The relativistic atomic many-body problem
International Nuclear Information System (INIS)
Brown, G.E.
1987-01-01
Problems connected with the infinite negative energy sea of electrons in the atomic many-body problem are discussed. It is shown that as long as one works in mean-field approximations, wave functions do not need to suffer from continuum dissociation. Various effects from virtual pairs in the wave functions are discussed. (orig.)
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)
On the special relativistic two-body problem
International Nuclear Information System (INIS)
Afanas'ev, G.N.; Asanov, R.A.
1979-01-01
The Poincare method is applied to the consideration of the two-body problem within the Special Relativity. The formulation of the theory contains two arbitrary functions of the Lorentz invariants. A specific choice of these functions leads to the correct description of three crucial experiments of the General Relativity. The expansion on the inverse powers of the light velocity being performed, the approximate Lorentz covariant two-body equations without retardation effects are obtained
Relativistic few body calculations
International Nuclear Information System (INIS)
Gross, F.
1988-01-01
A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ 5 γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40 Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs
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
International Nuclear Information System (INIS)
Bakalov, D.D.; Melezhik, V.S.
1987-01-01
The relativistic Hamiltonian for 3-spin particles with electromagnetic interaction has been represented in the form of a sum of terms with factorized dependence on spin, angular and spheroidal variable, and its matrix elements have been expressed in terms of the matrix elements of a small number of ''basic'' operators. The numerical values of the latter have been tabulated, thus allowing for the evaluation of the leading relativistic effects in any 3-body system (with unit particle charge) with and accuracy of ∼ 0(1/2M), where 1/2M=(M 1 -1 +M 2 -1 )/2(M 1 -1 +M 3 -1 ) is the small parameter of the adiabatic expansion (M i , i=1,2,3 being particle masses)
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.
A new approach to the semi-classical relativistic two-body problem for charged fermions
International Nuclear Information System (INIS)
Leiter, D.
1978-01-01
Generalizing from a recently developed hybrid formulation of classical electrodynamics with ''direct (charge-field) action'' structure an analogous semi-classical Dirac formulation of the theory is constructed, which is capable of describing the semi-classical quantum mechanics of two identical spin-1/2 particles. This semi-classical formulation is to be used as a heuristic aid in searching for the theoretical structure of a fully ''second quantized'' theory. The Pauli exclusion principle is incorporated by making the interaction fields (in the action principle) antisymmetric with respect to ''charge-field'' labeling. In this manner, ''position correlation'' effects associated with ''configuration interaction'' can also be accounted for. By studying the nature of the stationary-state solutions, the formalism is compared with the conventional quantum-mechanical one (to understand the similarities and the differences between this approach and the usual correlated Hartree-Fock approximation of ordinary relativistic quantum theory). The stationary-state solutions to the semi-classical formalism are shown to closely approximate the usual quantum-mechanical solutions when the wave functions are represented as a superposition of Slater determinants of Dirac-Coulombic-type wave functions with radial parts having a form which extremizes the total Breit energy. The manner in which this semi-classical theory might be extended to a fully ''second quantized'' formalism is sketched. (author)
Relativistic Descriptions of Few-Body Systems
International Nuclear Information System (INIS)
Karmanov, V. A.
2011-01-01
A brief review of relativistic effects in few-body systems, of theoretical approaches, recent developments and applications is given. Manifestations of relativistic effects in the binding energies, in the electromagnetic form factors and in three-body observables are demonstrated. The three-body forces of relativistic origin are also discussed. We conclude that relativistic effects in nuclei can be important in spite of small binding energy. At high momenta they clearly manifest themselves and are necessary to describe the deuteron e.m. form factors. At the same time, there is still a discrepancy in three-body observables which might be a result of less clarity in understanding the corresponding relativistic effects, the relativistic NN kernel and the three-body forces. Relativistic few-body physics remains to be a field of very intensive and fruitful researches. (author)
Some problems in relativistic thermodynamics
International Nuclear Information System (INIS)
Veitsman, E. V.
2007-01-01
The relativistic equations of state for ideal and real gases, as well as for various interface regions, have been derived. These dependences help to eliminate some controversies in the relativistic thermodynamics based on the special theory of relativity. It is shown, in particular, that the temperature of system whose velocity tends to the velocity of light in vacuum varies in accordance with the Ott law T = T 0 /√1 - v 2 /c 2 . Relativistic dependences for heat and mass transfer, for Ohm's law, and for a viscous flow of a liquid have also been derived
Relativistic Theory of Few Body Systems
Energy Technology Data Exchange (ETDEWEB)
Franz Gross
2002-11-01
Very significant advances have been made in the relativistic theory of few body systems since I visited Peter Sauer and his group in Hannover in 1983. This talk provides an opportunity to review the progress in this field since then. Different methods for the relativistic calculation of few nucleon systems are briefly described. As an example, seven relativistic calculations of the deuteron elastic structure functions, A, B, and T{sub 20}, are compared. The covariant SPECTATOR {copyright} theory, among the more successful and complete of these methods, is described in more detail.
Circular relativistic motion of two identical bodies
International Nuclear Information System (INIS)
Shavokhina, N.S.
1983-01-01
Circular relativistic motion of two bodies as a solution of the earlier obtained equations with a deflecting argument where the self-deflection of the argument is an unknown function of time is considered. In case of circular motion the argument deflection is independent from time and it is the root of the transcendental equation obtained in the paper
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 many-body theory of atomic transitions: the relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.N.
1981-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Relativistic many-body XMCD theory including core degenerate effects
Fujikawa, Takashi
2009-11-01
A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2. In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.
International Nuclear Information System (INIS)
Musielak, Z E; Quarles, B
2014-01-01
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. (review article)
The relativistic invariant and the Galilean mass of bodies
International Nuclear Information System (INIS)
Kapuscik, E.
1992-02-01
We generalize the concept of the Galilean mass to the relativistic case. In the case of inequality of Galilean and inertial masses we calculate the relativistic invariant being constant along the trajectory of the moving body. It enables us to define an invariant measure of inertia of bodies. 4 refs. (author)
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
Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.
1982-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
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)
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
International Nuclear Information System (INIS)
Alcaras, J.A.C.; Ferreira, J.L.
1975-01-01
A derivation of an angular basis for the A-body problem, suitable for the K-harmonics method, is presented. Those angular functions are obtained from homogeneous and harmonic polynomials, which are completely specified by labels associated to eigenvalues of the Casimir invariants of subgroups of the 3(A-1)-dimensional orthogonal group, among them, the total angular momentum and its z-projection [pt
Two centre problems in relativistic atomic physics
Energy Technology Data Exchange (ETDEWEB)
McConnell, Sean R.
2013-01-09
The work contained within this thesis is concerned with the explanation and usage of a set of theoretical procedures for the study of static and dynamic two-centre problems in the relativistic framework of Dirac's equation. Two distinctly different theories for handling time-dependent atomic interactions are reviewed, namely semi-classical perturbation theory and a non-perturbative numerical technique based on the coupled channel equation to directly solve the time-dependent, two-centre Dirac equation. The non-perturbative numerical technique has been developed independently and the calculations performed with it are entirely new. Calculations for ionisation cross sections and state occupancies are conducted for both these methods. The non-perturbative technique for relativistic two-centre problems is extensively explained and, given its novelty, a probity test is conducted between this technique and that of the well established perturbation theory in calculating K-and L-shell ionisation cross sections for the alpha decay of initially Hydrogen-like Polonium. To that end, an in depth outline of the perturbative technique is also made for both collision and decay processes. As well as the comparison test mentioned, this technique is also applied to the analysis of cross sections of the promotion of a single electron into the positive continuum from either a K- or L-shell due to the alpha decay of heavy, neutral nuclei (Gadolinium, Polonium and Thorium). Dirac-Coulomb eigenfunctions centred on the parent nucleus of the decay pair are taken as the basis for use in the cross section calculations utilising first order, semi-classical pertubation theory. The excellent congruence between both techniques justifies the usage of the non-perturbative algorithms in the subsequent analysis of collisions between very heavy, highly charged ions. As such, a set of calculations are performed examining the bound and continuum state occupancy of the electronic levels during a
Relativistic two-body forces in many-body systems
International Nuclear Information System (INIS)
Namyslowski, J.M.
1979-01-01
For the fully off-shell extension in the relativistic dynamics, based on a covariant light-front field theory, we define the relative momenta and their proper angular variables such that -1 < cos theta/sub α/ < 1. In terms of these variables and the timelike total momenta we write explicitly the Weinberg interaction, corresponding to the exchange of a spinless particle of mass μ. The total momentum dependence and the cluster decomposition property of the Weinberg interaction are presented in detail, together with its energy dependence and other nonlocal features. In the nonrelativistic limit we recover the Yukawa interaction, while for the finite masses the Weinberg interaction is a product of the Yukawa interaction and a form factor. The Weinberg two-body force goes to zero at large energies and is truly nonlocal, in spite of the fact that the underlying field theory has a local Lagrangian
Relativistic three-body model of pion-deuton elasic scattering
International Nuclear Information System (INIS)
Giraud, Noel.
1978-01-01
The Aaron-Amado-Young equations for the relativistic three-body problem are derived following the Blauckenbecker - Sugar method. The angular momentum reduction is carried out using suitable relative momenta. The pion-deuteron elastic scattering is calculated using the equations in which relativistic kinematics are retained only for the pion. After a general study of the observables in the energy range 25 to 256 MeV, detailed calculations are performed at 142 MeV [fr
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
Relativistic bound-state problem of a one-dimensional system
International Nuclear Information System (INIS)
Sato, T.; Niwa, T.; Ohtsubo, H.; Tamura, K.
1991-01-01
A Poincare-covariant description of the two-body bound-state problem in one-dimensional space is studied by using the relativistic Schrodinger equation. We derive the many-body Hamiltonian, electromagnetic current and generators of the Poincare group in the framework of one-boson exchange. Our theory satisfies Poincare algebra within the one-boson-exchange approximation. We numerically study the relativistic effects on the bound-state wavefunction and the elastic electromagnetic form factor. The Lorentz boost of the bound-state wavefunction and the two-body exchange current are shown to play an important role in guaranteeing the Lorentz invariance of the form factor. (author)
Fundamental problem in the relativistic approach to atomic structure theory
International Nuclear Information System (INIS)
Kagawa, Takashi
1987-01-01
It is known that the relativistic atomic structure theory contains a serious fundamental problem, so-called the Brown-Ravenhall (BR) problem or variational collapse. This problem arises from the fact that the energy spectrum of the relativistic Hamiltonian for many-electron systems is not bounded from below because the negative-energy solutions as well as the positive-energy ones are obtained from the relativistic equation. This report outlines two methods to avoid the BR problem in the relativistic calculation, that is, the projection operator method and the general variation method. The former method is described first. The use of a modified Hamiltonian containing a projection operator which projects the positive-energy solutions in the relativistic wave equation has been proposed to remove the BR difficulty. The problem in the use of the projection operator method is that the projection operator for the system cannot be determined uniquely. The final part of this report outlines the general variation method. This method can be applied to any system, such as relativistic ones whose Hamiltonian is not bounded from below. (Nogami, K.)
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
Relativistic analysis of four-body final states
International Nuclear Information System (INIS)
Adhikari, S.K.
1977-01-01
The constraints of unitarity and analyticity on four-body final states are studied. It is shown that unitarity alone forces the amplitudes to be coherent and have singular behaviour. The implementation of unitarity with total energy analyticity yields a set of relativistic linear integral equations for the four-body amplitude. This is the minimal set consistent with quantum mechanics and also is the full dynamical set of equations with two-body separable interactions. These equations will provide important ingredients for the phenomenological analysis of four-body final states using the isobar model. (Auth.)
Relativistic many-body bound systems. Monograph report
International Nuclear Information System (INIS)
Danos, M.; Gillet, V.
1975-04-01
The principles and the mathematical details of a fully relativistic nuclear theory are given. Since the concept of nuclear forces is a strictly non-relativistic construct, it must be abandoned, and the forces must be replaced explicitly by their physical origin, i.e., by the interaction between nucleons and mesons. Thus, in this monograph the description of a nucleus has been formulated as a problem of relativistic quantum field theory which is solved by nuclear physics methods; to wit: the physics is described by specifying a Lagrangian which is a functional of the constituent fields (= of the parton fields); the solutions for the physical systems then are obtained in a time-independent treatment as expansions in the parton fields: both particles and nuclei are composite systems, made up of parton configurations, which define a representation of the Hamiltonian (associated with the specified Lagrangian)
Relativistic initial conditions for N-body simulations
Energy Technology Data Exchange (ETDEWEB)
Fidler, Christian [Catholic University of Louvain—Center for Cosmology, Particle Physics and Phenomenology (CP3) 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Tram, Thomas; Crittenden, Robert; Koyama, Kazuya; Wands, David [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Rampf, Cornelius, E-mail: christian.fidler@uclouvain.be, E-mail: thomas.tram@port.ac.uk, E-mail: rampf@thphys.uni-heidelberg.de, E-mail: robert.crittenden@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: david.wands@port.ac.uk [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D–69120 Heidelberg (Germany)
2017-06-01
Initial conditions for (Newtonian) cosmological N-body simulations are usually set by re-scaling the present-day power spectrum obtained from linear (relativistic) Boltzmann codes to the desired initial redshift of the simulation. This back-scaling method can account for the effect of inhomogeneous residual thermal radiation at early times, which is absent in the Newtonian simulations. We analyse this procedure from a fully relativistic perspective, employing the recently-proposed Newtonian motion gauge framework. We find that N-body simulations for ΛCDM cosmology starting from back-scaled initial conditions can be self-consistently embedded in a relativistic space-time with first-order metric potentials calculated using a linear Boltzmann code. This space-time coincides with a simple ''N-body gauge'' for z < 50 for all observable modes. Care must be taken, however, when simulating non-standard cosmologies. As an example, we analyse the back-scaling method in a cosmology with decaying dark matter, and show that metric perturbations become large at early times in the back-scaling approach, indicating a breakdown of the perturbative description. We suggest a suitable ''forwards approach' for such cases.
Relativistic N-body simulations with massive neutrinos
Adamek, Julian; Durrer, Ruth; Kunz, Martin
2017-11-01
Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical simulations have to be developed. Due to their relativistic nature, neutrinos pose additional challenges when one tries to include them in N-body simulations that are traditionally based on Newtonian physics. Here we present the first numerical study of massive neutrinos that uses a fully relativistic approach. Our N-body code, gevolution, is based on a weak-field formulation of general relativity that naturally provides a self-consistent framework for relativistic particle species. This allows us to model neutrinos from first principles, without invoking any ad-hoc recipes. Our simulation suite comprises some of the largest neutrino simulations performed to date. We study the effect of massive neutrinos on the nonlinear power spectra and the halo mass function, focusing on the interesting mass range between 0.06 eV and 0.3 eV and including a case for an inverted mass hierarchy.
Particle acceleration and injection problem in relativistic and nonrelativistic shocks
International Nuclear Information System (INIS)
Hoshino, M.
2008-01-01
Acceleration of charged particles at the collisionless shock is believed to be responsible for production of cosmic rays in a variety of astrophysical objects such as supernova, AGN jet, and GRB etc., and the diffusive shock acceleration model is widely accepted as a key process for generating cosmic rays with non-thermal, power-law energy spectrum. Yet it is not well understood how the collisionless shock can produce such high energy particles. Among several unresolved issues, two major problems are the so-called '' injection '' problem of the supra-thermal particles and the generation of plasma waves and turbulence in and around the shock front. With recent advance of computer simulations, however, it is now possible to discuss those issues together with dynamical evolution of the kinetic shock structure. A wealth of modern astrophysical observations also inspires the dynamical shock structure and acceleration processes along with the theoretical and computational studies on shock. In this presentation, we focus on the plasma wave generation and the associated particle energization that directly links to the injection problem by taking into account the kinetic plasma processes of both non-relativistic and relativistic shocks by using a particle-in-cell simulation. We will also discuss some new particle acceleration mechanisms such as stochastic surfing acceleration and wakefield acceleration by the action of nonlinear electrostatic fields. (author)
Relativistic many-body theory of high density matter
International Nuclear Information System (INIS)
Chin, S.A.
1977-01-01
A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon--nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g 4 lng 2 are explicitly given. Effects of scalar-vector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined
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%
Relativistic many-body theory of atomic structures
International Nuclear Information System (INIS)
Cheng, K.T.
1983-01-01
The main objective of this program is to improve our understanding of the effect of relativity and electron correlations on atomic processes. Current efforts include hyperfine structure (hfs) studies using the multiconfiguration Dirac-Fock (MCDF) technique. Atomic hfs are known to be sensitive to relativity and electron correlations, and provide important tests of relativistic atomic many-body theories. Preliminary results on the hfs of the 4f 12 3 H ground state of 68 Er 167 are shown and are in good agreement with experiment. This shows that the MCDF technique can be an efficient and powerful method for atomic hfs studies. Further tests of this method are in progress. We are also studying the absorption spectra for Xe-like ions in the region of 4d → nf, epsilonf transitions
N-body bound state relativistic wave equations
International Nuclear Information System (INIS)
Sazdjian, H.
1988-06-01
The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability
Problems of describing the cumulative effect in relativistic nuclear physics
International Nuclear Information System (INIS)
Baldin, A.M.
1979-01-01
The problem of describing the cumulative effect i.e., the particle production on nuclei in the range kinematically forbidden for one-nucleon collisions, is studied. Discrimination of events containing cumulative particles fixes configurations in the wave function of a nucleus, when several nucleons are closely spaced and their quark-parton components are collectivized. For the cumulative processes under consideration large distances between quarks are very important. The fundamental facts and theoretical interpretation of the quantum field theory and of the condensed media theory in the relativistic nuclear physics are presented in brief. The collisions of the relativistic nuclei with low momentum transfers is considered in a fast moving coordinate system. The basic parameter determining this type of collisions is the energy of nucleon binding in nuclei. It has been shown that the short-range correlation model provides a good presentation of many characteristics of the multiple particle production and it may be regarded as an approximate universal property of hadron interactions
Solution of relativistic quantum optics problems using clusters of graphical processing units
Energy Technology Data Exchange (ETDEWEB)
Gordon, D.F., E-mail: daviel.gordon@nrl.navy.mil; Hafizi, B.; Helle, M.H.
2014-06-15
Numerical solution of relativistic quantum optics problems requires high performance computing due to the rapid oscillations in a relativistic wavefunction. Clusters of graphical processing units are used to accelerate the computation of a time dependent relativistic wavefunction in an arbitrary external potential. The stationary states in a Coulomb potential and uniform magnetic field are determined analytically and numerically, so that they can used as initial conditions in fully time dependent calculations. Relativistic energy levels in extreme magnetic fields are recovered as a means of validation. The relativistic ionization rate is computed for an ion illuminated by a laser field near the usual barrier suppression threshold, and the ionizing wavefunction is displayed.
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
Dynamics of relativistic point particles as a problem with constraints
International Nuclear Information System (INIS)
Todorov, I.T.
1976-01-01
The relativistic n-particle dynamics is studied as a problem with constraints of the type (2phisub(i)=)msub(i)sup(2)-psub(i)sup(2)+PHIsub(i)=0, i=1,...,n, (C) where PHIsub(i) are Poincare invariant functions of the particles' coordinates, momenta and spin components; PHIsib(i) is assumed to vanish asymptotically when the i-th particle coordinates tend to infinity. In the two particle case it is assumed in addition that the Poisson bracket [phi 1 , phi 2 ] vanishes on the surface (C). That allows us to give a formulation of the theory, invariant with respect to the choice of the time-parameter on each trajectory. The quantization of the relative two-particle motion is also discussed. It is pointed out that the stationary Schrodinger equation obtained in this manner is a local quasipotential equation
Fodor, Jerry A.
1981-01-01
Describes several different philosophies of mind with each philosophy's explanation of the mind-body problem. Philosophies discussed include dualism, materialism, functionalism, radical behaviorism, logical behaviorism and central-state identity. (DS)
On the basis of molecular orbitals for relativistic bound systems of many bodies
International Nuclear Information System (INIS)
Cook, A.H.
1987-09-01
The quasi-relativistic Hamiltonian for bound states of many bodies proposed in previous articles (Cook, 1986, 1987a) is shown to provide a basis for the molecular orbital scheme of constructing wavefunctions and calculating eigenenergies. (author). 5 refs
Relativistic n-body wave equations in scalar quantum field theory
International Nuclear Information System (INIS)
Emami-Razavi, Mohsen
2006-01-01
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields
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
Few-body problem in terms of correlated Gaussians
Silvestre-Brac, Bernard; Mathieu, Vincent
2007-10-01
In their textbook, Suzuki and Varga [Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems (Springer, Berlin, 1998)] present the stochastic variational method with the correlated Gaussian basis in a very exhaustive way. However, the Fourier transform of these functions and their application to the management of a relativistic kinetic energy operator are missing and cannot be found in the literature. In this paper we present these interesting formulas. We also give a derivation for formulations concerning central potentials.
Electromagnetic interactions in relativistic systems of many bodies
International Nuclear Information System (INIS)
Cook, A.H.
1987-09-01
In a previous report (Cook, 1986, 1987) on a formulation of a quasi-relativistic quantum mechanical equation of motion for many particles, little was said of the electromagnetic interactions that keep a set of particles in a bound state. That omission is to some extent repaired in this report. (author). 3 refs
The cosmic-ray shock structure problem for relativistic shocks
Webb, G. M.
1985-01-01
The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.
Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions
International Nuclear Information System (INIS)
Ishikawa, Y.; Quiney, H.M.
1993-01-01
A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence
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
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
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...
Two-body relativistic scattering with an O(1,1)-symmetric square-well potential
International Nuclear Information System (INIS)
Arshansky, R.; Horwitz, L.P.
1984-01-01
Scattering theory in the framework of a relativistic manifestly covariant quantum mechanics is applied to the relativistic analog of the nonrelativistic one-dimensional square-well potential, a two-body O(1,1)-symmetric hyperbolic square well in one space and one time dimension. The unitary S matrix is explicitly obtained. For well sizes large compared to the de Broglie wavelength of the reduced motion system, simple formulas are obtained for the associated sequence of resonances. This sequence has equally spaced levels and constant widths for higher resonances, and linearly increasing widths for lower-lying levels
Solved and unsolved problems in relativistic quantum chemistry
International Nuclear Information System (INIS)
Kutzelnigg, Werner
2012-01-01
Graphical abstract: The graphical abstract represents the Dirac-Coulomb Hamiltonian in Fock space in a diagrammatic notation. A line (vertical or slanted) with an upgoing arrow represents an eletron, with a downgoing arrow a positron. A cross in the first line means the potential created by a nucleus, a broken line represents the Coulomb interaction between electrons and positrons. Highlights: ► Relativistic many-electron theory needs a Fock space and a field-dependent vacuum. ► A good starting point is QED in Coulomb gauge without transversal photons. ► The Dirac underworld picture is obsolete. ► A kinetically balanced even-tempered Gaussian basis is complete. ► ‘Quantum chemistry in Fock space is preferable over QED. - Abstract: A hierarchy of approximations in relativistic many-electron theory is discussed that starts with the Dirac equation and its expansion in a kinetically balanced basis, via a formulation of non-interacting electrons in Fock space (which is the only consistent way to deal with negative-energy states). The most straightforward approximate Hamiltonian for interacting electrons is derived from quantum electrodynamics (QED) in Coulomb gauge with the neglect of transversal photons. This allows an exact (non-perturbative) decoupling of the electromagnetic field from the fermionic field. The electric interaction of the fermions is non-retarded and non-quantized. The quantization of the fermionic field leads to a polarizable vacuum. The simplest (but somewhat problematic) approximation is a no-pair projected theory with external-field projectors. The Dirac-Coulomb operator in configuration space (first quantization) is not acceptable, even if the Brown–Ravenhall disease is much less virulent than often claimed. Effects of transversal photons, such as the Breit interaction and renormalized self-interaction can be taken care of perturbatively at the end, but there are still many open questions.
Two-body problem for Weber-like interactions
International Nuclear Information System (INIS)
Clemente, R.A.; Assis, A.K.T.
1991-01-01
The problem of two moving bodies interacting through a Weber-like force is presented. Trajectories are obtained analytically once relativistic and quantic considerations are neglected. The main results are that in the case of limited trajectories, in general, they are not closed and in the case of open trajectories, the deflection angles are not the same for similar particles with given energies and angular momenta but opposite potentials. This last feature suggests the possibility of a direct verification of the validity of Weber's law of force for electromagnetic interactions
An su(1, 1) algebraic approach for the relativistic Kepler-Coulomb problem
International Nuclear Information System (INIS)
Salazar-Ramirez, M; Granados, V D; MartInez, D; Mota, R D
2010-01-01
We apply the Schroedinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the su(1, 1) Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.
Comment on 'analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation'
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1994-01-01
We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some straightforward variational procedure. (authors)
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 ...
International Nuclear Information System (INIS)
Karabut, P.V.; Chugreev, Yu.V.
1989-01-01
The relativistic theory of gravitation (RTG), which is constructed on the basis of Minkowski spacetime, the geometrization principle, and the notion of the gravitational field var-phi mn as a physical field in the spirit of Faraday and Maxwell, explains all known gravitational experiments and gives a new prediction for the evolution of the universe, collapse, etc. The RTG determines the structure of the gravitational field as a field possessing spins 2 and 0 and all conservation laws for energy, momentum, and angular momentum. An exact solution of the complete simultaneous system of equations of the relativistic theory of gravitation and Maxwell's equations is found in the axisymmetric case for an electrically charged rotating body. The uniqueness of this solution is proved
General relativistic dynamics of an extreme mass-ratio binary interacting with an external body
Yang, Huan; Casals, Marc
2017-10-01
We study the dynamics of a hierarchical three-body system in the general relativistic regime: an extreme mass-ratio inner binary under the tidal influence of an external body. The inner binary consists of a central Schwarzschild black hole and a test body moving around it. We discuss three types of tidal effects on the orbit of the test body. First, the angular momentum of the inner binary precesses around the angular momentum of the outer binary. Second, the tidal field drives a "transient resonance" when the radial and azimuthal frequencies are commensurable. In contrast with resonances driven by the gravitational self-force, this tidal-driven resonance may boost the orbital angular momentum and eccentricity (a relativistic version of the Kozai-Lidov effect). Finally, for an orbit-dynamical effect during the nonresonant phase, we calculate the correction to the innermost stable circular (mean) orbit due to the tidal interaction. Hierarchical three-body systems are potential sources for future space-based gravitational wave missions, and the tidal effects that we find could contribute significantly to their waveform.
Use of Genetic Algorithms to solve Inverse Problems in Relativistic Hydrodynamics
Guzmán, F. S.; González, J. A.
2018-04-01
We present the use of Genetic Algorithms (GAs) as a strategy to solve inverse problems associated with models of relativistic hydrodynamics. The signal we consider to emulate an observation is the density of a relativistic gas, measured at a point where a shock is traveling. This shock is generated numerically out of a Riemann problem with mildly relativistic conditions. The inverse problem we propose is the prediction of the initial conditions of density, velocity and pressure of the Riemann problem that gave origin to that signal. For this we use the density, velocity and pressure of the gas at both sides of the discontinuity, as the six genes of an organism, initially with random values within a tolerance. We then prepare an initial population of N of these organisms and evolve them using methods based on GAs. In the end, the organism with the best fitness of each generation is compared to the signal and the process ends when the set of initial conditions of the organisms of a later generation fit the Signal within a tolerance.
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
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
Few-body problem in celestial mechanics
Energy Technology Data Exchange (ETDEWEB)
Dermott, S F [Cornell Univ., Ithaca, NY (USA). Center for Radiophysics and Space Research
1984-03-26
The approaches taken by solar system dynamicists to various outstanding problems has changed considerably in recent years. Some problems for which few-body approaches have been tried in the past are now thought to involve collective phenomena. Observed features in Saturn's rings associated with resonances are examples. On the other hand, the problem of the origin of the Kirkwood gaps in the asteroid belt, for which a number of a many-body approaches (involving collisions or gas friction) have been tried, probably has a few-body solution and may involve chaos.
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)
Riemann problems and their application to ultra-relativistic heavy ion collisions
International Nuclear Information System (INIS)
Plohr, B.J.; Sharp, D.H.
1986-07-01
Heavy ion collisions at sufficiently high energies to form quark-gluon plasma are considered. The phase transformation from a quark-gluon phase to hadrons as the nuclear matter cools is modeled as a hydrodynamical flow. Nonlinear waves are the predominant feature of this type of flow and the Riemann problem of a relativistic gas undergoing a phase transformation is explored as a method to numerically model this phase transition process in nuclear matter. The solution of the Riemann problem is outlined and results of preliminary numerical computations of the flow are presented. 10 refs., 2 figs
Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics
Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert
1995-05-01
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.
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...
Interactions of relativistic heavy ions in thick heavy element targets and some unresolved problems
International Nuclear Information System (INIS)
Brandt, R.; Ditlov, V.A.; Pozharova, E.A.; Smirnitskij, V.A.
2005-01-01
Interactions of relativistic heavy ions with total energies above 30 GeV in thick Cu and Pb targets (≥2 cm) have been studied with various techniques. Radiochemical irradiation experiments using thick Cu targets, both in a compact form or as diluted '2π-Cu targets' have been carried out with several relativistic heavy ions, such as 44 GeV 12 C (JINR, Dubna) and 72 GeV 40 Ar (LBL, Berkeley, USA). Neutron measuring experiments using thick targets irradiated with various relativistic heavy ions up to 44 GeV 12 C have been performed at JINR. In addition, the number of 'black prongs' in nuclear interactions (due to protons with energies less than 30 MeV and emitted from the target-like interaction partner at rest) produced with 72 GeV 22 Ne ions in nuclear emulsion plates has been measured in the first nuclear interaction of the primary 22 Ne ion and in the following second nuclear interaction of the secondary heavy (Z>1) ion. Some essential results have been obtained. 1) Spallation products produced by relativistic secondary fragments in interactions ([44 GeV 12 C or 72 GeV 40 Ar]+Cu) within thick copper yield less products close to the target and much more products far away from the target as compared to primary beam interactions. This applies also to secondary particles emitted into large angles (Θ>10deg). 2) The neutron production of 44 GeV 12 C within thick Cu and Pb targets is beyond the estimated yield as based on experiments with 12 GeV 12 C. These rather independent experimental results cannot be understood with well-accepted nuclear reaction models. They appear to present unresolved problems
Lavine method applied to three body problems
International Nuclear Information System (INIS)
Mourre, Eric.
1975-09-01
The methods presently proposed for the three body problem in quantum mechanics, using the Faddeev approach for proving the asymptotic completeness, come up against the presence of new singularities when the potentials considered v(α)(x(α)) for two-particle interactions decay less rapidly than /x(α)/ -2 ; and also when trials are made for solving the problem with a representation space whose dimension for a particle is lower than three. A method is given that allows the mathematical approach to be extended to three body problem, in spite of singularities. Applications are given [fr
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
Periodic Solutions for Circular Restricted -Body Problems
Directory of Open Access Journals (Sweden)
Xiaoxiao Zhao
2013-01-01
Full Text Available For circular restricted -body problems, we study the motion of a sufficiently small mass point (called the zero mass point in the plane of equal masses located at the vertices of a regular polygon. By using variational minimizing methods, for some , we prove the existence of the noncollision periodic solution for the zero mass point with some fixed wingding number.
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...
Relativistic Dirac-Fock and many-body perturbation calculations on He, He-like ions, Ne, and Ar
International Nuclear Information System (INIS)
Ishikawa, Y.
1990-01-01
Relativistic Dirac-Fock and diagrammatic many-body perturbation-theory calculations have been performed on He, several He-like ions, Ne, and Ar. The no-pair Dirac-Coulomb Hamiltonian is taken as the starting point. A solution of the Dirac-Fock equations is obtained by analytic expansion in basis sets of Gaussian-type functions. Many-body perturbation improvements of Coulomb correlation are done to third order
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)
Savukov, I. M.; Filin, D. V.
2014-01-01
Many applications are in need of accurate photoionization cross sections, especially in the case of complex atoms. Configuration-interaction relativistic-many-body-perturbation theory (CI-RMBPT) has been successful in predicting atomic energies, matrix elements between discrete states, and other properties, which is quite promising, but it has not been applied to photoionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photoionization cross sections with minimal modifications of the codes is introduced and CI-RMBPT cross sections of Ne, Ar, Kr, and Xe are calculated. A consistent agreement with experiment is found. RMBPT corrections are particularly significant for Ar, Kr, and Xe and improve agreement with experimental results compared to the particle-hole CI method. As a result, the demonstrated conversion method can be applied to CI-RMBPT photoionization calculations for a large number of multivalence atoms and ions
Pavlov and the mind-body problem.
Windholz, G
1997-01-01
I. P. Pavlov claimed that the mind-body problem would ultimately be resolved by empirical methods, rather than by rational arguments. A committed monist, Pavlov was confronted by dualism in the case of an hysterical person. Under normal conditions, her body's left side was insensitive to pain, but when she was hypnotized, there was a reversal of her sensitivity to pain, with the right side becoming insensitive. Pavlov acknowledged that the divergence between stimulation and response suggested dualism, yet condemned his disciple G.P. Zelenyĭ as well as Charles S. Sherrington, for their dualistic tendencies. Pavlov's continuous adherence to monism it attributed to the influence of popular scientific books that he read during his adolescence. The books maintained that science was based upon monism. Pavlov proposed that by introducing the concept of emotions, an hysterical person's condition could be explained within the framework of his theory of higher nervous activity, thereby obviating the need to change his paradigm.
Pseudo-Newtonian planar circular restricted 3-body problem
International Nuclear Information System (INIS)
Dubeibe, F.L.; Lora-Clavijo, F.D.; González, Guillermo A.
2017-01-01
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.
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.
Moshinsky, M; Nikitin, A G; Smirnov, Yu F
1998-01-01
In 1945 Bhabha was probably the first to discuss the problem of a free relativistic particle with arbitrary spin in terms of a single linear equation in the four-momentum vector p subnu, but substituting the gamma supnu matrices of Dirac by other ones. He determined the latter by requiring that their appropriate Lorentz transformations lead to their formulation in terms of the generators of the O(5) group. His program was later extensively amplified by Krajcik, Nieto and others. We returned to this problem because we had an ab-initio procedure for deriving a Lorentz-invariant equation of arbitrary spin and furthermore could express the matrices appearing in them in terms of ordinary and what we called sign spins. Our procedure was similar to that of the ordinary and isotopic spin in nuclear physics that give rise to supermultiplets, hence the appearance of this word in the title. In the ordinary and sign spin formulation it is easy to transform our equation into one linear in both the p subnu and some of the ...
International Nuclear Information System (INIS)
Hines, D.F.; Frankel, N.E.
1979-01-01
The charged Bose has been previously studied as a many body problem of great intrinsic interest which can also serve as a model of some real physical systems, for example, superconductors, white dwarf stars and neutron stars. In this article the excitation spectrum of a relativistic spin-zero charged Bose gas is obtained in a dielectric response formulation. Relativity introduces a dip in the spectrum and consequences of this dip for the thermodynamic functions are discussed
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.)
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.)
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
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
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
Desplanques, B.
1986-07-01
We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs
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.
Relativistic instant-form approach to the structure of two-body composite systems
International Nuclear Information System (INIS)
Krutov, A.F.; Troitsky, V.E.
2002-01-01
An approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main feature of this approach is the method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz covariance of the current is ensured. In the electromagnetic case the current conservation law is also ensured. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for the lepton decay constant of pions
Relativistic field theory of neutron stars and their hyperon populations
International Nuclear Information System (INIS)
Glendenning, N.K.
1986-01-01
The nuclear many-body problem is examined by means of the formulation of an effective relativistic field theory of interacting hadrons. A relativistic field theory of hadronic matter is especially appropriate for the description of hot or dense matter, because of the appearance of antiparticles and higher baryon resonances and because it automatically respects causality. 8 refs., 7 figs., 1 tab
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
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.
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Key to good fit: body measurement problems specific to key ...
African Journals Online (AJOL)
Key to good fit: body measurement problems specific to key dimensions. ... to explore and describe the problems that the South African Clothing Industry currently ... A postal survey was conducted among South African apparel and footwear ...
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.)
Effective linear two-body method for many-body problems in atomic and nuclear physics
International Nuclear Information System (INIS)
Kim, Y.E.; Zubarev, A.L.
2000-01-01
We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)
The three body problem with energy dependent potentials
International Nuclear Information System (INIS)
Kim, Y.E.; McKay, C.M.; McKellar, B.H.J.
1975-10-01
It is shown how to generalize the three body equations of Faddeev, and of Karlsson and Zeiger, to include the case when the two body potential is energy dependent. Such generalizations will prove useful in the three nucleon problem and in three body models of nuclear reactions. (author)
Relativistic particle in a box
Alberto, P.; Fiolhais, Carlos; Gil, Victor
1996-01-01
The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case
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
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
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)
Renormalization-group study of the four-body problem
International Nuclear Information System (INIS)
Schmidt, Richard; Moroz, Sergej
2010-01-01
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
Internal or shape coordinates in the n-body problem
International Nuclear Information System (INIS)
Littlejohn, R.G.; Reinsch, M.
1995-01-01
The construction of global shape coordinates for the n-body problem is considered. Special attention is given to the three- and four-body problems. Quantities, including candidates for coordinates, are organized according to their transformation properties under so-called democracy transformations (orthogonal transformations of Jacobi vectors). Important submanifolds of shape space are identified and their topology studied, including the manifolds upon which shapes are coplanar or collinear, and the manifolds upon which the moment of inertia tensor is degenerate
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 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...
International Nuclear Information System (INIS)
Akhiezer, A.I.; Shul'ga, N.F.
1991-01-01
The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)
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...... pattern and obesity was higher among problem gamblers than among non-problem gamblers. The associations found in this study remained significant after adjustment for sex, age, educational and cohabiting status as well as other risk factors. Our findings highlight the presence of a potential, public health...... 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...
Handbook of relativistic quantum chemistry
International Nuclear Information System (INIS)
Liu, Wenjian
2017-01-01
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.
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.
Short history of nuclear many-body problem
International Nuclear Information System (INIS)
Köhler, H.S.
2014-01-01
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski–Scott separation method that was an important part of his early work. The core polarisation and his work related to effective interactions in general are also addressed
A psychiatric dialogue on the mind-body problem.
Kendler, K S
2001-07-01
Of all the human professions, psychiatry is most centrally concerned with the relationship of mind and brain. In many clinical interactions, psychiatrists need to consider both subjective mental experiences and objective aspects of brain function. This article attempts to summarize, in the form of a dialogue between a philosophically informed attending psychiatrist and three residents, the major philosophical positions on the mind-body problem. The positions reviewed include the following: substance dualism, property dualism, type identity, token identity, functionalism, eliminative materialism, and explanatory dualism. This essay seeks to provide a brief user-friendly introduction, from a psychiatric perspective, to current thinking about the mind-body problem.
Poincaré and the three body problem
Barrow-Green, June
1997-01-01
The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem-to describe the paths of three bodies in mutual gravitational interaction-is one of those which is simple to pose but impossible to solve precisely. Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincaré and the Three Body Problem opens with a discussion of the development of the th...
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.
Nuclear three-body problem and energy-dependent potentials
International Nuclear Information System (INIS)
Abdurakhmanov, A.; Akhmadkhodzhaev, B.; Zubarev, A.L.; Irgaziev, B.F.
1985-01-01
Energy-dependent potentials in the three-body problem are being considered. Three-particle equations for the case of pairing energy-dependent potentials are generalized and the problems related to this ambiguous generalization are investigated. In terms of the equations obtained the tritium binding energy and vertex coupling constants (Tdn) and (Tdν) are evaluated. The binding energy and, especially, coupling constants are shown to be sensitive to a shape of the energy-dependent potential
Continuum capture in the three-body problem
International Nuclear Information System (INIS)
Sellin, I.A.
1980-01-01
The three-body problem, especially the problem of electron capture to the continuum in heavy particle collisions is reviewed. Major topics covered include: second born-induced asymmetry in electron capture to the continuum; historical context, links to other tests of atomic scattering theory; experiments characterizing the velocity distribution of ECC electrons; other atomic physics tests of high velocity Born expansions; atom capture; capture by positrons; and pion capture to the continuum
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
The computationalist reformulation of the mind-body problem.
Marchal, Bruno
2013-09-01
Computationalism, or digital mechanism, or simply mechanism, is a hypothesis in the cognitive science according to which we can be emulated by a computer without changing our private subjective feeling. We provide a weaker form of that hypothesis, weaker than the one commonly referred to in the (vast) literature and show how to recast the mind-body problem in that setting. We show that such a mechanist hypothesis does not solve the mind-body problem per se, but does help to reduce partially the mind-body problem into another problem which admits a formulation in pure arithmetic. We will explain that once we adopt the computationalist hypothesis, which is a form of mechanist assumption, we have to derive from it how our belief in the physical laws can emerge from *only* arithmetic and classical computer science. In that sense we reduce the mind-body problem to a body problem appearance in computer science, or in arithmetic. The general shape of the possible solution of that subproblem, if it exists, is shown to be closer to "Platonist or neoplatonist theology" than to the "Aristotelian theology". In Plato's theology, the physical or observable reality is only the shadow of a vaster hidden nonphysical and nonobservable, perhaps mathematical, reality. The main point is that the derivation is constructive, and it provides the technical means to derive physics from arithmetic, and this will make the computationalist hypothesis empirically testable, and thus scientific in the Popperian analysis of science. In case computationalism is wrong, the derivation leads to a procedure for measuring "our local degree of noncomputationalism". Copyright © 2013 Elsevier Ltd. All rights reserved.
A new method for solving the two-center problem with relativistic potentials
International Nuclear Information System (INIS)
Gareev, F.A.; Gizzatkulov, M.Ch.
1977-01-01
A method has been proposed for the solution of the two-center problem with realistic potentials. It consists of two steps: first, a separable approximation to the single particle potentials is made and then the two-center problem with these separable potentials is solved exactly. The only approximations are introduced at the first stage in a well controllable way. As an example, we have calculated the single-particle energies and wave functions in the field of two 16 O like the Woods-Saxon potentials as functions of their distance R
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.
Modified Strum functions method in the nuclear three body problem
International Nuclear Information System (INIS)
Nasyrov, M.; Abdurakhmanov, A.; Yunusova, M.
1997-01-01
Fadeev-Hahn equations in the nuclear three-body problem were solved by modified Sturm functions method. Numerical calculations were carried out the square well potential. It was shown that the convergence of the method is high and the binding energy value is in agreement with experimental one (A.A.D.)
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Bulgac, Aurel; Carlson, Joseph A.; Engel, Jonathan; Fann, George; Furnstahl, Richard J.; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W.; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
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)
TOPICAL PROBLEMS OF PROVIDING LAWFULNESS IN PRELIMINARY INVESTIGATION BODIES
Directory of Open Access Journals (Sweden)
Elnara Islamova
2015-09-01
Full Text Available This article examines current problems of reviewing crime reports of private prosecution by the preliminary investigation bodies, and the role of the prosecutor in providing lawfulness in this process. Issues are formulated to be clarified by the prosecutor in exercising supervision over the enforcement of the law in the receipt, registration and reviewing of the crime reports of private prosecution.
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 ..... over duly by his mathematical intercourse with mere materials and this made him to found his .... Ed. (New York: McGraw Hill), 1993, p. 90. 19 Emefie ...
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.)
A New Class of Solvable Many-Body Problems
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-10-01
Full Text Available A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections. Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
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 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....
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.)
Energy Technology Data Exchange (ETDEWEB)
Antippa, Adel F [Departement de Physique, Universite du Quebec a Trois-Rivieres, Trois-Rivieres, Quebec G9A 5H7 (Canada)
2009-05-15
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 method that can be applied to a wide range of special relativistic problems of linear acceleration.
The changing features of the body-mind problem.
Agassi, Joseph
2007-01-01
The body-mind problem invites scientific study, since mental events are repeated and repeatable and invite testable explanations. They seemed troublesome because of the classical theory of substance that failed to solve its own central problems. These are soluble with the aid of the theory of the laws of nature, particularly in its emergentist version [Bunge, M., 1980. The Body-mind Problem, Pergamon, Oxford] that invites refutable explanations [Popper, K.R., 1959. The Logic of Scientific Discovery, Hutchinson, London]. The view of mental properties as emergent is a modification of the two chief classical views, materialism and dualism. As this view invites testable explanations of events of the inner world, it is better than the quasi-behaviorist view of self-awareness as computer-style self-monitoring [Minsky, M., Laske, O., 1992. A conversation with Marvin Minsky. AI Magazine 13 (3), 31-45].
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.
Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1983-01-01
We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly
Nuclear N body problem. Structure, dynamics, phase transitions and relativistic aspects
International Nuclear Information System (INIS)
Aouissat, Z.; Wambach, J.; Baldo, M.; Burgio, F.; Lombardo, U.; Rapisardo, A.; Chanfray, G.; Centelles, M.; Durand, M.; Piepenbring, R.; Protasov, K.V.; Schuck, P.; Dukesky, J.; Vinas, X.; Farine, M.; Nozieres, P.; Piperova, J.; Roepke, G.; Schnell, A.
1997-01-01
The multiphonon method has been applied to vibrational spherical nuclei with even numbers of particles. Using the quadrupole + pairing Hamiltonian, the inclusion of new terms in the expansion is investigated and they have been found to be important. For the construction of a new effective force of Gogny type, the recently developed variational Wigner Kirkwood (VWK) method is used. Self-consistent RPA theory has been further developed. It has been shown that conservation laws and f-sum rule are fulfilled as for standard RPA. Experimental studies on fusion-fission at SARA are being investigated theoretically with two models, one phenomenological, one more microscopic. The questions of friction, dissipation and extra push shall be clarified. The applicability of the wall formula is studied in another model using the Vlasov equation for large amplitude octupole motion. Neutron-proton pairing versus alpha-particle condensation is followed as a function of density. At very low densities α - particles win but at higher densities α particles are dissolved faster than the n-p Cooper pairs. The main defect of Walecka's σ - ω model is that it misses chiral symmetry. Using the chiral Lagrangian of the linear σ - model, the σ - meson is coupled to the π + - π - scattering sector. An RPA like Lippmann - Schwinger equation for π + - π - scattering is established which respects all constraints from chiral symmetry. The implementation into a generalized σ - ω model is on its way. (authors)
A dynamic contact problem between elasto-viscoplastic piezoelectric bodies
Directory of Open Access Journals (Sweden)
Tedjani Hadj ammar
2014-10-01
Full Text Available We consider a dynamic contact problem with adhesion between two elastic-viscoplastic piezoelectric bodies. The contact is frictionless and is described with the normal compliance condition. We derive variational formulation for the model which is in the form of a system involving the displacement field, the electric potential field and the adhesion field. We prove the existence of a unique weak solution to the problem. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed point arguments.
Generating families in the restricted three-body problem
Hénon, Michel
The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.
Addressing communications between Regulatory Body and TSO: perceptions and problems
International Nuclear Information System (INIS)
Salati de Almeida, I.P.
2007-01-01
The use of TSO assistance by the Regulatory Bodies is a way of facing the complexity of the technology and issues to be dealt with in the licensing and controlling process in the nuclear area. Although both TSO and Regulatory Body are well prepared and adjusted, the nature and environment of TSO work is rather different from the regulators. Some of the TSO members act as a consultant, giving expert advice to the regulators in a specific subject, some are in charge of inspections and audits, others do the job together with the regulators. The way that a TSO member perceives the work to be done, however, often creates different perspectives for questions related to the licensing and controlling process. These perceptions are usually a source of problems between the two partners, regulators and TSO members. In this paper some of this kind of problems are raised and suggestions of how to deal with them are proposed for discussion. (author)
Spectral sum rules for the three-body problem
International Nuclear Information System (INIS)
Bolle, D.; Osborn, T.A.
1982-01-01
This paper derives a number of sum rules for nonrelativistic three-body scattering. These rules are valid for any finite region μ in the six-dimensional coordinate space. They relate energy moments of the trace of the onshell time-delay operator to the energy-weighted probability for finding the three-body bound-state wave functions in the region μ. If μ is all of the six-dimensional space, the global form of the sum rules is obtained. In this form the rules constitute higher-order Levinson's theorems for the three-body problem. Finally, the sum rules are extended to allow the energy momtns have complex powers
Coulomb two-body problem with internal structure
International Nuclear Information System (INIS)
Kuperin, Yu.A.; Makarov, K.A.; Mel'nikov, Yu.B.
1988-01-01
The methods of the theory of extensions to an enlarged Hilbert space are used to construct a model of the interaction of the external (Coulomb) and internal (quark) channels in the two-body problem. The mutual influence of the spectra of the corresponding channel Hamiltonians is studied: it leads, in particular, to a rearrangement of the spectra of hadronic atoms. An explicit representation is obtained for the S matrix, and its singularities on the energy shell are studied
International Nuclear Information System (INIS)
Haberzettl, H.; Sandhas, W.
1981-01-01
Noclear reactions: Four-body problem. Effective two-body equations with exact (2+2)-subsystem contributions. Relation to field-theoretical model by Fonseca and Shanley. Three-body propagator with exchange effects. (orig.)
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.
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.
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...
International Nuclear Information System (INIS)
Nagornyj, S.I.; Kasatkin, Yu.A.; Zolenko, V.A.
1992-01-01
A study is made of the effects of Lorentz invariance and nuclear current conservation in calculations of the AΦ-asymmetry of the cross sections for (e,e',p) reactions on few-body systems. The AΦ-value is shown to be very sensitive to different relativistic effects and to nuclear current conservation. In the quasi-elastic region (q 2 /2mν∼1, P mis /m p cm >50 0 the AΦ-asymmetry is determined by both the reaction mechanisms and the intranuclear dynamics. 12 refs.; 3 figs. (author)
Nucleon many-body problem using quantum-mechanical few-body technique
International Nuclear Information System (INIS)
Horiuchi, Wataru
2016-01-01
A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)
Explicit solution to the N-body Calogero problem
Energy Technology Data Exchange (ETDEWEB)
Brink, L [Inst. of Theoretical Physics, CTH, Goeteborg (Sweden); Hansson, T H [Inst. of Theoretical Physics, Univ. Stockholm (Sweden); Vasiliev, M A [Dept. of Theoretical Physics, P.N. Lebedev Physical Inst., Moscow (Russia)
1992-07-23
We solve the N-body Calogero problem, i.e., N particles in one dimension subject to a two-body interaction of the form 1/2 {Sigma}{sub i,j} ((x{sub i}-x{sub j}){sup 2}+g/(x{sub i}-x{sub j}){sup 2}), by constructing annihilation and creation operators of the form a{sub i}{sup -+}=(1/{radical}2)(x{sub i}{+-}ip{sub i}) where p{sub i} is a modified momentum operator obeying Heisenberg-type commutation relations with x{sub i}, involving explicitly permutation operators. On the other hand, D{sub j}=ip{sub j} can be interpreted as a covariant derivative corresponding to a flat connection. The relation to fractional statistics in 1+1 dimensions and anyons in a strong magnetic field is briefly discussed. (orig.).
Computational nuclear quantum many-body problem: The UNEDF project
Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.
2013-10-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
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)
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
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.
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.
International Nuclear Information System (INIS)
de Jong, F.; Malfliet, R.
1991-01-01
Starting from a relativistic Lagrangian we derive a ''conserving'' approximation for the description of nuclear matter. We show this to be a nontrivial extension over the relativistic Dirac-Brueckner scheme. The saturation point of the equation of state calculated agrees very well with the empirical saturation point. The conserving character of the approach is tested by means of the Hugenholtz--van Hove theorem. We find the theorem fulfilled very well around saturation. A new value for compression modulus is derived, K=310 MeV. Also we calculate the occupation probabilities at normal nuclear matter densities by means of the spectral function. The average depletion κ of the Fermi sea is found to be κ∼0.11
International Nuclear Information System (INIS)
Latha, K V P; Angom, Dilip; Chaudhuri, Rajat K; Das, B P; Mukherjee, Debashis
2007-01-01
The electric dipole moments of closed-shell atoms are sensitive to the parity and time-reversal violating phenomena in the nucleus. The nuclear Schiff moment is one such property, it arises from the parity and time reversal violating quark-quark interactions and the quark-chromo electric dipole moments. We calculate the electric dipole moment of atomic 199 Hg arising from the nuclear Schiff moment using the relativistic coupled-cluster theory. This is the most accurate calculation of the quantity to date. Our calculations in combination with the experiment data provide important insights to the P and T violating coupling constants at the elementary particle level. In addition, a new limit on the tensor-pseudo tensor induced atomic EDM, calculated using the relativistic coupled-cluster theory is also presented
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.
Institutional Solutions to the ``Two-Body Problem"
Knezek, P.
2005-05-01
The Committee on the Status of Women (CSWA), in conjunction with the Employment Committee (EC), will hold a special session that will focus on institutional approaches to solving the ``two-body problem". In step with the national employment trend, for the majority of astronomers with partners, those partners work outside the home. This is particularly true for female astronomers, who generally are married to professionals (and often to other astronomers). Academic and professional institutions that employ the majority of astronomers are now beginning to recognize the importance of addressing what has come to be known as the ``two-body" problem in order to attract and retain the best scientists. A few of those institutions are making pioneering efforts to create pro-active approaches to the issue of dual-career couples. The special session will feature two or three speakers involved with the administration at institutions with pro-active policies. This special session will be coupled with the normal afternoon CSWA session, which will focus on the other side of the issue - how dual-career couples have successfully approached the issue at institutions that do NOT have proactive policies.
Energy Analysis in the Elliptic Restricted Three-body Problem
Qi, Yi; de Ruiter, Anton
2018-05-01
The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.
International Nuclear Information System (INIS)
Minesaki, Yukitaka
2013-01-01
For the restricted three-body problem, we propose an accurate orbital integration scheme that retains all conserved quantities of the two-body problem with two primaries and approximately preserves the Jacobi integral. The scheme is obtained by taking the limit as mass approaches zero in the discrete-time general three-body problem. For a long time interval, the proposed scheme precisely reproduces various periodic orbits that cannot be accurately computed by other generic integrators
International Nuclear Information System (INIS)
Kapshay, V.N.; Skachkov, N.B.
1979-01-01
A composite system of two relativistic particles is studied on the basis of the Kadyshevsky quasipotential equation, in which the ''Coulomb'' potential is taken in the form of a propagator of the massless-scalar-particle exchange. The obtained exact solutions to this equation are shown to be a geometrical generalization of nonrelativistic Coulomb wave functions in the sense of change of the Euclidean geometry of momentum space to the Lobachevsky geometry
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.
Resonating-group method for nuclear many-body problems
International Nuclear Information System (INIS)
Tang, Y.C.; LeMere, M.; Thompson, D.R.
1977-01-01
The resonating-group method is a microscopic method which uses fully antisymmetric wave functions, treats correctly the motion of the total center of mass, and takes cluster correlation into consideration. In this review, the formulation of this method is discussed for various nuclear many-body problems, and a complex-generator-coordinate technique which has been employed to evaluate matrix elements required in resonating-group calculations is described. Several illustrative examples of bound-state, scattering, and reaction calculations, which serve to demonstrate the usefulness of this method, are presented. Finally, by utilization of the results of these calculations, the role played by the Pauli principle in nuclear scattering and reaction processes is discussed. 21 figures, 2 tables, 185 references
Three-body problem in the ground-state representation
International Nuclear Information System (INIS)
Gonzalez, A.
1993-01-01
The ground-state probability density of a three-body system is used to construct a classical potential U whose minimum coincides exactly with the ground-state energy. The spectrum of excited states may approximately be obtained by imposing quasiclassical quantization conditions over the classical motion in U. We show nontrivial one-dimensional models in which either this quantization condition is exact or considerably improves the usual semiclassical quantization. For three-dimensional problems, the small-oscillation frequencies in states with total angular momentum L = 0 are computed. These frequencies could represent an improvement over the frequencies of triatomic molecules computed with the use of ordinary quasiclassics for the motion of the nuclei in the molecular term. By providing a semiclassical description of the first excited quantum states, the sketched approach rises some interesting questions such as, for example, the relevance (once again) of classical chaos to quantum mechanics
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
Approximate Coulomb effects in the three-body scattering problem
International Nuclear Information System (INIS)
Haftel, M.I.; Zankel, H.
1981-01-01
From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles
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.)
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
Nuclear many-body problem with repulsive hard core interactions
Energy Technology Data Exchange (ETDEWEB)
Haddad, L M
1965-07-01
The nuclear many-body problem is considered using the perturbation-theoretic approach of Brueckner and collaborators. This approach is outlined with particular attention paid to the graphical representation of the terms in the perturbation expansion. The problem is transformed to centre-of-mass coordinates in configuration space and difficulties involved in ordinary methods of solution of the resulting equation are discussed. A new technique, the 'reference spectrum method', devised by Bethe, Brandow and Petschek in an attempt to simplify the numerical work in presented. The basic equations are derived in this approximation and considering the repulsive hard core part of the interaction only, the effective mass is calculated at high momentum (using the same energy spectrum for both 'particle' and 'hole' states). The result of 0.87m is in agreement with that of Bethe et al. A more complete treatment using the reference spectrum method in introduced and a self-consistent set of equations is established for the reference spectrum parameters again for the case of hard core repulsions. (author)
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.
Logarithmic corrections of the two-body QED problem
International Nuclear Information System (INIS)
Khriplovich, I.B.; Mil'shtejn, A.I.; Elkhovskij, A.S.
1992-01-01
The logarithmic part of the Lamb shift, the contribution of the relative order α 3 log(1/α) to the atomic state energy, is related to the usual infrared divergence. For positronium, the calculated logarithmic correction does not vanish only in n 3 S 1 states and constitutes 5/24mα 6 log(1/α)/m 3 . Logarithmic corrections of the relative order α 2 log(1/α) to the positronium decay rate are also of the relativistic origin and can be easily computed within the same approach. 31 refs.; 11 figs
Contraint's theory and relativistic dynamics
International Nuclear Information System (INIS)
Longhi, G.; Lusanna, L.
1987-01-01
The purpose of this Workshop was to examine the current situation of relativistic dynamics. In particular, Dirac-Bergmann's theory of constraints, which lies at the heart of gauge theories, general relativity, relativistic mechanics and string theories, was chosen as the unifying theoretical framework best suited to investigate such a field. The papers discussed were on general relativity; relativistic mechanics; particle physics and mathematical physics. Also discussed were the problems of classical and quantum level, namely the identification of the classical observables of constrained systems, the equivalence of the nonequivalence of the various ways to quantize such systems; the problem of the anomalies; the best geometrical approach to the theory of constraints; the possibility of unifying all the treatments of relativistic mechanics. This book compiles the papers presented at proceedings of relativistic dynamics and constraints theory
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…
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 ...
Relativistic solitons and pulsars
Energy Technology Data Exchange (ETDEWEB)
Karpman, V I [Inst. of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Moscow; Norman, C A; ter Haar, D; Tsytovich, V N
1975-05-01
A production mechanism for stable electron bunches or sheets of localized electric fields is investigated which may account for pulsar radio emission. Possible soliton phenomena in a one-dimensional relativistic plasma are analyzed, and it is suggested that the motion of a relativistic soliton, or ''relaton'', along a curved magnetic-field line may produce radio emission with the correct polarization properties. A general MHD solution is obtained for relatons, the radiation produced by a relativistic particle colliding with a soliton is evaluated, and the emission by a soliton moving along a curved field line is estimated. It is noted that due to a number of severe physical restrictions, curvature radiation is not a very likely solution to the problem of pulsar radio emission. (IAA)
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...
International Nuclear Information System (INIS)
Gago-Alonso, A; Santiago-Moreno, L; Piñeiro-Díaz, L R
2008-01-01
We study finite nonlinear dynamical systems that are somehow more general and complex than the relativistic Toda lattice. Our dynamical systems have a matrix representation very similar to the ones that were previously studied. It is defined in terms of a one-parameter family (D(x), M(x)) of matrices, where D(x) is a Hessenberg matrix and M(x) is a lower triangular matrix. The Jordan matrix associated with M −1 (x)D(x) is a constant of motion and the auxiliary spectral data have explicit time evolution. Using the connection between Hessenberg matrices and general orthogonal polynomials we associated to our system a one-parameter family of scalar products that we use to prove the integrability of the system. In particular the inverse transform is given by an orthogonalization process on a given scalar product
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
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 m...... method is inspired by the novel algorithm by Einstein, Lichtblau, Strzebonski and Wagon and the Groebner basis approach by Roune....
Cognitive Neuroscience and the "Mind-Body problem"
Directory of Open Access Journals (Sweden)
Grega Repovš
2004-08-01
Full Text Available In recent years we have witnessed an upsurge of interest in the study of the human mind and how it relates to the material body, the brain. Cognitive neuroscience is a multidisciplinary science that tries to explain how the mind arises from the structure and workings of the brain. Can we equate the study of mind-body relationship with cognitive neuroscience? Are there aspects of mind-body relationship that are not covered by cognitive neuroscience? Is cognitive neuroscience able to explain human behaviour and experience? These are the questions that are addressed in this "Beginner's Guide to Cognitive neuroscience and it's relation to the Body-Mind question".
Safronova, U. I.; Safronova, M. S.
2014-05-01
Excitation energies of the [Xe]nd (n =5-9), [Xe]ns (n =6-10), [Xe]np (n =6-9), [Xe]nf (n =4-8), and [Xe]ng (n =5-8) states in La iii, where [Xe] = 1s22s22p63s23p63d104s24p64d105s25p6, are evaluated. Electric dipole matrix elements for the allowed transitions between the low-lying [Xe]nd, [Xe]ns, [Xe]np, [Xe]nf, and [Xe]ng states in the La iii ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar and tensor polarizabilities of the states listed above are evaluated. The uncertainties of the recommended values are estimated. Electric quadrupole and magnetic dipole matrix elements are calculated to determine lifetimes of the 5d5/2 and 6s metastable levels. The ground-state E1, E2, and E3 static polarizabilities are calculated. This work provides recommended values critically evaluated for their accuracy for a number of La iii atomic properties for use in planning and analysis of various experiments as well as theoretical modeling.
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...
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)
Semiclassical expansions of the nuclear relativistic Hartree-Fock theory
International Nuclear Information System (INIS)
Weigel, M.K.; Haddad, S.
1991-01-01
Semiclassical expansions for Green functions, self-energy, phase-space density and density are given and discussed. The many-body problem was treated in the relativistic Hartree-Fock approximation with a Lagrangian with a standard OBE potential structure including the possibility of space-dependent couplings. The expansions are obtained by formulating the many-body problem in the mixed position-momentum (Wigner) representation and application of the (h/2π)-Wigner-Kirkwood expansion scheme. The resulting self-consistency problems for the zeroth and second order are formulated in three versions. (author)
The exact solution of a four-body Coulomb problem
Ray, Hasi
2018-03-01
The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed. Contribution to the Topical Issue "Low Energy Positron and Electron Interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.
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.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
International Nuclear Information System (INIS)
Font, J. A.
2015-01-01
The relativistic astrophysics is the field of astrophysics employing the theory of relativity Einstein as physical-mathematical model is to study the universe. This discipline analyzes astronomical contexts in which the laws of classical mechanics of Newton's law of gravitation are not valid. (Author)
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)
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
A simple coordinate space approach to three-body problems ...
Indian Academy of Sciences (India)
problems – Examples: Halo nucleus and double-λ hypernucleus ... Department of Physics, Jadavpur University, Kolkata 700 032, India. £Banaras Hindu ..... thanks the Department of Atomic Energy, India for financial support. References.
The mind body problem: the hermeneutics of African philosophy ...
African Journals Online (AJOL)
Philosophers of different ages, epochs and ideological orientations have engaged themselves in a heated debate on the issue of the mind- body interaction. Indeed, there are two different but interactive entities in man with different modes of action yet interacting in themost subtlemanner as to produce in aman , amind able ...
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...
Optimization of the variational basis in the three body problem
International Nuclear Information System (INIS)
Simenog, I.V.; Pushkash, O.M.; Bestuzheva, A.B.
1995-01-01
The procedure of variational oscillator basis optimization is proposed to the calculation the energy spectra of three body systems. The hierarchy of basis functions is derived and energies of ground and excited states for three gravitating particles is obtained with high accuracy. 12 refs
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
Calogero, Francesco
2001-01-01
This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
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.
International Nuclear Information System (INIS)
Marks, R.
1985-09-01
Theoretical analysis is presented of a relativisic klystron; i.e. a high-relativistic bunched electron beam which is sent through a succession of tuned cavities and has its energy replenished by periodic induction accelerator units. Parameters are given for a full-size device and for an experimental device using the FEL at the ETA; namely the ELF Facility. 6 refs., 2 figs
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.
Core Problem: Does the CV Parent Body Magnetization require differentiation?
O'Brien, T.; Tarduno, J. A.; Smirnov, A. V.
2016-12-01
Evidence for the presence of past dynamos from magnetic studies of meteorites can provide key information on the nature and evolution of parent bodies. However, the suggestion of a past core dynamo for the CV parent body based on the study of the Allende meteorite has led to a paradox: a core dynamo requires differentiation, evidence for which is missing in the meteorite record. The key parameter used to distinguish core dynamo versus external field mechanisms is absolute field paleointensity, with high values (>>1 μT) favoring the former. Here we explore the fundamental requirements for absolute field intensity measurement in the Allende meteorite: single domain grains that are non-interacting. Magnetic hysteresis and directional data define strong magnetic interactions, negating a standard interpretation of paleointensity measurements in terms of absolute paleofield values. The Allende low field magnetic susceptibility is dominated by magnetite and FeNi grains, whereas the magnetic remanence is carried by an iron sulfide whose remanence-carrying capacity increases with laboratory cycling at constant field values, indicating reordering. The iron sulfide and FeNi grains are in close proximity, providing mineralogical context for interactions. We interpret the magnetization of Allende to record the intense early solar wind with metal-sulfide interactions amplifying the field, giving the false impression of a higher field value in some prior studies. An undifferentiated CV parent body is thus compatible with Allende's magnetization. Early solar wind magnetization should be the null hypothesis for evaluating the source of magnetization for chondrites and other meteorites.
The Quantum N-Body Problem and the Auxiliary Field Method
International Nuclear Information System (INIS)
Semay, C.; Buisseret, F.; Silvestre-Brac, B.
2011-01-01
Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and applied to the case of baryons in the large-N c limit. (author)
A new separable expansion for the two-body problem
International Nuclear Information System (INIS)
Haberzettl, H.
1988-07-01
We derive a new separable expansion of the two-body T matrix which represents the T matrix as a series of diagonal separable terms. The representation is exact half-on-shell at all energies even when truncated to one single term; moreover, the truncated expansion satisfies the full off-shell unitarity relation. The approach does not take recourse to some complete set of functions but rather uses properties of the Lippmann-Schwinger equation itself to arrive at the expansion. It is based on the W-matrix representation of the two-body T matrix introduced by Bartnik, Haberzettl, and Sandhas. That representation provides a splitting of the T matrix in one single separable term which contains all bound state poles and scatttering cuts and in a nonsingular, real remainder which vanishes half-on-shell. The method presented here yields a separable expansion of this remainder in which all its properties are preserved term by term. Any given n-term approximation can easily be refined to an (n+1)-term expansion by simply adding a new term. At each stage the amount of additional numerical work is constant. The method is applicable to any kind of short range potential, local, nonlocal or energy dependent. (orig.)
On the Stability of L4,5 in the Relativistic R3BP with Radiating ...
Indian Academy of Sciences (India)
Abstract. This paper discusses the motion of a test particle in the neigh- bourhood of the triangular points L4,5 by considering the less massive primary (secondary) as a source of radiation in the framework of the relativistic restricted three-body problem (R3BP). It is found that the positions and stability of the triangular point ...
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.
International Nuclear Information System (INIS)
Safronov, A.N.; Safronov, A.A.
2006-01-01
Full text: A nonperturbative character of QCD at low and intermediate energies generates serious mathematical difficulties in describing the dynamics of hadron-hadron interactions in terms quark-gluon degrees of freedom. Therefore much effort has gone in past years into developing QCD-motivated approaches that formulate the theory of strong interaction in terms of hadron degrees of freedom. The path-integral technique together with idea of spontaneous chiral-symmetry breaking leads to Effective Field Theory (EFT) [1]. Unfortunately EFT can be applied to description of hadron-hadron interactions only at very low energies. On the other hand, meson theories of nuclear forces have long since been used to describe the properties of nucleon systems and scattering processes. Now it is not quite clear, up to what distances the meson-exchange pattern of nuclear forces is valid. Recently the new relativistic approach to the problem of constructing effective hadron-hadron interaction operators has been proposed [2-4] on the basis of analytic S-matrix theory and Gelfand-Levitan-Marchenko-Martin methods for solving the inverse quantum scattering problem. In this approach effective potential is defined as a local operator in a partial-wave equation of the quasipotential type such that it generates on-shell relativistic (Feynman) scattering amplitude that has required discontinuities at dynamical cuts. The discontinuities of partial-wave amplitudes are determined by model-independent quantities (renormalized vertex constants and amplitudes of subprocesses involving on-mass-shell particles off the physical region) and can be calculated by methods of relativistic quantum field theory within various dynamical approaches. In particular, EFT can be used to calculate the discontinuities across dynamical-cut segments closest to the physical region. In [2-4] we have examined the basic features of the proposed approach. Attention has been given primarily to analyzing the new mechanism of
International Nuclear Information System (INIS)
Haberzettl, H.; Sandhas, W.
1981-01-01
Effective two-body equations for the four-body problem are derived within the general N-body theory of Alt, Grassberger, and Sandhas. In contrast to usual treatments, the final expressions do not require separable (2+2) subamplitudes but incorporate these exactly. All four-body amplitudes can be calculated from the solution of a single integral equation for the reaction (3+1)→(3+1). With single-term separable approximations for the two-particle and the (3+1) subsystem amplitudes the driving terms of the final equations are seen to reduce to those of the field-theoretical model by Fonseca and Shanley. Since our results are based on an exact and complete N-body theory, the investigation of subsystem reaction mechanisms is facilitated. As a consequence, we are led to a three-particle propagator which has the right pole behavior and includes exchange effects
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.
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
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
Gauge invariance and relativistic effects in X-ray absorption and scattering by solids
International Nuclear Information System (INIS)
Bouldi, N.; Brouder, C.
2017-01-01
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. (authors)
An initial boundary value problem for modeling a piezoelectric dipolar body
Marin, Marin; Öchsner, Andreas
2018-03-01
This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.
Relativistic distances, sizes, lengths
International Nuclear Information System (INIS)
Strel'tsov, V.N.
1992-01-01
Such notion as light or retarded distance, field size, formation way, visible size of a body, relativistic or radar length and wave length of light from a moving atom are considered. The relation between these notions is cleared up, their classification is given. It is stressed that the formation way is defined by the field size of a moving particle. In the case of the electromagnetic field, longitudinal sizes increase proportionally γ 2 with growing charge velocity (γ is the Lorentz-factor). 18 refs
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)
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
Qazi, Faisal; Fette, Don; Jafri, Syed S; I Padela, Aasim
2018-07-01
Famously posed by seventeenth-century French philosopher René Descartes, the mind-body problem remains unresolved in western philosophy and science, with both disciplines unable to move convincingly beyond the dualistic model. The persistence of dualism calls for a reframing of the problem through interdisciplinary modes of inquiry that include non-western points of view. One such perspective is Islamic theology of the soul, which, while approaching the problem from a distinct point of view, also adopts a position commensurate with (substance) dualism. Using this point of convergence as a conceptual starting point, we argue that bringing into dialogue contemporary neuroscientific, philosophy of mind, and Sunni Islamic theological discourses may provide a fruitful way of reframing the age-old mind-body problem. This paper provides an overview of how these three discourses have approached the issue of the mind-body (-soul) problem. Juxtaposing these three discourses, we hope, may ignite further scholarly dialogue and investigation.
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.
Relativistic magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Juan; Kovtun, Pavel [Department of Physics and Astronomy, University of Victoria,Victoria, BC, V8P 5C2 (Canada)
2017-05-02
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the “conventional” magnetohydrodynamics (formulated using Maxwell’s equations in matter) to those in the “dual” version of magnetohydrodynamics (formulated using the conserved magnetic flux).
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.
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.
Elasticity of Relativistic Rigid Bodies?
Smarandache, Florentin
2013-10-01
In the classical Twin Paradox, according to the Special Theory of Relativity, when the traveling twin blasts off from the Earth to a relative velocity v =√{/3 } 2 c with respect to the Earth, his measuring stick and other physical objects in the direction of relative motion shrink to half their lengths. How is that possible in the real physical world to have let's say a rigid rocket shrinking to half and then later elongated back to normal as an elastic material when it stops? What is the explanation for the traveler's measuring stick and other physical objects, in effect, return to the same length to their original length in the Stay-At-Home, but there is no record of their having shrunk? If it's a rigid (not elastic) object, how can it shrink and then elongate back to normal? It might get broken in such situation.
Proper time axis of a closed relativistic system
International Nuclear Information System (INIS)
Chernikov, N.A.; Fadeev, N.G.; Shavokhina, N.S.
1997-01-01
The definition of a proper time axis of a closed relativistic system of colliding particles is given. The solution of the proper time axis problem is presented. If the light velocity c equals the imaginary unit i, then in the case of a plane motion of the system the problem about the proper time axis turns out to be equivalent to the known in engineering mechanics problem about the reduction of any system of forces, applied to a rigid body, to the dynamic screw. In the general case, when c=i, the problem about the proper time axis turns out to be equivalent to the problem about the reduction to the dynamic screw of a system of forces, applied to a rigid body in a four-dimensional Euclidean space
The Kantian Attempt to Solve the Mind-Body Problem. A Critical Approach
Directory of Open Access Journals (Sweden)
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.
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.
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.)
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
Relativistic nuclear physics and quantum chromodynamics. Abstracts
International Nuclear Information System (INIS)
1994-01-01
The data of investigations on problems of high energy physics are given. Special attention pays to quantum chromodynamics at large distances, cumulative processes, multiquark states and relativistic nuclear collisions
The few-body problem - some thoughts after the 1980 International Conference
International Nuclear Information System (INIS)
Moravcsik, M.J.; Oregon Univ., Eugene
1981-01-01
Recent progress in the few-body problem, as considered at the Ninth International Conference on the Few-body Problem, Eugene, Oregon, August 1980, is discussed. It is shown that these developments help to-wards the understanding of some of the systems properties of these few-body configurations, contribute to the testing of quark theories, give evidence for the validity or violation of conservation laws, add to the present knowledge of nuclear properties, off-shell nucleon-nucleon interaction and other component laws and provide reliable predictions which may be useful in applications extrinsic to the few-body itself, such as astrophysics, space physics or chemistry. (U.K.)
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.
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.
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.
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.
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
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.
Graphs and an exactly solvable N-body problem in one dimension
Energy Technology Data Exchange (ETDEWEB)
Barucchi, G [Turin Univ. (Italy). Ist. di Fisica Matematica
1980-08-21
The one-dimensional N-body classical problem with inversely quadratic pair potential is considered. A method of explicit construction, by means of graphs, of the constants of the motion is given. It is then shown how to obtain, by means of a computer, the position variables of the particles as numerical functions of time.
Barger, R. L.
1977-01-01
Slender body methods were applied to some specialized problems associated with missile configurations with elliptic cross sections. Expressions are derived for computing the velocity distribution on the nose section when the ellipse eccentricity is varying longitudinally on the missile. The cross flow velocity on a triform fin section is also studied.
The black-body radiation inversion problem, its instability and a new universal function set method
International Nuclear Information System (INIS)
Ye, JiPing; Ji, FengMin; Wen, Tao; Dai, Xian-Xi; Dai, Ji-Xin; Evenson, William E.
2006-01-01
The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS
Algebraic internal wave solitons and the integrable Calogero--Moser--Sutherland N-body problem
International Nuclear Information System (INIS)
Chen, H.H.; Lee, Y.C.; Pereira, N.R.
1979-01-01
The Benjamin--Ono equation that describes nonlinear internal waves in a stratified fluid is solved by a pole expansion method. The dynamics of poles which characterize solitons is shown to be identical to the well-known integrable N-body problem of Calogero, Moser, and Sutherland
Universal algorithms and programs for calculating the motion parameters in the two-body problem
Bakhshiyan, B. T.; Sukhanov, A. A.
1979-01-01
The algorithms and FORTRAN programs for computing positions and velocities, orbital elements and first and second partial derivatives in the two-body problem are presented. The algorithms are applicable for any value of eccentricity and are convenient for computing various navigation parameters.
Chiral quark model with relativistic kinematics
International Nuclear Information System (INIS)
Garcilazo, H.; Valcarce, A.
2003-01-01
The nonstrange baryon spectrum is studied within a three-body model that incorporates relativistic kinematics. We found that the combined effect of relativistic kinematics together with the pion exchange between quarks is able to reverse the order of the first positive- and negative-parity nucleon excited states as observed experimentally. Including the chiral partner of the pion (the σ meson) leads to an overall good description of the spectrum
Chiral quark model with relativistic kinematics
Garcilazo, H.; Valcarce, A.
2003-01-01
The non-strange baryon spectrum is studied within a three-body model that incorporates relativistic kinematics. We found that the combined effect of relativistic kinematics together with the pion exchange between quarks is able to reverse the order of the first positive- and negative-parity nucleon excited states as observed experimentally. Including the chiral partner of the pion (the $\\sigma$ meson) leads to an overall good description of the spectrum.
Solution of the Chandler-Gibson equations for a three-body test problem
International Nuclear Information System (INIS)
Gibson, A.G.; Waters, A.J.; Berthold, G.H.; Chandler, C.
1991-01-01
The Chandler-Gibson (CG) N-body equations are tested by considering the problem of three nonrelativistic particles moving on a line and interacting through attractive delta-function potentials. In particular, the input Born and overlap matrix-valued functions are evaluated analytically, and the CG equations are solved using a B-spline collocation method. The computed scattering matrix elements are within 0.5% of the known exact solutions, and the corresponding scattering probabilities are within 0.001% of the exact probabilities, both below and above the 3-body breakup threshold. These results establish that the CG method is practical, as well as theoretically correct, and may be a valuable approach for solving certain more complicated N-body scattering problems
Sources of spurious force oscillations from an immersed boundary method for moving-body problems
Lee, Jongho; Kim, Jungwoo; Choi, Haecheon; Yang, Kyung-Soo
2011-04-01
When a discrete-forcing immersed boundary method is applied to moving-body problems, it produces spurious force oscillations on a solid body. In the present study, we identify two sources of these force oscillations. One source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion. The addition of mass source/sink together with momentum forcing proposed by Kim et al. [J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics 171 (2001) 132-150] reduces the spurious force oscillations by alleviating this pressure discontinuity. The other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion. The magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary. Four moving-body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant CFL number, respectively. It is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size, but they depend more on the grid spacing than on the computational time step size.
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
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.
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)
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...
Proceedings of the meeting on few-body problems in high and medium energy physics
International Nuclear Information System (INIS)
Yukawa, T.
1985-12-01
The study meeting on few-body problems in high and medium energy physics was held from October 3 to 5, 1985, at National Laboratory for High Energy Physics. Two meetings were held already concerning few body physics, but most of the participants were theorists. In this meeting, high priority was put on the attendance of experimental physicists. As a bridge between particle and nuclear physics, the few body physics in an intermediate energy region has become important recently. The topics in this meeting were meson spectroscopy, baryonium, kaon physics, muonic fusion, dibaryon, φNN system, quarks and skyrmions, NN correlation, and symmetry test in few-body system. The gists of the papers presented are collected in this book. (Kako, I.)
The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics
International Nuclear Information System (INIS)
Tremaine, Scott
2003-01-01
The gravitational N-body problem is to describe the evolution of an isolated system of N point masses interacting only through Newtonian gravitational forces. For N =2 the solution is due to Newton. For N =3 there is no general analytic solution, but the problem has occupied generations of illustrious physicists and mathematicians including Laplace, Lagrange, Gauss and Poincare, and inspired the modern subjects of nonlinear dynamics and chaos theory. The general gravitational N-body problem remains one of the oldest unsolved problems in physics. Many-body problems can be simpler than few-body problems, and many physicists have attempted to apply the methods of classical equilibrium statistical mechanics to the gravitational N-body problem for N >> 1. These applications have had only limited success, partly because the gravitational force is too strong at both small scales (the interparticle potential energy diverges) and large scales (energy is not extensive). Nevertheless, we now understand a rich variety of behaviour in large-N gravitating systems. These include the negative heat capacity of isolated, gravitationally bound systems, which is the basic reason why nuclear burning in the Sun is stable; Antonov's discovery that an isothermal, self-gravitating gas in a container is located at a saddle point, rather than a maximum, of the entropy when the gas is sufficiently dense and hence is unstable (the 'gravothermal catastrophe'); the process of core collapse, in which relaxation induces a self-similar evolution of the central core of the system towards (formally) infinite density in a finite time; and the remarkable phenomenon of gravothermal oscillations, in which the central density undergoes periodic oscillations by factors of a thousand or more on the relaxation timescale - but only if N ∼> 10 4 . The Gravitational Million-Body Problem is a monograph that describes our current understanding of the gravitational N-body problem. The authors have chosen to
Heggie, D.; Hut, P.
2003-10-01
The gravitational N-body problem is to describe the evolution of an isolated system of N point masses interacting only through Newtonian gravitational forces. For N =2 the solution is due to Newton. For N =3 there is no general analytic solution, but the problem has occupied generations of illustrious physicists and mathematicians including Laplace, Lagrange, Gauss and Poincaré, and inspired the modern subjects of nonlinear dynamics and chaos theory. The general gravitational N-body problem remains one of the oldest unsolved problems in physics. Many-body problems can be simpler than few-body problems, and many physicists have attempted to apply the methods of classical equilibrium statistical mechanics to the gravitational N-body problem for N gg 1. These applications have had only limited success, partly because the gravitational force is too strong at both small scales (the interparticle potential energy diverges) and large scales (energy is not extensive). Nevertheless, we now understand a rich variety of behaviour in large-N gravitating systems. These include the negative heat capacity of isolated, gravitationally bound systems, which is the basic reason why nuclear burning in the Sun is stable; Antonov's discovery that an isothermal, self-gravitating gas in a container is located at a saddle point, rather than a maximum, of the entropy when the gas is sufficiently dense and hence is unstable (the 'gravothermal catastrophe'); the process of core collapse, in which relaxation induces a self-similar evolution of the central core of the system towards (formally) infinite density in a finite time; and the remarkable phenomenon of gravothermal oscillations, in which the central density undergoes periodic oscillations by factors of a thousand or more on the relaxation timescale - but only if N gtrsim 104. The Gravitational Million-Body Problem is a monograph that describes our current understanding of the gravitational N-body problem. The authors have chosen to
Precise numerical results for limit cycles in the quantum three-body problem
International Nuclear Information System (INIS)
Mohr, R.F.; Furnstahl, R.J.; Hammer, H.-W.; Perry, R.J.; Wilson, K.G.
2006-01-01
The study of the three-body problem with short-range attractive two-body forces has a rich history going back to the 1930s. Recent applications of effective field theory methods to atomic and nuclear physics have produced a much improved understanding of this problem, and we elucidate some of the issues using renormalization group ideas applied to precise nonperturbative calculations. These calculations provide 11-12 digits of precision for the binding energies in the infinite cutoff limit. The method starts with this limit as an approximation to an effective theory and allows cutoff dependence to be systematically computed as an expansion in powers of inverse cutoffs and logarithms of the cutoff. Renormalization of three-body bound states requires a short range three-body interaction, with a coupling that is governed by a precisely mapped limit cycle of the renormalization group. Additional three-body irrelevant interactions must be determined to control subleading dependence on the cutoff and this control is essential for an effective field theory since the continuum limit is not likely to match physical systems (e.g., few-nucleon bound and scattering states at low energy). Leading order calculations precise to 11-12 digits allow clear identification of subleading corrections, but these corrections have not been computed
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George
2011-09-01
commission are to: * clarify the geometrical and dynamical concepts of fundamental astronomy within a relativistic framework, * provide adequate mathematical and physical formulations to be used in fundamental astronomy, * deepen the understanding of relativity among astronomers and students of astronomy, and * promote research needed to accomplish these tasks. The present book is intended to make a theoretical contribution to the efforts undertaken by this commission. The first three chapters of the book review the foundations of celestial mechanics as well as those of special and general relativity. Subsequent chapters discuss the theoretical and experimental principles of applied relativity in the solar system. The book is written for graduate students and researchers working in the area of gravitational physics and its applications inmodern astronomy. Chapters 1 to 3 were written by Michael Efroimsky and Sergei Kopeikin, Chapters 4 to 8 by Sergei Kopeikin, and Chapter 9 by George Kaplan. Sergei Kopeikin also edited the overall text. It hardly needs to be said that Newtonian celestial mechanics is a very broad area. In Chapter 1, we have concentrated on derivation of the basic equations, on explanation of the perturbed two-body problem in terms of osculating and nonosculating elements, and on discussion of the gauge freedom in the six-dimensional configuration space of the orbital parameters. The gauge freedom of the configuration space has many similarities to the gauge freedom of solutions of the Einstein field equations in general theory of relativity. It makes an important element of the Newtonian theory of gravity, which is often ignored in the books on classic celestial mechanics. Special relativity is discussed in Chapter 2. While our treatment is in many aspects similar to the other books on special relativity, we have carefully emphasised the explanation of the Lorentz and Poincaré transformations, and the appropriate transformation properties of geometric
The quantum n-body problem in dimension d ⩾ n – 1: ground state
Miller, Willard, Jr.; Turbiner, Alexander V.; Escobar-Ruiz, M. A.
2018-05-01
We employ generalized Euler coordinates for the n body system in dimensional space, which consists of the centre-of-mass vector, relative (mutual) mass-independent distances r ij and angles as remaining coordinates. We prove that the kinetic energy of the quantum n-body problem for can be written as the sum of three terms: (i) kinetic energy of centre-of-mass, (ii) the second order differential operator which depends on relative distances alone and (iii) the differential operator which annihilates any angle-independent function. The operator has a large reflection symmetry group and in variables is an algebraic operator, which can be written in terms of generators of the hidden algebra . Thus, makes sense of the Hamiltonian of a quantum Euler–Arnold top in a constant magnetic field. It is conjectured that for any n, the similarity-transformed is the Laplace–Beltrami operator plus (effective) potential; thus, it describes a -dimensional quantum particle in curved space. This was verified for . After de-quantization the similarity-transformed becomes the Hamiltonian of the classical top with variable tensor of inertia in an external potential. This approach allows a reduction of the dn-dimensional spectral problem to a -dimensional spectral problem if the eigenfunctions depend only on relative distances. We prove that the ground state function of the n body problem depends on relative distances alone.
[Anxiety and body image among women growing up in families with addiction problem].
Lelek, Agnieszka; Betkowska-Korpała, Barbara; Jabłoński, Marcin
2011-01-01
The aim of the study was to analyse the correlation between body image and anxiety symptoms as well as psychological discomfort experienced by women growing up in alcoholic families. The group of 61 women (27 years old on average) was surveyed with Body Self Questionnaire and MMPI-2 personality test questionnaires and the results were measured on Scale 7 (Pt). All the participants also attended psychotherapy sessions focused on disorders resulting from growing up in families with alcohol problems. The analysis showed negative correlation (p emotional spheres, as well as functioning cognitive schemes.
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.
LAGRANGE SOLUTIONS TO THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM
International Nuclear Information System (INIS)
Minesaki, Yukitaka
2013-01-01
There is no known integrator that yields exact orbits for the general three-body problem (G3BP). It is difficult to verify whether a numerical procedure yields the correct solutions to the G3BP because doing so requires knowledge of all 11 conserved quantities, whereas only six are known. Without tracking all of the conserved quantities, it is possible to show that the discrete general three-body problem (d-G3BP) yields the correct orbits corresponding to Lagrange solutions of the G3BP. We show that the d-G3BP yields the correct solutions to the G3BP for two special cases: the equilateral triangle and collinear configurations. For the triangular solution, we use the fact that the solution to the three-body case is a superposition of the solutions to the three two-body cases, and we show that the three bodies maintain the same relative distances at all times. To obtain the collinear solution, we assume a specific permutation of the three bodies arranged along a straight rotating line, and we show that the d-G3BP maintains the same distance ratio between two bodies as in the G3BP. Proving that the d-G3BP solutions for these cases are equivalent to those of the G3BP makes it likely that the d-G3BP and G3BP solutions are equivalent in other cases. To our knowledge, this is the first work that proves the equivalence of the discrete solutions and the Lagrange orbits.
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.
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.
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.)
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).
Stability and periodicity in the Sitnikov three-body problem when primaries are oblate spheroids
Rahman, M. A.; Garain, D. N.; Hassan, M. R.
2015-05-01
This paper deals with the effect of oblateness of the primaries of equal masses on the series solutions of the Sitnikov problem of three bodies. Effects of oblateness have also been shown on the stability of libration points and Poincare surface of section. Here series solutions have been developed with the help of iteration process of Green's function and by the Lindstedt-Poincare method. Following Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) we have checked the stability of the equilibrium points in the Sitnikov problem. Periodicity and quasi-periodicity have been examined by drawing the Poincare surfaces of section using the mathematical software.
11Li-12C scattering as a four-body problem
International Nuclear Information System (INIS)
Formanek, J.; Lombard, R.J.
1995-01-01
11 Li- 12 C scattering is described as a four-body problem. The succession of approximations required to obtain the simplified approach of Yabana et al(1992) is examined in detail. We found that whereas their simple model is roughly acceptable for total cross sections (with discrepancies of the order of a few per cent), it has dramatic effects on the differential cross section. Beyond the very forward angles, the problem has to be treated in its full complexity; the various possible intermediate approximations generate differential cross sections which deviate noticeably from the correct calculation. (author)
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.
Transformations of the perturbed two-body problem to unperturbed harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Szebehely, V; Bond, V
1983-05-01
Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations. 11 references.
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.
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)
A cluster expansion for bound three-alpha particles as a three-body problem
International Nuclear Information System (INIS)
Osman, A.
1981-08-01
A three-body model is proposed to study the nuclear bound states. The nucleus is described as a bound state of three clusters. A cluster expansion is introduced for the three cluster bound state problem. The present integral equations are treated by simple approximate solutions, which lead to effective potentials by using the present cluster expansion. The 12 C nucleus is described as a three-alpha particle bound state. The binding energy of 12 C is calculated numerically using the present cluster expansion as bound three-alpha clusters. The present three-body cluster expansion calculations are very near to the exact three-body calculations using separable potentials. The present theoretical calculations are in good agreement with the experimental measurements. (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.
How the carotid body works: Different strategies and preparations to solve different problems
ZAPATA, PATRICIO; LARRAÍN, CAROLINA
2005-01-01
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 p...
Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem
International Nuclear Information System (INIS)
Wei-Tao, Lu; Hua, Zhang; Shun-Jin, Wang
2008-01-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge–Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP. (general)
Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin
2008-07-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.
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.
Characteristic manifolds in relativistic hypoelasticity
Energy Technology Data Exchange (ETDEWEB)
Giambo, S [Messina Univ. (Italy). Istituto di Matematica
1978-10-02
The relativistic hypoelasticity is considered and the characteristic manifolds are determined by using the Cauchy-Kovalevski theorem for the Cauchy problem with analytic initial conditions. Taking into account that the characteristic manifold represents the image of the front-wave in the space-time, it is possible to determine the velocities of propagation. Three wave-species are obtained: material waves, longitudinal waves and transverse waves.
Energy Technology Data Exchange (ETDEWEB)
Minesaki, Yukitaka [Tokushima Bunri University, Nishihama, Yamashiro-cho, Tokushima 770-8514 (Japan)
2015-01-01
We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog that preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.
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.
International Nuclear Information System (INIS)
Lusanna, Luca
2011-01-01
After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators imply a kinematical non-locality and non-separability influencing the theory of relativistic entanglement and not connected with the standard quantum non-locality.
Geometric characterization for the least Lagrangian action of n-body problems
Institute of Scientific and Technical Information of China (English)
ZHANG; Shiqing
2001-01-01
［1］Manev, G., La gravitation et l'énergie au zéro, Comptes Rendus, 924, 78: 259.［2］Diacu, F. N., Near-collision dynamics for particle systems with quasihomogeneous potentials, J. of Diff. Equ., 996, 28: 58.［3］Ambrosetti, A., Coti Zelati, V., Periodic Solutions of Singular Lagrangian Systems, Basel: Birkhuser, 993.［4］Arnold, V., Kozlov, V., Neishtadt, A., Dynamical Systems (iii): Mathematical Aspects of Classical and Celestial Mechanics, Berlin: Springer-Verlag, 988.［5］Chenciner, A., Desolneux, N., Minima de l'intégrale d'action et équilibres relatifs de n corps, C R Acad. Sci. Paris, serie I, 998, 326: 209.［6］Coti Zelati, V., The periodic solutions of n-body type problems, Ann IHP Anal nonlinéaire, 990, 7: 477.［7］Euler, L., De motu rectilineo trium corprum se mutuo attrahentium, Novi. Comm. Acad. Sci. Imp. Petropll, 767: 45.［8］Gordon, W., A minimizing property of Keplerian orbits, Amer. J. Math., 977, 99: 96.［9］Lagrange, J., Essai sur le problé me des trois corps, 772, Ouvres, 783, 3: 229.［10］Long, Y., Zhang, S. Q., Geometric characterization for variational minimization solutions of the 3-body problem, Chinese Science Bulletin, 999, 44(8): 653.［11］Long, Y., Zhang, S. Q., Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy, J. of Diff. Equ., 2000, 60: 422.［12］Meyer, K., Hall, G., Introduction to Hamiltonian systems and the n-body problems, Berlin: Springer-Verlag,992.［13］Serra, E., Terracini, S., Collisionless periodic solutions to some three-body problems, Arch. Rational Mech. Anal., 992, 20: 305.［14］Siegle, C., Moser, J., Lectures on Celestial Mechanics, Berlin: Springer-Verlag, 97.［15］Wintner, A., Analytical Foundations of Celestial Mechanics, Princeton: Princeton University Press, 94.［16］Hardy, G., Littlewood, J., Pólya, G., Inequalities, 2nd ed., Cambridge: Combridge University Press, 952.
Hyperspherical Coulomb spheroidal basis in the Coulomb three-body problem
International Nuclear Information System (INIS)
Abramov, D. I.
2013-01-01
A hyperspherical Coulomb spheroidal (HSCS) representation is proposed for the Coulomb three-body problem. This is a new expansion in the set of well-known Coulomb spheroidal functions. The orthogonality of Coulomb spheroidal functions on a constant-hyperradius surface ρ = const rather than on a constant-internuclear-distance surface R = const, as in the traditional Born-Oppenheimer approach, is a distinguishing feature of the proposed approach. Owing to this, the HSCS representation proves to be consistent with the asymptotic conditions for the scattering problem at energies below the threshold for three-body breakup: only a finite number of radial functions do not vanish in the limit of ρ→∞, with the result that the formulation of the scattering problem becomes substantially simpler. In the proposed approach, the HSCS basis functions are considerably simpler than those in the well-known adiabatic hyperspherical representation, which is also consistent with the asymptotic conditions. Specifically, the HSCS basis functions are completely factorized. Therefore, there arise no problems associated with avoided crossings of adiabatic hyperspherical terms.
A complete basis for a perturbation expansion of the general N-body problem
International Nuclear Information System (INIS)
Laing, W Blake; Kelle, David W; Dunn, Martin; Watson, Deborah K
2009-01-01
We discuss a basis set developed to calculate perturbation coefficients in an expansion of the general N-body problem. This basis has two advantages. First, the basis is complete order-by-order for the perturbation series. Second, the number of independent basis tensors spanning the space for a given order does not scale with N, the number of particles, despite the generality of the problem. At first order, the number of basis tensors is 25 for all N, i.e. the problem scales as N 0 , although one would initially expect an N 6 scaling at first order. The perturbation series is expanded in inverse powers of the spatial dimension. This results in a maximally symmetric configuration at lowest order which has a point group isomorphic with the symmetric group, S N . The resulting perturbation series is order-by-order invariant under the N! operations of the S N point group which is responsible for the slower than exponential growth of the basis. In this paper, we demonstrate the completeness of the basis and perform the first test of this formalism through first order by comparing to an exactly solvable fully interacting problem of N particles with a two-body harmonic interaction potential
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…
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
International Nuclear Information System (INIS)
Mittelstaedt, P.
1983-01-01
on the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space. (author)
Relativistic motion in gamma-ray bursts
International Nuclear Information System (INIS)
Krolik, J.H.; Pier, E.A.
1991-01-01
Three fundamental problems affect models of gamma-ray bursts, i.e., the energy source, the ability of high-energy photons to escape the radiation region, and the comparative weakness of X-ray emission. It is indicated that relativistic bulk motion of the gamma-ray-emitting plasma generically provides a solution to all three of these problems. Results show that, if the plasma that produces gamma-ray bursts has a bulk relativistic velocity with Lorentz factor gamma of about 10, several of the most troubling problems having to do with gamma-ray bursts are solved. 42 refs
Symmetry and geometry of the N-body problem. Application to the nuclear physics
International Nuclear Information System (INIS)
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)
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
Semiclassical expansion of quantum characteristics for many-body potential scattering problem
International Nuclear Information System (INIS)
Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.
2007-01-01
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
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.
Robe's Restricted Problem of 2 + 2 Bodies with a Roche Ellipsoid - Triaxial System
Aggarwal, Rajiv; Kaur, Bhavneet; Yadav, Sushil
2018-03-01
This paper investigates the motion of two infinitesimal masses on the location and stability of the equilibrium points in Robe's restricted problem of 2 + 2 bodies with the bigger primary a Roche ellipsoid and the smaller a triaxial body. We suppose the bigger primary of mass m 1 to be filled with a homogeneous incompressible fluid of density ρ 1. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m 2 is describing a circle around m 1. The masses m 3 and m 4 mutually attract each other, do not influence the motion of m 1 and m 2 but are influenced by them. We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m 2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m 3 and m 4 and their linear stability are analyzed.
Leigh, Nathan W. C.; Wegsman, Shalma
2018-05-01
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction into a series of discrete transformations in energy- and angular momentum-space. Each time a transformation is applied, the system changes state as the particles re-distribute their energy and angular momenta. These diagrams have the virtue of containing all of the quantitative information needed to fully characterize most bound or unbound interactions through time and space, including the total duration of the interaction, the initial and final stable states in addition to every intervening temporary meta-stable state. As shown via an illustrative example for the bound case, prolonged excursions of one of the particles, which by far dominates the computational cost of the simulations, are reduced to a single discrete transformation in energy- and angular momentum-space, thereby potentially mitigating any computational expense. We further generalize our formalism to sequences of (unbound) three-body interactions, as occur in dense stellar environments during binary hardening. Finally, we provide a method for dynamically evolving entire populations of binaries via three-body scattering interactions, using a purely analytic formalism. In principle, the techniques presented here are adaptable to other three-body problems that conserve energy and angular momentum.
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
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.
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.)
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.
In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
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.
The inverse problem of brain energetics: ketone bodies as alternative substrates
International Nuclear Information System (INIS)
Calvetti, D; Occhipinti, R; Somersalo, E
2008-01-01
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
The inverse problem of brain energetics: ketone bodies as alternative substrates
Calvetti, D.; Occhipinti, R.; Somersalo, E.
2008-07-01
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.
Many-body effects in the mesoscopic x-ray edge problem
International Nuclear Information System (INIS)
Hentschel, Martina; Roeder, Georg; Ullmo, Denis
2007-01-01
Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray exciton of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. (author)
A method for solving a three-body problem with energy-dependent interactions
International Nuclear Information System (INIS)
Safronov, A.N.
1994-01-01
A method is proposed for solving a three-body problem with energy-dependent interactions. This method is based on introducing the dependence of scattering operators and state vectors on an additional external parameter. Effects caused by the energy dependence of the interaction operator are investigated by using the unitary condition for the amplitude of the 2 → 2 and 2 → 3 transitions. It is shown, in particular, that taking this dependence into account leads to a change in the relation between the asymptotic normalization factor of the wave function of the three-body bound state and the vertex constant of virtual dissociation (synthesis) of the system into two fragments. 15 refs
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.
Muonic molecules as three-body Coulomb problem in adiabatic approximation
International Nuclear Information System (INIS)
Decker, M.
1994-04-01
The three-body Coulomb problem is treated within the framework of the hyperspherical adiabatic approach. The surface functions are expanded into Faddeev-type components in order to ensure the equivalent representation of all possible two-body contributions. It is shown that this decomposition reduces the numerical effort considerably. The remaining radial equations are solved both in the extreme and the uncoupled adiabatic approximation to determine the binding energies of the systems (dtμ) and (d 3 Heμ). Whereas the ground state is described very well in the uncoupled adiabatic approximation, the excited states should be treated within the coupled adiabatic approximation to obtain good agreement with variational calculations. (orig.)
Changes in Body Mass Index and Stoma Related Problems in the Elderly
Skeps, Raymond; McMullen, Carmit K.; Wendel, Christopher S.; Bulkley, Joanna; Grant, Marcia; Mohler, Jane; Hornbrook, Mark C.; Krouse, Robert S.; Herrinton, Lisa J.
2012-01-01
Objectives Weight gain can cause retraction of an intestinal stoma, possibly resulting in difficulty with wafer and pouch fit, daily care challenges, and discomfort. This cross-sectional study examined the association between body mass index (BMI) and ostomy-related problems among long-term (>5 years post-diagnosis) colorectal cancer (CRC) survivors. Materials and Methods CRC survivors from three Kaiser Permanente Regions completed a mailed survey. The response rate for those with an ostomy was 53% (283/529). Questions included stoma-related problems and time to conduct daily ostomy care. Poisson regression evaluated associations between report of problems and change in BMI. Our analysis sample included 235 survivors. Results Sample was 76% ≥65 years of age. Since their surgeries, BMI remained stable in 44% (ST), decreased in 20% (DE), and increased in 35% (IN) of survivors. Compared to ST, male IN (RR 2.15 [1.09–4.25]) and female DE (RR 5.06 [1.26–25.0]) were more likely to spend more than 30 minutes per day on stoma care. IN (vs. ST) were more likely to report interference with clothing (RR 1.51 [1.06–2.17]) and other stoma-related problems (RR 2.32 [1.30–4.14]). Survivors who were obese at time of survey were more likely to report interference with clothing (RR 1.88 [1.38–2.56]) and other stoma-related problems (RR 1.68 [1.07–2.65]). Conclusion A change in BMI is associated with ostomy-related problems among long-term CRC survivors. Equipment and care practices may need to be adapted for changes in abdominal shape. Health care providers should caution that a significant increase or decrease in BMI may cause ostomy-related problems. PMID:24071496
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
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.
Norbury, John W.
1992-01-01
Nuclear fission reactions induced by the electromagnetic field of relativistic nuclei are studied for energies relevant to present and future relativistic heavy ion accelerators. Cross sections are calculated for U-238 and Pu-239 fission induced by C-12, Si-28, Au-197, and U-238 projectiles. It is found that some of the cross sections can exceed 10 b.
Relativistic Shock Acceleration
International Nuclear Information System (INIS)
Duffy, P.; Downes, T.P.; Gallant, Y.A.; Kirk, J.G.
1999-01-01
In this paper we briefly review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising some astrophysically interesting cases. We then present an overview of the theory of particle acceleration at such shocks describing the methods used to calculate the spectral indices of energetic particles. Recent results on acceleration at ultra-relativistic shocks are discussed. (author)
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
Two novel classes of solvable many-body problems of goldfish type with constraints
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , 00185 Rome (Italy); Gomez-Ullate, D [Departamento de Fisica Teorica II, Universidad Complutense, 28040 Madrid (Spain)
2007-05-18
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
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.
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.
Approach method of the solutions of algebraic models of the N body problem
International Nuclear Information System (INIS)
Dufour, M.
1986-09-01
We have studied a class of algebraic eigenvalue problems that generate tridiagonal matrices. The Lipkin Hamiltonian was chosen as representative. Three methods have been implemented, whose extension to more general many body problems seems possible i) Degenerate Linked Cluster Theory (LCT), which disregards special symmetries of the interaction and defines a hierarchy of approximation based on model spaces at fixed number of particle-hole excitation of the unperturbed Hamiltonian. The method works for small perturbations but does not yield a complete description. ii) A new linearization method that replaces the matrix to be diagonalized by local (tangent) approximations by harmonic matrices. This method generalizes LCT and is a posteriori reminiscent of semi-classical ones. However of is simpler, more precise and yields a complete description of spectra. iii) A global way to characterize spectra based on Gershgorine-Hadamard disks [fr
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.
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.
Central configurations of the collinear three-body problem and singular surfaces in the mass space
Energy Technology Data Exchange (ETDEWEB)
Xie, Zhifu, E-mail: zxie@vsu.edu [Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA 23806 (United States)
2011-09-12
This Letter is to provide a new approach to study the phenomena of degeneracy of the number of the collinear central configurations under geometric equivalence. A direct and simple explicit parametric expression of the singular surface H{sub 3} is constructed in the mass space (m{sub 1},m{sub 2},m{sub 3}) element of (R{sup +}){sup 3}. The construction of H{sub 3} is from an inverse respective, that is, by specifying positions for the bodies and then determining the masses that are possible to yield a central configuration. It reveals the relationship between the phenomena of degeneracy and the inverse problem of central configurations. We prove that the number of central configurations is decreased to 3!/2-1=2, m{sub 1}, m{sub 2}, and m{sub 3} are mutually distinct if m element of H{sub 3}. Moreover, we know not only the number of central configurations but also what the nonequivalent central configurations are. -- Highlights: → Provide a new method to study the degeneracy of number of CC. → Results advanced the understanding of number of central configurations. → Singular mass surface H{sub 3} is given by a direct and simple parametric expression. → The proof only requires some basic knowledge of linear algebra. → The method can be applied to some other collinear n-body problem.
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.
Draws on a relativistic pinch with a longitudinal magnetic field
International Nuclear Information System (INIS)
Trubnikov, B.A.
1991-01-01
The problems of draws on a relativistic pinch with longitudinal magnetic field are discussed. The absence of collisions promoting the energy exchange between different degrees of particle freedom is assumed. The calculations are conducted using the ideal relativistic anisotropic magnetic hydrodynamics equations. The spectrum of particles accelerated in the draws, is determined
Remarks on the relativistic magnetohydrodynamics of an anisotropic fluid
International Nuclear Information System (INIS)
Ignat, M.
1980-01-01
Considering a pressure tensor of a general form, a relativistic rarefied, anisotropic, infinite electrically conducting and nondissipative plasma is studied. For this purpose, the method of the orthonormal frame of reference is used. The choice of the frame of reference is made adequately to the problem. Some thermodynamical properties of such a relativistic, anisotropic plasma are also given. (author)
Energy Technology Data Exchange (ETDEWEB)
Arons, J.
1988-08-15
I outline particle simulations and theory of relativistic shock waves in an e/sup +-/ plasma. Magnetic reflection of particles is an essential role in the shock structure. Instability of the reflected particles in the shock front produces intense extraordinary mode radiation. Such shocks are candidates for the particle accelerator in plerions and in extragalactic jets only if the upstream Poynting flux composes no more than 10% of the total. I summarize analytical and numerical studies of radiation dominated accretion onto the magnetic poles of neutron stars. The upper limit to the photon luminosity depends upon magnetic confinement, not upon the dragging of photons into the star. Numerical solutions show the plasma forms large scale ''photon bubbles.'' I suggest the percolative loss of radiation controls the pressure and therefore the limits of magnetic confinement. Loss of magnetic confinement through resistive interchange instability is suggested as a means of generating TeV to PeV voltage drops along the magnetic field. 34 refs., 6 figs., 1 tab.
International Nuclear Information System (INIS)
Arons, J.
1988-01-01
I outline particle simulations and theory of relativistic shock waves in an e/sup +-/ plasma. Magnetic reflection of particles is an essential role in the shock structure. Instability of the reflected particles in the shock front produces intense extraordinary mode radiation. Such shocks are candidates for the particle accelerator in plerions and in extragalactic jets only if the upstream Poynting flux composes no more than 10% of the total. I summarize analytical and numerical studies of radiation dominated accretion onto the magnetic poles of neutron stars. The upper limit to the photon luminosity depends upon magnetic confinement, not upon the dragging of photons into the star. Numerical solutions show the plasma forms large scale ''photon bubbles.'' I suggest the percolative loss of radiation controls the pressure and therefore the limits of magnetic confinement. Loss of magnetic confinement through resistive interchange instability is suggested as a means of generating TeV to PeV voltage drops along the magnetic field. 34 refs., 6 figs., 1 tab
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 ...
Niemi, Antti H.; Bramwell, Jamie A.; Demkowicz, Leszek F.
2011-01-01
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
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.
International Nuclear Information System (INIS)
Hu Longfei; Fang Yang; Wang Yishun; Wang Long
2014-01-01
In prospecting and mining of a broken thick large uranium ore body, uncertain prospecting and shallow-hole shrinkage mining method resulted in large dilution rate and resource waste problems. Aimed at these problems, improvement schemes of enhancing the strength force of 'drilling prospecting instead of pit prospecting' and employing filling method stoping ore body were applied, and improvement result was analyzed. Experience was accumulated and evidence was provided for late prospecting and stoping work. (authors)
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.
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
Plasma relativistic microwave electronics
International Nuclear Information System (INIS)
Kuzelev, M.V.; Loza, O.T.; Rukhadze, A.A.; Strelkov, P.S.; Shkvarunets, A.G.
2001-01-01
One formulated the principles of plasma relativistic microwave electronics based on the induced Cherenkov radiation of electromagnetic waves at interaction of a relativistic electron beam with plasma. One developed the theory of plasma relativistic generators and accelerators of microwave radiation, designed and studied the prototypes of such devices. One studied theoretically the mechanisms of radiation, calculated the efficiencies and the frequency spectra of plasma relativistic microwave generators and accelerators. The theory findings are proved by the experiment: intensity of the designed sources of microwave radiation is equal to 500 μW, the frequency of microwave radiation is increased by 7 times (from 4 up to 28 GHz), the width of radiation frequency band may vary from several up to 100%. The designed sources of microwave radiation are no else compared in the electronics [ru
International Nuclear Information System (INIS)
Chen Baoqiu; Ma Zhongyu
1992-01-01
Relativistic microscopic optical potential of nucleon-nucleus is derived from the relativistic Brueckner-Bethe-Goldstone (RBBG) equation. The complex effective mass of a nucleon is determined by a fit to 200 MeV p- 40 Ca scattering data. The relativistic microscopic optical potentials with this effective mass are obtained from RBBG for p- 16O , 40 Ca, 90 Zr and 208 Pb scattering in energy range from 160 to 800 MeV. The microscopic optical potential is used to study the proton- 40 Ca scattering problem at 200 MeV. The results, such as differential cross section, analyzing power and spin rotation function are compared with those calculated from phenomenological relativistic optical potential
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.
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...
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 Chiral Mean Field Model for Finite Nuclei
Ogawa, Y.; Toki, H.; Tamenaga, S.; Haga, A.
2009-08-01
We present a relativistic chiral mean field (RCMF) model, which is a method for the proper treatment of pion-exchange interaction in the nuclear many-body problem. There the dominant term of the pionic correlation is expressed in two-particle two-hole (2p-2h) states with particle-holes having pionic quantum number, J^{π}. The charge-and-parity-projected relativistic mean field (CPPRMF) model developed so far treats surface properties of pionic correlation in 2p-2h states with J^{π} = 0^{-} (spherical ansatz). We extend the CPPRMF model by taking 2p-2h states with higher spin quantum numbers, J^{π} = 1^{+}, 2^{-}, 3^{+}, ... to describe the full strength of the pionic correlation in the intermediate range (r > 0.5 fm). We apply the RCMF model to the ^{4}He nucleus as a pilot calculation for the study of medium and heavy nuclei. We study the behavior of energy convergence with the pionic quantum number, J^{π}, and find convergence around J^{π}_{max} = 6^{-}. We include further the effect of the short-range repulsion in terms of the unitary correlation operator method (UCOM) for the central part of the pion-exchange interaction. The energy contribution of about 50% of the net two-body interaction comes from the tensor part and 20% comes from the spin-spin central part of the pion-exchange interaction.}
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
International Nuclear Information System (INIS)
Strange, P.
2010-01-01
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
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
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
On the photo-gravitational restricted four-body problem with variable mass
Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika
2018-05-01
This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.
Schwinger variational principle in the nuclear two-body problem and multichannel theory
International Nuclear Information System (INIS)
Zubarev, A.L.; Podkopaev, A.P.
1978-01-01
The aim of the investigation is to study the Schwinger variational principle in the nuclear two-body problem and the multichannel theory. An approach is proposed to problems of the potential scattering based on the substitution of the exact potential operator V by the finite rank operator Vsup((n)) with which the dynamic equations are solved exactly. The functionals obtained for observed values coincide with corresponding expressions derived by the Schwinger variational principle with the set of test functions. The determination of the Schwinger variational principle is given. The method is given for finding amplitude of the double-particle scattering with the potential Vsup((n)). The corresponding amplitudes are constructed within the framework of the multichannel potential model. Interpolation formula for determining amplitude, which describes with high accuracy a process of elastic scattering for any energies, is obtained. On the basis of the above method high-energy amplitude may be obtained within the range of small and large scattering angles
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.
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
On free fall of a relativistic particle
International Nuclear Information System (INIS)
Chernikov, N.A.; Paramonova, N.N.; Shavokhina, N.S.
2005-01-01
The free fall of a relativistic particle is considered: the well-known fact of the light velocity constancy is taken into account in the Galilean problem about the movement of a particle from nongravitational forces and its fall onto the ground. The velocity hodograph and the world line of the particle are found
Relativistic tunneling through two successive barriers
International Nuclear Information System (INIS)
Lunardi, Jose T.; Manzoni, Luiz A.
2007-01-01
We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called generalized Hartman effect, an effect observed in the context of nonrelativistic tunneling as well as in its counterparts and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the generalized Hartman effect. We compare our results with the nonrelativistic ones and discuss their interpretation
International Nuclear Information System (INIS)
Vilkas, Marius J; Ishikawa, Yasuyuki; Traebert, Elmar
2006-01-01
Many-body perturbation theory (MBPT) has been employed to calculate with high wavelength accuracy the extreme ultraviolet (EUV) spectra of F-like to P-like Xe ions. We discuss the reliability of the new calculations using the example of EUV beam-foil spectra of Xe, in which n = 3, Δn = 0 transitions of Na-, Mg-, Al- and Si-like ions have been found to dominate. A further comparison is made with spectra from an electron beam ion trap, that is, from a device with a very different (low density) excitation balance
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
International Nuclear Information System (INIS)
Nottale, Laurent
2003-01-01
The principle of relativity, when it is applied to scale transformations, leads to the suggestion of a generalization of fundamental dilations laws. These new special scale-relativistic resolution transformations involve log-Lorentz factors and lead to the occurrence of a minimal and of a maximal length-scale in nature, which are invariant under dilations. The minimal length-scale, that replaces the zero from the viewpoint of its physical properties, is identified with the Planck length l P , and the maximal scale, that replaces infinity, is identified with the cosmic scale L=Λ -1/2 , where Λ is the cosmological constant.The new interpretation of the Planck scale has several implications for the structure and history of the early Universe: we consider the questions of the origin, of the status of physical laws at very early times, of the horizon/causality problem and of fluctuations at recombination epoch.The new interpretation of the cosmic scale has consequences for our knowledge of the present universe, concerning in particular Mach's principle, the large number coincidence, the problem of the vacuum energy density, the nature and the value of the cosmological constant. The value (theoretically predicted ten years ago) of the scaled cosmological constant Ω Λ =0.75+/-0.15 is now supported by several different experiments (Hubble diagram of Supernovae, Boomerang measurements, gravitational lensing by clusters of galaxies).The scale-relativity framework also allows one to suggest a solution to the missing mass problem, and to make theoretical predictions of fundamental energy scales, thanks to the interpretation of new structures in scale space: fractal/classical transitions as Compton lengths, mass-coupling relations and critical value 4π 2 of inverse couplings. Among them, we find a structure at 3.27+/-0.26x10 20 eV, which agrees closely with the observed highest energy cosmic rays at 3.2+/-0.9x10 20 eV, and another at 5.3x10 -3 eV, which corresponds to the
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
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
Exact self-energy of the many-body problem from conserving approximations
International Nuclear Information System (INIS)
Takada, Y.
1995-01-01
A procedure is proposed to obtain the exact self-energy in the many-body problem. This algorithm is based on the formal analysis to reach the exact theory by repeated applications of an operator F to an arbitrarily chosen input self-energy represented as a functional of the dressed Green's function. The operator F is so defined that the microscopic conservation law for particle number is satisfied. The rigorous self-energy is obtained by the solution of an eigenfunction of F. Particular attention is paid to the relation between the present procedure and the Baym-Kadanoff framework of conserving approximations. By simplifying the procedure in F with use of the generalized Ward identity, we suggest a practical method to implement this algorithm rather easily in actual systems. In order to suggest future directions to improve on this practical method, the recently developed mean-field theory for the Hubbard model in the limit of high spatial dimensions is also discussed in the context of our theory
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.
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.
Relativistic quantum mechanics
International Nuclear Information System (INIS)
Ollitrault, J.Y.
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.)
Many body quantum physics at the condensed matter
International Nuclear Information System (INIS)
Llano, M. de
1981-01-01
The non-relativistic, continuous (as opposed to spin) many-body problem as it relates to condensed matter at absolute zero temperature is reviewed in simple, non-technical terms, mainly from the standpoint of infinite order perturbation theory, for physical systems where all the particles have the same mass but which otherwise interact with arbitrary short- or long-ranged two-body forces. (author)
International Nuclear Information System (INIS)
Tolstikhin, Oleg I.; Namba, Chusei
2003-08-01
A program to solve the quantum-mechanical collinear three-body Coulomb problem is described and illustrated by calculations for a number of representative systems and processes. In the internal region, the Schroedinger equation is solved in hyperspherical coordinates using the slow/smooth variable discretization method. In asymptotic regions, the solution is obtained in Jacobi coordinates using the asymptotic package GAILIT from the CPC library. Only bound states and scattering processes below the three-body disintegration threshold are considered here; resonances and fragmentation processes will be discussed in subsequent parts of this series. (author)
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)
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)
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
Relativistic heavy ion collisions
International Nuclear Information System (INIS)
Barz, H.W.; Kaempfer, B.; Schulz, H.
1984-12-01
An elementary introduction is given into the scenario of relativistic heavy ion collisions. It deals with relativistic kinematics and estimates of energy densities, extrapolations of the present knowledge of hadron-hadron and hadron-nuleus to nucleus-nucleus collisions, the properties of the quark-gluon plasma and the formation of the plasma and possible experimental signatures. Comments are made on a cosmic ray experiment which could be interpreted as a first indication of the quark-gluon phase of the matter. (author)
International Nuclear Information System (INIS)
Zhao Hongsheng; Li Baojiu; Bienayme, Olivier
2010-01-01
We derive a simple analytical expression for the two-body force in a subclass of modified Newtonian dynamics (MOND) theories and make testable predictions in the modification to the two-body orbital period, shape, precession rate, escape speed, etc. We demonstrate the applications of the modified Kepler's law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of the large Magellanic cloud, the M31 galaxy, and the merging bullet clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings, and shells.
The evolutionary origin of the vertebrate body plan: the problem of head segmentation.
Onai, Takayuki; Irie, Naoki; Kuratani, Shigeru
2014-01-01
The basic body plan of vertebrates, as typified by the complex head structure, evolved from the last common ancestor approximately 530 Mya. In this review, we present a brief overview of historical discussions to disentangle the various concepts and arguments regarding the evolutionary development of the vertebrate body plan. We then explain the historical transition of the arguments about the vertebrate body plan from merely epistemological comparative morphology to comparative embryology as a scientific treatment on this topic. Finally, we review the current progress of molecular evidence regarding the basic vertebrate body plan, focusing on the link between the basic vertebrate body plan and the evolutionarily conserved developmental stages (phylotypic stages).
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
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.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
International Nuclear Information System (INIS)
Contopoulos, G.
1983-01-01
In this paper, three main areas of relativistic stellar dynamics are reviewed: (a) The dynamics of clusters, or nuclei of galaxies, of very high density; (b) The dynamics of systems containing a massive black hole; and (c) The dynamics of particles (and photons) in an expanding Universe. The emphasis is on the use of orbit perturbations. (Auth.)
Directory of Open Access Journals (Sweden)
Bialynicki-Birula Iwo
2014-01-01
Full Text Available Original definition of the Wigner function can be extended in a natural manner to relativistic domain in the framework of quantum field theory. Three such generalizations are described. They cover the cases of the Dirac particles, the photon, and the full electromagnetic field.
Relativistic Polarizable Embedding
DEFF Research Database (Denmark)
Hedegård, Erik Donovan; Bast, Radovan; Kongsted, Jacob
2017-01-01
Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments s...
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.)
Fundamental Relativistic Rotator
International Nuclear Information System (INIS)
Staruszkiewicz, A.
2008-01-01
Professor Jan Weyssenhoff was Myron Mathisson's sponsor and collaborator. He introduced a class of objects known in Cracow as '' kreciolki Weyssenhoffa '', '' Weyssenhoff's rotating little beasts ''. The Author describes a particularly simple object from this class. The relativistic rotator described in the paper is such that its both Casimir invariants are parameters rather than constants of motion. (author)
Relativistic Quantum Mechanics
International Nuclear Information System (INIS)
Antoine, J-P
2004-01-01
The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic
Stability at Potential Maxima: The L-4 and L-5 Points of the Restricted Three-Body Problem.
Greenberg, Richard; Davis, Donald R.
1978-01-01
Describes a dynamical system which is stable at potential maxima. The maxima, called L-4 and L-5, are stable locations of the restricted three-body problem. Energy loss from the system will tend to drive it away from stability. (GA)
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 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.)
Is the relativistic approach really useful to nuclear reactions?
Miyazaki, K
2003-01-01
We have reconsidered the non-relativistic distorted-wave t-matrix approximation (NR-DWTA) for proton knockout (p,2p) reaction using modern high-quality phenomenological optical potentials and NN t-matrix. We have calculated 40Ca(p,2p) reactions at T_LAB=200MeV and compared the results with the relativistic distorted-wave impulse approximation (RDWIA) calculations. It is found that the NR-DWTA is superior to the RDWIA in consistent description of the cross section and the analyzing power. An immediate relativistic extension of the DWIA to the nuclear reaction has a problem.
Canonical quantization of spinning relativistic particle in external backgrounds
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica
2000-07-01
Full text follows: We revise the problem of the quantization of spinning relativistic particle pseudoclassical model, using a modified consistent canonical scheme. It allows one not only to include arbitrary electromagnetic and gravitational backgrounds in the consideration but to get in course of the quantization a consistent relativistic quantum mechanics, which reproduces literally the behavior of the one-particle sector of quantized spinor field. In particular, in a physical sector of the Hilbert space a complete positive spectrum of energies of relativistic particles and antiparticles is reproduced. Requirement to maintain all classical symmetries under the coordinate transformations and under U(1) transformations allows one to realize operator algebra without any ambiguities. (author)
Relativistic current sheets in electron-positron plasmas
International Nuclear Information System (INIS)
Zenitani, S.
2008-01-01
The current sheet structure with magnetic field reversal is one of the fundamental structure in space and astrophysical plasmas. It draws recent attention in high-energy astrophysical settings, where relativistic electron-positron plasmas are considered. In this talk we will review the recent progress of the physical processes in the relativistic current sheet. The kinetic stability of a single current sheet, the nonlinear behavior of these instabilities, and recent challenges on the multi current sheet systems are introduced. We will also introduce some problems of magnetic reconnection in these relativistic environments. (author)
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.
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica
2000-07-01
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)
Smith, C. W.
1992-01-01
The adaptation of the frozen stress photoelastic method to the determination of the distribution of stress intensity factors in three dimensional problems is briefly reviewed. The method is then applied to several engineering problems of practical significance.
Chrisler, Joan C.
2011-01-01
Reductionistic, misogynistic, and heterosexist views of women's bodies have been often expressed and widely shared, and psychology has not been immune to those views. Second-wave feminist psychologists had plenty of work to do to normalize and destigmatize women's bodies and to point out that cultural pressures, social constructions, and…
Non-extensive statistical effects in nuclear many-body problems
International Nuclear Information System (INIS)
Lavagno, A.; Quarati, P.
2007-01-01
Density and temperature conditions in many stellar core and in the first stage of relativistic heavy-ion collisions imply the presence of non-ideal plasma effects with memory and long-range interactions between particles. Recent progress in statistical mechanics indicates that Tsallis non-extensive thermostatistics could be the natural generalization of the standard classical and quantum statistics, when memory effects and long range forces are not negligible. In this framework, we show that in weakly non-ideal plasma non-extensive effects should be taken into account to derive the equilibrium distribution functions, the quantum fluctuations and correlations between the particles. The strong influence of these effects is discussed in the context of the solar plasma physics and in the high-energy nuclear-nuclear collision experiments. Although the deviation from Boltzmann-Gibbs statistics, in both cases, is very small, the stellar plasma and the hadronic gas are strongly influenced by the non-extensive feature and the discrepancies between experimental data and theoretical previsions are sensibly reduced. (authors)
The Hill's three-body problem: a new deduction of motion equations
International Nuclear Information System (INIS)
Fuente Marcos, C. de la.
1995-01-01
Although the Hill's problem has been considered traditionally as a particular case of the restricted problem, it is not but rather a different problem with the same degree of generality. In this paper it is presented a new derivation of the motion equations obtained originally by Hill in 1878 as well as a brief discussion about its possible applications. (Author) 13 refs
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)
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.
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
Relativistic gravitational instabilities
International Nuclear Information System (INIS)
Schutz, B.F.
1987-01-01
The purpose of these lectures is to review and explain what is known about the stability of relativistic stars and black holes, with particular emphases on two instabilities which are due entirely to relativistic effects. The first of these is the post-Newtonian pulsational instability discovered independently by Chandrasekhar (1964) and Fowler (1964). This effectively ruled out the then-popular supermassive star model for quasars, and it sets a limit to the central density of white dwarfs. The second instability was also discovered by Chandrasekhar (1970): the gravitational wave induced instability. This sets an upper bound on the rotation rate of neutron stars, which is near that of the millisecond pulsar PSR 1937+214, and which is beginning to constrain the equation of state of neutron matter. 111 references, 5 figures
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)
Breus, T. K.; Binhi, V. N.; Petrukovich, A. A.
2016-05-01
The body of current heliobiological evidence suggests that very weak variable magnetic fields due to solar- and geomagnetic-activities do have a biological effect. Geomagnetic disturbances can cause a nonspecific reaction in the human body - a kind of general adaptation syndrome which occurs due to any external stress factor. Also, specific reactions can develop. One of the reasons discussed for the similarity between biological and heliogeophysical rhythms is that geomagnetic variations have a direct influence on organisms, although exact magnetoreception mechanisms are not yet clear. The paper briefly reviews the current state of empirical and theoretical work on this fundamental multidisciplinary problem.
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.
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...... 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....
Relativistic heavy ion reactions
Energy Technology Data Exchange (ETDEWEB)
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.
Bratek, Łukasz
2015-01-01
Two particularly simple ideal clocks exhibiting intrinsic circular motion with the speed of light and opposite spin alignment are described. The clocks are singled out by singularities of an inverse Legendre transformation for relativistic rotators of which mass and spin are fixed parameters. Such clocks work always the same way, no matter how they move. When subject to high accelerations or falling in strong gravitational fields of black holes, the clocks could be used to test the clock hypo...
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
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.
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.
Relativistic theory of surficial Love numbers
Landry, Philippe; Poisson, Eric
2014-06-01
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
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.
Directory of Open Access Journals (Sweden)
Jagadish Singh
2012-01-01
Full Text Available This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.
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.
Weinstein, Galina
2015-01-01
Between 1935 and 1936, Einstein was occupied with the Schwarzschild solution and the singularity within it while working in Princeton on the unified field theory and with his assistant Nathan Rosen, on the theory of the Einstein-Rosen bridges. He was also occupied with quantum theory. He believed that quantum theory was an incomplete representation of real things. Together with Rosen and Boris Podolsky he invented the EPR paradox. I demonstrate that the two-body problem in general relativity ...
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...
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
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
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
Local distortion techniques and unitarity of the S-matrix for the 2-body problem
International Nuclear Information System (INIS)
Babbitt, D.; Balslev, E.
1976-01-01
The two-body S-matrix for an interaction with exponential decay at infinity is defined in a time-independent way and its unitarity is proved directly by local distortion techniques. Complete sets of incoming and outgoing states or delicate resolvent estimates are not needed for the proof
Concentration of frequencies of trapped waves in problems on freely floating bodies
Energy Technology Data Exchange (ETDEWEB)
Nazarov, Sergei A [Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St.-Petersburg (Russian Federation)
2012-09-30
It is shown that by choosing the shape of two identical bodies floating freely in a channel with symmetric cross-section it is possible to form any pre-assigned number of linearly independent trapped waves (localized solutions). Bibliography: 27 titles.
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
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
Energy Technology Data Exchange (ETDEWEB)
Abramowicz, M A; Jaroszynski, M; Sikora, M [Polska Akademia Nauk, Warsaw
1978-02-01
An analytic theory of the hydrodynamical structure of accreting disks (without self-gravitation but with pressure) orbiting around an 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 r/sub ms/ and r/sub 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/sub 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.
Directory of Open Access Journals (Sweden)
Takashi Ito
2016-01-01
Full Text Available Terms in the analytic expansion of the doubly averaged disturbing function for the circular restricted three-body problem using the Legendre polynomial are explicitly calculated up to the fourteenth order of semimajor axis ratio (α between perturbed and perturbing bodies in the inner case (α1. The expansion outcome is compared with results from numerical quadrature on an equipotential surface. Comparison with direct numerical integration of equations of motion is also presented. Overall, the high-order analytic expansion of the doubly averaged disturbing function yields a result that agrees well with the numerical quadrature and with the numerical integration. Local extremums of the doubly averaged disturbing function are quantitatively reproduced by the high-order analytic expansion even when α is large. Although the analytic expansion is not applicable in some circumstances such as when orbits of perturbed and perturbing bodies cross or when strong mean motion resonance is at work, our expansion result will be useful for analytically understanding the long-term dynamical behavior of perturbed bodies in circular restricted three-body systems.
Malafeyev, O. A.; Redinskikh, N. D.
2018-05-01
The problem of finding optimal temperature control of the material body state under the unknown in advance parameters of the external medium is formalized and studied in this paper. The problems of this type arise frequently in the real life. An optimal thermal regime is necessary to apply at the soil thawing or freezing, drying the building materials, heating the concrete to obtain the required strength, and so on. Problems of such type one can analyze making use the apparatus and methods of game theory. For describing the influence of external medium on the characteristics of different materials we make use the many-step two person zero-sum game in this paper. The compromise solution is taken as the optimality principle. The numerical example is given.
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.
Lattice Methods and the Nuclear Few- and Many-Body Problem
Lee, Dean
This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.
Relativistic Outflows from ADAFs
Becker, Peter; Subramanian, Prasad; Kazanas, Demosthenes
2001-04-01
Advection-dominated accretion flows (ADAFs) have a positive Bernoulli parameter, and are therefore gravitationally bound. The Newtonian ADAF model has been generalized recently to obtain the ADIOS model that includes outflows of energy and angular momentum, thereby allowing accretion to proceed self-consistently. However, the utilization of a Newtonian gravitational potential limits the ability of this model to describe the inner region of the disk, where any relativistic outflows are likely to originate. In this paper we modify the ADIOS scenario to incorporate a seudo - Newtonian potential, which approximates the effects of general relativity. The analysis yields a unique, self - similar solution for the structure of the coupled disk/wind system. Interesting features of the new solution include the relativistic character of the outflow in the vicinity of the radius of marginal stability, which represents the inner edge of the quasi-Keplerian disk in our model. Our self - similar model may therefore help to explain the origin of relativistic jets in active galaxies. At large distances the radial dependence of the accretion rate approachs the unique form dot M ∝ r^1/2, with an associated density variation given by ρ ∝ r-1. This density variation agrees with that implied by the dependence of the X-ray hard time lags on the Fourier frequency for a number of accreting galactic black hole candidates. While intriguing, the results of our self-similar model need to be confirmed in the future by incorporating a detailed physical description of the energization mechanism that drives the outflow, which is likely to be powered by the shear of the underlying accretion disk.
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
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
Benson, Christopher R; Maffeo, Christopher; Fatila, Elisabeth M; Liu, Yun; Sheetz, Edward G; Aksimentiev, Aleksei; Singharoy, Abhishek; Flood, Amar H
2018-05-07
The coordinated motion of many individual components underpins the operation of all machines. However, despite generations of experience in engineering, understanding the motion of three or more coupled components remains a challenge, known since the time of Newton as the "three-body problem." Here, we describe, quantify, and simulate a molecular three-body problem of threading two molecular rings onto a linear molecular thread. Specifically, we use voltage-triggered reduction of a tetrazine-based thread to capture two cyanostar macrocycles and form a [3]pseudorotaxane product. As a consequence of the noncovalent coupling between the cyanostar rings, we find the threading occurs by an unexpected and rare inchworm-like motion where one ring follows the other. The mechanism was derived from controls, analysis of cyclic voltammetry (CV) traces, and Brownian dynamics simulations. CVs from two noncovalently interacting rings match that of two covalently linked rings designed to thread via the inchworm pathway, and they deviate considerably from the CV of a macrocycle designed to thread via a stepwise pathway. Time-dependent electrochemistry provides estimates of rate constants for threading. Experimentally derived parameters (energy wells, barriers, diffusion coefficients) helped determine likely pathways of motion with rate-kinetics and Brownian dynamics simulations. Simulations verified intercomponent coupling could be separated into ring-thread interactions for kinetics, and ring-ring interactions for thermodynamics to reduce the three-body problem to a two-body one. Our findings provide a basis for high-throughput design of molecular machinery with multiple components undergoing coupled motion.
Relativistic klystrons for high-gradient accelerators
International Nuclear Information System (INIS)
Westenskow, G.A.; Aalberts, D.P.; Boyd, J.K.; Deis, G.A.; Houck, T.L.; Orzechowski, T.J.; Ryne, R.D.; Yu, S.S.; Allen, M.A.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Hoag, H.A.; Koontz, R.F.; Lavine, T.L.; Loew, G.A.; Miller, R.H.; Ruth, R.D.; Vlieks, A.E.; Wang, J.W.; Hopkins, D.B.; Sessler, A.M.; Haimson, J.; Mecklenburg, B.
1991-01-01
Experimental work is being performed by collaborators at LLNL, SLAC, and LBL to investigate relativistic klystrons as a possible rf power source for future high-gradient accelerators. The authors have learned how to overcome their previously reported problem of high power rf pulse shortening and have achieved peak rf power levels of 330 MW using an 11.4-GHz high-gain tube with multiple output structures. In these experiments the rf pulse is of the same duration as the beam current pulse. In addition, experiments have been performed on two short sections of a high-gradient accelerator using the rf power from a relativistic klystron. An average accelerating gradient of 84 MV/m has been achieved with 80-MW of rf power
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.)
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
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...
Relativistic twins or sextuplets?
International Nuclear Information System (INIS)
Sheldon, Eric
2003-01-01
A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back
Relativistic twins or sextuplets?
Sheldon, E S
2003-01-01
A recent study of the relativistic twin 'paradox' by Soni in this journal affirmed that 'A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks' but entailed a pedagogic hurdle which the present treatment aims to surmount. Two scenarios are presented: the first 'flight-plan' is akin to that depicted by Soni, with constant-velocity segments, while the second portrays an alternative mission undertaken with sustained acceleration and deceleration, illustrated quantitatively for a two-way spacecraft flight from Earth to Polaris (465.9 light years distant) and back.
Relativistic quantum cryptography
Kaniewski, Jedrzej
Special relativity states that information cannot travel faster than the speed of light, which means that communication between agents occupying distinct locations incurs some minimal delay. Alternatively, we can see it as temporary communication constraints between distinct agents and such constraints turn out to be useful for cryptographic purposes. In relativistic cryptography we consider protocols in which interactions occur at distinct locations at well-defined times and we investigate why such a setting allows to implement primitives which would not be possible otherwise. (Abstract shortened by UMI.).
Localization of relativistic particles
International Nuclear Information System (INIS)
Omnes, R.
1997-01-01
In order to discuss localization experiments and also to extend the consistent history interpretation of quantum mechanics to relativistic properties, the techniques introduced in a previous paper [J. Math. Phys. 38, 697 (1997)] are applied to the localization of a photon in a given region of space. An essential requirement is to exclude arbitrarily large wavelengths. The method is valid for a particle with any mass and spin. Though there is no proper position operator for a photon, one never needs one in practice. Causality is valid up to exponentially small corrections. copyright 1997 American Institute of Physics
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
Relativistic quarkonium dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1985-06-01
We present, in the framework of relativistic quantum mechanics of two interacting particles, a general model for quarkonium systems satisfying the following four requirements: confinement, spontaneous breakdown of chiral symmetry, soft explicit chiral symmetry breaking, short distance interactions of the vector type. The model is characterized by two arbitrary scalar functions entering in the large and short distance interaction potentials, respectively. Using relationships with corresponding quantities of the Bethe-Salpeter equation, we also present the normalization condition of the wave functions, as well as the expressions of the meson decay coupling constants. The quark masses appear in this model as free parameters
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)
Relativistic nuclear collisions: theory
International Nuclear Information System (INIS)
Gyulassy, M.
1980-07-01
Some of the recent theoretical developments in relativistic (0.5 to 2.0-GeV/nucleon) nuclear collisions are reviewed. The statistical model, hydrodynamic model, classical equation of motion calculations, billiard ball dynamics, and intranuclear cascade models are discussed in detail. Inclusive proton and pion spectra are analyzed for a variety of reactions. Particular attention is focused on how the complex interplay of the basic reaction mechanism hinders attempts to deduce the nuclear matter equation of state from data. 102 references, 19 figures
[Relativistic heavy ion research
International Nuclear Information System (INIS)
1991-01-01
The present document describes our second-year application for a continuation grant on relativistic heavy-ion research at Nevis Laboratories, Columbia University, over the two-year period starting from November 15, 1990. The progress during the current budget year is presented. This year, construction of RHIC officially began. As a result, the entire Nevis nuclear physics group has made a coherent effort to create new proposal for an Open Axially Symmetric Ion Spectrometer (OASIS) proposal. Future perspectives and our plans for this proposal are described
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
The stress distribution in shell bodies and wings as an equilibrium problem
Wagner, H
1937-01-01
This report treats the stress distribution in shell-shaped airplane components (fuselage, wings) as an equilibrium problem; it includes both cylindrical and non-cylindrical shells. In particular, it treats the stress distribution at the point of stress application and at cut-out points.
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
Relativistic dynamics without conservation laws
Rothenstein, Bernhard; Popescu, Stefan
2006-01-01
We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.
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.
On the relativistic quantum mechanics of two interacting spinless particles
International Nuclear Information System (INIS)
Rizov, V.A.; Sazdjian, H.; Todorov, I.T.
1984-05-01
The L 2 -scalar product ∫ PHI*(x)PSI(x) d 3 x is not appropriate for the space of states describing the center-of-mass relative motion of two relativistic particles whose interaction is given by an energy dependent quasipotential. The problem already appears in the relativistic quantum mechanics of a Klein-Gordon charged particle in an external field. We extend the methods developed for that case to study a two-particle system with an energy independent scalar interaction as well as the relativistic Coulomb problem. We write down a Poincare invariant inner product for which the eigenfunctions corresponding to different energy eigenvalues are orthogonal. We also construct a perturbative expansion for bound-state energy eigenvalues corresponding to an arbitrary energy dependent (quasipotential) correction to an unperturbed Hamiltonian with a known spectrum. The description of observables and transition probabilities for eigenvalue problems with a polynomial dependence on the spectral parameter is also discussed
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.
Relativistic heavy ion physics
International Nuclear Information System (INIS)
Hill, J.C.; Wohn, F.K.
1992-01-01
In 1992 a proposal by the Iowa State University experimental nuclear physics group entitled ''Relativistic Heavy Ion Physics'' was funded by the US Department of Energy, Office of Energy Research, for a three-year period beginning November 15, 1991. This is a progress report for the first six months of that period but, in order to give a wider perspective, we report here on progress made since the beginning of calendar year 1991. In the first section, entitled ''Purpose and Trends,'' we give some background on the recent trends in our 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 Programs,'' is divided into three parts. First, we discuss our participation in the program to develop a large detector named PHENIX for the RHIC accelerator. Second, we outline progress made in the study of electromagnetic dissociation (ED). A highlight of this endeavor is experiments carried out with the 197 Au beam from the AGS accelerator in April 1991. Third, we discuss progress in completion of our nuclear structure studies. In the final section a list of publications, invited talks and contributed talks starting in 1991 is given
Some exact solutions to the translation-invariant N-body problem
International Nuclear Information System (INIS)
Hall, R.L.
1978-01-01
It is shown that Schroedinger's equation for a translation-invariant system consisting of N particles with arbitrary masses interacting via Hooke's law pair potentials with the same coupling constant can be solved exactly; explicit solutions are found for the case N = 3. Exact solutions are also found explicitly for the translation-invariant problem in which a particle with mass m 0 interacts with N identical particles of mass m 1 via Hooke's law pair potential with coupling constant k 0 2 , and the identical particles interact with each other via Hooke's law pair potentials with coupling constant k 1 2 . The latter solution provides a basis problem for an energy lower-bound method for translation-invariant atom-like systems. (author)
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.
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 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.
X-ray morphology of the eburnated vertebral body - diagnostic and differential diagnostic problems
Energy Technology Data Exchange (ETDEWEB)
Krug, B; Lorenz, R; Steinbrich, W
1988-08-01
1. Numerous diseases may become manifest as eburnated vertebral bodies, and hence the X-ray morphological sign of eburnation is an unspecific one. Isolated characteristics such as the involvement of one or several vertebrae, an intact vertebral space, a broadening of the paravertebral accompanying shadow, and the remaining radiological skeletal status enable narrowing down the differential diagnosis, although anamnesis and clinical findings will supply the main pointers. 2. In primary tumorous eburnations radiotherapy or chemotherapy will render an X-ray morphological assessment of therapeutic success impossible. 3. In primary diagnosis of an eburnated vertebral body it is possible to apply sonography. CT and MR as diagnostic tools step by step to narrow down the differential diagnosis by detecting or excluding pathological abdominal processes such as liver or lymphatic node metastases, paravertebral or intraspinal soft-part dense space-occupying growths or bone infiltration, but it will only rarely be possible to classify the phenomenon properly as being caused by a well-defined process, even if CT and MR are employed.
Ferrari, Fabio; Lavagna, Michèle
2018-06-01
The design of formations of spacecraft in a three-body environment represents one of the most promising challenges for future space missions. Two or more cooperating spacecraft can greatly answer some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.
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
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/
Electron capture in proton collisions with alkali atoms as a three-body problem
International Nuclear Information System (INIS)
Avakov, G.V.; Blokhintsev, L.D.; Kadyrov, A.S.; Mukhamedzhanov, A.M.
1992-01-01
A previous paper proposed an approach to the calculation of electron transfer reactions in ion-atomic collisions based on the Faddeev three-body equations written in the Alt-Grassberger-Sandhas form. In the present work this approach is used to describe the electron capture in proton collisions with alkali atoms. The results of calculation of the total and partial cross sections for charge exchange in proton collisions with Li, Na, K and Rb atoms are presented. The calculated total cross sections are in good agreement with experiment for light target atoms. In going over to heavier targets, the theoretical total cross sections, while agreeing in form, tend to be larger than the experimental ones. The calculated partial cross sections for electron capture into the 2s state of the H atom are also in agreement with experiment. Some other partial cross sections were also calculated. (author)
Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
International Nuclear Information System (INIS)
Braden, H W; Enolski, V Z; Fedorov, Yu N
2013-01-01
We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve. (paper)
Study of stochastic approaches of the n-bodies problem: application to the nuclear fragmentation
International Nuclear Information System (INIS)
Guarnera, A.
1996-01-01
In the last decade nuclear physics research has found, with the observation of phenomena such as multifragmentation or vaporization, the possibility to get a deeper insight into the nuclear matter phase diagram. For example, a spinodal decomposition scenario has been proposed to explain the multifragmentation: because of the initial compression, the system may enter a region, the spinodal zone, in which the nuclear matter is no longer stable, and so any fluctuation leads to the formation of fragments. This thesis deals with spinodal decomposition within the theoretical framework of stochastic mean filed approaches, in which the one-body density function may experience a stochastic evolution. We have shown that these approaches are able to describe phenomena, such as first order phase transitions, in which fluctuations and many-body correlations plan an important role. In the framework of stochastic mean-filed approaches we have shown that the fragment production by spinodal decomposition is characterized by typical time scales of the order of 100 fm/c and by typical size scales around the Neon mass. We have also shown that these features are robust and that they are not affected significantly by a possible expansion of the system or by the finite size of nuclei. We have proposed as a signature of the spinodal decomposition some typical partition of the largest fragments. The study and the comparison with experimental data, performed for the reactions Xe + Cu at 45 MeV/A and Xe + Sn at 50 MeV/A, have shown a remarkable agreement. Moreover we would like to stress that the theory does not contain any adjustable parameter. These results seem to give a strong indication of the possibility to observe a spinodal decomposition of nuclei. (author)
Electronic structure of molecules using relativistic effective core potentials
International Nuclear Information System (INIS)
Hay, P.J.
1983-01-01
In this review an approach is outlined for studying molecules containing heavy atoms with the use of relativistic effective core potentials (RECP's). These potentials play the dual roles of (1) replacing the chemically-inert core electrons and (2) incorporating the mass velocity and Darwin term into a one-electron effective potential. This reduces the problem to a valence-electron problem and avoids computation of additional matrix elements involving relativistic operators. The spin-orbit effects are subsequently included using the molecular orbitals derived from the RECP calculation as a basis
International Nuclear Information System (INIS)
Bray, I.; Stelbovics, A.T.
1992-01-01
Convergence as a function of the number of states is studied and demonstrated for the Poet-Temkin model of electron-hydrogen scattering. In this Coulomb three-body problem only the l=0 partial waves are treated. By taking as many as thirty target states, obtained by diagonalizing the target Hamiltonian in a Laguerre basis, complete agreement with the smooth results of Poet is obtained at all energies. We show that the often-encountered pseudoresonance features in the cross sections are simply an indication of an inadequate target state representation
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
Relativistic transport theory for hadronic matter
International Nuclear Information System (INIS)
Shun-Jin Wang; Bao-An Li; Bauer, W.; Randrup, J.
1991-01-01
We derive coupled equations of motion for the density matrices for nucleons, Δ resonances, and π mesons, as well as for the pion--baryon interaction vertex function for the description of nuclear reactions at intermediate energies. We start from an effective hadronic Lagrangian density with minimal coupling between baryons and mesons. By truncating at the level of three-body correlations and using the G-matrix method to solve the equations of motion for the two-body correlation functions, a closed equation of motion for the one-body density matrices is obtained. A subsequent Wigner transformation then leads to a tractable set of relativistic transport equations for interacting nucleons, deltas, and pions. copyright 1991 Academic Press, Inc
Efficient solution of three-body quantum collision problems: Application to the Temkin-Poet model
International Nuclear Information System (INIS)
Jones, S.; Stelbovics, Andris T.
2002-01-01
We have developed a variable-spacing finite-difference algorithm that rapidly propagates the general solution of Schroedinger's equation to large distances (whereupon it can be matched to asymptotic solutions, including the ionization channel, to extract the desired scattering quantities). The present algorithm, when compared to Poet's corresponding fixed-spacing algorithm [R. Poet, J. Phys. B 13, 2995 (1980); S. Jones and A. T. Stelbovics, Phys. Rev. Lett. 84, 1878 (2000)], reduces storage by 98% and computation time by 99.98%. The method is applied to the Temkin-Poet electron-hydrogen model collision problem. Complete results (elastic, inelastic, and ionization) are obtained for low (17.6 eV), intermediate (27.2, 40.8, and 54.4 eV), and high (150 eV) impact energies
Four-body problem for four bound alpha particles in 16O
International Nuclear Information System (INIS)
Osman, A.
1980-02-01
The alpha cluster model is used in considering the 16 O nucleus as a bound state of four alpha particles. This problem is represented by integral equations which are exact effective two-particle equations. These equations have the form of two-particle Lippmann-Schwinger equations. The separable expressions are used in approximating the scattering amplitudes in the separable potential model to include also few and small non-separable rest parts of the interactions. The integral equations obtained are manageable and suitable for computations. Numerical calculations are carried out for the 16 O nucleus, with the structure of four bound alpha particles. The obtained binding energy of 16 O with that structure is 16.86 MeV which is in good agreement with the experimental value. (author)
The Schwinger variational principle in the quantum-mechanical three-body problem
International Nuclear Information System (INIS)
Podkopaev, A.P.; Subarev, A.I.; Wrzecionko, J.
1978-01-01
The Schwinger variational principle (SVP) is applied to problems of atomic (e + H scattering), mesoatomic (p(dμ) scattering) and nuclear (pion-deuteron scattering) physics. The convergence of the Schwinger variational iterative method is investigated. It is shown that in some cases there occurs a pathological convergence. It means that the iterative procedure is convergent, but not to the exact solution. The method of strong coupling of channels is reformulated on the basis of SVP. it permits the summation over all closed channels. The obtained equations are applied to the calculations of the low energy scattering parameters of the following processes: e + H → e + H; πd → πd. The dependence on πN scattering lengths and effective radii is investigated. It is shown that the contribution of closed channels to the π - d scattering length is 30 percent
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
Photoionization at relativistic energies
International Nuclear Information System (INIS)
Ionescu, D.C.; Technische Univ. Dresden; Soerensen, A.H.; Belkacem, A.
2000-11-01
At MeV energies and beyond the inner-shell vacancy production cross section associated with the photoelectric and Compton effect decrease with increasing photon energy. However, when the photon energy exceeds twice the rest energy of the electron, ionization of a bound electron may be catalyzed by the creation of an electron-positron pair. Distinctly different from all other known mechanisms for inner-shell vacancy production by photons, we show that the cross section for this ''vacuum-assisted photoionization'' increases with increasing photon energy and then saturates. As a main result, we predict that vacuum-assisted photoionization will dominate the other known photoionization mechanisms in the highly relativistic energy regime. (orig.)
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
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 plasma dispersion functions
International Nuclear Information System (INIS)
Robinson, P.A.
1986-01-01
The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived
International Nuclear Information System (INIS)
Feuvret, L.; Jammet, P.; Campana, F.; Cosset, J.M.; Fourquet, A.
1994-01-01
From december 1991 to september 1992, 20 patients due to receive total body irradiation (TBI) prior to allogeneic or autologous bone marrow transplantation were given granisetron (Kytril) in order to prevent intestinal (nausea and vomiting) early intolerance, TBI regimen was delivered on a fractional basis of six fractions, over 3 days. Twelve grays were delivered with a lung protection decreasing the pulmonary dose to 9 Gy Granisetron (3 mg) was administered by a 5-min intravenous infusion, 1 h before TBI. Up to two further infusions were given if nausea or vomiting occurred. The pretreatment perfusion was sufficient to prevent nausea and vomiting in 10/20 patients, one additional post-treatment perfusion was necessary in 7/20 patients, and two in 1/20 patients. In 2/20 cases, nausea and vomiting persisted in spite of three perfusions. Excellent or good efficacy was noted in 15/20 patients and a minor (or no) efficacy in five. Granisetron appears to be superior to the conventional anti emetic schemes to prevent nausea and vomiting in patients receiving TBI for bone marrow transplantation. 15 Refs
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.
International Nuclear Information System (INIS)
Kipping, David
2017-01-01
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.
Guzzo, Massimiliano; Lega, Elena
2018-06-01
The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.
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.
Van Oudenhove, Lukas; Cuypers, Stefaan E
2010-01-01
Parallel to psychiatry, "philosophy of mind" investigates the relationship between mind (mental domain) and body/brain (physical domain). Unlike older forms of philosophy of mind, contemporary analytical philosophy is not exclusively based on introspection and conceptual analysis, but also draws upon the empirical methods and findings of the sciences. This article outlines the conceptual framework of the "mind-body problem" as formulated in contemporary analytical philosophy and argues that this philosophical debate has potentially far-reaching implications for psychiatry as a clinical-scientific discipline, especially for its own autonomy and its relationship to neurology/neuroscience. This point is illustrated by a conceptual analysis of the five principles formulated in Kandel's 1998 article "A New Intellectual Framework for Psychiatry." Kandel's position in the philosophical mind-body debate is ambiguous, ranging from reductive physicalism (psychophysical identity theory) to non-reductive physicalism (in which the mental "supervenes" on the physical) to epiphenomenalist dualism or even emergent dualism. We illustrate how these diverging interpretations result in radically different views on the identity of psychiatry and its relationship with the rapidly expanding domain of neurology/neuroscience.
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 Poisson equation at second order in relativistic cosmology
International Nuclear Information System (INIS)
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.
2013-01-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field
Solar sail trajectory design in the Earth-Moon circular restricted three body problem
Das, Ashwati
The quest to explore the Moon has helped resolve scientific questions, has spurred leaps in technology development, and has revealed Earth's celestial companion to be a gateway to other destinations. With a renewed focus on returning to the Moon in this decade, alternatives to chemical propulsion systems are becoming attractive methods to efficiently use scarce resources and support extended mission durations. Thus, an investigation is conducted to develop a general framework, that facilitates propellant-free Earth-Moon transfers by exploiting sail dynamics in combination with advantageous transfer options offered in the Earth-Moon circular restricted multi-body dynamical model. Both periodic orbits in the vicinity of the Earth-Moon libration points, and lunar-centric long-term capture orbits are incorporated as target destinations to demonstrate the applicability of the general framework to varied design scanarios, each incorporating a variety of complexities and challenges. The transfers are comprised of three phases - a spiral Earth escape, a transit period, and, finally, the capture into a desirable orbit in the vicinity of the Moon. The Earth-escape phase consists of spiral trajectories constructed using three different sail steering strategies - locally optimal, on/off and velocity tangent. In the case of the Earth-libration point transfers, naturally occurring flow structures (e.g., invariant manifolds) arising from the mutual gravitational interaction of the Earth and Moon are exploited to link an Earth departure spiral with a destination orbit. In contrast, sail steering alone is employed to establish a link between the Earth-escape phase and capture orbits about the Moon due to a lack of applicable natural structures for the required connection. Metrics associated with the transfers including flight-time and the influence of operational constraints, such as occultation events, are investigated to determine the available capabilities for Earth
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.
Relativistic description of atomic nuclei
International Nuclear Information System (INIS)
Krutov, V.A.
1985-01-01
Papers on the relativistic description of nuclei are reviewed. The Brown and Rho ''small'' bag'' model is accepted for hardrons. Meson exchange potentials of the nucleon-nucleon interaction have been considered. Then the transition from a system of two interacting nucleons has been performed to the relativistic nucleus description as a multinucleon system on the basis of OBEP (one-boson exchange potential). The proboem of OPEP (one-pion-exchange potential) inclusion to a relativistic scheme is discussed. Simplicity of calculations and attractiveness of the Walecka model for specific computations and calculations was noted. The relativistic model of nucleons interacting through ''effective'' scalar and vector boson fields was used in the Walacka model for describing neutronaand nuclear mater matters
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
International Nuclear Information System (INIS)
Mani, B. K.; Angom, D.; Latha, K. V. P.
2009-01-01
We have carried out a detailed and systematic study of the correlation energies of inert gas atoms Ne, Ar, Kr, and Xe using relativistic many-body perturbation theory and relativistic coupled-cluster theory. In the relativistic coupled-cluster calculations, we implement perturbative triples and include these in the correlation energy calculations. We then calculate the dipole polarizability of the ground states using perturbed coupled-cluster theory.
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.
Relativistic gravitational potential and its relation to mass-energy
International Nuclear Information System (INIS)
Voracek, P.
1979-01-01
From the general theory of relativity a relation is deduced between the mass of a particle and the gravitational field at the position of the particle. For this purpose the fall of a particle of negligible mass in the gravitational field of a massive body is used. After establishing the relativistic potential and its relationship to the rest mass of the particle, we show, assuming conservation of mass-energy, that the difference between two potential-levels depends upon the value of the radial metric coefficient at the position of an observer. Further, it is proved that the relativistic potential is compatible with the general concept of the potential also from the standpoint of kinematics. In the third section it is shown that, although the mass-energy of a body is a function of the distance from it, this does not influence the relativistic potential of the body itself. From this conclusion it follows that the mass-energy of a particle in a gravitational field is anisotropic; isotropic is the mass only. Further, the possibility of an incidental feed-back between two masses is ruled out, and the law of the composition of the relativistic gravitational potentials is deduced. Finally, it is shown, by means of a simple model, that local inhomogeneities in the ideal fluid filling the Universe have negligible influence on the total potential in large regions. (orig.)
Relativistic heavy-ion physics
Herrera Corral, G
2010-01-01
The study of relativistic heavy-ion collisions is an important part of the LHC research programme at CERN. This emerging field of research focuses on the study of matter under extreme conditions of temperature, density, and pressure. Here we present an introduction to the general aspects of relativistic heavy-ion physics. Afterwards we give an overview of the accelerator facility at CERN and then a quick look at the ALICE project as a dedicated experiment for heavy-ion collisions.
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.
An introduction to relativistic hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Font, Jose A [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)
2007-11-15
We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, particularly within the test-fluid approximation but also for dynamical spacetimes. While such advances also hold true in the case of the MHD equations, the astrophysical applications investigated so far are still limited, yet the field is bound to witness major developments in the near future. The article also presents a brief overview of numerical techniques, providing state-of-the-art examples of their applicability to general relativistic fluids and magneto-fluids in characteristic scenarios of relativistic astrophysics.
Radiation dominated relativistic current sheets
International Nuclear Information System (INIS)
Jaroschek, C.H.
2008-01-01
Relativistic Current Sheets (RCS) feature plasma instabilities considered as potential key to magnetic energy dissipation and non-thermal particle generation in Poynting flux dominated plasma flows. We show in a series of kinetic plasma simulations that the physical nature of non-linear RCS evolution changes in the presence of incoherent radiation losses: In the ultra-relativistic regime (i.e. magnetization parameter sigma = 104 defined as the ratio of magnetic to plasma rest frame energy density) the combination of non-linear RCS dynamics and synchrotron emission introduces a temperature anisotropy triggering the growth of the Relativistic Tearing Mode (RTM). As direct consequence the RTM prevails over the Relativistic Drift Kink (RDK) Mode as competitive RCS instability. This is in contrast to the previously studied situation of weakly relativistic RCS (sigma ∼ 1) where the RDK is dominant and most of the plasma is thermalized. The simulations witness the typical life cycle of ultra-relativistic RCS evolving from a violent radiation induced collapse towards a radiation quiescent state in rather classical Sweet-Parker topology. Such a transition towards Sweet-Parker configuration in the late non-linear evolution has immediate consequences for the efficiency of magnetic energy dissipation and non-thermal particle generation. Ceasing dissipation rates directly affect our present understanding of non-linear RCS evolution in conventional striped wind scenarios. (author)
Relativistic theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1986-01-01
In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday--Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly fulfilled for the energy-moment and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just ''flat.'' This suggests that in the universe a ''missing mass'' should exist in a form of matter
Relativistic theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvilli, M.A.
1985-01-01
In the present paper a relativistic theory of gravitation (RTG) is constructed in a unique way on the basis of the special relativity and geometrization principle. In this, a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG, the conservation laws are strictly fulfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravitation. In virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTg leads to an exceptionally strong prediction: The Universe is not closed but just ''flat''. This suggests that in the Universe a ''hidden mass'' should exist in some form of matter
Relativistic gravitation theory
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1984-01-01
On the basis of the special relativity and geometrization principle a relativistic gravitation theory (RGT) is unambiguously constructed with the help of a notion of a gravitational field as a physical field in Faraday-Maxwell spirit, which posesses energy momentum and spins 2 and 0. The source of gravitation field is a total conserved energy-momentum tensor for matter and for gravitation field in Minkowski space. In the RGT conservation laws for the energy momentum and angular momentum of matter and gravitational field hold rigorously. The theory explains the whole set of gravitation experiments. Here, due to the geometrization principle the Riemannian space is of a field origin since this space arises effectively as a result of the gravitation field origin since this space arises effectively as a result of the gravitation field action on the matter. The RGT astonishing prediction is that the Universe is not closed but ''flat''. It means that in the Universe there should exist a ''missing'' mass in some form of matter
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
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.
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)
Focusing of relativistic electron bunch, moving in cylindrical plasma waveguide
International Nuclear Information System (INIS)
Amatuni, A.Ts.; Ehlbakyan, S.S.; Sekhpossyan, E.V.
1994-01-01
The problem on the focusing of electron bunches moving with the relativistic velocity along the axis of cylindrical overdense plasma waveguide with the conducting internal surface is considered. The existence of periodic and nonperiodic components of the fields, generated in the plasma is shown. The conditions of electron bunch self-focusing by transverse electrical field and azimuthal magnetic field are derived. The possibility of the acceleration and focusing of electron or positron bunches by driving electron bunch wake field is discussed. The conditions, when the bunch in plasma waveguide moves without wake fields generating are obtained, which could be of the interest for the transport of relativistic electron (positron) bunches. 5 refs
Quasi-relativistic effects in barrier-penetration processes
International Nuclear Information System (INIS)
Anchishkin, D.V.
1991-01-01
The problem of a particle tunneling through the potential barrier is solved within quasi-relativistic Schroedinger equation. It is shown that the subbarrier relativistic effects give a significant addition to penetration coefficient when some relations between parameters of the barrier and mass of a tunneling particle are satisfied. For instance an account of these effects for penetration of low energy π + -mesons through Coulomb barrier of the 298 U nuclei would give the increasing of penetration coefficient to 30 percent as compared to the nonrelativistic one. Also we give the criteria under which the contribution of the ''under barrier relativism'' to penetration coefficient becomes essential. 3 refs.; 6 figs. (author)
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
Relativistic positioning systems: perspectives and prospects
Coll Bartolomé
2013-11-01
Relativistic positioning systems are interesting technical objects for applications around the Earth and in the Solar system. But above all else, they are basic scientific objects allowing developing relativity from its own concepts. Some past and future features of relativistic positioning sys- tems, with special attention to the developments that they suggest for an epistemic relativity (relativistic experimental approach to physics), are analyzed. This includes relativistic stereometry, which, together with relativistic positioning systems, allows to introduce the general relativistic notion of (finite) laboratory (space-time region able to perform experiments of finite size).
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.
International Nuclear Information System (INIS)
Nissen, K.L.
1988-06-01
Two computer codes for the analysis of fuel rod behavior have been developed. Fuel rod mechanics is treated by a two-dimensional, axisymmetric finite element method. The program KONTAKT is used for detailed examinations on fuel rod sections, whereas the second program METHOD2D allows instationary calculations of whole fuel rods. The mechanical contact of fuel and cladding during heating of the fuel rod is very important for it's integrity. Both computer codes use a Newton-Raphson iteration for the solution of the nonlinear solid body contact problem. A constitutive equation is applied for the dependency of contact pressure on normal approach of the surfaces which are assumed to be rough. If friction is present on the contacting surfaces, Coulomb's friction law is used. Code validation is done by comparison with known analytical solutions for special problems. Results of the contact algorithm for an elastic ball pressing against a rigid surface are confronted with Hertzian theory. Influences of fuel-pellet geometry as well as influences of discretisation of displacements and stresses of a single fuel pellet are studied. Contact of fuel and cladding is calculated for a fuel rod section with two fuel pellets. The influence of friction forces between fuel and cladding on their axial expansion is demonstrated. By calculation of deformations and temperatures during an instationary fuel rod experiment of the CABRI-series the feasibility of two-dimensional finite element analysis of whole fuel rods is shown. (orig.) [de
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).
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
Relativistic ''potential model'' for N-particle systems
International Nuclear Information System (INIS)
Noyes, H.P.
1986-08-01
Neither quantum field theory nor S-Matrix theory have a well defined procedure for going over to an approximation that can be reliably used in non-relativistic models for nuclear physics. We meet the problem here by constructing a finite particle number relativistic scattering theory for (scalar) particles and mesons using integral equations of the Faddeev-Yakubovsky type. Restricted to N particles and one meson, we can go from the relativistic theory to a ''potential theory'' in the integral equation formulation by using boundary states which do not contain the meson asymptotically. The meson-particle input amplitudes contain a pole at the particle mass, and the particle-particle input amplitudes are null. This gives unique definition (numerically calculable) to the particle-particle off-shell amplitude, and hence to the covariant ''scattering potential'' (but not to the noninvariant concept of ''potential energy''). As we have commented before, if we take these scattering amplitudes as iput for relativistic Faddeev equations, the results are identical to those obtained from the same model starting from three particles and one meson. In this paper we explore how far we can extend this relativistic ''potential model'' to higher numbers of particles and mesons. 10 refs
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)
Development of the relativistic impulse approximation
International Nuclear Information System (INIS)
Wallace, S.J.
1985-01-01
This talk contains three parts. Part I reviews the developments which led to the relativistic impulse approximation for proton-nucleus scattering. In Part II, problems with the impulse approximation in its original form - principally the low energy problem - are discussed and traced to pionic contributions. Use of pseudovector covariants in place of pseudoscalar ones in the NN amplitude provides more satisfactory low energy results, however, the difference between pseudovector and pseudoscalar results is ambiguous in the sense that it is not controlled by NN data. Only with further theoretical input can the ambiguity be removed. Part III of the talk presents a new development of the relativistic impulse approximation which is the result of work done in the past year and a half in collaboration with J.A. Tjon. A complete NN amplitude representation is developed and a complete set of Lorentz invariant amplitudes are calculated based on a one-meson exchange model and appropriate integral equations. A meson theoretical basis for the important pair contributions to proton-nucleus scattering is established by the new developments. 28 references