuclear physics. Mean-field models have strong analogies with the first order of the perturbative many-body problem and the currently used effective interactions are adjusted at the mean-field level. In this work, we analyze the renormalizability of the nuclear many-body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters can renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. To achieve renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.
Realizing all reduced syzygy sequences in the planar three-body problem
International Nuclear Information System (INIS)
Moeckel, Richard; Montgomery, Richard
2015-01-01
The configuration space of the planar three-body problem, reduced by rotations and with collisions excluded, has a rich topology which supports a large set of free homotopy classes. These classes have a simple description in terms of syzygy (or eclipse) sequences. Each homotopy class corresponds to a unique ‘reduced’ syzygy sequence. We prove that each reduced syzygy sequence is realized by a periodic solution of the rotation-reduced Newtonian planar three-body problem. The realizing solutions have small, nonzero angular momentum, repeatedly come very close to triple collision, and have lots of ‘stutters’—repeated syzygies of the same type, which cancel out up to homotopy. The heart of the proof stems from the work by one of us on symbolic dynamics arising out of the central configurations after the triple collision is blown up using McGehee's method. We end with a list of open problems. (paper)
Vereshchagin, Gregory V.; Aksenov, Alexey G.
2017-02-01
Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.
Solving the Quantum Many-Body Problem via Correlations Measured with a Momentum Microscope
Hodgman, S. S.; Khakimov, R. I.; Lewis-Swan, R. J.; Truscott, A. G.; Kheruntsyan, K. V.
2017-06-01
In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s -wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system—the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.
Ni, Xiao-Ting; Wu, Xin
2014-10-01
The time-transformed leapfrog scheme of Mikkola & Aarseth was specifically designed for a second-order differential equation with two individually separable forms of positions and velocities. It can have good numerical accuracy for extremely close two-body encounters in gravitating few-body systems with large mass ratios, but the non-time-transformed one does not work well. Following this idea, we develop a new explicit symplectic integrator with an adaptive time step that can be applied to a time-dependent Hamiltonian. Our method relies on a time step function having two distinct but equivalent forms and on the inclusion of two pairs of new canonical conjugate variables in the extended phase space. In addition, the Hamiltonian must be modified to be a new time-transformed Hamiltonian with three integrable parts. When this method is applied to the elliptic restricted three-body problem, its numerical precision is explicitly higher by several orders of magnitude than the nonadaptive one's, and its numerical stability is also better. In particular, it can eliminate the overestimation of Lyapunov exponents and suppress the spurious rapid growth of fast Lyapunov indicators for high-eccentricity orbits of a massless third body. The present technique will be useful for conservative systems including N-body problems in the Jacobian coordinates in the the field of solar system dynamics, and nonconservative systems such as a time-dependent barred galaxy model in a rotating coordinate system.
Mosquera, Martín A.
2017-10-01
Provided the initial state, the Runge-Gross theorem establishes that the time-dependent (TD) external potential of a system of non-relativistic electrons determines uniquely their TD electronic density, and vice versa (up to a constant in the potential). This theorem requires the TD external potential and density to be Taylor-expandable around the initial time of the propagation. This paper presents an extension without this restriction. Given the initial state of the system and evolution of the density due to some TD scalar potential, we show that a perturbative (not necessarily weak) TD potential that induces a non-zero divergence of the external force-density, inside a small spatial subset and immediately after the initial propagation time, will cause a change in the density within that subset, implying that the TD potential uniquely determines the TD density. In this proof, we assume unitary evolution of wavefunctions and first-order differentiability (which does not imply analyticity) in time of the internal and external force-densities, electronic density, current density, and their spatial derivatives over the small spatial subset and short time interval.
Relativistic Length Agony Continued
Redzic, D. V.
2014-06-01
We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redzic 2008b), we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the 'pole in a barn' paradox.
Relativistic GLONASS and geodesy
Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.
2016-12-01
GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.
Weakly relativistic plasma expansion
Energy Technology Data Exchange (ETDEWEB)
Fermous, Rachid, E-mail: rfermous@usthb.dz; Djebli, Mourad, E-mail: mdjebli@usthb.dz [Theoretical Physics Laboratory, Faculty of Physics, USTHB, B.P. 32 Bab-Ezzouar, 16079 Algiers (Algeria)
2015-04-15
Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.
Yaparova, N.
2017-10-01
We consider the problem of heating a cylindrical body with an internal thermal source when the main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. We can control the surface temperature and the heat flow from the surface inside the cylinder, but it is impossible to measure the temperature on axis and the initial temperature in the entire body. This problem is associated with the temperature measurement challenge and appears in non-destructive testing, in thermal monitoring of heat treatment and technical diagnostics of operating equipment. The mathematical model of heating is represented as nonlinear parabolic PDE with the unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given and it is required to calculate the temperature values at the internal points of the body. To solve this problem, we propose the numerical method based on using of finite-difference equations and a regularization technique. The computational scheme involves solving the problem at each spatial step. As a result, we obtain the temperature function at each internal point of the cylinder beginning from the surface down to the axis. The application of the regularization technique ensures the stability of the scheme and allows us to significantly simplify the computational procedure. We investigate the stability of the computational scheme and prove the dependence of the stability on the discretization steps and error level of the measurement results. To obtain the experimental temperature error estimates, computational experiments were carried out. The computational results are consistent with the theoretical error estimates and confirm the efficiency and reliability of the proposed computational scheme.
Properties of compressible elastica from relativistic analogy.
Oshri, Oz; Diamant, Haim
2016-01-21
Kirchhoff's kinetic analogy relates the deformation of an incompressible elastic rod to the classical dynamics of rigid body rotation. We extend the analogy to compressible filaments and find that the extension is similar to the introduction of relativistic effects into the dynamical system. The extended analogy reveals a surprising symmetry in the deformations of compressible elastica. In addition, we use known results for the buckling of compressible elastica to derive the explicit solution for the motion of a relativistic nonlinear pendulum. We discuss cases where the extended Kirchhoff analogy may be useful for the study of other soft matter systems.
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Kaplan, George
2011-01-01
This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic r
Equations of motion in relativistic gravity
Lämmerzahl, Claus; Schutz, Bernard
2015-01-01
The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...
Low-Thrust Orbital Transfers in the Two-Body Problem
Directory of Open Access Journals (Sweden)
A. A. Sukhanov
2012-01-01
Full Text Available Low-thrust transfers between given orbits within the two-body problem are considered; the thrust is assumed power limited. A simple method for obtaining the transfer trajectories based on the linearization of the motion near reference orbits is suggested. Required calculation accuracy can be reached by means of use of a proper number of the reference orbits. The method may be used in the case of a large number of the orbits around the attracting center; no averaging is necessary in this case. The suggested method also is applicable to the cases of partly given final orbit and if there are constraints on the thrust direction. The method gives an optimal solution to the linearized problem which is not optimal for the original nonlinear problem; the difference between the optimal solutions to the original and linearized problems is estimated using a numerical example. Also examples illustrating the method capacities are given.
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2009-01-01
contact response. In this paper, we present a new approach to contact force determination. We reformulate the contact force problem as a nonlinear root search problem, using a Fischer function. We solve this problem using a generalized Newton method. Our new Fischer - Newton method shows improved......n interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating each other. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. The result is visual artifacts such as viscous or damped...... qualities for specific configurations where the most widespread alternative, the Projected Gauss-Seidel method, fails. Experiments show superior convergence properties of the exact Fischer - Newton method....
Dissipative relativistic hydrodynamics
International Nuclear Information System (INIS)
Imshennik, V.S.; Morozov, Yu.I.
1989-01-01
Using the comoving reference frame in the general non-inertial case, the relativistic hydrodynamics equations are derived with an account for dissipative effects in the matter. From the entropy production equation, the exact from for the dissipative tensor components is obtained. As a result, the closed system of equations of dissipative relativistic hydrodynamics is obtained in the comoving reference frame as a relativistic generalization of the known Navier-Stokes equations for Lagrange coordinates. Equations of relativistic hydrodynamics with account for dissipative effects in the matter are derived using the assocoated reference system in general non-inertial case. True form of the dissipative tensor components is obtained from entropy production equation. Closed system of equations for dissipative relativistic hydrodynamics is obtained as a result in the assocoated reference system (ARS) - relativistic generalization of well-known Navier-Stokes equations for Lagrange coordinates. Equation system, obtained in this paper for ARS, may be effectively used in numerical models of explosive processes with 10 51 erg energy releases which are characteristic for flashes of supernovae, if white dwarf type compact target suggested as presupernova
The magnetosphere in relativistic physics
International Nuclear Information System (INIS)
Zapffe, C.A.
1982-01-01
The present paper takes off from the author's earlier epistemological analysis and criticism of the Special Theory of Relativity, identifies the problem as lying in Einstein's choice of the inertial frame of Newtonian mechanics rather than the electromagnetic frame of the locally embedding Maxwellian field when discussing electrodynamics, then proposes this Maxwellian field of the magnetosphere as the specific rest frame proper to all experimentation of optical or electromagnetic sort conducted within its bounds. The result is shown to remove all paradoxes from relativistic physics. (author)
Relativistic theory of tidal Love numbers
International Nuclear Information System (INIS)
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
The quantum N-body problem in the mean-field and semiclassical regime.
Golse, François
2018-04-28
The present work discusses the mean-field limit for the quantum N -body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).
A frictional contact problem with damage and adhesion for an electro elastic-viscoplastic body
Directory of Open Access Journals (Sweden)
Adel Aissaoui
2014-01-01
Full Text Available We consider a quasistatic frictional contact problem for an electro elastic-viscopalastic body with damage and adhestion. The contact is modelled with normal compliance. The adhesion of the contact surfaces is taken into account and modelled by a surface variable. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field, the damage field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, differential equations and fixed point.
Numerical Solution of Problem for Non-Stationary Heat Conduction in Multi-Layer Bodies
Directory of Open Access Journals (Sweden)
R. I. Еsman
2007-01-01
Full Text Available A mathematical model for non-stationary heat conduction of multi-layer bodies has been developed. Dirac’s δ-function is used to take into account phase and chemical transformations in one of the wall layers. While formulating a problem non-linear heat conduction equations have been used with due account of dependence of thermal and physical characteristics on temperature. Solution of the problem is realized with the help of methods of a numerical experiment and computer modeling.
Transient effects in a relativistic quantum system
Energy Technology Data Exchange (ETDEWEB)
Sadurni, E.; Moshinsky, M. [IFUNAM, Departamento de Fisica Teorica, A.P. 20-364, 01000 Mexico D.F. (Mexico)]. e-mail: sadurni@fisica.unam.mx
2007-12-15
The spectral decomposition of propagators is useful in the study of dynamical problems in the Schroedinger picture. However, relativistic problems exhibit complicated spectra containing positive and negative energies. In this work we write an appropriate spectral decomposition for the propagator of the Dirac oscillator. With such propagator we study the dynamical problem of sudden frequency change related to processes in which the isospin projection of the particle is modified. (Author)
Series solutions of the Sitnikov restricted N+1-body problem: elliptic case
Shahbaz Ullah, M.; Majda, B.; Ullah, M. Zafar; Shahnawaz Ullah, M.
2015-06-01
Following Giacaglia (1967), in Sect. 2 we have developed equation of motion of the Sitnikov restricted N+1-body problem in elliptic case. We assumed that the primaries are at the vertices of a regular N-gon so the distances of the primaries from center of mass are time depending. In Sect. 3 we have linearized the equation of motion to obtain the Hill's type equation and then find the approximate solution. In Sects. 4 and 5 the series solutions of the Sitnikov restricted N+1-body problem have been developed by the method of Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the two series solutions have been compared graphically by putting N=2, 3 and 4 for different eccentricity.
Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets
International Nuclear Information System (INIS)
Aquilanti, Vincenzo; Tonzani, Stefano
2004-01-01
Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known 'symmetric' and 'asymmetric' parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems
Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem
Minesaki, Yukitaka
2018-04-01
We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.
Penkov, V. B.; Levina, L. V.; Novikova, O. S.; Shulmin, A. S.
2018-03-01
Herein we propose a methodology for structuring a full parametric analytical solution to problems featuring elastostatic media based on state-of-the-art computing facilities that support computerized algebra. The methodology includes: direct and reverse application of P-Theorem; methods of accounting for physical properties of media; accounting for variable geometrical parameters of bodies, parameters of boundary states, independent parameters of volume forces, and remote stress factors. An efficient tool to address the task is the sustainable method of boundary states originally designed for the purposes of computerized algebra and based on the isomorphism of Hilbertian spaces of internal states and boundary states of bodies. We performed full parametric solutions of basic problems featuring a ball with a nonconcentric spherical cavity, a ball with a near-surface flaw, and an unlimited medium with two spherical cavities.
Lagrangian solutions to the three-body problem with forces r sup(-p) (p integer)
International Nuclear Information System (INIS)
Azeredo Campos, R. de; Ferreira, P.L.
1979-08-01
The exact solutions to the three-body problem in Celestial Mechanics, due to Lagrange (triangular solutions) and Euler (collinear solutions), are generalized to the case of forces r sup( - p) (p being an integer). The stability of the system is also investigated in a local sense (small variations about steady motion) for triangular and collinear solutions and conditions restricting the values of p for which there are stable oscillatory modes of vibration are obtained. Furthermore, for the solutions under consideration, Bohr or Bohr-Sommerfeld quantization is performed and compared, for some cases of interest, with the WKB approximation, derived from an Hamiltonian of the system obtained by reducing it to a one-body problem under the action of a central force at the system's center of mass. (Author) [pt
Dynamic contact problem with adhesion and damage between thermo-electro-elasto-viscoplastic bodies
Hadj ammar, Tedjani; Saïdi, Abdelkader; Azeb Ahmed, Abdelaziz
2017-05-01
We study of a dynamic contact problem between two thermo-electro-elasto-viscoplastic bodies with damage and adhesion. The contact is frictionless and is modeled with normal compliance condition. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.
Action minimizers under topological constraints in the planar equal-mass four-body problem
Yan, Duokui
2018-04-01
It is shown that in the planar equal-mass four-body problem, there exist two sets of action minimizers connecting two planar boundary configurations with fixed symmetry axes and specific order constraints: a double isosceles configuration and an isosceles trapezoid configuration, while order constraints are introduced on the boundary configurations. By applying the level estimate method, these minimizers are shown to be collision-free and they can be extended to two new sets of periodic or quasi-periodic orbits.
Construction of an exactly solvable model of the many-body problem
Energy Technology Data Exchange (ETDEWEB)
Zettili, N. [King Fahd Univ. of Petrolium and Minerals, Dhahran (Saudi Arabia). Dept. of Phys.]|[Institut de Physique, Universite de Blida, Blida (Algeria); Bouayad, N. [Institut de Physique, Universite de Blida, Blida (Algeria)
1996-11-11
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model`s Hamiltonian by means of vector operators that are the generators of an SO(2,1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum. (orig.).
A Riemann-Hilbert problem for the shape of a body dissolving in flow
Moore, Nick; Huang, Jinzi Mac; Ristroph, Leif; Applied Math Lab, Courant Institute Team
2014-11-01
As is familiar to anyone who has stirred sugar into coffee, fluid flow can enhance the dissolution of solid material. This effect plays an important role in contexts as varied as landscape formation and drug delivery within the body, but such processes are not well understood due to the interaction between evolving surfaces and flow. By performing experiments with hard-candy bodies dissolving in fast flowing water, we find that different initial geometries converge to the same final shape as they vanish. By modeling both the separated flow around the body and the molecular diffusion of material within the boundary layer, we obtain a Riemann-Hilbert problem for the terminal shape. The solution predicts a front surface of nearly constant curvature, in agreement with experimental measurements. Once formed, this geometry dissolves self-similarly in time and vanishes with a power-law predicted by the model.
Coulomb effects in deuteron stripping reactions as a three-body problem
International Nuclear Information System (INIS)
Osman, A.
1981-08-01
Deuteron stripping nuclear reactions are reconsidered as a three-body problem. The Coulomb effects between the proton and the target nucleus are investigated. The mathematical formalism introduces three-body integral equations which can be exactly calculated for such simple models. These coupled integral equations suitably include the Coulomb effects due to replusive or attractive Coulomb potential. Numerical calculations of the differential cross-sections of the reactions 28 Si(d,p) 29 Si and 40 Ca(d,p) 41 Ca are carried out showing the importance of the Coulomb effects. The angular distributions of these reactions are theoretically calculated and fitted to the experimental data. From this fitting, reasonable spectroscopic factors are obtained. Inclusion of Coulomb force in the three-body model are found to improve the results by a percentage of about 6.826%. (author)
Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems
Jia, C. J.; Wang, Y.; Mendl, C. B.; Moritz, B.; Devereaux, T. P.
2018-03-01
We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
Connecting orbits and invariant manifolds in the spatial restricted three-body problem
Gómez, G.; Koon, W. S.; Lo, M. W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.
2004-09-01
The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material between primary bodies for separate three-body systems. These tubes can be used to construct new spacecraft trajectories, such as a 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. This work extends the results to the three-dimensional case. Besides providing a full description of different kinds of libration motions in a large vicinity of these points, this paper numerically demonstrates the existence of heteroclinic connections between pairs of libration orbits, one around the libration point L1 and the other around L2. Since these connections are asymptotic orbits, no manoeuvre is needed to perform the transfer from one libration point orbit to the other. A knowledge of these orbits can be very useful in the design of missions such as the Genesis Discovery Mission, and may provide the backbone for other interesting orbits in the future.
Detector issues for relativistic heavy ion experimentation
International Nuclear Information System (INIS)
Gordon, H.
1986-04-01
Several aspects of experiments using relativistic heavy ion beams are discussed. The problems that the current generation of light ion experiments would face in using gold beams are noted. A brief review of colliding beam experiments for heavy ion beams is contrasted with requirements for SSC detectors. 11 refs., 13 figs
RELATIVISTIC HEAVY ION PHYSICS: A THEORETICAL OVERVIEW.
Energy Technology Data Exchange (ETDEWEB)
KHARZEEV,D.
2004-03-28
This is a mini-review of recent theoretical work in the field of relativistic heavy ion physics. The following topics are discussed initial conditions and the Color Glass Condensate; approach to thermalization and the hydrodynamic evolution; hard probes and the properties of the Quark-Gluon Plasma. Some of the unsolved problems and potentially promising directions for future research are listed as well.
Stars with relativistic speeds in the Hills scenario
Dremova, G. N.; Dremov, V. V.; Tutukov, A. V.
2017-07-01
The dynamical capture of a binary system consisting of a supermassive black hole (SMBH) and an ordinary star in the gravitational field of a central (more massive) SMBH is considered in the three-body problem in the framework of a modified Hills scenario. The results of numerical simulations predict the existence of objects whose spatial speeds are comparable to the speed of light. The conditions for and constraints imposed on the ejection speeds realized in a classical scenario and the modified Hills scenario are analyzed. The star is modeled using an N-body approach, making it possible to treat it as a structured object, enabling estimation of the probability that the object survives when it is ejected with relativistic speed as a function of the mass of the star, the masses of both SMBHs, and the pericenter distance. It is possible that the modern kinematic classification for stars with anomalously high spatial velocities will be augmented with a new class—stars with relativistic speeds.
Koenig, Linda J.; Wasserman, Erika L.
1995-01-01
Explored whether the links of depression, eating problems, and body image that apply to women also apply to men. A study of 234 male and female college students showed depression was higher in those with negative body image for both men and women. Depression accounted for significant variability in eating problems only in women. (GR)
Time-frequency analysis of the restricted three-body problem: transport and resonance transitions
International Nuclear Information System (INIS)
Vela-Arevalo, Luz V; Marsden, Jerrold E
2004-01-01
A method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space
Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.; Tang, Qi
2017-08-01
A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added-mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.
Relativistic and non-relativistic studies of nuclear matter
Banerjee, MK; Tjon, JA
2002-01-01
We point out that the differences between the results of the non-relativistic lowest order Brueckner theory (LOBT) and the relativistic Dirac-Brueckner analysis predominantly arise from two sources. Besides effects from a nucleon mass modification M* in nuclear medium we have in a relativistic
Non-singular orbital elements for special perturbations in the two-body problem
Baù, Giulio; Bombardelli, Claudio; Peláez, Jesús; Lorenzini, Enrico
2015-12-01
Seven spatial elements and a time element are proposed as the state variables of a new special perturbation method for the two-body problem. The new elements hold for zero eccentricity and inclination and for negative values of the total energy. They are developed by combining a spatial transformation into projective coordinates (as in the Burdet-Ferrándiz regularization) with a time transformation in which the exponent of the orbital radius is equal to one instead of two (as commonly done in the literature). By following this approach, we discover a new linearization of the two-body problem, from which the orbital elements can be generated by the variation of parameters method. The geometrical significance of the spatial quantities is revealed by a new intermediate frame which differs from a local vertical local horizontal frame by one rotation in the instantaneous orbital plane. Four elements parametrize the attitude in space of this frame, which in turn defines the orientation of the orbital plane and fixes the departure direction for the longitude of the propagated body. The remaining three elements determine the motion along the radial unit vector and the orbital longitude. The performance of the method, tested using a series of benchmark orbit propagation scenarios, is extremely good when compared to several regularized formulations, some of which have been modified and improved here for the first time.
The Coriolis asymmetry in the classical restricted 3-body problem and the Jacobian integral
Innanen, K. A.
1980-01-01
Certain aspects of the restricted three-body problem are reexamined and several new results are derived. A more complete analytical derivation of the formulae used in an earlier paper (Innanen, 1979) is supplied, together with a generalization to include inclined orbits. The important results are summarized in equations (23), (24) and (30) and in Fig. 4. It is shown, in the limit, that the condition of zero relative acceleration between the particle bound to one of the finite masses supplies a stronger restriction on the Jacobi integral than does the zero velocity criterion, for direct orbits. Stable retrograde orbits populate the entire space of the zero velocity "Fig. 8" envelopes of the 3-body problem (Fig. 5). The behavior of the galaxy IC 10 (Cohen, 1979; Huchtmeir, 1979) may be explained if there is a ring or disk of H I in retrograde motion about the main body of that galaxy. The plane of that ring (disk) defines the galactic orbit plane of IC 10, as in the case of the Sculptor galaxy (Innanen and Papp, 1979). The equation of motion for small oscillations of the particle perpendicular to its orbit plane is briefly mentioned, as are several other possible applications.
Relativistic quantum mechanics
International Nuclear Information System (INIS)
Wolschin, Georg
2016-01-01
This course is a concise introduction to the foundations of relativistic quantum mechanics. It is concipated as one-semester, two-hour arrangement for bachelor and master students; some of the advanced parts can be also of interest or promovings. Primary adressates are studyings from the fourth semester upwards, which have already worked out the basic course of quantum mechanics and want beyond to get to know relativistic wave equations. In the introduction I draw first the development, the result of which was the establishment of Lorentz-invariant relativistic wave equations by Schroedinger, Klein, Gordon, and Dirac. After a chapter about the connection to the Galilei-invariant nonrelativistic quantum mechanics follow the presentations of the Klein-Gordon and Dirac and the study of the Dirac theory in view of invariances concerning parity, charge conjugation, ant time-reversal transformation. A short introduction to the principles of quantum field theory, especially quantum electrodynamics, follows.
Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.
2018-02-01
As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi
Global solutions to the electrodynamic two-body problem on a straight line
Bauer, G.; Deckert, D.-A.; Dürr, D.; Hinrichs, G.
2017-06-01
The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260:6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence—a result that had been obtained by Bauer (Ein Existenzsatz für die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, München, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.
BOOK REVIEW: Relativistic Figures of Equilibrium
Mars, M.
2009-08-01
Compact fluid bodies in equilibrium under its own gravitational field are abundant in the Universe and a proper treatment of them can only be carried out using the full theory of General Relativity. The problem is of enormous complexity as it involves two very different regimes, namely the interior and the exterior of the fluid, coupled through the surface of the body. This problem is very challenging both from a purely theoretical point of view, as well as regarding the obtaining of realistic models and the description of their physical properties. It is therefore an excellent piece of news that the book 'Relativistic Figures of Equilibrium' by R Meinel, M Ansorg, A Kleinwächter, G Neugebauer and D Petroff has been recently published. This book approaches the topic in depth and its contents will be of interest to a wide range of scientists working on gravitation, including theoreticians in general relativity, mathematical physicists, astrophysicists and numerical relativists. This is an advanced book that intends to present some of the present-day results on this topic. The most basic results are presented rather succinctly, and without going into the details, of their derivations. Although primarily not intended to serve as a textbook, the presentation is nevertheless self-contained and can therefore be of interest both for experts on the field as well as for anybody wishing to learn more about rotating self-gravitating compact bodies in equilibrium. It should be remarked, however, that this book makes a rather strong selection of topics and concentrates fundamentally on presenting the main results obtained by the authors during their research in this field. The book starts with a chapter where the fundamental aspects of rotating fluids in equilibrium, including its thermodynamic properties, are summarized. Of particular interest are the so-called mass-shedding limit, which is the limit where the body is rotating so fast that it is on the verge of starting
Jasper, Stefanie; Rennekampff, Hans-Oliver; de Zwaan, Martina
2013-11-01
Due to progress in burn treatment, more patients even with severe burn injuries survive. Despite this positive development, however, there are still negative somatic and mental consequences. These include the life-long care of scars and pain. In addition, posttraumatic-stress disorder and depression are common consequences. Also distress due to disfigurement and body image problems have to be considered, since this is likely to result in social withdrawal, low self-esteem, and reduction of quality of life. Overall, the impact of mental strain on burn victims is quite high. Therefore, psychotherapeutic treatment approaches should be integrated into the care of patients with burns. This might be helpful for both coping and compliance with long-term treatment. This paper provides a review of the mental co-morbidity of burn victims and of psychotherapeutic treatment approaches focusing on changes in body image and the respective social consequences. © Georg Thieme Verlag KG Stuttgart · New York.
The inverse problem of brain energetics: ketone bodies as alternative substrates
Energy Technology Data Exchange (ETDEWEB)
Calvetti, D; Occhipinti, R [Case Western Reserve University, Department of Mathematics, 10900 Euclid Avenue, Cleveland, OH 44106 (United States); Somersalo, E [Helsinki University of Technology, Institute of Mathematics, P. O. Box 1100, FIN-02015 HUT (Finland)], E-mail: daniela.calvetti@case.edu, E-mail: rossana.occhipinti@case.edu, E-mail: erkki.somersalo@tkk.fi
2008-07-15
Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing.
Highly eccentric hip-hop solutions of the 2 N-body problem
Barrabés, Esther; Cors, Josep M.; Pinyol, Conxita; Soler, Jaume
2010-02-01
We show the existence of families of hip-hop solutions in the equal-mass 2 N-body problem which are close to highly eccentric planar elliptic homographic motions of 2 N bodies plus small perpendicular non-harmonic oscillations. By introducing a parameter ɛ, the homographic motion and the small amplitude oscillations can be uncoupled into a purely Keplerian homographic motion of fixed period and a vertical oscillation described by a Hill type equation. Small changes in the eccentricity induce large variations in the period of the perpendicular oscillation and give rise, via a Bolzano argument, to resonant periodic solutions of the uncoupled system in a rotating frame. For small ɛ≠0, the topological transversality persists and Brouwer’s fixed point theorem shows the existence of this kind of solutions in the full system.
CSIR Research Space (South Africa)
Bogaers, Alfred EJ
2016-09-01
Full Text Available -surface flow problem with an advancing wave front and a solid-body contact problem. 2 Partitioned FSI Fluid-structure interactions can be defined as a two-field coupled problem, involving a fluid domain Ωf and a solid domain Ωs sharing a common interface ΓFSI...
Basic Problems of a Microscopic Theory of a Many Body Quantum System
Jain, Y. S.
2002-01-01
Basic problems of a microscopic theory of many body quantum systems and different aspects of a new approach which can help in solving them are discussed in detail. To this effect we make a critical study of the wave mechanics of two hard core quantum particles and discover its several untouched aspects, viz.: (i) the useful details of \\psi_k(r) (representing the relative motion of two particles), (ii) the expectation value of hard core (HC) repulsion (), (iii) the inconsistency of the stateme...
On the Coplanar Integrable Case of the Twice-Averaged Hill Problem with Central Body Oblateness
Vashkov'yak, M. A.
2018-01-01
The twice-averaged Hill problem with the oblateness of the central planet is considered in the case where its equatorial plane coincides with the plane of its orbital motion relative to the perturbing body. A qualitative study of this so-called coplanar integrable case was begun by Y. Kozai in 1963 and continued by M.L. Lidov and M.V. Yarskaya in 1974. However, no rigorous analytical solution of the problem can be obtained due to the complexity of the integrals. In this paper we obtain some quantitative evolution characteristics and propose an approximate constructive-analytical solution of the evolution system in the form of explicit time dependences of satellite orbit elements. The methodical accuracy has been estimated for several orbits of artificial lunar satellites by comparison with the numerical solution of the evolution system.
Shape space figure-8 solution of three body problem with two equal masses
Yu, Guowei
2017-06-01
In a preprint by Montgomery (https://people.ucsc.edu/~rmont/Nbdy.html), the author attempted to prove the existence of a shape space figure-8 solution of the Newtonian three body problem with two equal masses (it looks like a figure 8 in the shape space, which is different from the famous figure-8 solution with three equal masses (Chenciner and Montgomery 2000 Ann. Math. 152 881-901)). Unfortunately there is an error in the proof and the problem is still open. Consider the α-homogeneous Newton-type potential, 1/rα, using action minimization method, we prove the existence of this solution, for α \\in (1, 2) ; for α=1 (the Newtonian potential), an extra condition is required, which unfortunately seems hard to verify at this moment.
Tails and bridges in the parabolic restricted three-body problem
Barrabés, Esther; Cors, Josep M.; Garcia-Taberner, Laura; Ollé, Mercè
2017-12-01
After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the so-called parabolic restricted three-body problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we show that the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.
Relativistic treatment of mesonic contributions to quasielastic (e,e')
International Nuclear Information System (INIS)
Blunden, P.G.; Butler, M.N.
1988-03-01
Meson exchange currents play an important role in the description of observables in electron scattering. The authors use a relativistic model with pseudovector pion coupling to study the exchange current contributions, with emphasis on quasielastic kinematics. Starting with the Lagrangian for nucleons interacting with a scalar and vector mason along with pseudovector coupling to pions, they derive the one and two-body electromagnetic currents. They then calculate the longitudinal and transverse pieces of the quasielastic cross section for various nuclei and kinematics. The effects of meson exchange currents are found to be much more important in a relativistic model than in a non-relativistic one
International Nuclear Information System (INIS)
Safronov, A.N.
2007-01-01
Full text: The pion-nucleon dynamics is one of the most fundamental problems in nuclear and particle physics. It is now widely believed that QCD is fundamental theory of strong interactions. On this basis all hadron-hadron interactions are completely determined by the underlying quark-gluon dynamics. However, due to the formidable mathematical problems raised by the non-perturbative character of QCD at low and intermediate energies, we are still far from a quantitative understanding hadron-hadron interactions from this point of view. Recently the relativistic approaches to constructing effective interaction operators between strongly interacting composite particles has been proposed on the basis of analytic S-matrix theory and methods for solving the inverse quantum scattering problem. The kernel of Marchenko equation in theory of inverse scattering problem can be expressed in terms of the discontinuity of the partial wave amplitude on dynamic cut in the complex s=k 2 plane, k being the relative momentum of colliding particles. The discontinuities of partial-wave amplitudes are determined by model-independent quantities (renormalized vertex constants and amplitudes of sub-processes involving on-mass-shell particles off physical region) and can be calculated by methods of relativistic quantum field theory within various dynamical approaches. In particular, effective field theory can be used to calculate the discontinuities across dynamical cuts closest to physical region. In present work a new manifestly Poincare-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. With the help of N/D-equations it was earlier shown that solution of a scattering problem in case of nonzero angular momentum does not exist for arbitrary discontinuity of partial-wave amplitude. The method is elaborated allowing to determine contributions of
Slices of theoretical astrophysics: planetary dynamics and relativistic explosions
Pan, Margaret Whei-Jie
This thesis presents studies in two distinct areas of theoretical astrophysics: dynamics of planetary systems and relativistic fluid flows from shocks emerging from stellar envelopes. The first pertains to the early solar system, planet formation, and extrasolar planets; the second is related to extreme explosions like gamma-ray bursts and supernovae.We present two investigations of the dynamics and population evolution of small solar system bodies. First, we explore the dynamics of mean-motion resonances for a test particle moving in a highly eccentric long-period orbit in the restricted circular planar three-body problem --- a scenario relevant to the scattered Kuiper belt and the formation of the Oort cloud. We find an infinite number of analogues to the Lagrange points; a simple explanation for the presence and absence of asymmetric librations in particular mean-motion resonances; and a criterion for the onset of chaotic motion at large semimajor axes.Second, we study the size distribution of Kuiper belt objects (KBOs), which is observed to be a broken power law. We apply a simple mass conservation argument to the KBO collisional cascade to get the power-law slope for KBOs below the break; our result agrees well with observations if we assume KBOs are held together by self-gravity rather than material strength. We also explain the location and time evolution of the break in the size distribution.We also present investigations of the flow which results when a relativistic shock propagates through and then breaks out of a stellar envelope with a polytropic density profile. This work informs predictions of the speed of and energy carried by the relativistic ejecta in supernovae and perhaps in gamma-ray bursts. We find the asymptotic solution for the flow as the shock reaches the star's edge and find a new self-similar solution for flow of hot fluid after the shock breakout. Since the post-breakout flow acclerates by converting its thermal energy into bulk kinetic
Solving the three-body Coulomb breakup problem using exterior complex scaling
Energy Technology Data Exchange (ETDEWEB)
McCurdy, C.W.; Baertschy, M.; Rescigno, T.N.
2004-05-17
Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a ''reduction to computation'' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations, and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wave function can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.
Relativistic configuration interaction approach
Indian Academy of Sciences (India)
(and requirement for) ab-initio calculation of electronic structure providing a high level of reliability and accuracy in accounting for both relativistic and correlation effects associated with these properties has gained importance. In this paper, we will compute one of the P, T-odd interaction constants, the so-called Wd, which is.
Relativistic length agony continued
Directory of Open Access Journals (Sweden)
Redžić D.V.
2014-01-01
Full Text Available We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redžić 2008b, we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the ‘pole in a barn’ paradox. [Projekat Ministarstva nauke Republike Srbije, br. 171028
Relativistic Coulomb excitation
International Nuclear Information System (INIS)
Winther, A.; Alder, K.
1979-01-01
Coulomb excitation of both target and projectile in relativistic heavy ion collisions is evaluated including the lowest order correction for the deviation from a straight line trajectory. Explicit results for differential and total cross sections are given in the form of tables and figures. (Auth.)
International Nuclear Information System (INIS)
Mrowczynski, S.
1989-01-01
The physics of relativistic elementary atoms,i.e. of Coulomb bound states of elementary particles, like positronium, pionium or an atom of μ + π - , is presented. The atom lifetimes and processes, in which the atoms are produced, are discussed. The interaction of the atoms with matter is also described. A simple derivation of most results is given. 33 refs. (author)
Relativistic effects on plasma expansion
Energy Technology Data Exchange (ETDEWEB)
Benkhelifa, El-Amine; Djebli, Mourad, E-mail: mdjebli@usthb.dz [USTHB, Faculty of Physics, Theoretical Physics Laboratory, B.P. 32 Bab-Ezzouar, 16079 Algiers (Algeria)
2014-07-15
The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.
Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.
2018-01-01
Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.
Gauge fields in the separation of rotations and internal motions in the n-body problem
International Nuclear Information System (INIS)
Littlejohn, R.G.; Reinsch, M.
1997-01-01
The problem of separating rotations from internal motions in systems such as macroscopic flexible bodies, atoms, molecules, nuclei, and solar systems is an old one, with many applications in physics, chemistry, and engineering. A new element, however, which has not been appreciated until fairly recently, is the existence of certain gauge fields on the reduced configuration space for such systems. These (non-Abelian) gauge fields arise in the open-quotes falling catclose quotes problem, in which changes in shape induce changes in external orientation; but they also have a dynamical significance, and enter as gauge potentials in the Lagrangian or Hamiltonian describing the internal or reduced dynamics. Physically these gauge fields represent Coriolis effects. This review concentrates on the case of nonrelativistic, n-body systems not subject to external torques, and develops the gauge theory of rotations and internal motions in detail. Both classical and quantum treatments are given. The gauge theory is developed from the standpoint of classical, coordinate-based tensor analysis; more abstract mathematical notation is generally not used, although the basic geometrical ideas of fiber-bundle theory are developed as needed. Certain old results, such as the Wilson-Howard-Watson Hamiltonian of molecular physics, are examined from a gauge-theoretical standpoint; and several new results are presented, including field equations of the Kaluza-Klein type satisfied by the gauge fields, and geometrical interpretations of the Eckart frame. copyright 1997 The American Physical Society
Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem
Peng, Hao; Bai, Xiaoli; Xu, Shijie
2017-06-01
Starting from resonant Halo orbits in the Circular Restricted Three-Body Problem (CRTBP), Multi-revolution Elliptic Halo (ME-Halo) orbits around L1 and L2 points in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are generated systematically. Three pairs of resonant parameters M5N2, M7N3 and M9N4 are tested. The first pair shows special features and is investigated in detail. Three separated characteristic curves of periodic orbit around each libration point are obtained, showing the eccentricity varies non-monotonically along these curves. The eccentricity of the Sun-Mercury system can be achieved by continuation method in just a few cases. The stability analysis shows that these orbits are all unstable and the complex instability occurs with certain parameters. This paper shows new periodic orbits in both the CRTBP and the ERTBP. Totally four periodic orbits with parameters M5N2 around each libration points are extracted in the Sun-Mercury ERTBP.
The Lie–Poisson structure of the reduced n-body problem
International Nuclear Information System (INIS)
Dullin, Holger R
2013-01-01
The classical n-body problem in d-dimensional space is invariant under the Galilean symmetry group. We reduce by this symmetry group using the method of polynomial invariants. One novelty of our approach is that we do not fix the centre of mass but rather use a momentum shifting trick to change the kinetic part of the Hamiltonian to arrive at a new, dynamically equivalent Hamiltonian which is easier to reduce. As a result we obtain a reduced system with a Lie–Poisson structure which is isomorphic to sp(2n-2), independently of d. The reduction preserves the natural form of the Hamiltonian as a sum of kinetic energy that depends on velocities only and a potential that depends on positions only. This splitting allows us to construct a Poisson integrator for the reduced n-body problem which is efficient away from collisions for n = 3. In particular, we could integrate the figure eight orbit in 18 time steps. (paper)
Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator
Directory of Open Access Journals (Sweden)
Takibayev N.Zh.
2010-04-01
Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two ﬁxed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two ﬁxed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei ﬁxed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.
Periodic orbits for space-based reflectors in the circular restricted three-body problem
Salazar, F. J. T.; McInnes, C. R.; Winter, O. C.
2017-05-01
The use of space-based orbital reflectors to increase the total insolation of the Earth has been considered with potential applications in night-side illumination, electric power generation and climate engineering. Previous studies have demonstrated that families of displaced Earth-centered and artificial halo orbits may be generated using continuous propulsion, e.g. solar sails. In this work, a three-body analysis is performed by using the circular restricted three body problem, such that, the space mirror attitude reflects sunlight in the direction of Earth's center, increasing the total insolation. Using the Lindstedt-Poincaré and differential corrector methods, a family of halo orbits at artificial Sun-Earth L_2 points are found. It is shown that the third order approximation does not yield real solutions after the reflector acceleration exceeds 0.245 mm s^{-2}, i.e. the analytical expressions for the in- and out-of-plane amplitudes yield imaginary values. Thus, a larger solar reflector acceleration is required to obtain periodic orbits closer to the Earth. Derived using a two-body approach and applying the differential corrector method, a family of displaced periodic orbits close to the Earth are therefore found, with a solar reflector acceleration of 2.686 mm s^{-2}.
Meson spectra using relativistic quark models
International Nuclear Information System (INIS)
Eggers, M.C.
1985-01-01
The complexity of QCD has led to the use of simpler, phenomenological models for hadrons, notably potential models. A short overview of the origin, rationale, merits and demerits of such models is given. Nonrelativistic models and scaling laws are discussed using the WKB technique for illustrative purposes. The failure of nonrelativistic models to describe the lighter mesons motivates the introduction of relativistic equations. Relativistic kinematics are incorporated into a Schroedinger formalism using equations derived by A. Barut, while two-body kinematics are brought into a one-body form via a substitution related to the Todorov equation. The potential used involves a semi-analytic solution to a harmonic oscillator modified by a spin-spin interaction term. The results seem to indicate that such a harmonic oscillator is unsuitable to describe diquark systems adequately
Relativistic covariant wave equations and acausality in external fields
International Nuclear Information System (INIS)
Pijlgroms, R.B.J.
1980-01-01
The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)
Rayleigh-Brillouin spectrum in special relativistic hydrodynamics
International Nuclear Information System (INIS)
Garcia-Perciante, A. L.; Garcia-Colin, L. S.; Sandoval-Villalbazo, A.
2009-01-01
In this paper we calculate the Rayleigh-Brillouin spectrum for a relativistic simple fluid according to three different versions available for a relativistic approach to nonequilibrium thermodynamics. An outcome of these calculations is that Eckart's version predicts that such spectrum does not exist. This provides an argument to question its validity. The remaining two results, which differ one from another, do provide a finite form for such spectrum. This raises the rather intriguing question as to which of the two theories is a better candidate to be taken as a possible version of relativistic nonequilibrium thermodynamics. The answer will clearly require deeper examination of this problem.
The large - $Z$ behaviour of pseudo-relativistic atoms
Ostergaard-Sorensen, T
2004-01-01
In this paper we study the large - $Z$ behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy $\\sqrt{p^{2}c^{2}+m^{2}c^{4}}-mc^{2}$. We prove that to leading order in $Z$ the energy is the same as in the non-relativistic case, given by (non-relativistic) Thomas-Fermi theory. For the problem to make sense, we keep the product $Z\\alpha$ fixed (here $\\alpha$ is Sommerfeld's fine structure constant), and smaller than, or equal to, $2/\\pi$, which means that as $Z$ tends to infinity, $\\alpha$ tends to zero.
Dissipation in relativistic pair-plasma reconnection: revisited
Zenitani, Seiji
2018-01-01
Basic properties of relativistic magnetic reconnection in electron–positron pair plasmas are investigated by using a particle-in-cell (PIC) simulation. We first revisit a problem by Hesse and Zenitani (2007 Phys. Plasmas 14 112102), who examined the kinetic Ohm’s law across the X line. We formulate a relativistic Ohm’s law by decomposing the stress–energy tensor. Then, the role of the new term, called the heat-flow inertial term, is examined in the PIC simulation data. We further evaluate the energy balance in the reconnection system. These analyses demonstrate physically transparent ways to diagnose relativistic kinetic data.
Directory of Open Access Journals (Sweden)
Biyu Shen
2015-01-01
Full Text Available SLE might affect all aspects of life including sexual functioning; previous study found that body image disturbance (BID was the most powerful predictors of impaired partner relationships and sexual function. The current study investigated the relationship among disease parameters, quality of life, the psychological status, BID, and sexual problems in Chinese patients with SLE. A self-report survey design was administered to 168 SLE patients and 210 healthy individuals. Our results showed that 86 (55.1% SLE patients reported impaired relationships with a sexual partner or partners, and 100 (64.1% patients reported impaired sexual function which were significantly higher than the control group (31.6%, 35.7%, rep.. Age, marital status, depression, and BIDQ were the most powerful predictors of impaired partner relationships, while BIDQ3 and education, disease activity, and depression were the most significant causes of impaired sexual function. The study for first time reported Chinese SLE patients had sexual problems and BID was associated with sexual problems. So, early detection and interventions might not only rehabilitate the patients and their loved ones, but also improve overall health outcomes and reduce the direct and indirect costs of their medical care.
L^1 -optimality conditions for the circular restricted three-body problem
Chen, Zheng
2016-11-01
In this paper, the L^1 -minimization for the translational motion of a spacecraft in the circular restricted three-body problem (CRTBP) is considered. Necessary conditions are derived by using the Pontryagin Maximum Principle (PMP), revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, recalling the existence of the Fuller phenomenon according to the theories developed in (Marchal in J Optim Theory Appl 11(5):441-486, 1973; Zelikin and Borisov in Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering. Birkhäuser, Basal 1994; in J Math Sci 114(3):1227-1344, 2003). The sufficient optimality conditions for the L^1 -minimization problem with fixed endpoints have been developed in (Chen et al. in SIAM J Control Optim 54(3):1245-1265, 2016). In the current paper, we establish second-order conditions for optimal control problems with more general final conditions defined by a smooth submanifold target. In addition, the numerical implementation to check these optimality conditions is given. Finally, approximating the Earth-Moon-Spacecraft system by the CRTBP, an L^1 -minimization trajectory for the translational motion of a spacecraft is computed by combining a shooting method with a continuation method in (Caillau et al. in Celest Mech Dyn Astron 114:137-150, 2012; Caillau and Daoud in SIAM J Control Optim 50(6):3178-3202, 2012). The local optimality of the computed trajectory is asserted thanks to the second-order optimality conditions developed.
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.
2000-01-01
Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)
Evolution of the halo family in the radial solar sail circular restricted three-body problem
Verrier, Patricia; Waters, Thomas; Sieber, Jan
2014-12-01
We present a detailed investigation of the dramatic changes that occur in the halo family when radiation pressure is introduced into the Sun-Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. in Int J Bifurc Chaos 1:493-520, 1991) the families can be fully mapped out as the parameter is increased. Interestingly, the emergence of a branch point in the retrograde satellite family around the Earth at acts to split the halo family into two new families. As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at , resulting in a third new family. The linear stability of the families changes rapidly at low values of , with several small regions of neutral stability appearing and disappearing. By using existing methods within AUTO to continue branch points and period-doubling bifurcations, and deriving a new boundary-value problem formulation to continue the folds and Krein collisions, we track bifurcations and changes in the linear stability of the families in the parameter and provide a comprehensive overview of the halo family in the presence of radiation pressure. The results demonstrate that even at small values of there is significant difference to the classical CRTBP, providing opportunity for novel solar sail trajectories. Further, we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case.
Relativistic mean field model for entrainment in general relativistic superfluid neutron stars
International Nuclear Information System (INIS)
Comer, G.L.; Joynt, R.
2003-01-01
General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of 'relativistic': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons
FBS Colloquium Hyperspherical-Harmonics Methods for Few-Body Problems
Krivec, R.
A review of hyperspherical-harmonics (HH) methods from the standpoint of their applications is given. In the first lecture, the symmetrized and unsymmetrized HH bases and symmetrization methods are presented. The physical obstacles to the straightforward application of the HH expansion are discussed, and expansion acceleration methods are described. In the second lecture, the main HH methods are described, including the correlation function hyperspherical harmonic method (CFHHM), the potential harmonic (PH) methods, and the correlated HH methods (PHH, CHH). The third lecture discusses the advantages and limitations of different HH methods in applications, and compares the results for specific few-body problems obtained by HH methods as well as non-HH methods.
21st International Conference on Few-Body Problems in Physics
2015-01-01
The 21st International Conference on Few-Body Problems in Physics (FB21) will take place at the Crowne Plaza Chicago Metro Downtown Hotel in the West Loop area of Chicago, Illinois, USA, from May 18th to 22nd, 2015. The first conference of this series took place in London in 1959 and subsequent meetings were held in Brela (1967), Birmingham (1969), Budapest (1971), Los Angeles (1972), Laval (1974), Delhi (1976), Graz (1978), Eugene (1980), Karlsruhe (1983), Sendai (1986), Vancouver (1989), Adelaide (1992), Williamsburg (1994), Groningen (1997), Taipei (2000), Durham (2003),Santos (2006),Bonn (2009),and Fukuoka (2012) see also "History". FB21 will be conducted with the principles passed by the General Assembly in 2008. In particular, no bona fide scientist will be excluded from participation on the grounds of national origin, nationality, or political considerations unrelated to science.
Motions of Kepler circumbinary planets in restricted three-body problem under radiating primaries
Energy Technology Data Exchange (ETDEWEB)
Dermawan, B., E-mail: budider@as.itb.ac.id; Hidayat, T., E-mail: taufiq@as.itb.ac.id [Astronomy Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia); Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id; Mandey, D., E-mail: mandey.de@gmail.com; Utama, J. A., E-mail: judhistira@yahoo.com; Tampubolon, I., E-mail: ihsan.tampubolon@gmail.com [Department of Astronomy, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia); Wibowo, R. W., E-mail: ridlo.w.wibowo@gmail.com [Department of Computational Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia)
2015-09-30
By observing continuously a single field of view in the sky, Kepler mission reveals outstanding results on discoveries of exoplanets. One of its recent progress is the discoveries of circumbinary planets. A circumbinary planet is an exoplanet that moves around a binary system. In this study we investigate motions of Kepler circumbinary planets belong to six binary systems, namely Kepler-16, -34, -35, -38, -47, and -413. The motions are considered to follow the Restricted Three-Body Problem (RTBP). Because the primaries (central massive objects) are stars, they are both radiatives, while the planet is an infinitesimal object. The primaries move in nearly circular and elliptic orbits with respect to their center of masses. We describe, in general, motions of the circumbinary planets in RTBP under radiating primaries. With respect to the averaged zero velocity curves, we show that motions of the exoplanets are stable, in accordance with their Hill stabilities.
The problem of the motion of bodies a historical view of the development of classical mechanics
Capecchi, Danilo
2014-01-01
This book focuses on the way in which the problem of the motion of bodies has been viewed and approached over the course of human history. It is not another traditional history of mechanics but rather aims to enable the reader to fully understand the deeper ideas that inspired men, first in attempting to understand the mechanisms of motion and then in formulating theories with predictive as well as explanatory value. Given this objective, certain parts of the history of mechanics are neglected, such as fluid mechanics, statics, and astronomy after Newton. On the other hand, due attention is paid, for example, to the history of thermodynamics, which has its own particular point of view on motion. Inspired in part by historical epistemology, the book examines the various views and theories of a given historical period (synchronic analysis) and then makes comparisons between different periods (diachronic analysis). In each period, one or two of the most meaningful contributions are selected for particular attent...
Spatial Double Choreographies of the Newtonian 2n-Body Problem
Yu, Guowei
2018-01-01
In this paper, for the spatial Newtonian 2n-body problem with equal masses, by proving that the minimizers of the action functional under certain symmetric, topological and monotone constraints are collision-free, we found a family of spatial double choreographies, which have the common feature that half of the masses are circling around the z-axis clockwise along a spatial loop, while the motions of the other half of the masses are given by a rotation of the first half around the x-axis by π. Both loops are simple, without any self-intersection, and symmetric with respect to the xz-plane and yz-plane. The set of intersection points between the two loops is non-empty and contained in the xy-plane. The number of such double choreographies grows exponentially as n goes to infinity.
Relativistic heavy ion reactions
International Nuclear Information System (INIS)
Brink, D.M.
1989-08-01
The theory of quantum chromodynamics predicts that if nuclear matter is heated to a sufficiently high temperature then quarks might become deconfined and a quark-gluon plasma could be produced. One of the aims of relativistic heavy ion experiments is to search for this new state of matter. These lectures survey some of the new experimental results and give an introduction to the theories used to interpret them. 48 refs., 4 tabs., 11 figs
Basilio, Ralph Ramos
Spacecraft formation flying involves operating multiple spacecraft in a pre-determined geometrical shape such that the configuration yields both individual and system benefits. One example is an over-flight of the same spatial position by spacecraft in geocentric orbit with the intent to create a complementary data set of remotely sensed observables. Another example is controlling to a high degree of accuracy the distance between spacecraft in heliocentric orbit to create a virtual, large-diameter interferometer telescope. Although Keplerian orbits provide the basic framework for general and precision spacecraft formation flying they also present limitations. Spacecraft are generally constrained to operate only in circular and elliptical orbits, parabolic paths, or hyperbolic trajectories around celestial bodies. Applying continuation methods and bifurcation theory techniques to the circular, restricted three-body problem - where stable and unstable periodic orbits exist around equilibrium points - creates an environment that is more orbit rich. After surmounting a similar challenge with test particles in the circular, restricted three-vortex problem in fluid mechanics as a proof-of-concept, it was shown that spacecraft traveling in uncontrolled motion along separate and distinct planar or three-dimensional periodic orbits could be placed in controlled motion, i.e. a controller is enabled and later disabled at precisely the proper positions, to have them phase-locked on a single periodic orbit. Although it was possible to use this controller in a resonant frequency/orbit approach to establish a formation, it was clearly shown that a separate controller could be used in conjunction with the first to expedite the formation establishment process. Creation of these dynamically natural spacecraft formations or multi-spacecraft platforms will enable the 'loiter, synchronize/coordinate, and observe' approach for future engineering and scientific missions where flexibility
Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J
2013-09-27
Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.
Full Two-Body Problem Mass Parameter Observability Explored Through Doubly Synchronous Systems
Davis, Alex Benjamin; Scheeres, Daniel
2018-04-01
The full two-body problem (F2BP) is often used to model binary asteroid systems, representing the bodies as two finite mass distributions whose dynamics are influenced by their mutual gravity potential. The emergent behavior of the F2BP is highly coupled translational and rotational mutual motion of the mass distributions. For these systems the doubly synchronous equilibrium occurs when both bodies are tidally-locked and in a circular co-orbit. Stable oscillations about this equilibrium can be shown, for the nonplanar system, to be combinations of seven fundamental frequencies of the system and the mutual orbit rate. The fundamental frequencies arise as the linear periods of center manifolds identified about the equilibrium which are heavily influenced by each body’s mass parameters. We leverage these eight dynamical constraints to investigate the observability of binary asteroid mass parameters via dynamical observations. This is accomplished by proving the nonsingularity of the relationship between the frequencies and mass parameters for doubly synchronous systems. Thus we can invert the relationship to show that given observations of the frequencies, we can solve for the mass parameters of a target system. In so doing we are able to predict the estimation covariance of the mass parameters based on observation quality and define necessary observation accuracies for desired mass parameter certainties. We apply these tools to 617 Patroclus, a doubly synchronous Trojan binary and flyby target of the LUCY mission, as well as the Pluto and Charon system in order to predict mutual behaviors of these doubly synchronous systems and to provide observational requirements for these systems’ mass parameters
Gravitationally confined relativistic neutrinos
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
Relativistic tidal disruption events
Directory of Open Access Journals (Sweden)
Levan A.
2012-12-01
Full Text Available In March 2011 Swift detected an extremely luminous and long-lived outburst from the nucleus of an otherwise quiescent, low luminosity (LMC-like galaxy. Named Swift J1644+57, its combination of high-energy luminosity (1048 ergs s−1 at peak, rapid X-ray variability (factors of >100 on timescales of 100 seconds and luminous, rising radio emission suggested that we were witnessing the birth of a moderately relativistic jet (Γ ∼ 2 − 5, created when a star is tidally disrupted by the supermassive black hole in the centre of the galaxy. A second event, Swift J2058+0516, detected two months later, with broadly similar properties lends further weight to this interpretation. Taken together this suggests that a fraction of tidal disruption events do indeed create relativistic outflows, demonstrates their detectability, and also implies that low mass galaxies can host massive black holes. Here, I briefly outline the observational properties of these relativistic tidal flares observed last year, and their evolution over the first year since their discovery.
Point form relativistic quantum mechanics and relativistic SU(6)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Hadron spectra from a non-relativistic model with confining harmonic potential
Directory of Open Access Journals (Sweden)
Cuervo-Reyes Eduardo
2003-01-01
Full Text Available Hadron spectra and other properties of quark systems are studied in the framework of a non-relativistic spinindependent phenomenological model. The chosen confining potential is harmonic, which allowed us to obtain analytical solutions for both meson and baryon (of equal constituent quarks spectra. The introduced parameters are fixed from the low-lying levels of heavy quark mesons. The requirement of flavor independence is imposed, and it restricts the possible choices of inter-quark potentials. The hyper-spherical coordinates are considered for the solution of the three-body problem.
A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential
International Nuclear Information System (INIS)
Hamzavi, M.; Ikhdair, S.M.; Rajabi, A.A.
2013-01-01
By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for an arbitrary l-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schroedinger-Woods-Saxon problem for an arbitrary l-state and the exact s-wave (l=0). (authors)
How the carotid body works: Different strategies and preparations to solve different problems
Directory of Open Access Journals (Sweden)
PATRICIO ZAPATA
2005-01-01
Full Text Available This is a review of the different experimental approaches developed to solve the problems in our progress towards a comprehensive understanding of how arterial chemoreceptors operate. An analysis is performed of the bases, advantages and limits of the following preparations: studies of ventilatory reflexes originated from carotid bodies (CBs in the entire animal; recordings of CB chemosensory discharges in situ; CB preparations perfused in situ; CB explants in oculo; CB explants in ovo; CB preparations incubated in vitro; CB preparations superfused in vitro; CB preparations perfused and superfused in vitro; CB tissue slices in vitro; cells acutely dissociated from CBs; CB cells in tissue culture; petrosal ganglia superfused in vitro; petrosal ganglion cells in tissue culture; and co-cultures of CB and sensory ganglion cells. A brief historical account is given of the passage from one preparation to the next one. Emphasis is placed on personal experience with the different preparations whenever possible. Examples are given of the importance of selecting the appropriate experimental preparation for solving each particular theoretical problem. In fact, brilliant ideas on how the CB works have been unproductive until finding the adequate experimental approach to explore the validity of such ideas.
The rectilinear three-body problem as a basis for studying highly eccentric systems
Voyatzis, G.; Tsiganis, K.; Gaitanas, M.
2018-01-01
The rectilinear elliptic restricted three-body problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity e'=1, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (AIAA J 7:1003-1009, 1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter μ =0.5 (equal masses of the primaries). We found that all orbits obtained by Broucke are linearly unstable. We extend Broucke's computations by using a finer search for symmetric periodic orbits and computing their linear stability. We found a large number of periodic orbits, but only eight of them were found to be linearly stable and are associated with particular mean motion resonances. These stable orbits are used as generating orbits for continuation with respect to μ and e'systems of very highly eccentric orbits can be found in stable resonant configurations. As an application we present a stability study for the planetary system HD7449.
Gedney, Stephen D.; Mittra, Raj
1990-01-01
The enhancement of the computational efficiency of the body of revolution (BOR) scattering problem is discused with a view to making it practical for solving large-body problems. The problem of EM scattering by a perfectly conducting BOR is considered, although the methods can be extended to multilayered dielectric bodies as well. Typically, the generation of the elements of the moment method matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements to permit efficient FFT computation. A technique for extracting the singularity of the Green function that appears within the integrands of the matrix diagonal is also presented, further enhancing the usefulness of the FFT. The computation time can thus be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms.
Relativistic thermodynamics of Fluids. l
International Nuclear Information System (INIS)
Havas, P.; Swenson, R.J.
1979-01-01
In 1953, Stueckelberg and Wanders derived the basic laws of relativistic linear nonequilibrium thermodynamics for chemically reacting fluids from the relativistic local conservation laws for energy-momentum and the local laws of production of substances and of nonnegative entropy production by the requirement that the corresponding currents (assumed to depend linearly on the derivatives of the state variables) should not be independent. Generalizing their method, we determine the most general allowed form of the energy-momentum tensor T/sup alphabeta/ and of the corresponding rate of entropy production under the same restriction on the currents. The problem of expressing this rate in terms of thermodynamic forces and fluxes is discussed in detail; it is shown that the number of independent forces is not uniquely determined by the theory, and seven possibilities are explored. A number of possible new cross effects are found, all of which persist in the Newtonian (low-velocity) limit. The treatment of chemical reactions is incorporated into the formalism in a consistent manner, resulting in a derivation of the law for rate of production, and in relating this law to transport processes differently than suggested previously. The Newtonian limit is discussed in detail to establish the physical interpretation of the various terms of T/sup alphabeta/. In this limit, the interpretation hinges on that of the velocity field characterizing the fluid. If it is identified with the average matter velocity following from a consideration of the number densities, the usual local conservation laws of Newtonian nonequilibrium thermodynamics are obtained, including that of mass. However, a slightly different identification allows conversion of mass into energy even in this limit, and thus a macroscopic treatment of nuclear or elementary particle reactions. The relation of our results to previous work is discussed in some detail
Spacecraft trajectories to the L3 point of the Sun-Earth three-body problem
Tantardini, Marco; Fantino, Elena; Ren, Yuan; Pergola, Pierpaolo; Gómez, Gerard; Masdemont, Josep J.
2010-11-01
Of the three collinear libration points of the Sun-Earth Circular Restricted Three-Body Problem (CR3BP), L3 is that located opposite to the Earth with respect to the Sun and approximately at the same heliocentric distance. Whereas several space missions have been launched to the other two collinear equilibrium points, i.e., L1 and L2, taking advantage of their dynamical and geometrical characteristics, the region around L3 is so far unexploited. This is essentially due to the severe communication limitations caused by the distant and permanent opposition to the Earth, and by the gravitational perturbations mainly induced by Jupiter and the close passages of Venus, whose effects are more important than those due to the Earth. However, the adoption of a suitable periodic orbit around L3 to ensure the necessary communication links with the Earth, or the connection with one or more relay satellites located at L4 or L5, and the simultaneous design of an appropriate station keeping-strategy, would make it possible to perform valuable fundamental physics and astrophysics investigations from this location. Such an opportunity leads to the need of studying the ways to transfer a spacecraft (s/c) from the Earth’s vicinity to L3. In this contribution, we investigate several trajectory design methods to accomplish such a transfer, i.e., various types of two-burn impulsive trajectories in a Sun-s/c two-body model, a patched conics strategy exploiting the gravity assist of the nearby planets, an approach based on traveling on invariant manifolds of periodic orbits in the Sun-Earth CR3BP, and finally a low-thrust transfer. We examine advantages and drawbacks, and we estimate the propellant budget and time of flight requirements of each.
Stabilities of regular motion in the relativistic standard map
International Nuclear Information System (INIS)
Nomura, Y.; Ichikawa, Y.H.; Horton, W.
1991-02-01
Analysis of the relativistic standard map is one of the important problems to understand nonlinear interaction between waves and charged particles in the relativistic dynamics. In the relativistic standard map, in general, chaotic motion is strongly suppressed and regular motion such as periodic orbit plays dominant roles in the phase space. Location of periodic points is predicted by use of symmetry lines of the map. Local stability of periodic points is investigated by introducing the residue of the orbit which characterizes the eigenvalue of the area-preserving map. It is found that the exchange of stable and unstable points takes place at some value of the relativistic parameter. Special behavior of the residue of the Poincare-Birkhoff period-4 points are also examined and related bifurcations are clarified. (author)
International Nuclear Information System (INIS)
Abramowicz, M.A; Jaroszynski, M.; Sikora, M.
1978-01-01
An analytic theory of the hydrodynamical structure of accreting disks (without self-gravitation but with pressure) orbiting around and axially symmetric, stationary, compact body (e.g. black hole) is presented. The inner edge of the marginally stable accreting disk (i.e. disk with constant angular momentum density) has a sharp cusp located on the equatorial plane between rsub(ms) and rsub(mb). The existence of the cusp is also typical for any angular momentum distribution. The physical importance of the cusp follows from the close analogy with the case of a close binary system (L 1 Lagrange point on the Roche lobe). The existence of the cusp is thus a crucial phenomenon in such problems as boundary condition for the viscous stresses, accretion rate etc. (orig.) [de
Nonuniform currents and spins of relativistic electron vortices in a magnetic field
van Kruining, Koen; Hayrapetyan, Armen G.; Götte, Jörg B.
2017-01-01
We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonp...
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
International Nuclear Information System (INIS)
Araujo, Wilson Roberto Barbosa de
1995-01-01
In this dissertation, we present a model for the nucleon, which is composed by three relativistic quarks interacting through a contract force. The nucleon wave-function was obtained from the Faddeev equation in the null-plane. The covariance of the model under kinematical null-plane boots is discussed. The electric proton form-factor, calculated from the Faddeev wave-function, was in agreement with the data for low-momentum transfers and described qualitatively the asymptotic region for momentum transfers around 2 GeV. (author)
Finite-Temperature Relativistic Time-Blocking Approximation for Nuclear Strength Functions
Wibowo, Herlik; Litvinova, Elena
2017-09-01
This work presents an extension of the relativistic nuclear field theory (RNFT) developed throughout the last decade as an approach to the nuclear many-body problem, based on QHD meson-nucleon Lagrangian and relativistic field theory. The unique feature of RNFT is a consistent connection of the high-energy scale of heavy mesons, the medium-energy range of pion, and the low-energy domain of emergent collective vibrations (phonons). RNFT has demonstrated a very good performance in various nuclear structure calculations across the nuclear chart and, in particular, provides a consistent input for description of the two phases of r-process nucleosynthesis: neutron capture and beta decay. Further inclusion of finite temperature effects presented here allows for an extension of the method to highly excited compound nuclei. The covariant response theory in the relativistic time-blocking approximation (RTBA) is generalized for thermal effects, adopting the Matsubara Green's function formalism to the RNFT framework. The finite-temperature RTBA is implemented numerically to calculate multipole strength functions in medium-mass and heavy nuclei. The obtained results will be discussed in comparison to available experimental data and in the context of possible consequences for astrophysics.
Relativistic dynamics, Green function and pseudodifferential operators
Energy Technology Data Exchange (ETDEWEB)
Cirilo-Lombardo, Diego Julio [National Institute of Plasma Physics (INFIP), Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires 1428 (Argentina); Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna (Russian Federation)
2016-06-15
The central role played by pseudodifferential operators in relativistic dynamics is known very well. In this work, operators like the Schrodinger one (e.g., square root) are treated from the point of view of the non-local pseudodifferential Green functions. Starting from the explicit construction of the Green (semigroup) theoretical kernel, a theorem linking the integrability conditions and their dependence on the spacetime dimensions is given. Relativistic wave equations with arbitrary spin and the causality problem are discussed with the algebraic interpretation of the radical operator and their relation with coherent and squeezed states. Also we perform by means of pure theoretical procedures (based in physical concepts and symmetry) the relativistic position operator which satisfies the conditions of integrability: it is a non-local, Lorentz invariant and does not have the same problems as the “local”position operator proposed by Newton and Wigner. Physical examples, as zitterbewegung and rogue waves, are presented and deeply analyzed in this theoretical framework.
Exact Relativistic Magnetized Haloes around Rotating Disks
Directory of Open Access Journals (Sweden)
Antonio C. Gutiérrez-Piñeres
2015-01-01
Full Text Available The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.
Transport theory for relativistic ionized gases
International Nuclear Information System (INIS)
Georgiou, A.
1985-01-01
The phenomenological non-equilibrium thermodynamics is adapted to the description of relativistic multicomponent plasmas. The general and special forms of matter energy-momentum tensor are given and the physical meaning of the different terms are discussed. A delicate problem of such theories, the contribution of ionized components of plasmas to the electromagnetic energy-momentum tensor is analyzed and illustrated by special examples. The relativistic form of Gibbs equation leads to the balance equation of entropy density. The theory is compared to the nonrelativistic one. The linear transport equations are derived by assuming the linear dependence of currents on deviations. The thermodynamical fluxes and forces are identified and the interference of cross phenomena is discussed. (D.Gy.)
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Body dysmorphic factors and mental health problems in people seeking rhinoplastic surgery.
Javanbakht, M; Nazari, A; Javanbakht, A; Moghaddam, L
2012-02-01
There has been increasing number of requests for cosmetic rhinoplastic surgery among Iranian people in different age groups in recent years. One risk for people who undergo such plastic operations is the presence of body dysmorphic disorder (BDD), which can complicate the result and decrease the rate of satisfaction from surgery. This study aimed to investigate mental health problems in people seeking rhinoplastic surgery. In this case-control study, the scores of General Health Questionnaire (GHQ) and DCQ (Dysmorphic Concerns Questionnaire) were obtained from 50 individuals who were candidates for rhinoplasty, and the results were compared with a normal control group. The total GHQ score and scores in anxiety, depression, and social dysfunction sub-scales were higher among the study group. This was the same for the DCQ score. However, the scores of somatization sub-scale of GHQ were not significantly different between the two groups. Psychiatric evaluation of candidates for rhinoplasty seems necessary for prevention of unnecessary and repetitive surgical operations.
Good clinical practice in dubious head trauma – the problem of retained intracranial foreign bodies
Directory of Open Access Journals (Sweden)
Fischer BR
2012-10-01
Full Text Available Bernhard R Fischer,1 Yousef Yasin,2 Markus Holling,2 Volker Hesselmann31Department of Neurotraumatology, BG-University Hospital Bergmannsheil, Ruhr-University Bochum, Bochum, Germany; 2Department of Neurosurgery, 3Institute for Clinical Radiology, University Hospital of Muenster, Muenster, GermanyObjective: In young people, traumatic head and brain injuries are the leading cause of morbidity and mortality. In some cases, no neurological deficits are present, even after penetrating trauma. These patients have a greater risk of suffering from secondary injuries due to secondary infections, brain edema, and hematomas. We present a case report which illustrates that brain injuries that do not induce neurological deficits can still result in a fatal clinical course and death, with medicolegal consequences.Clinical presentation: A 19-year-old patient was admitted to hospital suffering from a head injury due to an assault. He reported that he was attacked from behind. Medical examination showed no neurological deficits, and only a small occipital wound. Neuroimaging of the cranium revealed that a knife blade was penetrating the cranial bone and touching the superior sagittal sinus.Intervention: After removing the foreign body, magnetic resonance imaging showed that the superior sagittal sinus remained open.Conclusion: We want to stress that possible problems can arise due to the retention of objects in the cranium, while also highlighting the risk of superficial clinical examination.Keywords: head trauma, guidelines, retained object, neuroimaging
AbdulJabbar, Mustafa Abdulmajeed
2017-05-11
Reduction of communication and efficient partitioning are key issues for achieving scalability in hierarchical N-Body algorithms like Fast Multipole Method (FMM). In the present work, we propose three independent strategies to improve partitioning and reduce communication. First, we show that the conventional wisdom of using space-filling curve partitioning may not work well for boundary integral problems, which constitute a significant portion of FMM’s application user base. We propose an alternative method that modifies orthogonal recursive bisection to relieve the cell-partition misalignment that has kept it from scaling previously. Secondly, we optimize the granularity of communication to find the optimal balance between a bulk-synchronous collective communication of the local essential tree and an RDMA per task per cell. Finally, we take the dynamic sparse data exchange proposed by Hoefler et al. [1] and extend it to a hierarchical sparse data exchange, which is demonstrated at scale to be faster than the MPI library’s MPI_Alltoallv that is commonly used.
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
'Antigravity' Propulsion and Relativistic Hyperdrive
Felber, Franklin S.
2006-01-01
Exact payload trajectories in the strong gravitational fields of compact masses moving with constant relativistic velocities are calculated. The strong field of a suitable driver mass at relativistic speeds can quickly propel a heavy payload from rest to a speed significantly faster than the driver, a condition called hyperdrive. Hyperdrive thresholds and maxima are calculated as functions of driver mass and velocity.
Relativistic hypernuclei: old problems and new prospects
Czech Academy of Sciences Publication Activity Database
Majling, Lubomír; Lukstins, J.; Parfenov, AN.; Chren, D.; Solar, M.; Sopko, B.
2003-01-01
Roč. 53, č. 8 (2003), s. 667-677 ISSN 0011-4626 R&D Projects: GA ČR GA202/02/0930; GA AV ČR KSK1048102 Keywords : quantum wave -guides * Schrödinger-operators * Dirichlet Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 0.263, year: 2003
DEFF Research Database (Denmark)
Simonsen, L; Bülow, J; Madsen, Jan Lysgård
1993-01-01
The effects of an oral glucose load of 75 g on the local forearm and whole-body energy thermogenesis were measured in normal subjects during the 4 h after the glucose intake. Simultaneous assessment of substrate metabolism in the forearm was performed. Energy expenditure (EE) increased after.......17) to 0.63 (0.17) 30 min after the glucose load (P problems in the measurement of local forearm RQ. The whole-body RQ...
Slices of theoretical astrophysics: Solar system dynamics and relativistic explosions
Pan, Margaret
This thesis presents studies in two distinct areas of theoretical astrophysics: dynamics of planetary systems and relativistic fluid flows from shocks emerging from stellar envelopes. The first pertains to the early solar system, planet formation, and extrasolar planets; the second is related to extreme explosions like gamma-ray bursts and supernovae. We present two investigations of the dynamics and population evolution of solar system bodies. First, we explore the dynamics of mean-motion resonances for a test particle in a highly eccentric long-period orbit in the restricted circular planar three-body problem---a scenario relevant to the scattered Kuiper belt and the formation of the Oort cloud. We find infinitely many analogues to the Lagrange points; an explanation for the presence of asymmetric librations in particular mean-motion resonances; and a criterion for the onset of chaos at large semimajor axes. Second, we study the size distribution of Kuiper belt objects (KBOs), which is observed to be a broken power law. We apply a simple mass conservation argument to the KBO collisional cascade to get the power-law slope for KBOs below the break in the distribution; our result agrees well with observations if KBOs are held together by self-gravity rather than material strength. We then explain the location and time evolution of the break. We also present investigations of the flow that results when a relativistic shock propagates through and breaks out of a stellar envelope with a polytropic density profile. This work informs predictions of the speed of and energy carried by the relativistic ejecta in supernovae and perhaps in gamma-ray bursts. We find the asymptotic solution for the flow as the shock reaches the star's edge and find a new self-similar solution for the flow of hot fluid after breakout. Since the post-breakout flow acclerates by converting thermal energy into bulk kinetic energy, the fluid eventually cools to nonrelativistic temperatures. We
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
Energy Technology Data Exchange (ETDEWEB)
Batchelor, M T [Department of Theoretical Physics, RSPSE and Department of Mathematics, MSI, Australian National University, Canberra ACT 0200 (Australia)
2005-04-08
Heisenberg spin chain, the Hubbard model, exchange models, the Calogero-Sutherland models and models with ground state wavefunctions of product form. One of my favourites is chapter 7, dealing with the consistency conditions for two-body scattering operators involving the Yang-Baxter equations. The strength of the book lies in the pedagogical approach, with the underlying emphasis on integrability and the Bethe ansatz. Sutherland brings his own insights to these problems, and as such there is also something to be gained by specialist readers. Given the author's aims, the book is not meant to be a complete and historic review of the field. Rather, the intention is that the general references given will point the reader in the right direction. Sutherland quite wisely gives an up-front apology to any authors he has left out. Certainly such historical omissions can be found. Two obvious examples are the origins of the condition of non-diffraction and twisted boundary conditions. Setting such minor points aside, Beautiful Models is a most welcome book. It does a great service to a fascinating, enduring and increasingly relevant field by highlighting not only the beauty, but also the magic of integrability. (book review)
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
International Nuclear Information System (INIS)
Batchelor, M T
2005-01-01
-Sutherland models and models with ground state wavefunctions of product form. One of my favourites is chapter 7, dealing with the consistency conditions for two-body scattering operators involving the Yang-Baxter equations. The strength of the book lies in the pedagogical approach, with the underlying emphasis on integrability and the Bethe ansatz. Sutherland brings his own insights to these problems, and as such there is also something to be gained by specialist readers. Given the author's aims, the book is not meant to be a complete and historic review of the field. Rather, the intention is that the general references given will point the reader in the right direction. Sutherland quite wisely gives an up-front apology to any authors he has left out. Certainly such historical omissions can be found. Two obvious examples are the origins of the condition of non-diffraction and twisted boundary conditions. Setting such minor points aside, Beautiful Models is a most welcome book. It does a great service to a fascinating, enduring and increasingly relevant field by highlighting not only the beauty, but also the magic of integrability. (book review)
Relativistic centrifugal instability
Gourgouliatos, Konstantinos N.; Komissarov, Serguei S.
2018-03-01
Near the central engine, many astrophysical jets are expected to rotate about their axis. Further out they are expected to go through the processes of reconfinement and recollimation. In both these cases, the flow streams along a concave surface and hence, it is subject to the centrifugal force. It is well known that such flows may experience the centrifugal instability (CFI), to which there are many laboratory examples. The recent computer simulations of relativistic jets from active galactic nuclei undergoing the process of reconfinement show that in such jets CFI may dominate over the Kelvin-Helmholtz instability associated with velocity shear (Gourgouliatos & Komissarov). In this letter, we generalize the Rayleigh criterion for CFI in rotating fluids to relativistic flows using a heuristic analysis. We also present the results of computer simulations which support our analytic criterion for the case of an interface separating two uniformly rotating cylindrical flows. We discuss the difference between CFI and the Rayleigh-Taylor instability in flows with curved streamlines.
Energy Technology Data Exchange (ETDEWEB)
Ujevic, Maximiliano [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil). Centro de Ciencias Naturais e Humanas; Letelier, Patricio S.; Vogt, Daniel [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Matematica, Estatistica e Computacao Cientifica. Dept. de Matematica Aplicada
2011-07-01
Full text: Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. This was achieved by inflating previously constructed Newtonian ring potentials using the transformation |z|{yields}{radical}z{sup 2} + b{sup 2}, and then finding their relativistic analog. The models presented have infinite extension but the physical quantities decays very fast with the distance, and in principle, one could make a cut-off radius to consider it finite. In particular, we present systems with one ring, two rings and a disc with a ring. Also, the circular velocity of a test particle and its stability when performing circular orbits are presented in all these models. Using the Rayleigh criterion of stability of a fluid at rest in a gravitational field, we find that the different systems studied present a region of non-stability that appears in the intersection of the disc and the ring, and between the rings when they become thinner. (author)
Relativistic Planck-scale polymer
Directory of Open Access Journals (Sweden)
Giovanni Amelino-Camelia
2017-12-01
Full Text Available Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is usually assumed that the discrete polymer structure should lead to a breakdown of relativistic symmetries. We here focus for simplicity on a one-spatial-dimension polymer model and show that relativistic symmetries are deformed, rather than being broken. The specific type of deformed relativistic symmetries which we uncover appears to be closely related to analogous descriptions of relativistic symmetries in some noncommutative spacetimes. This also contributes to an ongoing effort attempting to establish whether the âquantum-Minkowski limitâ of Loop Quantum Gravity is a noncommutative spacetime.
Wegner, Franz J.
2007-01-01
Explicit solutions of the two-dimensional floating body problem (bodies that can float in all positions) for relative density different from 1/2 and of the tire track problem (tire tracks of a bicycle, which do not allow to determine, which way the bicycle went) are given, which differ from circles. Starting point is the differential equation given by the author in archive physics/0205059 and Studies in Appl. Math. 111 (2003) 167-183. The curves are also trajectories of charges in a perpendic...
Relativistic and separable classical hamiltonian particle dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1981-01-01
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
Relativistic fluid formulation and theory of intense relativistic electron beams
International Nuclear Information System (INIS)
Siambis, J.G.
1984-01-01
A new general relativistic fluid formulation has been obtained for intense relativistic electron beams (IREB) with arbitrarily high relativistic mass factor γ. This theory is valid for confined IREB equilibria such as those found inside high energy accelerators as well as in the pinched and ion-focused regimes of beam propagation in plasma channels. The new relativistic fluid formulation is based on the covariant relativistic fluid formulation of Newcomb with the parameter lambda identical to 1, in order to allow for realistic confined equilibria. The resulting equilibrium constraints require that the beam has a slow rotational velocity around its direction of propagation and that the off-diagonal thermal stress element, associated with these two directions of motion, be nonzero. The effective betatron oscillation frequency of the fluid elements of the beam is modified by the radial gradient and anisotropies in the thermal stress elements of the beam fluid. The wave equation, for sausage, hose and filamentation excitations on the relativistic fluid beam, is found to be formally identical to that obtained from the Vlasov equation approach, hence phase-mixing damping is a generic and self-consistent correlate of the new relativistic fluid formulation
Electron-deuteron scattering in a relativistic theory of hadrons
International Nuclear Information System (INIS)
Phillips, D.
1998-11-01
The author reviews a three-dimensional formalism that provides a systematic way to include relativistic effects including relativistic kinematics, the effects of negative-energy states, and the boosts of the two-body system in calculations of two-body bound-states. He then explains how to construct a conserved current within this relativistic three-dimensional approach. This general theoretical framework is specifically applied to electron-deuteron scattering both in impulse approximation and when the ρπγ meson-exchange current is included. The experimentally-measured quantities A, B, and T 20 are calculated over the kinematic range that is probed in Jefferson Lab experiments. The role of both negative-energy states and meson retardation appears to be small in the region of interest
Method of resonating groups in the Faddeev-Hahn equation formalism for three-body nuclear problem
Nasirov, M Z
2002-01-01
The Faddeev-Hahn equation formalism for three-body nuclear problem is considered. For solution of the equations the method of resonant groups have applied. The calculations of tritium binding energy and doublet nd-scattering length have been carried out. The results obtained shows that Faddeev-Hahn equation formalism is very simple and effective. (author)
Relativistic heavy ion physics
International Nuclear Information System (INIS)
Hill, J.C.; Wohn, F.K.
1993-01-01
This is a progress report for the period May 1992 through April 1993. The first section, entitled ''Purpose and Trends, gives background on the recent trends in the research program and its evolution from an emphasis on nuclear structure physics to its present emphasis on relativistic heavy ion and RHIC physics. The next section, entitled ''Physics Research Progress'', is divided into four parts: participation in the program to develop a large detector named PHENIX for the RHIC accelerator; joining E864 at the AGS accelerator and the role in that experiment; progress made in the study of electromagnetic dissociation highlight of this endeavor is an experiment carried out with the 197 Au beam from the AGS accelerator in April 1992; progress in completion of the nuclear structure studies. In the final section a list of publications, invited talks, and contributed talks is given
Relativistic thermodynamics of fluids
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-05-01
The relativistic covariant definition of a statistical equilibrium, applied to a perfect gas, involves a 'temperature four-vector', whose direction is the mean velocity of the fluid, and whose length is the reciprocal temperature. The hypothesis of this 'temperature four-vector' being a relevant variable for the description of the dissipative motions of a simple fluid is discussed. The kinematics is defined by using a vector field and measuring the number of molecules. Such a dissipative fluid is subject to motions involving null entropy generation; the 'temperature four-vector' is then a Killing vector; the equations of motion can be completely integrated. Perfect fluids can be studied by this way and the classical results of Lichnerowicz are obtained. In weakly dissipative motions two viscosity coefficient appear together with the heat conductibility coefficient. Two other coefficients perharps measurable on real fluids. Phase transitions and shock waves are described with using the model [fr
International Nuclear Information System (INIS)
Nemenov, L.
2001-01-01
The Coulomb interaction which occurs in the final state between two particles with opposite charges allows for creation of the bound state of these particles. In the case when particles are generated with large momentum in lab frame, the Lorentz factors of the bound state will also be much larger than one. The relativistic velocity of the atoms provides the opportunity to observe bound states of (π + μ - ), (π + π - ) and (π + K - ) with a lifetime as short as 10 -16 s, and to measure their parameters. The ultrarelativistic positronium atoms (A 2e ) allow us to observe the e.ect of superpenetration in matter, to study the effects caused by the formation time of A 2e from virtual e + e - pairs and to investigate the process of transformation of two virtual particles into the bound state
Energy Technology Data Exchange (ETDEWEB)
Kipping, David, E-mail: dkipping@astro.columbia.edu [Department of Astronomy, Columbia University, 550 W. 120th St., New York, NY 10027 (United States)
2017-06-01
One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail’s acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail’s motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot , we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.
Kipping, David
2017-06-01
One proposed method for spacecraft to reach nearby stars is by accelerating sails using either solar radiation pressure or directed energy. This idea constitutes the thesis behind the Breakthrough Starshot project, which aims to accelerate a gram-mass spacecraft up to one-fifth the speed of light toward Proxima Centauri. For such a case, the combination of the sail’s low mass and relativistic velocity renders previous treatments incorrect at the 10% level, including that of Einstein himself in his seminal 1905 paper introducing special relativity. To address this, we present formulae for a sail’s acceleration, first in response to a single photon and then extended to an ensemble. We show how the sail’s motion in response to an ensemble of incident photons is equivalent to that of a single photon of energy equal to that of the ensemble. We use this principle of ensemble equivalence for both perfect and imperfect mirrors, enabling a simple analytic prediction of the sail’s velocity curve. Using our results and adopting putative parameters for Starshot, we estimate that previous relativistic treatments underestimate the spacecraft’s terminal velocity by ∼10% for the same incident energy. Additionally, we use a simple model to predict the sail’s temperature and diffraction beam losses during the laser firing period; this allows us to estimate that, for firing times of a few minutes and operating temperatures below 300°C (573 K), Starshot will require a sail that absorbs less than one in 260,000 photons.
Lattice Boltzmann scheme for relativistic fluids
Mendoza, M.; Boghosian, B.; Herrmann, H. J.; Succi, S.
2009-01-01
A Lattice Boltzmann formulation for relativistic fluids is presented and numerically verified through quantitative comparison with recent hydrodynamic simulations of relativistic shock-wave propagation in viscous quark-gluon plasmas. This formulation opens up the possibility of exporting the main advantages of Lattice Boltzmann methods to the relativistic context, which seems particularly useful for the simulation of relativistic fluids in complicated geometries.
The Affection Vs. Intercourse Problem or All He Wants Is My Body.
Knox, David
This paper discusses the problems of affection versus intercourse in a male/female relationship, with differing degrees or periods of sexual interest listed as the most frequent sexual problem reported by students studied who were living together and by married couples. The problem occurs when one partner is refused while trying to initiate sexual…
Generic stability of dissipative non-relativistic and relativistic fluids
International Nuclear Information System (INIS)
Ván, Peter
2009-01-01
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium is asymptotically stable in both cases due to purely thermodynamic restrictions; the only requirements are the thermodynamic stability and the non-negativity of the transport coefficients
Riggs, Christina
2010-01-01
The human body is both the physical form inhabited by an individual “self” and the medium through which an individual engages with society. Hence the body both shapes and is shaped by an individual’s social roles. In contrast to the cognate fields of archaeology, anthropology, and classics, there has been little explicit discussion or theorization of the body in Egyptology. Some recent works, discussed here, constitute an exception to this trend, but there is much more scope for exploring anc...
Proton-proton virtual bremsstrahlung in a relativistic covariant model
Martinus, GH; Scholten, O; Tjon, J
1999-01-01
Lepton-pair production (virtual bremsstrahlung) in proton-proton scattering is investigated using a relativistic covariant model. The effects of negative-energy slates and two-body currents are studied. These are shown to have large effects in some particular structure functions, even at the
Problem of diagnosis and extraction of a foreign body in orbit associated with pain
Directory of Open Access Journals (Sweden)
Jovanović Miloš
2002-01-01
Full Text Available The aim of this study was to present the troubles and significance of a proper diagnosis of a foreign body which caused a double perforation of the eyeball and was retained in the orbit. Another reason for this case report was the intensive pain associated with the existing foreign body in the orbit. A male, 54 years old, had a perforating wound of the eyeball caused by a metal foreign body, which stayed in the orbit close to the scierai wall. X-ray and echographic examinations of the orbit were not conclusive regarding the question whether this foreign body was situated within or outside the eyeball. Only CT imaging showed that foreign body produced a double perforation of the eyeball and was externally close to the sciera. Foreign body was extracted by tran-sconjunctival anterior orbitotomy through the inferior fornix, using the electromagnetic probe. Since the first day of injury and up to the eighth day, the patient had intensive deep orbital pain, which was alleviated only partially by analgetics. It could not be explained by secondary glaucoma because IOP was normal or by an inflammatory process, or in any other way. Only the extraction of foreign body from the orbit led to the complete relief of pain. We believe that the pain was caused by compression of foreign body to some of scierai sensory nerves. X-ray and echographic examinations of the orbit are not always a reliable proof in the proper evaluation whether foreign body is within or outside the eyeball in the orbit. Precise diagnosis can be made only by CT imaging. The pain in the orbit may be caused by compression of foreign body to sensory nerves.
Shirmin, G. I.
Within the range of a model obtained from the twice-restricted circular four-body problem with the help of the Fatou averaging method the influence of a perturbing body attraction on the infinitesimal mass motion is considered.
Conductivity of a relativistic plasma
International Nuclear Information System (INIS)
Braams, B.J.; Karney, C.F.F.
1989-03-01
The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. This formulation is used to calculate the electrical conductivity. 13 refs., 1 fig., 1 tab
Conductivity of a relativistic plasma
Energy Technology Data Exchange (ETDEWEB)
Braams, B.J.; Karney, C.F.F.
1989-03-01
The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. This formulation is used to calculate the electrical conductivity. 13 refs., 1 fig., 1 tab.
Energy Technology Data Exchange (ETDEWEB)
Chau, H.T.P
2002-10-01
One of the main goals of classical and quantum physics is to solve the many-body problem. In nuclear theory, several methods have been developed and provide accurate results. In this thesis, we remind how symmetry can be used to obtain analytical solutions of the quantum many-body problem. We emphasize that unitary Lie algebras play a crucial role in quantum mechanics and propose and implement a method to build irreducible representations of this algebra from its highest-weight state. Calculations of bosonic and fermionic spectra are performed with realistic and with random interactions. Studies with rotational invariant two-body random interactions have unveiled high degree of order (a marked statistical preference is found for ground states with angular momentum equal to zero). In the second chapter of this thesis, it is argued that the spectral properties of this kind of interaction depend on the choice of the valence space. In particular, we propose a geometrical method to predict the properties of the ground state in certain cases. We also present numerical results when the geometrical approach can not be applied. In the third chapter, we study the link between quantum chaos and nuclear spectra calculated with realistic interactions. (author)
Relativistic quantum mechanics and field theory
Gross, Franz
1999-01-01
An accessible, comprehensive reference to modern quantum mechanics and field theory.In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field.
Juip, Micki; Fitzner, Karen
2012-06-01
People with diabetes require skills and knowledge to adhere to medication regimens and self-manage this complex disease. Effective self-management is contingent upon effective problem solving and decision making. Gaps existed regarding useful approaches to problem solving by individuals with very low and very high body mass index (BMI) who self-administer insulin injections. This article addresses those gaps by presenting findings from a patient survey, a symposium on the topic of problem solving, and recent interviews with diabetes educators to facilitate problem-solving approaches for people with diabetes with high and low BMI who inject insulin and/or other medications. In practice, problem solving involves problem identification, definition, and specification; goal and barrier identification are a prelude to generating a set of potential strategies for problem resolution and applying these strategies to implement a solution. Teaching techniques, such as site rotation and ensuring that people with diabetes use the appropriate equipment, increase confidence with medication adherence. Medication taking is more effective when people with diabetes are equipped with the knowledge, skills, and problem-solving behaviors to effectively self-manage their injections.
Rivolta, Davide; Lawson, Rebecca P; Palermo, Romina
2017-02-01
It has been estimated that one out of 40 people in the general population suffer from congenital prosopagnosia (CP), a neurodevelopmental disorder characterized by difficulty identifying people by their faces. CP involves impairment in recognizing faces, although the perception of non-face stimuli may also be impaired. Given that social interaction depends not only on face processing, but also on the processing of bodies, it is of theoretical importance to ascertain whether CP is also characterized by body perception impairments. Here, we tested 11 CPs and 11 matched control participants on the Body Identity Recognition Task (BIRT), a forced-choice match-to-sample task, using stimuli that require processing of body-specific, not clothing-specific, features. Results indicated that the group of CPs were as accurate as controls on the BIRT, which is in line with the lack of body perception complaints by CPs. However, the CPs were slower than controls, and when accuracy and response times were combined into inverse efficiency scores (IESs), the group of CPs were impaired, suggesting that the CPs could be using more effortful cognitive mechanisms to be as accurate as controls. In conclusion, our findings demonstrate that CP may not generally be limited to face processing difficulties, but may also extend to body perception.
New theories of relativistic hydrodynamics in the LHC era
Florkowski, Wojciech; Heller, Michal P.; Spaliński, Michał
2018-04-01
The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our review presents these developments from the perspective of the underlying microscopic physics, using the language of quantum field theory, relativistic kinetic theory, and holography. We discuss the gradient expansion, the phenomenon of hydrodynamization, as well as several models of hydrodynamic evolution equations, highlighting the interplay between collective long-lived and transient modes in relativistic matter. Our aim to provide a unified presentation of this vast subject—which is naturally expressed in diverse mathematical languages—has also led us to include several new results on the large-order behaviour of the hydrodynamic gradient expansion.
New theories of relativistic hydrodynamics in the LHC era.
Florkowski, Wojciech; Heller, Michal P; Spaliński, Michał
2018-04-01
The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our review presents these developments from the perspective of the underlying microscopic physics, using the language of quantum field theory, relativistic kinetic theory, and holography. We discuss the gradient expansion, the phenomenon of hydrodynamization, as well as several models of hydrodynamic evolution equations, highlighting the interplay between collective long-lived and transient modes in relativistic matter. Our aim to provide a unified presentation of this vast subject-which is naturally expressed in diverse mathematical languages-has also led us to include several new results on the large-order behaviour of the hydrodynamic gradient expansion.
Relativistic multiwave Cerenkov generator
Bugaev, S. P.; Kanavets, V. I.; Klimov, A. I.; Koshelev, V. I.; Cherepenin, V. A.
1983-11-01
The design and operation of a multiwave Cerenkov generator using a relativistic electron beam are reported. The device comprises a 3-cm-radius tubular graphite cathode fed with a 1-microsec 1-2.5-MW pulse from a Marx generator; a 5.6-cm-radius anode; an increasing 14-32-kG magnetic field; a 3.4-cm-aperture-radius graphite collimating iris; a stainless-steel semitoroidal-iris-loaded slow-wave structure of maximum length 48.6 cm, inside radius 4.2 cm, iris aperture radius 3.0 cm, iris minor radius 3 mm, and period 1.5 cm; a stainless-steel cone collector; and a vacuum-tight 60-cm-radius window. At 2.5 MV and 21 kG, output power at wavelength 3.15 + or - 0.1 cm is measured as about 5 GW, with baseline pulse length 30-50 nsec and efficiency up to about 10 percent.
Practical Relativistic Bit Commitment.
Lunghi, T; Kaniewski, J; Bussières, F; Houlmann, R; Tomamichel, M; Wehner, S; Zbinden, H
2015-07-17
Bit commitment is a fundamental cryptographic primitive in which Alice wishes to commit a secret bit to Bob. Perfectly secure bit commitment between two mistrustful parties is impossible through an asynchronous exchange of quantum information. Perfect security is, however, possible when Alice and Bob each split into several agents exchanging classical information at times and locations suitably chosen to satisfy specific relativistic constraints. In this Letter we first revisit a previously proposed scheme [C. Crépeau et al., Lect. Notes Comput. Sci. 7073, 407 (2011)] that realizes bit commitment using only classical communication. We prove that the protocol is secure against quantum adversaries for a duration limited by the light-speed communication time between the locations of the agents. We then propose a novel multiround scheme based on finite-field arithmetic that extends the commitment time beyond this limit, and we prove its security against classical attacks. Finally, we present an implementation of these protocols using dedicated hardware and we demonstrate a 2 ms-long bit commitment over a distance of 131 km. By positioning the agents on antipodal points on the surface of Earth, the commitment time could possibly be extended to 212 ms.
Ion G. Motofei; David L. Rowland
2015-01-01
In a previous published paper, we initiated in this journal discussion about new perspectives regarding the organization and functioning of the mind, as a premise for addressing the mind-body problem. In this article, we continue focussing discussion on two distinct but interrelated concepts, internal-mental existence/ entity and internal-mental reality. These two psycho-physiological subunits of the mind interact each other in the form of an internal-mental interaction, having no sense if...
Directory of Open Access Journals (Sweden)
A. Narayan
2013-01-01
Full Text Available The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.
Apparent paradoxes in classical electrodynamics: relativistic transformation of force
International Nuclear Information System (INIS)
Kholmetskii, A L; Yarman, T
2007-01-01
In this paper, we analyse a number of paradoxical teaching problems of classical electrodynamics, dealing with the relativistic transformation of force for complex macro systems, consisting of a number of subsystems with nonzero relative velocities such as electric circuits that change their shape in the course of time
Equilibria of the three-body problem with rigid dumb-bell satellite
International Nuclear Information System (INIS)
Elipe, A.; Palacios, M.; Pretka-Ziomek, H.
2008-01-01
This paper is concerned with the orbital-rotational motion of an asymmetric dumb-bell (two masses with fixed distance among them) under the attraction of a central body. For this model, we find some equilibria and give sufficient conditions for their stability
The Slender Imbalance: An Overview of Body Image Related Problems and Solutions.
McBride, Leslie
The current emphasis on thinness has had a negative impact on many women and girls who suffer from a negative body image, poor self-concept, and depression, three conditions that often manifest themselves behaviorally through chronic dieting, compulsive exercise, and eating disorders. Socio-cultural factors that have contributed to this emphasis…
On the linear problem arising from motion of a fluid around a moving rigid body
Czech Academy of Sciences Publication Activity Database
Nečasová, Šárka; Wolf, J.
2015-01-01
Roč. 140, č. 2 (2015), s. 241-259 ISSN 0862-7959 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : incompressible fluid * rotating rigid body * strong solution Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144329
Relativistic three-particle dynamical equations: II. Application to the trinucleon system
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.
1993-11-01
The contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy is calculated employing five sets tri nucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (author)
Julié, Félix-Louis
2018-01-01
Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a ν deformation (where ν =0 is the test mass limit) of the analytically known ST Hamiltonian of a test particle. This ST-EOB Hamiltonian leads to a simple (yet canonically equivalent) formulation of the conservative 2PK two-body problem, but also defines a resummation of the dynamics which is well-suited to ST regimes that depart strongly from general relativity (GR) and which may provide information on the strong field dynamics; in particular, the ST innermost stable circular orbit location and associated orbital frequency. Results will be compared and contrasted with those deduced from the ST-deformation of the (5PN) GR-EOB Hamiltonian previously obtained in [Phys. Rev. D 95, 124054 (2017), 10.1103/PhysRevD.95.124054].
VEBA relativistic electron accelerator
International Nuclear Information System (INIS)
Parker, R.K.; Ury, M.
1975-01-01
The VEBA high-current, relativistic electron accelerator was designed and constructed at NRL for applications in the study of high-power microwave sources. To meet the requirements of this study, the accelerator was designed for operation in either a short (60 nsec) or long (2.2 μsec) pulse mode. The short-pulse mode has been in operation for nearly two years and has proven to be an extremely reliable design. The design of the long-pulse mode is now complete and component fabrication will soon be underway. The pulse-forming network in the short-pulse mode is an unbalanced, water Blumlein with an output impedance of 9.2 Ω. The Blumlein is pulse charged by a 17 stage Marx generator which has a series capacitance of 29.4 nF. By transmission along a tapered coaxial line, the output pulse is transformed to 20 Ω, and the voltage developed across a matched load increases to a maximum of 2.3 MV. The proposed conversion to the long-pulse mode will require the Blumlein and transformer sections be removed and the diode assembly be attached directly to the oversized Marx tank. The direct coupling between the Marx and the Blumlein will then be replaced by two nested water capacitors, which are shunted by spiral inductors. When coupled in series with the Marx, this output filter will form a three-section, voltage-fed, Guillemin (type A), pulse-forming network with a characteristic impedance of 40 Ω and a maximum output voltage of 0.9 MV. (auth)
Present status of the theoretical relativistic plasma SHF electronics
International Nuclear Information System (INIS)
Kuzelev, M.V.; Rukhadze, A.A.
2000-01-01
Paper presents a review of theoretical investigations into powerful sources of SHF waves grounded on the forced emission of relativistic electron beams in plasma wave guides and resonator. Emission sources operating under amplification of a certain inlet signal and under generation mode were studied. Two mechanisms of forced emission: resonance Cherenkov radiation of relativistic electron beams in plasma and nonresonance Pierce emission resulting from evolution of high-frequency Pierce instability, were studied. Paper discusses theoretical problems only, all evaluations and calculations are made for the parameters of the exact experiments, the theoretical results are compared with the available experimental data. Factors affecting formation of spectrum of waves excited by relativistic electron beam in plasma systems are discussed [ru
Statistical thermodynamics of a two-dimensional relativistic gas.
Montakhab, Afshin; Ghodrat, Malihe; Barati, Mahmood
2009-03-01
In this paper we study a fully relativistic model of a two-dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for x and y components of velocity in the rest frame (Gamma) as well as the moving frame (Gamma;{'}) . Our results confirm that Jüttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter beta for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).
Introduction to the renormalization group study in relativistic quantum field theory
International Nuclear Information System (INIS)
Mignaco, J.A.; Roditi, I.
1985-01-01
An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt
Manifestation of sleeping-instability in partially-compensated relativistic electron beams
International Nuclear Information System (INIS)
Karbushev, N.I.; Rukhadze, A.A.; Udivichenko, S.Yu.
1984-01-01
Problem of sleeping-instability in partially-compensated relativistic electron beam is exactly solved for the ring waveguide. Nonuniformity of beam velocity is conditioned by electrostatic potential sagging
CAFE: A NEW RELATIVISTIC MHD CODE
Energy Technology Data Exchange (ETDEWEB)
Lora-Clavijo, F. D.; Cruz-Osorio, A. [Instituto de Astronomía, Universidad Nacional Autónoma de México, AP 70-264, Distrito Federal 04510, México (Mexico); Guzmán, F. S., E-mail: fdlora@astro.unam.mx, E-mail: aosorio@astro.unam.mx, E-mail: guzman@ifm.umich.mx [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo. Edificio C-3, Cd. Universitaria, 58040 Morelia, Michoacán, México (Mexico)
2015-06-22
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin–Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin–Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
CAFE: A New Relativistic MHD Code
Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzmán, F. S.
2015-06-01
We introduce CAFE, a new independent code designed to solve the equations of relativistic ideal magnetohydrodynamics (RMHD) in three dimensions. We present the standard tests for an RMHD code and for the relativistic hydrodynamics regime because we have not reported them before. The tests include the one-dimensional Riemann problems related to blast waves, head-on collisions of streams, and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the two-dimensional (2D) and 3D tests without magnetic field, we include the 2D Riemann problem, a one-dimensional shock tube along a diagonal, the high-speed Emery wind tunnel, the Kelvin-Helmholtz (KH) instability, a set of jets, and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability, and a 3D magnetic field advection loop. The code uses high-resolution shock-capturing methods, and we present the error analysis for a combination that uses the Harten, Lax, van Leer, and Einfeldt (HLLE) flux formula combined with a linear, piecewise parabolic method and fifth-order weighted essentially nonoscillatory reconstructors. We use the flux-constrained transport and the divergence cleaning methods to control the divergence-free magnetic field constraint.
Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T
2017-01-01
The problem of physical interpretation of the nonlocal relativistic diffusion (NoRD model) for cosmic ray transport in the Galaxy is discussed. The model accounts for the turbulent character of the interstellar medium and the relativistic principle of the speed limitation. Involving fractional calculus and non-Gaussian Lévy statistics yields numerical results compatible with observation data. A special attention is paid to the knee problem. The relativistic speed limit requirement steepens theoretical background spectrum at certain energies, and the position of the break, its sharpness and slopes of asymptotes depend on D α ( E ) and α . (paper)
Theory of relativistic heat polynomials and one-sided Lévy distributions
Dattoli, G.; Górska, K.; Horzela, A.; Penson, K. A.; Sabia, E.
2017-06-01
The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These types of equations are pivotal elements to treat problems in anomalous diffusion and in relativistic quantum mechanics. In this paper, we report on new links between fractional diffusion, quantum relativistic equations, and particular families of polynomials, linked to the Bessel polynomials in Carlitz form and playing the role of relativistic heat polynomials. We introduce generalizations of these polynomial families and point out their specific use for the solutions of problems of practical importance.
Hyperspherical functions and quantum-mechanical three-body problem with application to carbon 12
International Nuclear Information System (INIS)
Letz, H.
1975-01-01
In this work a system of three identical particles (bosons) interacting by a particular two-body force is discussed. Using the complete set of the hyperspherical functions (K-harmonics), analytical expressions for eigenvalues and wave functions of the stationary states are found. The numerical evaluation gives a level sequence for a definite pair of potential parameters similar to that of the nucleus carbon 12
The self-consistent field method in the study of many-body problems
International Nuclear Information System (INIS)
Campos, V.B.F. de.
1976-01-01
Properties of many-body systems in special quantum liquids (T=O 0 K), utilizing the self-consistent field method (SCFM) are calculated. The SCFM is applied to quantum systems compounds by neutral and charged (electrons) particles, studying the generalized susceptibility of the system. Thus, properties as the structure factor, pair correlation function, excitation energy spectra, sound velocity, etc are obtained self-consistently (L.C.) [pt
The mind body problem, part three: ascension of sexual function to cerebral level
Ion G. Motofei; David L. Rowland
2016-01-01
Physiologically, the somatic nervous system intervenes in external interaction between the body and environment, while autonomic nervous system ensures the functioning of internal organs. We present in this paper a psycho-physiological perspective suggesting that mental function (somatic in nature, because coordinates environmental interaction) is closer to and more aligned with the physiologic functioning of autonomic nervous system (due to autonomy, duality, etc.). At opposite end, sexual f...
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.
1979-01-01
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt
Collision orbits and chaos in the free-fall three-body problem.
Tanikawa, K.; Umehara, H.
In this short report, the authors want to stress the chaotic nature of the final motions of the problem with reference to the distribution of binary collision curves and triple collision points. The calculation extends to the escapes at the first three collapses of the triple system. The Aarseth code to obtain the final motions is used.
Non-Relativistic Superstring Theories
Energy Technology Data Exchange (ETDEWEB)
Kim, Bom Soo
2007-12-14
We construct a supersymmetric version of the 'critical' non-relativistic bosonic string theory [1] with its manifest global symmetry. We introduce the anticommuting bc CFT which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider 'noncritical' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.
Relativistic description of deformed nuclei
International Nuclear Information System (INIS)
Price, C.E.
1988-01-01
The author has shown that relativistic Hartree calculations using parameters that have been fit to the properties of nuclear matter can provide a good description of both spherical and axially deformed nuclei. The quantitative agreement with experiment is equivalent to that which was obtained in non-relativistic calculations using Skyrme interactions. The equilibrium deformation is strongly correlated with the size of the spin-orbit splitting, and that parameter sets which give roughly the correct value for this splitting provide the best agreement with the quadrupole moments in the s-d shell. Finally, for closed shell +/- 1 nuclei, it was shown that the self-consistent calculations are able to reproduce the experimental magnetic moments. This was not possible in relativistic calculations which include only the effects of the valence orbital
Computational Relativistic Astrophysics Using the Flow Field-Dependent Variation Theory
Richardson, G. A.; Chung, T. J.
2002-01-01
We present our method for solving general relativistic nonideal hydrodynamics. Relativistic effects become pronounced in such cases as jet formation from black hole magnetized accretion disks which may lead to the study of gamma-ray bursts. Nonideal flows are present where radiation, magnetic forces, viscosities, and turbulence play an important role. Our concern in this paper is to reexamine existing numerical simulation tools as to the accuracy and efficiency of computations and introduce a new approach known as the flow field-dependent variation (FDV) method. The main feature of the FDV method consists of accommodating discontinuities of shock waves and high gradients of flow variables such as occur in turbulence and unstable motions. In this paper, the physics involved in the solution of relativistic hydrodynamics and solution strategies of the FDV theory are elaborated. The general relativistic astrophysical flow and shock solver (GRAFSS) is introduced, and some simple example problems for computational relativistic astrophysics (CRA) are demonstrated.
Directory of Open Access Journals (Sweden)
Peterson Kelly
2007-04-01
Full Text Available Abstract Background Despite the increasing prevalence of overweight/obesity and its association to eating patterns in adolescents and adults, little is known about the relationship between problematic eating behaviours and body weight in the preschool years within the context of various social factors. This research aims to analyze the relationship between social factors, mothers' perceptions of their child's eating behaviour (picky eating and overeating, and body weight in preschool years, in a population-based cohort of preschoolers from Québec (Canada. Methods Analyses were performed on 1498 children from the Longitudinal Study of Child Development in Québec, a representative sample of children born in 1998 in the Canadian province of Québec. Eating behaviours (picky eating and overeating were derived from questionnaires at 2.5, 3.5, and 4.5 years of age. BMI was calculated from children's measured height and weight at 4.5 years. Children's sex and birth weight, mothers' age, immigrant status, smoking status during pregnancy, and education level, family type, annual household income and income sufficiency, the number of overweight/obese parents, children's day-care attendance, and food insufficiency were part of the analysis. Multivariate logistic regressions were used to determine odds ratios for different body weight profiles (underweight, normal weight, at risk of overweight, overweight, and one-way analysis-of-variances (ANOVA allowed for group comparisons of means. Results The proportion of children reported for each eating behaviour category remained quite stable across the years studied. Picky eating and overeating related to body weight among 4.5-year-old children, even when social and parental factors were accounted for in multivariate analysis. Picky eaters were twice as likely to be underweight at 4.5 years as children who were never picky eaters. Adjusted odds ratios revealed overeaters were 6 times more likely to be overweight
Communication: An N-body solution to the problem of Fock exchange.
Challacombe, Matt; Bock, Nicolas
2014-03-21
We report an N-Body approach to computing the Fock exchange matrix with and without permutational symmetry. The method achieves an O(NlgN) computational complexity through an embedded metric-query, allowing hierarchical application of direct SCF criteria. The advantages of permutational symmetry are found to be 4-fold for small systems, but decreasing with increasing system size and/or more permissive neglect criteria. This work sets the stage for: (1) the introduction of range queries in multi-level multipole schemes for rank reduction, and (2) recursive task parallelism.
SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION
Energy Technology Data Exchange (ETDEWEB)
Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)
2016-12-20
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Special Relativistic Hydrodynamics with Gravitation
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Multibaryon interactions at relativistic energies
International Nuclear Information System (INIS)
Baldin, A.M.
1980-01-01
Having discussed the basic notions and quantities used when considering multibaryon interactions in the relativistic range, attention is focussed on particle production in the region of limiting fragmentation of nuclei which is kinematically forbidden for one-nucleon collisions (the cumulative region). Multibaryon configurations responsible for the cumulative effect are examined with especial reference to the possible existence of metastable multiquark systems, for example of dibaryons. Finally the present status and perspectives of studies in the field of relativistic nuclear physics at the Joint Institute for Nuclear Research are discussed. (UK)
Application of the CIP Method to Strongly Nonlinear Wave-Body Interaction Problems
Zhu, Xinying
2006-01-01
Water entry and exit, green water on deck, sloshing in tanks and capsizing in intact and damaged conditions are examples on violent fluid motion. The combination of model tests, theoretical analysis and Computational Fluid Dynamics (CFD) methods is emphasized in treating these problems. Because mixing of air and liquid may occur, the interaction between the flow in the air and in the liquid ought to be considered in numerical simulations. Further, the mixing of air and liquid represents a sca...
Existence of solutions for the dynamic frictional contact problem of isotropic viscoelastic bodies
Czech Academy of Sciences Publication Activity Database
Eck, C.; Jarušek, Jiří
2003-01-01
Roč. 53, č. 2 (2003), s. 157-181 ISSN 0362-546X R&D Projects: GA AV ČR IAA1075005; GA AV ČR IAA1075707 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : dynamic contact problem * parabolic equation * Coulomb law of friction Subject RIV: BA - General Mathematics Impact factor: 0.354, year: 2003
The relativistic feedback discharge model of terrestrial gamma ray flashes
Dwyer, Joseph R.
2012-02-01
As thunderclouds charge, the large-scale fields may approach the relativistic feedback threshold, above which the production of relativistic runaway electron avalanches becomes self-sustaining through the generation of backward propagating runaway positrons and backscattered X-rays. Positive intracloud (IC) lightning may force the large-scale electric fields inside thunderclouds above the relativistic feedback threshold, causing the number of runaway electrons, and the resulting X-ray and gamma ray emission, to grow exponentially, producing very large fluxes of energetic radiation. As the flux of runaway electrons increases, ionization eventually causes the electric field to discharge, bringing the field below the relativistic feedback threshold again and reducing the flux of runaway electrons. These processes are investigated with a new model that includes the production, propagation, diffusion, and avalanche multiplication of runaway electrons; the production and propagation of X-rays and gamma rays; and the production, propagation, and annihilation of runaway positrons. In this model, referred to as the relativistic feedback discharge model, the large-scale electric fields are calculated self-consistently from the charge motion of the drifting low-energy electrons and ions, produced from the ionization of air by the runaway electrons, including two- and three-body attachment and recombination. Simulation results show that when relativistic feedback is considered, bright gamma ray flashes are a natural consequence of upward +IC lightning propagating in large-scale thundercloud fields. Furthermore, these flashes have the same time structures, including both single and multiple pulses, intensities, angular distributions, current moments, and energy spectra as terrestrial gamma ray flashes, and produce large current moments that should be observable in radio waves.
Transport models for relativistic heavy-ion collisions at Relativistic ...
Indian Academy of Sciences (India)
2015-04-29
Apr 29, 2015 ... We review the transport models that are widely used to study the properties of the quark-gluon plasma formed in relativistic heavy-ion collisions at RHIC and LHC. We show that transport model analysis of two important and complementary observables, the anisotropic flow of bulk hadrons and suppression ...
Directory of Open Access Journals (Sweden)
Richard Anantua
2018-03-01
Full Text Available This work summarizes a program intended to unify three burgeoning branches of the high-energy astrophysics of relativistic jets: general relativistic magnetohydrodynamic (GRMHD simulations of ever-increasing dynamical range, the microphysical theory of particle acceleration under relativistic conditions, and multiwavelength observations resolving ever-decreasing spatiotemporal scales. The process, which involves converting simulation output into time series of images and polarization maps that can be directly compared to observations, is performed by (1 self-consistently prescribing models for emission, absorption, and particle acceleration and (2 performing time-dependent polarized radiative transfer. M87 serves as an exemplary prototype for this investigation due to its prominent and well-studied jet and the imminent prospect of learning much more from Event Horizon Telescope (EHT observations this year. Synthetic observations can be directly compared with real observations for observational signatures such as jet instabilities, collimation, relativistic beaming, and polarization. The simplest models described adopt the standard equipartition hypothesis; other models calculate emission by relating it to current density or shear. These models are intended for application to the radio jet instead of the higher frequency emission, the disk and the wind, which will be subjects of future investigations.
Morse index for figure-eight choreographies of the planar equal mass three-body problem
Fukuda, Hiroshi; Fujiwara, Toshiaki; Ozaki, Hiroshi
2018-04-01
We report on numerical calculations of the Morse index for figure-eight choreographic solutions to a system of three identical bodies in a plane interacting through the homogeneous potential, -1/r a , or through the Lennard-Jones-type (LJ) potential, 1/r12 - 1/r6 , where r is a distance between the bodies. The Morse index is a number of independent variational functions giving negative second variation S (2) of action functional S. We calculated three kinds of Morse indices, N, N c and N e, in the domain of the periodic, the choreographic and the figure-eight choreographic function, respectively. For the homogeneous system, we obtain N = 4 for 0 ≤slant a periodic solution found by Simó through S (2). For the LJ system, we calculated the index for the solution tending to the figure-eight solution of the a = 6 homogeneous system for the period T \\to ∞ . We obtain N, N c and N e as monotonically increasing functions of T from T \\to ∞ , which start with N=N_c=N_e=0 , jump at the smallest T by 1, and reach N = 12, N_c=4 , and N_e=1 for T \\to ∞ in the other branch.
The general problem of the motion of coupled rigid bodies about a fixed point
Leimanis, Eugene
1965-01-01
In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.
Radiatively-driven general relativistic jets
Indian Academy of Sciences (India)
Mukesh K. Vyas
2018-02-10
Feb 10, 2018 ... Abstract. We use moment formalism of relativistic radiation hydrodynamics to obtain equations of motion of radial jets and solve them using polytropic equation of state of the relativistic gas. We consider curved space- time around black holes and obtain jets with moderately relativistic terminal speeds.
Relativistic generalization of strong plasma turbulence
International Nuclear Information System (INIS)
Chian, A.C.-L.
1982-01-01
Two fundamental electrostatic modes of an unmagnetized plasma, namely, ion acoustic mode and Langumir mode are studied. Previous theories are generalized to include the effect of relativistic mass variations. The existence of relativistic ion acoustic solitons is demonstrated. In addition, it is shown that simple, relativistic Langumir solitons do not exist in a infinite plasma. (L.C.) [pt
Apparent unambiguousness of relativistic time dilation
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1992-01-01
It is indicated on the definite analogy between the dependence of visible sizes of relativistic objects and period of the wave, emitted by the moving source from the observation conditions ('retradition factor'). It is noted that the definition of time for moving extended objects, led to relativistic dilation, corresponds to the definition of the relativistic (radar) length led to the 'elongation formula'. 10 refs
Arnot, C. S.; McInnes, C. R.; McKay, R. J.; Macdonald, M.; Biggs, J.
2018-02-01
This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δ v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.
Relativistic correlations in atoms
International Nuclear Information System (INIS)
Dietz, K.
1987-01-01
Atoms are particularly well-suited objects when it comes to testing certain concepts of many-body theories. They play a unique role in this respect because of two constructively interfering reasons: first of all, the laws describing the interactions of their constituents are the ones best known in all of Physics; secondly, their structure is comparatively simple and amenable to concise theoretical treatment. Because of these two reasons, physically motivated many-body approximation schemes, ordered in a systematic hierarchy of precision, can be carefully tested; discrepancies between theory and experiment are due to many-body effects and are never masked by uncertainties in the constituent-interaction (needless to say, the very small hadronic contributions to atomic structure is left out. Many-body effects in atoms are solely produced by the electron-electron interaction which derives from the laws of Quantum Electrodynamics or, in a very good approximation from the repulsive Coulomb potential; in the general nomenclature they are named correlations. The material is organized in two chapters: chapter 1 deals with a general introduction and discussion of g-Hartree mean-field theories, chapter 2 deals with applications. The role of vacuum fluctuations and deformations of the Dirac sea in a consistent construction of mean-fields is emphasized and their explicit form in the g-Hartree theory is given. 21 references, 5 figures, 3 tables
Many-body problem in quantum mechanics and quantum statistical mechanics
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/
The mind body problem, part three: ascension of sexual function to cerebral level
Directory of Open Access Journals (Sweden)
Ion G. Motofei
2016-04-01
Full Text Available Physiologically, the somatic nervous system intervenes in external interaction between the body and environment, while autonomic nervous system ensures the functioning of internal organs. We present in this paper a psycho-physiological perspective suggesting that mental function (somatic in nature, because coordinates environmental interaction is closer to and more aligned with the physiologic functioning of autonomic nervous system (due to autonomy, duality, etc.. At opposite end, sexual function (autonomic in nature, erection for example being a parasympathetic vasodilatory reflex seems to be compatible and even dependent by a somatic participation (erectile response is rather induced by environmental stimuli than internal visceral stimuli. The perspective presented here is that the mind and sexuality are two distinct relational processes which, being related to the same environmental stimuli/ peripheral afferents, should be supported by a common (somatic-autonomic neurobiological substrate.
Helium double photoionisation: an accurate solution of a three-body Coulomb problem
International Nuclear Information System (INIS)
Kheifets, A.S.; Bray, I.
1998-01-01
We present here the solution of the helium double photoionisation problem by the convergent close-coupling (CCC) method. This method allows us to obtain the most detailed description of the double photoionisation process in the form of the fully resolved triply differential cross section (TDCS). The accuracy of our model is tested by calculating the TDCS in the three different forms of the electromagnetic operator which produces essentially identical results. We compare our calculation with the most accurate experimental and theoretical data available to date. Copyright (1998) CSIRO Australia
Proof of the Spin Statistics Connection 2: Relativistic Theory
Santamato, Enrico; De Martini, Francesco
2017-12-01
The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.
The convergent close-coupling method for a Coulomb three-body problem
International Nuclear Information System (INIS)
Bray, I.; Stelbovics, A.T.
1994-09-01
The close-coupling method relies on the reformulation of the Schroedinger equation into an infinite set of coupled-channel equations by expanding over the complete set of target states. The difficulty in applying this approach is that the continuum channels are known to be very important in the intermediate-energy region and coupling to them must be included with little approximation. The application of the Convergent Close-Coupling (CCC) method is discussed which allows the continuum to be treated in a systematic manner via the use of square-integrable states. The CCC method utilizes an expansion of the target in a complete set of orthogonal L 2 functions which form a basis for the underlying Hilbert space. The utility of the method relies on being able to demonstrate convergence in the scattering amplitudes of interest as the basis size is increased. Numerical examples for the well known Temkin-Poet problem are used to illustrate the method. It is estimated the methods may be readily applied to full electron-atom scattering problem. 17 refs., 4 figs
Particle Acceleration in Relativistic Outflows
Bykov, Andrei; Gehrels, Neil; Krawczynski, Henric; Lemoine, Martin; Pelletier, Guy; Pohl, Martin
2012-01-01
In this review we confront the current theoretical understanding of particle acceleration at relativistic outflows with recent observational results on various source classes thought to involve such outflows, e.g. gamma-ray bursts, active galactic nuclei, and pulsar wind nebulae. We highlight the possible contributions of these sources to ultra-high-energy cosmic rays.
Future relativistic heavy ion experiments
International Nuclear Information System (INIS)
Pugh, H.G.
1980-12-01
Equations of state for nuclear matter and ongoing experimental studies are discussed. Relativistic heavy ion physics is the only opportunity to study in the laboratory the properties of extended multiquark systems under conditions such that quarks might run together into new arrangements previously unobserved. Several lines of further study are mentioned
Thermal effects in relativistic plasmas
International Nuclear Information System (INIS)
Castaldo, C.; Fedele, R.; Angelis, U. de; Bingham, R.
1990-11-01
A kinetic approach is used for a description of a plasma in the presence of a large amplitude wave (ie relativistic electrons). The case of a ''small'' momentum spread around an average momentum is considered and corrections to the cold plasma case (zero spread) are given. (author)
Relativistic electron beams above thunderclouds
DEFF Research Database (Denmark)
Füellekrug, M.; Roussel-Dupre, R.; Symbalisty, E. M. D.
2011-01-01
of electrons partially discharge the lightning electric field above thunderclouds and thereby gain a mean energy of similar to 7MeV to transport a total charge of similar to-10mC upwards. The impulsive current similar to 3 x 10(-3) Am-2 associated with relativistic electron beams above thunderclouds...
Fast lattice Boltzmann solver for relativistic hydrodynamics.
Mendoza, M; Boghosian, B M; Herrmann, H J; Succi, S
2010-07-02
A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.
The problem with weighing: effects on mood, self-esteem and body image.
Ogden, J; Evans, C
1996-03-01
To examine the effect of weighing and comparison with social norms on self-esteem, mood and body dissatisfaction. An experimental design was used. Seventy-four normal weight individuals took part in the study. Subjects completed a set of measures before and after being weighed and sequentially allocated to either the under, average or over weight conditions according to a fictional height-weight chart. The results showed that subjects allocated to the overweight group showed an increase in depression and a decrease in self esteem following the manipulation, compared to subjects in the average weight group who reported improvements in these measures and the underweight group who similarly showed decreased depression, but showed some deterioration of their self-esteem. Weighing and comparison with height weight charts of weight norms is used both to detect and treat overweight and obesity. The results from this study indicate that this procedure may not be as benign as believed and may contribute to the negative psychological state of the individual.
Solving three-body-breakup problems with outgoing-flux asymptotic conditions
International Nuclear Information System (INIS)
Randazzo, J. M.; Frapiccini, A. L.; Colavecchia, F. D.; Buezas, F.; Gasaneo, G.
2011-01-01
An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys. 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.
The many-body level density; Densite de niveaux du probleme a n-corps
Energy Technology Data Exchange (ETDEWEB)
Roccia, J
2007-09-15
We investigate the many-body level density {rho}{sub MB} for fermion and boson gases. We establish its behavior as a function of the temperature and the number of particles. We deal with correction terms due to finite number of particles effects for {rho}{sub MB}: for fermions, it seems that it exists only one behavior. We propose a semiclassical expression of {rho}{sub MB} for two types of particles with an angular momentum. It is decomposed into a smooth part coming from the saddle point method plus corrective terms due to the expansion of the number of partitions for two types of particles and an oscillating part coming from the fluctuations of the single-particle level density. Our model is validated by a numerical study. For the case of the atomic nucleus, the oscillating part of {rho}{sub MB} is controlled by a temperature factor which depends on the chaotic or integrable nature of the system and on the fluctuation of the ground state energy. This leads to consider in more detail this last quantity. For an isolated system, we give the general expression of the mean value for fixed potentials. We treat the self-bound system case through the example of the three dimensional harmonic oscillator (3DHO). Furthermore we study the oscillating part of {rho}{sub MB} for bosons in the low temperature regime for billiards and for isotropic 3DHO. We note the oscillations disappear leading to a power law correction. In the case of the isotropic 3DHO, these corrections have the same order of magnitude as the smooth part. In the same way, for the high temperature regime we show the oscillating part of {rho}{sub MB} is exponentially negligible compared to the smooth part. (author)
The Hubbard dimer: a density functional case study of a many-body problem.
Carrascal, D J; Ferrer, J; Smith, J C; Burke, K
2015-10-07
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the 'failure' of the Kohn-Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree-Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.
Directory of Open Access Journals (Sweden)
Smirnov S.A.,
2016-04-01
Full Text Available The paper analyses the issue of a popular trend called ‘life outsourcing’ which affects the structure of personality in an individual. Basing on the works of L.S. Vygotsky and others, the author explores the methodology of the concept of cultural development as a process of formation of an embodied personality or non-organic body. He outlines the search for the approaches to the process of cultural development and for its descriptions in terms of personality construction and ‘soul organism’ which can be traced down in Vygotsky’s works. According to these works, cultural-historical psychology employed a concept of tool- and activity-based personality body, or soul organism. As it is argued in the paper, this concept is to a certain extent incomplete. What happens to the individual’s personality body in a situation of increasingly popular life outsourcing, i.e. when more and more basic functions and actions are transferred from the individual to various devices? Using artistic creativity as an example, the author explores the artist’s transition from working with natural materials to working with devices and focuses on the problem of the artist’s ‘smart body’ losing the feeling of texture and form. The issue is to be continued in the second paper.
Silverberg, Jesse; Ng, Pei Ying; Baron, Roland; Yin, Peng
Most research on in vivocytoskeletal mechanics focuses on what happens in a single cell context. This foundational work has opened up new avenues to study higher-order problems, such as what happens when cells physically interact. For example, osteoclasts, one of the cell types responsible for maintaining healthy skeletal structure, are formed when 10 or more mononuclear cells fuse into a multinuclear behemoth. But how does the cytoskeleton of two or more cells fuse? And what is the role of mechanics in understanding the resulting cytoskeletal organization? In this work, we use the multiscale multiplexed Molecular Atlas Platform to image and study the cytoskeletal mechanics of cell-cell fusion. Our work documents the processes involved and uses observed structures to infer mechanical events during these interactions. Broadly this work takes a technology-driven approach to perform fundamental exploratory work, and uses current state-of-the-art cytoskeletal mechanical modeling to interpret our observations. National Cancer Institute of the National Institutes of Health under Award Number F32CA204038.
Wang, Shoucheng; Huang, Guoqing; Wu, Xin
2018-02-01
In this paper, we survey the effect of dissipative forces including radiation pressure, Poynting–Robertson drag, and solar wind drag on the motion of dust grains with negligible mass, which are subjected to the gravities of the Sun and Jupiter moving in circular orbits. The effect of the dissipative parameter on the locations of five Lagrangian equilibrium points is estimated analytically. The instability of the triangular equilibrium point L4 caused by the drag forces is also shown analytically. In this case, the Jacobi constant varies with time, whereas its integral invariant relation still provides a probability for the applicability of the conventional fourth-order Runge–Kutta algorithm combined with the velocity scaling manifold correction scheme. Consequently, the velocity-only correction method significantly suppresses the effects of artificial dissipation and a rapid increase in trajectory errors caused by the uncorrected one. The stability time of an orbit, regardless of whether it is chaotic or not in the conservative problem, is apparently longer in the corrected case than in the uncorrected case when the dissipative forces are included. Although the artificial dissipation is ruled out, the drag dissipation leads to an escape of grains. Numerical evidence also demonstrates that more orbits near the triangular equilibrium point L4 escape as the integration time increases.
Güémez, J.; Fiolhais, M.
2018-05-01
We apply the four-vector formalism of special relativity to describe various interaction processes of photons with a solar sail, in two cases: when the sail’s surface is a perfect mirror, and when it is a body coated with a totally absorbing material. We stress the pedagogical value of implementing simultaneously both the linear momentum and the energy conservation in a covariant fashion, as our formalism inherently does. It also allows for a straightforward change of the description of a certain process in different inertial reference frames.
Relativistic particle in a box: Klein-Gordon versus Dirac equations
Alberto, Pedro; Das, Saurya; Vagenas, Elias C.
2018-03-01
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
Niemi, Antti H.
2011-02-01
We study the applicability of the discontinuous Petrov-Galerkin (DPG) variational framework for thin-body problems in structural mechanics. Our numerical approach is based on discontinuous piecewise polynomial finite element spaces for the trial functions and approximate, local computation of the corresponding \\'optimal\\' test functions. In the Timoshenko beam problem, the proposed method is shown to provide the best approximation in an energy-type norm which is equivalent to the L2-norm for all the unknowns, uniformly with respect to the thickness parameter. The same formulation remains valid also for the asymptotic Euler-Bernoulli solution. As another one-dimensional model problem we consider the modelling of the so called basic edge effect in shell deformations. In particular, we derive a special norm for the test space which leads to a robust method in terms of the shell thickness. Finally, we demonstrate how a posteriori error estimator arising directly from the discontinuous variational framework can be utilized to generate an optimal hp-mesh for resolving the boundary layer. © 2010 Elsevier B.V.
Slowly rotating general relativistic superfluid neutron stars with relativistic entrainment
International Nuclear Information System (INIS)
Comer, G.L.
2004-01-01
Neutron stars that are cold enough should have two or more superfluids or supercondutors in their inner crusts and cores. The implication of superfluidity or superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect; i.e., the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modeling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic σ-ω mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit
General-relativistic celestial mechanics. II. Translational equations of motion
International Nuclear Information System (INIS)
Damour, T.; Soffel, M.; Xu, C.
1992-01-01
The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) 4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies
Mass, matter, and energy. A relativistic approach
International Nuclear Information System (INIS)
Bitsakis, E.
1991-01-01
The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if one rejects this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation
The relativistic electron wave equation
International Nuclear Information System (INIS)
Dirac, P.A.M.
1977-08-01
The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)
Relativistic quantum mechanics of bosons
International Nuclear Information System (INIS)
Ghose, P.; Home, D.; Sinha Roy, M.N.
1993-01-01
We show that it is possible to use the Klein-Gordon, Proca and Maxwell formulations to construct multi-component relativistic configuration space wavefunctions of spin-0 and spin-1 bosons in an external field. These wavefunctions satisfy the first-order Kemmer-Duffin equation. The crucial ingredient is the use of the future-causal normal n μ (n μ n μ =1, n 0 >0) to the space-like hypersurfaces foliating space-time, inherent in the concept of a relativistic wavefunction, to construct a conserved future-causal probability current four-vector from the second-rank energy-momentum tensor, following Holland's prescription. The existence of a Hermitian position operator, localized solutions, compatibility with the second quantized theories and the question of interpretation are discussed. (orig.)
Double Relativistic Electron Accelerating Mirror
Directory of Open Access Journals (Sweden)
Saltanat Sadykova
2013-02-01
Full Text Available In the present paper, the possibility of generation of thin dense relativistic electron layers is shown using the analytical and numerical modeling of laser pulse interaction with ultra-thin layers. It was shown that the maximum electron energy can be gained by optimal tuning between the target width, intensity and laser pulse duration. The optimal parameters were obtained from a self-consistent system of Maxwell equations and the equation of motion of electron layer. For thin relativistic electron layers, the gaining of maximum electron energies requires a second additional overdense plasma layer, thus cutting the laser radiation off the plasma screen at the instant of gaining the maximum energy (DREAM-schema.
Volatility smile as relativistic effect
Kakushadze, Zura
2017-06-01
We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution (1) is properly normalized and (2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black-Scholes-Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no ;speed limit; and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Lévy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Gravity waves from relativistic binaries
Levin, Janna; O'Reilly, Rachel; Copeland, E. J.
1999-01-01
The stability of binary orbits can significantly shape the gravity wave signal which future Earth-based interferometers hope to detect. The inner most stable circular orbit has been of interest as it marks the transition from the late inspiral to final plunge. We consider purely relativistic orbits beyond the circular assumption. Homoclinic orbits are of particular importance to the question of stability as they lie on the boundary between dynamical stability and instability. We identify thes...
Asymptotics of relativistic spin networks
International Nuclear Information System (INIS)
Barrett, John W; Steele, Christopher M
2003-01-01
The stationary phase technique is used to calculate asymptotic formulae for SO(4) relativistic spin networks. For the tetrahedral spin network this gives the square of the Ponzano-Regge asymptotic formula for the SU(2) 6j-symbol. For the 4-simplex (10j-symbol) the asymptotic formula is compared with numerical calculations of the spin network evaluation. Finally, we discuss the asymptotics of the SO(3, 1) 10j-symbol
Relativistic gravitational deflection of photons
Saca, J M
2002-01-01
A relativistic analysis of the deflection of a light ray due to a massive attractive centre is here developed by solving a differential equation of the orbit of photons. Results are compared with a widely known approximate formula for the deflection obtained by Einstein in 1916. Finally, it is concluded that the results here obtained, although very close to Einstein's values, could stand out as a conclusive reference for comparison with future direct measurements of the deflection.
General relativistic collapse of textures
International Nuclear Information System (INIS)
Durrer, R.; Heusler, M.; Jetzer, P.; Straumann, N.
1991-01-01
We present an exact self-similar solution of the coupled Einstein-σ model equations which describes the general relativistic collapse of global textures. In one coordinate system the texture geometry has a simple interpretation in terms of a deficit solid angle. We also briefly discuss the behavior of matter and light in this geometry. In particular we show that the weak field approximation for the metric perturbations of flat space texture solutions is quantitatively quite reliable. (orig.)
Relativistic beaming and quasar statistics
International Nuclear Information System (INIS)
Orr, M.J.L.; Browne, I.W.A.
1982-01-01
The statistical predictions of a unified scheme for the radio emission from quasars are explored. This scheme attributes the observed differences between flat- and steep-spectrum quasars to projection and the effects of relativistic beaming of the emission from the nuclear components. We use a simple quasar model consisting of a compact relativistically beamed core with spectral index zero and unbeamed lobes, spectral index - 1, to predict the proportion of flat-spectrum sources in flux-limited samples selected at different frequencies. In our model this fraction depends on the core Lorentz factor, γ and we find that a value of approximately 5 gives satisfactory agreement with observation. In a similar way the model is used to construct the expected number/flux density counts for flat-spectrum quasars from the observed steep-spectrum counts. Again, good agreement with the observations is obtained if the average core Lorentz factor is about 5. Independent estimates of γ from observations of superluminal motion in quasars are of the same order of magnitude. We conclude that the statistical properties of quasars are entirely consistent with the predictions of simple relativistic-beam models. (author)
Frontiers in Relativistic Celestial Mechanics, Vol. 2, Applications and Experiments
Kopeikin, Sergei
2014-08-01
Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This second volume of a two-volume series covers applications of the theory as well as experimental verifications. From tools to determine light travel times in curved space-time to laser ranging between earth and moon and between satellites, and impacts on the definition of time scales and clock comparison techniques, a variety of effects is discussed. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: J. Simon, A. Fienga: Victor Brumberg and the French school of analytical celestial mechanics T. Fukushima: Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy P. Teyssandier: New tools for determining the light travel time in static, spherically symmetric spacetimes beyond the order G2 J. Müller, L. Biskupek, F. Hofmann and E. Mai: Lunar laser ranging and relativity N. Wex: Testing relativistic celestial mechanics with radio pulsars I. Ciufolini et al.: Dragging of inertial frames, fundamental physics, and satellite laser ranging G. Petit, P. Wolf, P. Delva: Atomic time, clocks, and clock comparisons in relativistic spacetime: a review
Jaromi, Melinda; Nemeth, Andrea; Kranicz, Janos; Laczko, Tamas; Betlehem, Jozsef
2012-06-01
The purpose of the study was to measure the effectiveness of a spine training programme (Back School) in nurses who have been living with chronic low back pain. It was hypothesised that active therapy, ergonomics and education called Back School will significantly decrease the pain intensity levels and improve the body posture of the study participants. A chronic low back pain is a significant work-related health problem among healthcare workers around the world. Proper body posture is essential for decreasing pain in healthcare workers who have history of chronic low back pain. By teaching proper body posture and with the creation of occupational settings that are 'spine-friendly' hospitals and other healthcare settings can significantly lower the suffering of their nursing staff. Single-blinded randomised controlled trial was utilised with six- and 12-months follow-up. The study was carried out at the University of Pecs, Faculty of Health Sciences from 2007 to 2008 involving 124 nurses with low back pain. Participants were randomly assigned to the study group (who have received ergonomics training and education called Back School) with an intervention conducted once a week for a six-week period. The control group received passive physiotherapy once a week for a six-week period. Further follow-up measurements were conducted at six and 12 months, respectively. The study variables and outcome measures were pain intensity and body posture (angle of thoracic kyphosis and lumbar lordosis). The pain intensity was investigated with the Visual Analogue Scale. Body posture was recorded and analysed with the Zebris biomechanical motion analysis system. The statistical analysis of repeated measures indicated a significant decrease in back pain intensity after the therapy in both groups, compared with measurements before the therapy; however, the BS group showed significantly better results during the six-month and one-year follow-up period. The biomechanical analysis of
Cao, Wei-Guang; Zhou, Tian-Yi; Xie, Yi
2017-10-01
As a continuing investigation of an earlier work that establishes the collinear solutions to the three-body problem with general masses under a scalar-tensor theory, we study these solutions and prove their uniqueness up to the first order post-Newtonian approximation. With the help of observed bounds on the scalar field in the Solar System, we show that the seventh-order polynomial equation determining the distance ratio among the three masses has either one or three positive roots. However, in the case with three positive roots, it is found that two positive roots break down the slow-motion condition for the post-Newtonian approximation so that only one positive root is physically valid. The resulting uniqueness suggests that the locations of the three masses are very close to their Newtonian positions with post-Newtonian corrections of general relativity and the scalar field. We also prove that, in the framework of the scalar-tensor theory, the angular velocity of the collinear configuration is always less than the Newtonian one when all other parameters are fixed. These results are valid only for three-body systems where upper-bounds on the scalar field are compatible with those of the Solar System. Supported by the National Natural Science Foundation of China under Grant Nos. 11573015 and J1210039, and the Innovation Training Project for Undergraduates of Nanjing University, China
Directory of Open Access Journals (Sweden)
Svetoslav Ganchev Nikolov
2015-07-01
Full Text Available The study of the dynamic behavior of a rigid body with one fixed point (gyroscope has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1 to outline the characteristic features of the theory of dynamical systems and 2 to reveal the specific properties of the motion of a rigid body with one fixed point (gyroscope.This article consists of six sections. The first section addresses the main concepts of the theory of dynamical systems. Section two presents the main theoretical results (obtained so far concerning the dynamic behavior of a solid with one fixed point (gyroscope. Section three examines the problem of gyroscopic stabilization. Section four deals with the non-linear (chaotic dynamics of the gyroscope. Section five is a brief analysis of the gyroscope applications in engineering. The final section provides conclusions and generalizations on why the theory of dynamical systems should be used in the study of the movement of gyroscopic systems.
Celletti, A; Lega, E
2003-01-01
The stability of some asteroids, in the framework of the restricted three- body problem, has been recently proved in \\cite{CC03} by developing an isoenergetic KAM theorem. More precisely, having fixed a level of energy related to the motion of the asteroid, the stability can be obtained by showing the existence of nearby trapping invariant tori living on the same energy level. The analytical results are compatible with the astronomical observations, since the theorem is valid for the realistic mass-ratio of the primaries. The model adopted in \\cite{CC03} is the planar, circular, restricted three-body model, in which only the most significant contributions of the Fourier development of the perturbation are retained. In this paper we investigate numerically the stability of the same asteroids considered in \\cite{CC03} (namely, Iris, Victoria and Renzia). In particular, we implement the nowadays standard method of frequency- map analysis and we compare our investigation with the analytical results on the planar,...
Quark-Parton Model and Relativistic Quantum Mechanics
Directory of Open Access Journals (Sweden)
Kostenko Boris
2018-01-01
Full Text Available An attempt to treat the asymptotic freedom and the quark confinement as a self-consistent problem in the framework of relativistic quantum mechanics is realized. It is shown that the confinement of quarks induces a change of their helicities together with a simultaneous alteration of orbital momenta, so that the total angular momentum of each quark is conserved. This observation may cast light on the so-called proton spin puzzle after some additional numerical estimations.
Nonlinear dynamics of the relativistic standard map
International Nuclear Information System (INIS)
Nomura, Y.; Ichikawa, Y.H.; Horton, W.
1991-04-01
Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map. The question arises as to how the relativistic effects change the nonlinear dynamical behavior described by the classical standard map. The relativistic standard map is a two parameter (K, Β = ω/kc) family of dynamical systems reducing to the standard map when Β → 0. For Β ≠ 0 the relativistic mass increase suppresses the onset of stochasticity. It shown that the speed of light limits the rate of advance of the phase in the relativistic standard map and introduces KAM surfaces persisting in the high momentum region. An intricate structure of mixing in the higher order periodic orbits and chaotic orbits is analyzed using the symmetry properties of the relativistic standard map. The interchange of the stability of the periodic orbits in the relativistic standard map is also observed and is explained by the local linear stability of the orbits. 12 refs., 16 figs
Directory of Open Access Journals (Sweden)
Tian Zhipeng
2015-01-01
Full Text Available In the car company, the painted body storage (PBS is set up between the paint shop and the assembly shop. It stores the vehicles in production and reorders the vehicles sequence. To improve production efficiency of assembly shop, a mathematical model is developed aiming at minimizing the consumption rate of options and the total overtime and idle time. As the PBS sequencing process contains upstream sequence inbound and downstream sequence outbound, this paper proposes an algorithm with two phases. In the first phase, the discrete small-world optimization algorithm (DSWOA is applied to schedule the inbound sequence by employing the short-range nodes and the long-range nodes in order to realize the global searching. In the second phase, the heuristic algorithm is applied to schedule the outbound sequencing. The proposed model and algorithm are applied in an automobile enterprise. The results indicate that the two-phase algorithm is suitable for the PBS sequencing problem and the DSWOA has a better searching performance than GA in this problem. The sensitivity of model parameters is analyzed as well.
Radiation Hazard of Relativistic Interstellar Flight
Semyonov, Oleg G.
2006-01-01
From the point of view of radiation safety, interstellar space is not an empty void. Interstellar gas and cosmic rays, which consist of hydrogen and helium nucleons, present a severe radiation hazard to crew and electronics aboard a relativistic interstellar ship. Of the two, the oncoming relativistic flow of interstellar gas produces the most intence radiation. A protection shield will be needed to block relativistic interstellar gas that can also absorb most of the cosmic rays which, as a r...
Modeling relativistic jets and cosmic-ray acceleration processes
International Nuclear Information System (INIS)
Globus, Noemie
2011-01-01
This thesis explores various issues related to relativistic jets associated with black holes. Their formation as well as the acceleration and collimation processes, are studied using a fluid approximation within a global description of the flow. The general relativistic magnetohydrodynamic equations can be integrated using the 3+1 formalism, and the covariant equations can be transposed to a vectorial form, where the physical vectorial quantities are measured by an Eulerian observer comoving with the rotation, the so-called zero angular momentum observer. This formalism allows us to study the physics of the magnetosphere surrounding a Kerr black hole, i.e., the physics of a strongly magnetized plasma in differential rotation in curved space-time. This formalism enabled me to develop a self-similar meridional model in the Kerr metric that allows us to obtain relativistic jet solutions, and to describe the dynamics, and the geometry of the flow close to the rotational axis. In particular, I have investigated how the rotation of the black hole affects the collimation process. I have found solutions for T Tauri stars in the Newtonian approximation in order to study magnetic braking, and to compare them with their generalization in the Kerr metric. Relativistic jets could also be the seat of high-energy corpuscular and photon emission. In particular, gamma-ray bursts could be possible sources of ultra-high-energy cosmic rays. This problem requires the use of a local description of the flow. Finally, we have investigated the propagation of ultra high energy cosmic rays in these shocks, taking into account the competition between relativistic Fermi acceleration and energy loss due to interaction with the gamma ray background, in order to ascertain whether the observed energies can be obtained in this way. (author)
Atomic physics using relativistic H- beams
International Nuclear Information System (INIS)
Bryant, H.C.
2005-01-01
Full text: An 8 GeV hydrogen atom can traverse a focused laser beam of width of 1 micron in a time of 353 attoseconds in its rest frame. A design is currently underway at Fermilab for a superconducting linear accelerator that will accelerate H - ions to 8 GeV. This 'Proton Driver' beam is intended to be injected, after stripping down to protons, into the 120 GeV Main Injector for the mass production of neutrinos aimed at a neutrino detector (MINOS) in a mine shaft in Soudan, Minnesota (USA) for the study of neutrino oscillations. It has not passed unnoticed that with some advance planning a few nanoamps from the up-to-250 mA beam could be diverted for atomic physics experiments. Relativistic kinematics enable the creation of extreme conditions for a beam atom. For example, the Doppler shift allows a very large tuning range in the atom's rest frame of a laser beam that is fixed- frequency in the lab. At 8 GeV the rest frame Doppler shift ranges from a factor of 19 in the forward direction to 0.05 backward. The laser intensity is enhanced by the square of the Doppler shift, so that the world's most intense laser beam would be amplified by a factor of 360 in the atom's rest frame. Furthermore, although there are extreme changes in the frequency and intensity in the atom's frame as one changes the intersection angle, the ponderomotive potential remains constant, as it is a relativistic invariant. One of the interesting problems that arises in the planning for this accelerator is the stripping of electrons from the negative ions by photodetachment from Doppler shifted thermal photons. We estimate that, if the transfer lines are kept at 300 K (room temperature), the mean free path at 8 GeV for stripping from collisions with cavity radiation is about 1300 km. The physics of the interactions of such a beam with very thin material foils, again in the attosecond regime, has been treated theoretically, but has not been studied experimentally at such high energies. We will
RELATIVISTIC CYCLOTRON INSTABILITY IN ANISOTROPIC PLASMAS
Energy Technology Data Exchange (ETDEWEB)
López, Rodrigo A.; Moya, Pablo S.; Muñoz, Víctor; Valdivia, J. Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Navarro, Roberto E.; Araneda, Jaime A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Viñas, Adolfo F., E-mail: rlopez186@gmail.com [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, MD 20771 (United States)
2016-11-20
A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show a good agreement with simulations results.
A fully relativistic definition of the geoid
Laemmerzahl, C.; Hackmann, E.; Perlick, V.; Philipp, D.; Puetzfeld, D.
2016-12-01
The present definition of the geoid is based on the Newtonian potential together with the potential related to centrifugal force of the rotating Earth. All time-dependencies due to, e.g., seasonal variations are removed from this definition. The geoid is defined as to be related to the rigid part of the rotating Earth. Upcoming high precision gravimeters and gradiometers as well as optical clocks and clock networks make it necessary to propose a definition of the geoid solely in terms of General Relativity.The new definition of the geoid will be stated within the framework of General Relativity. In this framework we model atomic clocks by standard clocks showing the proper time along their worldline, and we model the Earth in terms of a rigidly rotating gravitating body. The second assumption gives that space-time is equipped with a time-like Killing vector. The norm of this Killing vector is a scalar function which (i) describes the acceleration of freely falling bodies on the surface of the Earth, and (ii) gives the redshift of atomic clocks whose ticking rate can be compared using connecting light rays or optical fibers. It can be shown that in the nonrelativistic limit this generalized potential gives the usual Newtonian potential. Therefore, this scalar function can be taken as the basis for a natural and fully general relativistic generalization of the geoid based on Newtonian gravitational physics. Finally, for certain space-times we will present examples for the geoid.
Electromagnetic responses of relativistic electrons
de Carvalho, C. A. A.; Reis, D. M.
2018-02-01
We compute the real and imaginary parts of the electric permittivities and magnetic permeabilities of relativistic electrons from quantum electrodynamics at finite temperatures and densities, for weak fields, neglecting electron-electron interactions. For non-zero temperatures, electromagnetic responses are reduced to one-dimensional integrals computed numerically. For zero temperature, we find analytic expressions for both their real/dispersive and imaginary/absorptive parts. As an application of our results, we obtain the dispersion relation for longitudinal electric plasmons. Present calculations support our recent claim that, at low frequencies and long wavelengths, the system will exhibit simultaneously negative electric and magnetic responses.
Chaotic distributions for relativistic particles
Mustafa, Dawan; Wennberg, Bernt
2015-01-01
We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function $\\phi(v)$, $v \\in \\mathbb{R}$. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is $Ce^{-z_0\\phi(v)}$-chaotic, $C,z_0 \\in \\mathbb{R}_+$. The kinetic energy for relativistic particles is a special case. A generalization to the case $v\\in \\mathbb{R}^d$ which involves conservation momentum is also formally discussed.
Relativistic heavy ion facilities: worldwide
International Nuclear Information System (INIS)
Schroeder, L.S.
1986-05-01
A review of relativistic heavy ion facilities which exist, are in a construction phase, or are on the drawing boards as proposals is presented. These facilities span the energy range from fixed target machines in the 1 to 2 GeV/nucleon regime, up to heavy ion colliders of 100 GeV/nucleon on 100 GeV/nucleon. In addition to specifying the general features of such machines, an outline of the central physics themes to be carried out at these facilities is given, along with a sampling of the detectors which will be used to extract the physics. 22 refs., 17 figs., 3 tabs
Unlimited Relativistic Shock Surfing Acceleration
International Nuclear Information System (INIS)
Ucer, D.; Shapiro, V. D.
2001-01-01
Nonrelativistic shock surfing acceleration at quasiperpendicular shocks is usually considered to be a preacceleration mechanism for slow pickup ions to initiate diffusive shock acceleration. In shock surfing, the particle accelerates along the shock front under the action of the convective electric field of the plasma flow. However, the particle also gains kinetic energy normal to the shock and eventually escapes downstream. We consider the case when ions are accelerated to relativistic velocities. In this case, the ions are likely to be trapped for infinitely long times, because the energy of bounce oscillations tends to decrease during acceleration. This suggests the possibility of unlimited acceleration by shock surfing
Pousse, Alexandre; Robutel, Philippe; Vienne, Alain
2017-08-01
In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term "quasi-satellite" more and more present in the literature. However, some authors rather use the term "retrograde satellite" when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.
MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation
Pashkevich, V. V.
2017-03-01
The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.
Mukherjee, Debashis; Sahoo, B. K.; Nataraj, H. S.; Das, B. P.
2009-01-01
A relativistic many-body theory for the electric dipole moment (EDM) of paramagnetic atoms arising from the electric dipole moment of the electron is presented and implemented. The relativistic coupled-cluster method with single and double excitations (RCCSD) using the Dirac-Coulomb Hamiltonian and
Relativistic ls coupling in scalar potential
International Nuclear Information System (INIS)
Martem'yanov, B.V.; Shchepkin, M.G.
1987-01-01
On fermion example ls-splitting of the levels in scalar potential in the general case including relativistic range is considered. The derived formulas are compared with the classical ones for the energy concerned with the Thomas spin precession. It is shown that in the relativistic range ls-coupling causes change of rotational excitation spectrum
Relativistic heavy-ion physics: Experimental overview
Indian Academy of Sciences (India)
The field of relativistic heavy-ion physics is reviewed with emphasis on new results and highlights from the first run of the relativistic heavy-ion collider at BNL and the 15 year research programme at the super proton synchrotron ...... to the charged particle spectra at high momentum (cf. §3.2). A similar suppression pattern.
Relativistic calculations of coalescing binary neutron stars
Indian Academy of Sciences (India)
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and ...
Relativistic calculations of coalescing binary neutron stars
Indian Academy of Sciences (India)
We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested ... We find that the amount of mass ejected from the system, much less than a per cent, is greatly reduced by the inclusion of relativistic gravitation.
Relativistic heavy-ion physics: Experimental overview
Indian Academy of Sciences (India)
Abstract. The ﬁeld of relativistic heavy-ion physics is reviewed with emphasis on new results and highlights from the ﬁrst run of the relativistic heavy-ion collider at BNL and the 15 year research programme at the super proton synchrotron (SPS) at CERN and the AGS at BNL.
Einstein Never Approved of Relativistic Mass
Hecht, Eugene
2009-01-01
During much of the 20th century it was widely believed that one of the significant insights of special relativity was "relativistic mass." Today there are two schools on that issue: the traditional view that embraces speed-dependent "relativistic mass," and the more modern position that rejects it, maintaining that there is only one mass and it's…
Wiedemann, Ashley A; Saules, Karen K
2013-12-01
Weight problem perception (WPP) refers to the belief that one is overweight. Previous research suggests that WPP, even in the absence of actual overweight status, is associated with disordered eating, binge eating, and body image dissatisfaction. However, the relationship between emotional eating, BMI, and WPP has not yet been explored. This investigation recruited a total of 409 college students who completed a web-based survey. An additional 76 participants were recruited to complete an identical survey with the addition of a depression measure to evaluate the contribution of this potentially important covariate. As hypothesized, WPP was associated with emotional eating, while actual BMI was not. In the second sample, WPP remained significantly associated with emotional eating, even after depression was included as a covariate. Results suggest that non-overweight young adults who express the belief that they are overweight may be at risk for emotional eating, which, over the long term, could indeed adversely impact BMI. Cognitive approaches to address disordered eating may benefit from addressing WPP. © 2013 Elsevier Ltd. All rights reserved.
Physical processes in relativistic plasmas
International Nuclear Information System (INIS)
Svensson, R.
1984-01-01
The continuum emission in many active galactic nuclei (AGNs) extend to 100 keV and beyond (e.g. Rothschild et al. 1983). In thermal models of the continuum emission this implies temperatures above 10 9 K or kT of order mc 2 . In such a plasma the electrons are at least mildly relativistic and furthermore the particles and the photons are energetic enough to produce electron-positron pairs. The physics of such hot plasmas has only recently been studied in any detail and here we review the results of those studies. Significant electron-positron pair production may also occur in non-thermal models of the continuum emission if the optical depth to photon-photon pair production is greater than unity. We review the few results obtained regarding this interesting but not very well studied possibility. First, however, we briefly discuss the processes taking place in relativistic plasmas and the standard models for the continuum emission from AGNs. We then summarize the effects pair production have on these models and the observational implications of the presence of electron-positron pairs. (orig./WL)
Example of a relativistic, completely integrable, Hamiltonian system
International Nuclear Information System (INIS)
Lund, F.
1977-01-01
The initial value problem for a system of two relativistic scalar fields in two space-time dimensions is solved. One of them has a self-interaction of the sine-Gordon type, while the other is massless and moves in a background geometry which has a dynamical evolution of its own. The system has soliton solutions and is shown to be completely integrable using the inverse scattering method. The appropriate linear equations are found by thinking of the problem as the isometric embedding of a surface in a three-dimensional Euclidean space
Relativistic wave equations and compton scattering
International Nuclear Information System (INIS)
Sutanto, S.H.; Robson, B.A.
1998-01-01
Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula
Non-relativistic model for interaction of dark particles with matter
Takibayev, Nurgali
2014-01-01
A non-relativistic quantum mechanical model for interaction of dark particles with matter is proposed; the model describes resonant amplification of effective interaction between two massive bodies at large distances between them. The phenomenon is explained by catalytic action by a third dark particle scattered at a system of two heavy bodies. It is shown that effective interaction between the heavy bodies is changed at large distances and can transform into repulsion contributing in that ca...
The nuclear N-body problem and the effective interaction in self-consistent mean-field methods
International Nuclear Information System (INIS)
Duguet, Thomas
2002-01-01
This work deals with two aspects of mean-field type methods extensively used in low-energy nuclear structure. The first study is at the mean-field level. The link between the wave-function describing an even-even nucleus and the odd-even neighbor is revisited. To get a coherent description as a function of the pairing intensity in the system, the utility of the formalization of this link through a two steps process is demonstrated. This two-steps process allows to identify the role played by different channels of the force when a nucleon is added in the system. In particular, perturbative formula evaluating the contribution of time-odd components of the functional to the nucleon separation energy are derived for zero and realistic pairing intensities. Self-consistent calculations validate the developed scheme as well as the derived perturbative formula. This first study ends up with an extended analysis of the odd-even mass staggering in nuclei. The new scheme allows to identify the contribution to this observable coming from different channels of the force. The necessity of a better understanding of time-odd terms in order to decide which odd-even mass formulae extracts the pairing gap the most properly is identified. These terms being nowadays more or less out of control, extended studies are needed to make precise the fit of a pairing force through the comparison of theoretical and experimental odd-even mass differences. The second study deals with beyond mean-field methods taking care of the correlations associated with large amplitude oscillations in nuclei. Their effects are usually incorporated through the GCM or the projected mean-field method. We derive a perturbation theory motivating such variational calculations from a diagrammatic point of view for the first time. Resuming two-body correlations in the energy expansion, we obtain an effective interaction removing the hard-core problem in the context of configuration mixing calculations. Proceeding to a
Wickrama, Kandauda K A S; O'Neal, Catherine Walker; Oshri, Assaf
2014-07-01
Although previous research has documented the adverse influence of early socioeconomic disadvantage on youths' physical health outcomes and the increase in health inequalities over the early life course, little is known about genetically informed sequential life course developmental processes leading to health outcomes. Consistent with the life course-stress process perspective, we hypothesized that early socioeconomic adversity initiates a stress process over the early life course. This process involves the disrupted transition from adolescence to young adulthood, which increases the risk of health problems during young adulthood. Behavioral, psychosocial, and genetic data were collected from 12,424 adolescents (53 % female) over a period of 13 years participating in the nationally representative National Longitudinal Study of Adolescent Health (Add Health). Early cumulative socioeconomic adversity and the polygenic influence were measured using composite indices. The study provided evidence for stressful developmental processes of adolescents, involving parental rejection, depressive symptoms, and adolescents' precocious transition. This longitudinal process was initiated by early cumulative socioeconomic adversity and eventuated with young adults' increased body mass index (BMI). Furthermore, the study provided evidence for the influence of life context-gene interactions (G × E) on adolescents' precocious development and young adult BMI (after controlling for the lagged measure) amplifying the stress process over the early life course. These findings emphasize the need for incorporating individual genetic characteristics in a longitudinal context into life course stress research. Furthermore, policies focused on eradicating childhood/adolescent adversities are necessary as well as youth programs and policies that promote youth competencies that aid in their successful transition to young adulthood.
From the self-force problem to the radiation reaction formula
International Nuclear Information System (INIS)
Mino, Yasushi
2005-01-01
We review recent theoretical progress in the so-called self-force problem of a general relativistic two-body system. Although a two-body system in Newtonian gravity is a very simple problem, some fundamental issues are involved in relativistic gravity. Besides, because of recent projects for gravitational wave detection, it has become possible to see those phenomena directly via gravitational waves, and the self-force problem becomes one of urgent and highly-motivated problems in general relativity. Roughly speaking, there are two approaches to investigate this problem; the so-called post-Newtonian approximation, and a black-hole perturbation. In this paper, we review theoretical progress in the self-force problem using a black-hole perturbation. Although the self-force problem seems to be just a problem to calculate a self-force, we discuss that the real problem is to define a gauge-invariant concept of a motion in a gauge-dependent metric perturbation
Relativistic hydrodynamics in the presence of puncture black holes
International Nuclear Information System (INIS)
Faber, Joshua A.; Etienne, Zachariah B.; Shapiro, Stuart L.; Taniguchi, Keisuke; Baumgarte, Thomas W.
2007-01-01
Many of the recent numerical simulations of binary black holes in vacuum adopt the moving puncture approach. This successful approach avoids the need to impose numerical excision of the black hole interior and is easy to implement. Here we wish to explore how well the same approach can be applied to moving black hole punctures in the presence of relativistic hydrodynamic matter. First, we evolve single black hole punctures in vacuum to calibrate our Baumgarte-Shapiro-Shibata-Nakamura implementation and to confirm that the numerical solution for the exterior spacetime is invariant to any junk (i.e., constraint-violating) initial data employed in the black hole interior. Then we focus on relativistic Bondi accretion onto a moving puncture Schwarzschild black hole as a numerical test bed for our high-resolution shock-capturing relativistic hydrodynamics scheme. We find that the hydrodynamical equations can be evolved successfully in the interior without imposing numerical excision. These results help motivate the adoption of the moving puncture approach to treat the binary black hole-neutron star problem using conformal thin-sandwich initial data
Decay law of relativistic particles: Quantum theory meets special relativity
Directory of Open Access Journals (Sweden)
K. Urbanowski
2014-10-01
Full Text Available Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-exponential form of the survival amplitude, occur much earlier than it follows from the classical standard approach boiled down to replace time t by t/γL (where γL is the relativistic Lorentz factor in the formula for the survival probability. The consequence is that fluctuations of the corresponding decay curves can appear much earlier and much more unstable particles have a chance to survive up to these times or later. It is also shown that fluctuations of the instantaneous energy of the moving unstable particles have a similar form as the fluctuations in the particle rest frame but they are seen by the observer in his rest system much earlier than one could expect replacing t by t/γL in the corresponding expressions for this energy and that the amplitude of these fluctuations can be even larger than it follows from the standard approach. All these effects seem to be important when interpreting some accelerator experiments with high energy unstable particles and the like (possible connections of these effects with GSI anomaly are analyzed and some results of astrophysical observations.
Uncertainty dimension and basin entropy in relativistic chaotic scattering
Bernal, Juan D.; Seoane, Jesús M.; Sanjuán, Miguel A. F.
2018-04-01
Chaotic scattering is an important topic in nonlinear dynamics and chaos with applications in several fields in physics and engineering. The study of this phenomenon in relativistic systems has received little attention as compared to the Newtonian case. Here we focus our work on the study of some relevant characteristics of the exit basin topology in the relativistic Hénon-Heiles system: the uncertainty dimension, the Wada property, and the basin entropy. Our main findings for the uncertainty dimension show two different behaviors insofar as we change the relativistic parameter β , in which a crossover behavior is uncovered. This crossover point is related with the disappearance of KAM islands in phase space, which happens for velocity values above the ultrarelativistic limit, v >0.1 c . This result is supported by numerical simulations and by qualitative analysis, which are in good agreement. On the other hand, the computation of the exit basins in the phase space suggests the existence of Wada basins for a range of β value for β ≈0.2 . This last quantity is related to the uncertainty in the prediction of the final fate of the system. Finally, our work is relevant in galactic dynamics, and it also has important implications in other topics in physics such as as in the Störmer problem, among others.
Relativistic heavy-ion collisions
Bhalerao, Rajeev S.
The field of relativistic heavy-ion collisions is introduced to the high-energy physics students with no prior knowledge in this area. The emphasis is on the two most important observables, namely the azimuthal collective flow and jet quenching, and on the role fluid dynamics plays in the interpretation of the data. Other important observables described briefly are constituent quark number scaling, ratios of particle abundances, strangeness enhancement, and sequential melting of heavy quarkonia. Comparison is made of some of the basic heavy-ion results obtained at LHC with those obtained at RHIC. Initial findings at LHC which seem to be in apparent conflict with the accumulated RHIC data are highlighted.
Thermodynamic laws and equipartition theorem in relativistic Brownian motion.
Koide, T; Kodama, T
2011-06-01
We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.
Energy Dependence of Near-relativistic Electron Spectrum at ...
Indian Academy of Sciences (India)
the Relativistic Electron Dropouts (REDs) and the Relativistic Electron Enhancements. (REEs) observed at the geosynchronous altitudes. The sudden drop in the relativistic electron flux often by two orders of magnitude is called RED which is usually pre- ceded by the gradual enhancement in the relativistic electron fluxes, ...
Relativistic klystron research for linear colliders
International Nuclear Information System (INIS)
Allen, M.A.; Callin, R.S.; Deruyter, H.
1988-09-01
Relativistic klystrons are being developed as a power source for high gradient accelerator applications which include large linear electron-positron colliders, compact accelerators, and FEL sources. We have attained 200 MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. We report here on the design of our relativistic klystrons, the results of our experiments so far, and some of our plans for the near future. 5 refs., 9 figs., 1 tab
New derivation of relativistic dissipative fluid dynamics
International Nuclear Information System (INIS)
Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
2012-01-01
Relativistic dissipative hydrodynamics has been quite successful in explaining the spectra and azimuthal anisotropy of particles produced in heavy-ion collisions at the RHIC and recently at the LHC. The first-order dissipative fluid dynamics or the relativistic Navier-Stokes (NS) theory involves parabolic differential equations and suffers from a causality and instability. The second-order or Israel-Stewart (IS) theory with its hyperbolic equations restores causality but may not guarantee stability. The correct formulation of relativistic viscous fluid dynamics is far from settled and is under intense investigation
Local density approximations for relativistic exchange energies
International Nuclear Information System (INIS)
MacDonald, A.H.
1986-01-01
The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented
The de Sitter relativistic top theory
International Nuclear Information System (INIS)
Armenta, J.; Nieto, J.A.
2005-01-01
We discuss the relativistic top theory from the point of view of the de Sitter (or anti-de Sitter) group. Our treatment rests on the Hanson-Regge spherical relativistic top Lagrangian formulation. We propose an alternative method for studying spinning objects via Kaluza-Klein theory. In particular, we derive the relativistic top equations of motion starting with the geodesic equation for a point particle in 4+N dimensions. We compare our approach with Fukuyama's formulation of spinning objects, which is also based on Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D dimensional theory
Holographic Aspects of a Relativistic Nonconformal Theory
Directory of Open Access Journals (Sweden)
Chanyong Park
2013-01-01
Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.
On the physics of relativistic double layers
International Nuclear Information System (INIS)
Carlqvist, P.
1982-06-01
A model of a strong, time-independent, and relativistic double layer is studied. Besides double layers having the electric field parallel to the current the model also describes a certain type of oblique double layers. The 'Langmuir condition' (ratio of ion current density to electron current density) as well as an expression for the potential drop of the double layer are derived. Furthermore, the distribution of charged particles, electric field, and potential within the double layer are clarified and discussed. It is found that the properties of relativistic double layers differ substantially from the properties of corresponding non-relativistic double layers. (Author)
The $q \\bar{q}$ relativistic interaction in the Wilson loop approach
Brambilla, Nora; Vairo, Antonio
1997-01-01
We study the $q \\bar{q}$ relativistic interaction starting from the Feynman-Schwinger representation of the gauge-invariant quark-antiquark Green function. We focus on the one-body limit and discuss the obtained non-perturbative interaction kernel of the Dirac equation.
Exact results for the many-body problem in one dimension with repulsive delta-function interaction
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S/sub N/. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation
Instabilities constraint and relativistic mean field parametrization
International Nuclear Information System (INIS)
Sulaksono, A.; Kasmudin; Buervenich, T.J.; Reinhard, P.-G.; Maruhn, J.A.
2011-01-01
Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria 20 determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors. (author)
Hyperbolic theory of relativistic conformal dissipative fluids
Lehner, Luis; Reula, Oscar A.; Rubio, Marcelo E.
2018-01-01
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism described in [R. Geroch and L. Lindblom, Phys. Rev. D 41, 1855 (1990), 10.1103/PhysRevD.41.1855, S. Pennisi, Some considerations on a non linear approach to extended thermodynamics and in Proceedings of Symposium of Kinetic Theory and Extended Thermodynamics, Bologna, 1987.]. This type of theory is fully described in terms of evolution variables whose dynamics are governed by total divergence-type conservation laws. Specifically, we give a characterization of the whole family of conformal fluids in terms of a single master scalar function defined up to second-order corrections in dissipative effects, which we explicitly find in general form. This allows us to identify the equilibrium states of the theory and derive constitutive relations and a Fourier-like law for the corresponding first-order theory heat flux. Finally, we show that among this class of theories—and near equilibrium configurations—there exist symmetric hyperbolic ones, implying that for them one can define well-posed initial value problems.
International Nuclear Information System (INIS)
Breuer, R.A.; Rudolph, E.
1982-01-01
The force between two well-separated bodies is calculated in a fully dynamic system of two extended bodies up to and including the second post-Newtonian approximation (PNA). The iteration procedure as formulated by Anderson and Decanio is used in a version whose divergences have been pushed to the third PNA. The following are shown: (i) The force law assumes the ''Newtonian form'' if a second approximation in 1/(separation of the bodies) is made; (ii) the mass terms appearing in the force law are the (Tolman) masses of the individual bodies expanded up the second PNA; the internal masses equal the (passive and active) gravitational masses of the bodies in order considered; they are all constants of the motion; (iii) the self-fields of the bodies vanish in the second PNA; hence there is no Nordvedt effect in the second PNA; (iv) the compactness of the bodies, i.e., (gravitational radius)/(body size), does not appear in the force law; only the relation between mass and the matter variables is changed in the PNA as compared with the corresponding Newtonian result. (author)
Investigations of instabilities in nuclear matter in stochastic relativistic models
International Nuclear Information System (INIS)
Ayik, S.; Yilmaz, O.; Acar, F.; Danisman, B.; Er, N.; Gokalp, A.
2011-01-01
The spinodal instabilities for symmetric nuclear matter at finite temperature are studied within different relativistic mean-field models in the semi-classical approximation and the relativistic results are compared with Skyrme type non-relativistic calculations. Qualitatively similar results appear in the unstable response of the system in both non-relativistic and relativistic descriptions. Furthermore, the early growth of baryon, scalar and current density correlation functions are calculated for hot symmetric nuclear matter.
A unified treatment of the non-relativistic and relativistic hydrogen atom: Pt. 2
International Nuclear Information System (INIS)
Swainson, R.A.; Drake, G.W.F.
1991-01-01
This is the second in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. In this paper the non-relativistic Green function is examined in detail; new functional forms are presented and a clear mathematical progression is show to link these and most other known forms. A linear transformation of the four radial parts of the relativistic Green function is given which allows for the presentation of this function as a simple generalization of the non-relativistic Green function. Thus, many properties of the non-relativistic Green function are shown to have simple relativistic generalizations. In particular, new recursion relations of the radial parts of both the non-relativistic and relativistic Green functions are presented, along with new expressions for the double Laplace transforms and recursion relations between the radial matrix elements. (author)
International Nuclear Information System (INIS)
Barford, Thomas; Birse, Michael C
2005-01-01
A distorted-wave version of the renormalization group is applied to scattering by an inverse-square potential and to three-body systems. In attractive three-body systems, the short-distance wavefunction satisfies a Schroedinger equation with an attractive inverse-square potential, as shown by Efimov. The resulting oscillatory behaviour controls the renormalization of the three-body interactions, with the renormalization-group flow tending to a limit cycle as the cut-off is lowered. The approach used here leads to single-valued potentials with discontinuities as the bound states are cut off. The perturbations around the cycle start with a marginal term whose effect is simply to change the phase of the short-distance oscillations, or the self-adjoint extension of the singular Hamiltonian. The full power counting in terms of the energy and two-body scattering length is constructed for short-range three-body forces
Relativistic Boltzmann theory for a plasma
International Nuclear Information System (INIS)
Erkelens, H. van.
1984-01-01
This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)
Nucleon relativistic phenomenological and microscopic optical potential
International Nuclear Information System (INIS)
Shen Qingbiao; Feng Dachun; Zhuo Yizhong
1991-01-01
In this talk, both the phenomenological and microscopic nucleon relativistic optical potentials are presented. The global neutron relativistic phenomenological optical potential (RPOP) based on the available experimental data for various nuclei ranging from C to U with incident energies En=20-1000 MeV has been obtained through automatic search of the best parameters by computer. Then the nucleon relativistic microscopic optical potential (RMOP) is studied by utilizing effective lagrangian based on popular Walecka model. Through comparison between the theoretical results and experimental data we have shed some insight into both the RMOP and RPOP. We have concluded that both the phenomenological and microscopic relativistic optical potentials proposed here can be extensively used for intermediate energy nucleon data evaluation. Further improvement concerning how to combine the phenomenological potential with the microscopic one in order to reduce the number of free parameters appearing in RPOP is suggested. (author). 33 refs, 24 figs
Fourth sound in relativistic superfluidity theory
International Nuclear Information System (INIS)
Vil'chinskij, S.I.; Fomin, P.I.
1995-01-01
The Lorentz-covariant equations describing propagation of the fourth sound in the relativistic theory of superfluidity are derived. The expressions for the velocity of the fourth sound are obtained. The character of oscillation in sound is determined
On the origin of relativistic bond contraction
International Nuclear Information System (INIS)
Ziegler, T.; Snijders, J.G.; Baerends, E.J.
1980-01-01
The origin of the well-established relativistic bond contractions is investigated in the Au 2 , AuH and AuCl model systems. It is shown that, contrary to popular belief, this contraction is not caused ba relativistic orbital contractions. Rather it has to be ascribed to a relaxation of kinetic repulsion, which is quite independent of changes in the form of the orbitals. (orig.)
Relativistic klystron research at SLAC and LLNL
International Nuclear Information System (INIS)
Allen, M.A.; Callin, R.S.; Deruyter, H.
1988-06-01
We are developing relativistic klystrons as a power source for high gradient accelerator applications such as large linear electron-positron colliders and compact accelerators. We have attained 200 MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. We report here briefly on our experiments so far. 5 refs., 1 fig., 1 tab
Relativistic particles on quantum space-time
Energy Technology Data Exchange (ETDEWEB)
Stern, A., E-mail: astern@bama.ua.edu [Dept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, AL 35487 (United States)
2011-06-20
We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators. -- Highlights: → Anomalies can appear in the reparametrization symmetry of a relativistic particle. → The anomalies are signaled by noncommutative space-time. → The space-time algebra can have discrete representations. → A discrete spatial lattice emerges from one gauge. → A discrete time spectrum emerges in another gauge.
Dechanneling function for relativistic axially channeled electrons
International Nuclear Information System (INIS)
Muralev, V.A.; Telegin, V.I.
1981-01-01
Behaviour of the x(t) dechanneling function depending on the depth is theoretically studied. Theoretical consideration of x(t) for axial channeled relativistic electrons in anisotropic medium results in two-dimensional kinetic equation with mixed derivatives of the parabolic type. The kinetic equation in the approximation of the continuous Lindchard model for relativistic axial channeled electrons is numerically solved. The depth dependence of the x(t) dechanneling function is obtained [ru
Limits and signatures of relativistic spaceflight
Yurtsever, Ulvi; Wilkinson, Steven
2018-01-01
While special relativity imposes an absolute speed limit at the speed of light, our Universe is not empty Minkowski spacetime. The constituents that fill the interstellar/intergalactic vacuum, including the cosmic microwave background photons, impose a lower speed limit on any object travelling at relativistic velocities. Scattering of cosmic microwave photons from an ultra-relativistic object may create radiation with a characteristic signature allowing the detection of such objects at large distances.
Summary of the relativistic heavy ion sessions
International Nuclear Information System (INIS)
Harris, J.W.
1988-01-01
The topics covered in the Relativistic Heavy Ion Sessions span four orders of magnitude in energy in the laboratory and a few more in theory. In the two years since the last Intersections conference, experiments in the field of very high energy heavy ion research have begun at CERN and Brookhaven. The prime motivation for these experiments is the possibility of forming quark matter. This paper is a review of the topics covered in the Relativistic Heavy Ion Sessions
Localization and Entanglement in Relativistic Quantum Physics
Yngvason, Jakob
2014-01-01
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum Field Theory but less well known outside this community. The paper is intended as a concise survey of some selected aspects of relativistic quantum physics, in particular regarding localization and entanglement.
Timelike Killing Fields and Relativistic Statistical Mechanics
Klein, David; Collas, Peter
2008-01-01
For spacetimes with timelike Killing fields, we introduce a "Fermi-Walker-Killing" coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, derived both independently and as the Newtonian limit of our formula. We also find the relativistic the...
Ohm's Law for a Relativistic Pair Plasma
Blackman, Eric G.; Field, George B.
1994-01-01
We derive the fully relativistic Ohm's law for an electron-positron plasma. The absence of non-resistive terms in Ohm's law and the natural substitution of the 4-velocity for the velocity flux in the relativistic bulk plasma equations do not require the field gradient length scale to be much larger than the lepton inertial lengths, or the existence of a frame in which the distribution functions are isotropic.
Post-Newtonian reference ellipsoid for relativistic geodesy
Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena
2016-02-01
We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to
The relativistic geoid: redshift and acceleration potential
Philipp, Dennis; Lämmerzahl, Claus; Puetzfeld, Dirk; Hackmann, Eva; Perlick, Volker
2017-04-01
We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars. By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence. We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.
Relativistic quasiparticle random phase approximation in deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Shelton, Wayne
2013-01-01
This article discusses how the paradigm of Cartesian mind-body dualism has shaped the cultural and institutional life of modern science and medicine. John Dewey (1859-1952) made this case in a speech to the New York Academy of Medicine in 1927, "Preoccupation with the Disconnected," an expanded version of which was published as "Body and Mind" in the Bulletin of the New York Academy of Medicine in January 1928. From the perspective of Dewey's broader philosophy, the most urgent aspect of mind-body dualism is of a practical, not theoretical, nature. Medicine at present has an opportunity in both education and practice to reconcile internally disparate trends that result from mind-body dualism and to renew its mission.
A density-dependent effective interaction for relativistic Hartree-Fock calculations
International Nuclear Information System (INIS)
Marcos, S.; Mathiot, J.F.; Lopez-Quelle, M.; Niembro, R.; Bernardos, P.
1996-01-01
We present a general method to derive density-dependent effective interactions to be used in the relativistic Hartree-Fock approximation. In the non-relativistic limit (i.e. at low density), this method is identical to the usual variational ansatz with a two-body correlation function whose range is used as a variational parameter. At normal nuclear matter density, it provides a useful prescription to fit relativistic Brueckner-Hartree-Fock calculations. It provides in particular a physical way to deal with the zero-range pieces of π and ρ interactions in the medium. We apply our method to infinite symmetric nuclear matter. This effective interaction is also particularly well suited for calculations in finite nuclei. (orig.)
Structure and applications of point form relativistic quantum mechanics
International Nuclear Information System (INIS)
Klink, W.H.
2003-01-01
The framework of point form relativistic quantum mechanics is used to construct mass and current operators for hadronic systems with finite degree of freedom. For the point form all of the interactions are in the four-momentum operator and, since Lorentz transformations are kinematic, the theory is manifestly covariant. In the Bakamjian-Thomas version of the point form the four-momentum operator is written as a product of the four-velocity operator and mass operator, where the mass operator is the sum of free and interacting mass operators. Interacting mass operators can be constructed from vertices, matrix elements of local field operators evaluated at the space-time point zero, where the states are eigenstates of the four-velocity. Applications include the study of the spectra and widths of vector mesons, viewed as bound states of quark-antiquark pairs. Besides mass operators, current operators are needed to compute form factors. Form factors are matrix elements of current operators on mass operator eigenstates and are often calculated with one-body current operators (in the point form this is called the point form spectator approximation); but in a properly relativistic theory there must also be many-body current operators. Minimal currents needed to satisfy current conservation in the presence of hadronic interactions (called dynamically determined currents) are shown to be easily calculated in the point form. (author)
Hu, Jinniu; Toki, Hiroshi; Shen, Hong
2016-10-18
We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around -3 and -5 MeV at saturation density, while it becomes -8 and -12 MeV in relativistic framework with 1 S 0 , 3 S 1 , and 3 D 1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1 S 0 channel with isospin T = 1 case.
Fakis, Demetrios; Kalvouridis, Tilemahos
2017-09-01
The regular polygon problem of (N+1) bodies deals with the dynamics of a small body, natural or artificial, in the force field of N big bodies, the ν=N-1 of which have equal masses and form an imaginary regular ν -gon, while the Nth body with a different mass is located at the center of mass of the system. In this work, instead of considering Newtonian potentials and forces, we assume that the big bodies create quasi-homogeneous potentials, in the sense that we insert to the inverse square Newtonian law of gravitation an inverse cube corrective term, aiming to approximate various phenomena due to their shape or to the radiation emitting from the primaries. Based on this new consideration, we apply a general methodology in order to investigate by means of the zero-velocity surfaces, the regions where 3D motions of the small body are allowed, their evolutions and parametric variations, their topological bifurcations, as well as the existing trapping domains of the particle. Here we note that this process is definitely a fundamental step of great importance in the study of many dynamical systems characterized by a Jacobian-type integral of motion in the long way of searching for solutions of any kind.
Masago, Bruna Yukiko Pinheiro Lopes; Prado, Antonio Fernando Bertachini de Almeida; Chiaradia, Ana Paula Marins; Gomes, Vivian Martins
2016-02-01
Space missions to visit small bodies of the Solar System are important steps to improve our knowledge of the Solar System. Usually those bodies do not have well known characteristics, as their gravity field, which make the mission planning a difficult task. The present paper has the goal of studying orbits around the triple asteroid 2001SN263, a Near-Earth Asteroid (NEA). A mission to this system allows the exploration of three bodies in the same trip. The distances reached by the spacecraft from those three bodies have fundamental importance in the quality of their observations. Therefore, the present research has two main goals: (i) to develop a semi-analytical mathematical model, which is simple, but able to represent the main characteristics of that system; (ii) to use this model to find orbits for a spacecraft with the goal of remaining the maximum possible time near the three bodies of the system, without the need of space maneuvers. This model is called ;Precessing Inclined Bi-Elliptical Problem with Radiation Pressure; (PIBEPRP). The use of this model allow us to find important natural orbits for the exploration of one, two or even the three bodies of the system. These trajectories can be used individually or combined in two or more parts using orbital maneuvers.
Non-relativistic and relativistic quantum kinetic equations in nuclear physics.
Botermans, Wilhelmus Martinus Maria
1989-01-01
In this thesis, we discussed the derivation of quantum kinetic equations appropriate for applications in nuclear physics, both in a non-relativistic and in a relativistic context. In each case we obtained a kinetic equation together with an equation for the effective interaction. The latter serves
Classical relativistic spinning particle with anomalous magnetic moment: The precession of spin
International Nuclear Information System (INIS)
Barut, A.O.; Cruz, M.G.
1993-05-01
The theory of classical relativistic spinning particles with c-number internal spinor variables, modelling accurately the Dirac electron, is generalized to particles with anomalous magnetic moments. The equations of motion are derived and the problem of spin precession is discussed and compared with other theories of spin. (author). 32 refs
Plasma heating in a long solenoid by a laser or a relativistic electron beam
International Nuclear Information System (INIS)
Tajima, T.
1975-01-01
Advances in the technology of a large energy laser and/or relativistic electron beam (REB) generator have made it possible to seriously consider a long solenoid reactor concept. This concept has been reviewed. The physical problems in the plasma heating of the long solenoid by a laser or a REB are studied
Relativistic corrections to the algebra of position variables and spin-orbital interaction
International Nuclear Information System (INIS)
Deriglazov, Alexei A.; Pupasov-Maksimov, Andrey M.
2016-01-01
In the framework of vector model of spin, we discuss the problem of a covariant formalism [35] concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non-commutativity of a position accounts the discrepancy on the classical level, without appeal to the Dirac equation and Foldy–Wouthuysen transformation.
Relativistic corrections to the algebra of position variables and spin-orbital interaction
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, Alexei A., E-mail: alexei.deriglazov@ufjf.edu.br [Departamento de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation); Pupasov-Maksimov, Andrey M., E-mail: pupasov.maksimov@ufjf.edu.br [Departamento de Matemática, ICE, Universidade Federal de Juiz de Fora, MG (Brazil)
2016-10-10
In the framework of vector model of spin, we discuss the problem of a covariant formalism [35] concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non-commutativity of a position accounts the discrepancy on the classical level, without appeal to the Dirac equation and Foldy–Wouthuysen transformation.
RIS3: A program for relativistic isotope shift calculations
Nazé, C.; Gaidamauskas, E.; Gaigalas, G.; Godefroid, M.; Jönsson, P.
2013-09-01
An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program RIS3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined. Program summaryProgram title:RIS3 Catalogue identifier: ADEK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEK_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5147 No. of bytes in distributed program, including test data, etc.: 32869 Distribution format: tar.gz Programming language: Fortran 77. Computer: HP ProLiant BL465c G7 CTO. Operating system: Centos 5.5, which is a Linux distribution compatible with Red Hat Enterprise Advanced Server. Classification: 2.1. Catalogue identifier of previous version: ADEK_v1_0 Journal reference of previous version: Comput. Phys. Comm. 100 (1997) 81 Subprograms used: Cat Id Title Reference ADZL_v1_1 GRASP2K VERSION 1_1 to be published. Does the new version supersede the previous version?: Yes Nature of problem: Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions. Solution method: The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |Ψ>=∑μcμ|Φ(γμPJMj)>, where P, J and MJ are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as ∑cμcν where V is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied