On the Galilean Non-Invariance of Classical Electromagnetism

Science.gov (United States)

Preti, Giovanni; de Felice, Fernando; Masiero, Luca

2009-01-01

When asked to explain the Galilean non-invariance of classical electromagnetism on the basis of pre-relativistic considerations alone, students--and sometimes their teachers too--may face an impasse. Indeed, they often argue that a pre-relativistic physicist could most obviously have provided the explanation "at a glance", on the basis of the…

Anisotropic Weyl invariance

Energy Technology Data Exchange (ETDEWEB)

Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)

2017-07-15

We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)

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

Non-relativistic spinning particle in a Newton-Cartan background

Science.gov (United States)

Barducci, Andrea; Casalbuoni, Roberto; Gomis, Joaquim

2018-01-01

We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.

Poincaré invariance in low-energy EFTs for QCD

Directory of Open Access Journals (Sweden)

Hwang Sungmin

2017-01-01

Full Text Available We present the calculations on deriving constraints between the Wilson coefficients in non-relativistic quantum chromodynamics and potential non-relativistic quantum chromodynamics by exploiting the symmetry of its fundamental theory, Poincaré invariance in particular. Implications of the constraints are briefly discussed in the context of the effective string theory.

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.)

A new perspective on relativistic transformation for Maxwell's equations of electrodynamics

International Nuclear Information System (INIS)

Huang, Y.-S.

2009-01-01

A new scheme for relativistic transformation of the electromagnetic fields is formulated through relativistic transformation in the wavevector space, instead of the space-time space. Maxwell's equations of electrodynamics are shown to be form-invariant among inertial frames in accordance with this new scheme of relativistic transformation. This new perspective on relativistic transformation not only fulfills the principle of relativity, but is also compatible with quantum theory.

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)

Leading order relativistic chiral nucleon-nucleon interaction

Science.gov (United States)

Ren, Xiu-Lei; Li, Kai-Wen; Geng, Li-Sheng; Long, Bingwei; Ring, Peter; Meng, Jie

2018-01-01

Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the {}1S0 and {}3P0 phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta J≥slant 1, the relativistic results are almost the same as their leading order non-relativistic counterparts. )

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.

Canonical analysis of non-relativistic particle and superparticle

Energy Technology Data Exchange (ETDEWEB)

Kluson, Josef [Masaryk University, Department of Theoretical Physics and Astrophysics, Faculty of Science, Brno (Czech Republic)

2018-02-15

We perform canonical analysis of non-relativistic particle in Newton-Cartan Background. Then we extend this analysis to the case of non-relativistic superparticle in the same background. We determine constraints structure of this theory and find generator of κ-symmetry. (orig.)

A new perspective on relativistic transformation: formulation of the differential Lorentz transformation based on first principles

International Nuclear Information System (INIS)

Huang, Young-Sea

2010-01-01

The differential Lorentz transformation is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz transformation transforms physical quantities, instead of space-time coordinates, to keep laws of nature form-invariant among inertial frames. The new relativistic transformation fulfills the principle of relativity, whereas the usual Lorentz transformation of space-time coordinates does not. Furthermore, the new relativistic transformation is compatible with quantum mechanics. The formulation herein provides theoretical foundations for the differential Lorentz transformation as the fundamental relativistic transformation.

Relativistic quantum mechanics

CERN Document Server

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...

Quantum phase space for an ideal relativistic gas in d spatial dimensions

International Nuclear Information System (INIS)

Hayashi, M.; Vera Mendoza, H.

1992-01-01

We present the closed formula for the d-dimensional invariant phase-space integral for an ideal relativistic gas in an exact integral form. In the particular cases of the nonrelativistic and the extreme relativistic limits the phase-space integrals are calculated analytically. Then we consider the d-dimensional invariant phase space with quantum statistic and derive the cluster decomposition for the grand canonical and canonical partition functions as well as for the microcanonical and grand microcanonical densities of states. As a showcase, we consider the black-body radiation in d dimensions (Author)

Relativistic quantum kinetic analysis of a pion--nucleon system

International Nuclear Information System (INIS)

Alonso, J.D.

1985-01-01

A relativistic plasma of nucleons interacting through pions via the usual isospin-invariant Yukawa coupling is analyzed in the framework of the covariant Wigner function technique. The method is manifestly covariant and the temperature effects are considered. The relativistic quantum BBGKY hierarchy for the pion--nucleon system is derived. By generalizing the Bogolioubov analysis of the classical BBGKY hierarchy a non-perturbative renormalizable method is elaborated which allows the solution of the kinetic problem in form of power series of two cluster parameters which measure the importance of correlations. In the lowest order of the cluster expansion (Hartree approximation of zero-order approximation) the quasi-nucleon Fock space is introduced, the fermion Wigner function in the thermodynamic equilibrium is obtained and the vacuum effects are renormalized. In this approximation the plasma behaves as a perfect Fermi gas of nucleons and antinucleons, but there exists an abnormal configuration with a uniform pion condensate which is unstable. In the next approximation (quadratic in the small parameters) the quasi-pion dispersion relation is obtained and the vacuum polarization tensor is renormalized. The quasi-pion rest-mass spectra (''plasma frequency'') and the effective-coupling behaviour as functions of the thermodynamic state are given. By estimating the size of the cluster parameters the self-consistency of the approximation scheme is proved. The quasi-pion Fock space is introduced and the quasi-pion equilibrium Wigner function is obtained. From these results the problem of the higher-order corrections to the Hartree thermodynamics is outlined

CPT invariance and the spin-statistics connection

CERN Document Server

Bain, Jonathan

2016-01-01

This book seeks to answer the question "What explains CPT invariance and the spin-statistics connection?" These properties play foundational roles in relativistic quantum field theories (RQFTs), are supported by high-precision experiments, and figure into explanations of a wide range of phenomena, from antimatter, to the periodic table of the elements, to superconductors and superfluids. They can be derived in RQFTs by means of the famous CPT and Spin-Statistics theorems; but, the author argues, these theorems cannot be said to explain these properties, at least under standard philosophical accounts of scientific explanation. This is because there are multiple, in some cases incompatible, ways of deriving these theorems, and, secondly, because the theorems fail for the types of theories that underwrite the empirical evidence: non-relativistic quantum theories, and realistic interacting RQFTs. The goal of this book is to work towards an understanding of CPT invariance and the spin-statistics connection by firs...

Slow feature analysis: unsupervised learning of invariances.

Science.gov (United States)

Wiskott, Laurenz; Sejnowski, Terrence J

2002-04-01

Invariant features of temporally varying signals are useful for analysis and classification. Slow feature analysis (SFA) is a new method for learning invariant or slowly varying features from a vectorial input signal. It is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative. It is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features, which are ordered by their degree of invariance. SFA can be applied hierarchically to process high-dimensional input signals and extract complex features. SFA is applied first to complex cell tuning properties based on simple cell output, including disparity and motion. Then more complicated input-output functions are learned by repeated application of SFA. Finally, a hierarchical network of SFA modules is presented as a simple model of the visual system. The same unstructured network can learn translation, size, rotation, contrast, or, to a lesser degree, illumination invariance for one-dimensional objects, depending on only the training stimulus. Surprisingly, only a few training objects suffice to achieve good generalization to new objects. The generated representation is suitable for object recognition. Performance degrades if the network is trained to learn multiple invariances simultaneously.

Relativistic density matrix in the diagonal momentum representation. Bose-gas

International Nuclear Information System (INIS)

Makhlin, A.N.; Sinyukov, Yu.M.

1984-01-01

The relativistic-invariance treatment of the ideal Bose-system arising from the diagonal momentum representation for the density matrix is developed. The average occupation members and their correlators for statistical systems in arbitrary inertial frames are found on the equal-time hypersurfaces. The relativistic partition function method for the calculation of thermodynamic properties of gases moving as a whole is constructed

Classical and relativistic dynamics of supersolids: variational principle

International Nuclear Information System (INIS)

Peletminskii, A S

2009-01-01

We present a phenomenological Lagrangian and Poisson brackets for obtaining nondissipative hydrodynamic theory of supersolids. A Lagrangian is constructed on the basis of unification of the principles of non-equilibrium thermodynamics and classical field theory. The Poisson brackets, governing the dynamics of supersolids, are uniquely determined by the invariance requirement of the kinematic part of the found Lagrangian. The generalization of Lagrangian is discussed to include the dynamics of vortices. The obtained equations of motion do not account for any dynamic symmetry associated with Galilean or Lorentz invariance. They can be reduced to the original Andreev-Lifshitz equations to require Galilean invariance. We also present a relativistic-invariant supersolid hydrodynamics, which might be useful in astrophysical applications

Sensitivity of relativistic impulse approximation proton-nucleus elastic scattering calculations on relativistic mean-field parameterizations

International Nuclear Information System (INIS)

Hojsik, M.; Gmuca, S.

1998-01-01

Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use

OPE convergence in non-relativistic conformal field theories

Energy Technology Data Exchange (ETDEWEB)

Goldberger, Walter D.; Khandker, Zuhair University; Prabhu, Siddharth [Department of Physics, Yale University,New Haven, CT 06511 (United States); Physics Department, Boston University,Boston, MA 02215 (United States)

2015-12-09

Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NRCFT, in particular the mapping between operators and states in a non-relativistic “radial quantization” Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2,d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.

Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum

Directory of Open Access Journals (Sweden)

Ольга Юрьевна Хецелиус

2014-11-01

Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.

A Comprehensive Comparison of Relativistic Particle Integrators

Science.gov (United States)

Ripperda, B.; Bacchini, F.; Teunissen, J.; Xia, C.; Porth, O.; Sironi, L.; Lapenta, G.; Keppens, R.

2018-03-01

We compare relativistic particle integrators commonly used in plasma physics, showing several test cases relevant for astrophysics. Three explicit particle pushers are considered, namely, the Boris, Vay, and Higuera–Cary schemes. We also present a new relativistic fully implicit particle integrator that is energy conserving. Furthermore, a method based on the relativistic guiding center approximation is included. The algorithms are described such that they can be readily implemented in magnetohydrodynamics codes or Particle-in-Cell codes. Our comparison focuses on the strengths and key features of the particle integrators. We test the conservation of invariants of motion and the accuracy of particle drift dynamics in highly relativistic, mildly relativistic, and non-relativistic settings. The methods are compared in idealized test cases, i.e., without considering feedback onto the electrodynamic fields, collisions, pair creation, or radiation. The test cases include uniform electric and magnetic fields, {\\boldsymbol{E}}× {\\boldsymbol{B}} fields, force-free fields, and setups relevant for high-energy astrophysics, e.g., a magnetic mirror, a magnetic dipole, and a magnetic null. These tests have direct relevance for particle acceleration in shocks and in magnetic reconnection.

Kinetic analysis of thermally relativistic flow with dissipation

International Nuclear Information System (INIS)

Yano, Ryosuke; Suzuki, Kojiro

2011-01-01

Nonequilibrium flow of thermally relativistic matter with dissipation is considered in the framework of the relativistic kinetic theory. As an object of the analysis, the supersonic rarefied flow of thermally relativistic matter around the triangle prism is analyzed using the Anderson-Witting model. Obtained numerical results indicate that the flow field changes in accordance with the flow velocity and temperature of the uniform flow owing to both effects derived from the Lorentz contraction and thermally relativistic effects, even when the Mach number of the uniform flow is fixed. The profiles of the heat flux along the stagnation streamline can be approximated on the basis of the relativistic Navier-Stokes-Fourier (NSF) law except for a strong nonequilibrium regime such as the middle of the shock wave and the vicinity of the wall, whereas the profile of the heat flux behind the triangle prism cannot be approximated on the basis of the relativistic NSF law owing to rarefied effects via the expansion behind the triangle prism. Additionally, the heat flux via the gradient of the static pressure is non-negligible owing to thermally relativistic effects. The profile of the dynamic pressure is different from that approximated on the basis of the NSF law, which is obtained by the Eckart decomposition. Finally, variations of convections of the mass and momentum owing to the effects derived from the Lorentz contraction and thermally relativistic effects are numerically confirmed.

Proof of the relativistic covariance of the fermion Green function in QED

International Nuclear Information System (INIS)

Nguyen Suan Han.

1995-02-01

This paper is devoted to the calculation of the fermion Green function in QED in the framework of the Minimal Quantization Method, based on an explicit solution of the constraint equations and the gauge-invariance principle. The relativistic invariant expression for the fermion Green function which has the right analytical properties is obtained. (author). 24 refs

The Post-Newtonian Approximation for Relativistic Compact Binaries

Directory of Open Access Journals (Sweden)

Futamase Toshifumi

2007-03-01

Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.

Relativistic dynamical reduction models: General framework and examples

International Nuclear Information System (INIS)

Ghirardi, G.C.; Grassi, R.

1990-04-01

The formulation of a relativistic theory of statevector reduction is proposed and analyzed, and its conceptual consequences are elucidated. In particular, a detailed discussion of stochastic invariance and of local and nonlocal aspects at the level of individual systems is presented. (author). 35 refs, 5 figs

Three-body forces mandated by Poincare invariance

International Nuclear Information System (INIS)

Coester, F.

1986-01-01

Poincare invariant models for the three-nucleon system are examined which have the same heuristic relation to field theories as the nonrelativistic nuclear models. The generators of the infinitesimal dynamical transformations can be obtained as functions of the kinematic generators, the invariant mass operator of the interacting system, and additional operators. These additional operators are the components of the Newton-Wigner position operator in the instant form, and the transverse components of the spin in the front form. The relativistic dynamics of Poincare transformations is examined, and then these concepts are applied to two-nucleon systems. The transition to a fully interacting three-nucleon system is made

Relativistic and non-relativistic studies of nuclear matter

NARCIS (Netherlands)

Banerjee, MK; Tjon, JA

2002-01-01

We point out that the differences between the results of the non-relativistic lowest order Brueckner theory (LOBT) and the relativistic Dirac-Brueckner analysis predominantly arise from two sources. Besides effects from a nucleon mass modification M* in nuclear medium we have in a relativistic

Non-Noether Conserved Quantity for Relativistic Nonholonomic System with Variable Mass

International Nuclear Information System (INIS)

Qiao Yongfen; Li Renjie; Ma Yongsheng

2005-01-01

Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Path integral for a relativistic-particle theory

International Nuclear Information System (INIS)

Fradkin, E.S.; Gitman, D.M.; Shvartsman, S.M.

1991-01-01

An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + ∞ limits

Hiding Lorentz invariance violation with MOND

International Nuclear Information System (INIS)

Sanders, R. H.

2011-01-01

Horava-Lifshitz gravity is an attempt to construct a renormalizable theory of gravity by breaking the Lorentz invariance of the gravitational action at high energies. The underlying principle is that Lorentz invariance is an approximate symmetry and its violation by gravitational phenomena is somehow hidden to present limits of observational precision. Here I point out that a simple modification of the low-energy limit of Horava-Lifshitz gravity in its nonprojectable form can effectively camouflage the presence of a preferred frame in regions where the Newtonian gravitational field gradient is higher than cH 0 ; this modification results in the phenomenology of modified Newtonian dynamics (MOND) at lower accelerations. As a relativistic theory of MOND, this modified Horava-Lifshitz theory presents several advantages over its predecessors.

Invariant subspaces

CERN Document Server

Radjavi, Heydar

2003-01-01

This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,

What’s hampering measurement invariance: Detecting non-invariant items using clusterwise simultaneous component analysis

Directory of Open Access Journals (Sweden)

Kim eDe Roover

2014-06-01

Full Text Available The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA framework, methods have been proposed to trace such non-invariant items, but these methods have some disadvantages in that they require researchers to run a multitude of analyses and in that they imply assumptions that are often questionable. In this paper, we propose an alternative strategy which builds on clusterwise simultaneous component analysis (SCA. Clusterwise SCA, being an exploratory technique, assigns the groups under study to a few clusters based on differences and similarities in the covariance matrices, and thus based on the component structure of the items. Non-invariant items can then be traced by comparing the cluster-specific component loadings via congruence coefficients, which is far more parsimonious than comparing the component structure of all separate groups. In this paper we present a heuristic for this procedure. Afterwards, one can return to the multigroup CFA framework and check whether removing the non-invariant items or removing some of the equality restrictions for these items, yields satisfactory invariance test results. An empirical application concerning cross-cultural emotion data is used to demonstrate that this novel approach is useful and can co-exist with the traditional CFA approaches.

Exact quantisation of the relativistic Hopfield model

Energy Technology Data Exchange (ETDEWEB)

Belgiorno, F., E-mail: francesco.belgiorno@polimi.it [Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo 32, IT-20133 Milano (Italy); INdAM-GNFM (Italy); Cacciatori, S.L., E-mail: sergio.cacciatori@uninsubria.it [Department of Science and High Technology, Università dell’Insubria, Via Valleggio 11, IT-22100 Como (Italy); INFN sezione di Milano, via Celoria 16, IT-20133 Milano (Italy); Dalla Piazza, F., E-mail: f.dallapiazza@gmail.com [Università “La Sapienza”, Dipartimento di Matematica, Piazzale A. Moro 2, I-00185, Roma (Italy); Doronzo, M., E-mail: m.doronzo@uninsubria.it [Department of Science and High Technology, Università dell’Insubria, Via Valleggio 11, IT-22100 Como (Italy)

2016-11-15

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

Path integral for a relativistic-particle theory

Energy Technology Data Exchange (ETDEWEB)

Fradkin, E.S. (AN SSSR, Moscow (SU)); Gitman, D.M. (Moskovskij Inst. Radiotekhniki, Ehlektroniki i Automatiki, Moscow (SU)); Shvartsman, S.M. (Tomskij Pedagogicheskij Inst., Tomsk (SU))

1991-06-01

An action of a relativistic spinning particle written in reparametrization and local super-invariant form is consistently determined by using the path integral representation for the Green's function of the spinor field. It is shown that, to obtain the causal propagator, the integration over the null mode of the onebein variable must be performed in the (0, + {infinity}) limits.

Supersymmetric solutions for non-relativistic holography

International Nuclear Information System (INIS)

Donos, Aristomenis; Gauntlett, Jerome P.

2009-01-01

We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z≥4 and z≥3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)

All-sky analysis of the general relativistic galaxy power spectrum

Science.gov (United States)

Yoo, Jaiyul; Desjacques, Vincent

2013-07-01

We perform an all-sky analysis of the general relativistic galaxy power spectrum using the well-developed spherical Fourier decomposition. Spherical Fourier analysis expresses the observed galaxy fluctuation in terms of the spherical harmonics and spherical Bessel functions that are angular and radial eigenfunctions of the Helmholtz equation, providing a natural orthogonal basis for all-sky analysis of the large-scale mode measurements. Accounting for all the relativistic effects in galaxy clustering, we compute the spherical power spectrum and its covariance matrix and compare it to the standard three-dimensional power spectrum to establish a connection. The spherical power spectrum recovers the three-dimensional power spectrum at each wave number k with its angular dependence μk encoded in angular multipole l, and the contributions of the line-of-sight projection to galaxy clustering such as the gravitational lensing effect can be readily accommodated in the spherical Fourier analysis. A complete list of formulas for computing the relativistic spherical galaxy power spectrum is also presented.

Global operator expansions in conformally invariant relativistic quantum field theory

International Nuclear Information System (INIS)

Schoer, B.; Swieca, J.A.; Voelkel, A.H.

1974-01-01

A global conformal operator expansions in the Minkowski region in several models and their formulation in the general theory is presented. Whereas the vacuum expansions are termwise manisfestly conformal invariant, the expansions away from the vacuum do not share this property

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)

Report of seminar on relativistic approach to nuclear reaction and nuclear structure

International Nuclear Information System (INIS)

1986-05-01

A seminar on 'Relativistic Approach to Nuclear Reaction and Nuclear Structure' was held in 1985 at Osaka University. This booklet includes twenty-four reports given at the seminar, which deal with: Conventional Nonrelativistic Description of Nuclear Matter and Nuclear Spin-Orbit Interactions; Relativistic Approach to Nuclear Structure; Atomic and Molecular Structure Calculations; Electromagnetic Interaction in Nucleus and Relativistic Effect; Nuclear Magnetic Moment in the Relativistic Mean Field Theory, Effective Mass and Particle-Vibration Coupling in the Relativistic σ-ω Model; Gauge Invariance in Relativistic Many-Body Theory; Relativistic Description of Nucleon-Nucleon Interaction in Review; σ-Particle in NN Interaction; Nuclear Optical Potentials Based on the Brueckner-Hartree-Fock Approach; Elastic Backscattering and Optical Potential; Description of Intermediate-Energy Nuclear Reactions; Dirac Phenomenology at E(p) = 65 MeV; Relativistic Impulse Approximation; Reaction Studies with Intermediate Energy Deuterons at SATURNE; Folding Model for Intermediate-Energy Deutron Scattering; Folding Model for Polarized Deutron Scattering at 700 MeV; Dirac Approach Problems and a Different Viewpoint; Relativistic Approach and EMC Effect; Quasielastic Electron Scattering; Response Function of Quasielastic Electron Scattering; Relativistic Hartree Response Function for Quasielastic Electron Scattering on 12 C and 40 Ca; Backflow-, Retardation- and Relativistic Effects on the Longitudinal Response Function of Nuclear Matter; Pion-Photoproduction in the σ-ω Model. (Nogami, K.)

The first Donaldson invariant as the winding number of a Nicolai map

International Nuclear Information System (INIS)

Mansfield, P.

1988-01-01

The authors show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

Science.gov (United States)

Klink, William H.; Schweiger, Wolfgang

2018-03-01

This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

Relativistic U(3) symmetry and pseudo-U(3) symmetry of the Dirac Hamiltonian

International Nuclear Information System (INIS)

Ginocchio, Joseph N.

2010-01-01

The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry of the Dirac Hamiltonian. The spin limit occurs when the scalar potential is equal to the vector potential plus a constant, and the pseudospin limit occurs when the scalar potential is equal in magnitude but opposite in sign to the vector potential plus a constant. Like the non-relativistic harmonic oscillator, each of these limits has a higher symmetry. For example, for the spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3) symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of these two limits and derive the relativistic generators for the U(3) and pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a nucleus, the spectrum will have approximate spin and U(3) symmetry.

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.

Relativistic implications of the quantum phase

International Nuclear Information System (INIS)

Low, Stephen G

2012-01-01

The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics. We put aside the relativistic symmetry and show that the maximal quantum symmetry that leaves the Heisenberg commutation relations invariant is the projective representations of the conformally scaled inhomogeneous symplectic group. The Weyl-Heisenberg group and noncommutative structure arises directly because the quantum phase requires projective representations. We then consider the relativistic implications of the quantum phase that lead to the Born line element and the projective representations of an inhomogeneous unitary group that defines a noninertial quantum theory. (Understanding noninertial quantum mechanics is a prelude to understanding quantum gravity.) The remarkable properties of this symmetry and its limits are studied.

First quantized noncritical relativistic Polyakov string

International Nuclear Information System (INIS)

Jaskolski, Z.; Meissner, K.A.

1994-01-01

The first quantization of the relativistic Brink-DiVecchia-Howe-Polyakov (BDHP) string in the range 1 < d 25 is considered. It is shown that using the Polyakov sum over bordered surfaces in the Feynman path integral quantization scheme one gets a consistent quantum mechanics of relativistic 1-dim extended objects in the range 1 < d < 25. In particular, the BDHP string propagator is exactly calculated for arbitrary initial and final string configurations and the Hilbert space of physical states of noncritical BDHP string is explicitly constructed. The resulting theory is equivalent to the Fairlie-Chodos-Thorn massive string model. In contrast to the conventional conformal field theory approach to noncritical string and random surfaces in the Euclidean target space the path integral formulation of the Fairlie-Chodos-Thorn string obtained in this paper does not rely on the principle of conformal invariance. Some consequences of this feature for constructing a consistent relativistic string theory based on the ''splitting-joining'' interaction are discussed. (author). 42 refs, 1 fig

A gauge model describing N relativistic particles bound by linear forces

International Nuclear Information System (INIS)

Filippov, A.T.

1988-01-01

A relativistic model of N particles bound by linear forces is obtained by applying the gauging procedure to the linear canonical symmteries of a simple (rudimentary) nonrelativistic N-particle Lagrangian extended to relativistic phase space. The new (gauged) Lagrangian is formally Poincare invariant, the Hamiltonian is a linear combination of first-class constraints which are closed with respect to Pisson brackets and generate the localized canonical symmteries. The gauge potentials appear as the Lagrange multipliers of the constraints. Gauge fixing and quantization of the model are also briefly discussed. 11 refs

General relativistic chaos and nonlinear dynamics

Energy Technology Data Exchange (ETDEWEB)

Barrow, J D [California Univ., Berkeley (USA). Dept. of Physics

1982-06-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations.

General relativistic chaos and nonlinear dynamics

International Nuclear Information System (INIS)

Barrow, J.D.

1982-01-01

How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations. (author)

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

Energy Technology Data Exchange (ETDEWEB)

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' or ''dressing'' of these parameters to connect them to the boundary states.

Nucleon-nucleus inelastic scattering using a relativistic impulse approximation with exchange

International Nuclear Information System (INIS)

Rost, E.; Shepard, J.R.

1987-01-01

We formulate a microscopic relativistic treatment of nucleon-nucleus inelastic scattering in a distorted wave impulse approximation. The interaction is taken from a Lorentz invariant formulation with explicit direct and exchange terms constrained by fitting to experimental NN amplitudes. This procedure allows us to apply the theory in the lower range of intermediate energies (100--400 MeV) where exchange effects are likely to be important. Application to inelastic scattering uses this interaction for both the distorting potentials and the transition interaction. Effects of explicit exchange are studied and a preliminary analysis of /sup 12/C(p,p') data is presented

Exact solutions of the dirac equation for an electron in magnetic field with shape invariant method

International Nuclear Information System (INIS)

Setare, M.R.; Hatami, O.

2008-01-01

Based on the shape invariance property we obtain exact solutions of the Virac equation for an electron moving in the presence of a certain varying magnetic Geld, then we also show its non-relativistic limit. (authors)

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

Energy Technology Data Exchange (ETDEWEB)

Wu, Kailiang [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn [HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)

2017-01-01

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.

Basic Theory of Fractional Conformal Invariance of Mei Symmetry and its Applications to Physics

Science.gov (United States)

Luo, Shao-Kai; Dai, Yun; Yang, Ming-Jing; Zhang, Xiao-Tian

2018-04-01

In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method's applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry.

3D Product authenticity model for online retail: An invariance analysis

Directory of Open Access Journals (Sweden)

Algharabat, R.

2010-01-01

Full Text Available This study investigates the effects of different levels of invariance analysis on three dimensional (3D product authenticity model (3DPAM constructs in the e- retailing context. A hypothetical retailer website presents a variety of laptops using 3D product visualisations. The proposed conceptual model achieves acceptable fit and the hypothesised paths are all valid. We empirically investigate the invariance across the subgroups to validate the results of our 3DPAM. We concluded that the 3D product authenticity model construct was invariant for our sample across different gender, level of education and study backgrounds. These findings suggested that all our subgroups conceptualised the 3DPAM similarly. Also the results show some non-invariance results for the structural and latent mean models. The gender group posits a non-invariance latent mean model. Study backgrounds group reveals a non-invariance result for the structural model. These findings allowed us to understand the 3DPAMs validity in the e-retail context. Managerial implications are explained.

Anomalous magnetohydrodynamics in the extreme relativistic domain

CERN Document Server

Giovannini, Massimo

2016-01-01

The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physic...

Gauge-invariant formalism of cosmological weak lensing

Science.gov (United States)

Yoo, Jaiyul; Grimm, Nastassia; Mitsou, Ermis; Amara, Adam; Refregier, Alexandre

2018-04-01

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer rest-frame. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.

A note on Fujikawa's method of determining the critical dimension of the relativistic string

International Nuclear Information System (INIS)

Petcher, D.N.; Holten, J.W. van.

1987-04-01

Fujikawa's derivation of the critical dimension of the relativistic string in the path integral formulation is reconsidered. It is shown that the correct prescription for choosing the functional measure is obtained by requiring standard BRST-invariance without modifications and that Fujikawa's choice of measure is not unique. We find a one-parameter family of BRST-invariant measures even after fixing a gauge for local Weyl rescalings. Gauge independence of the resulting theory is demonstrated in the critical number of dimensions. 13 refs

On the Relativistic Origin of Pseudo spin Symmetry in Nuclei

International Nuclear Information System (INIS)

Leviatan, A.

1998-01-01

We review the concept of pseudo spin symmetry and its role in nuclear spectroscopy. We survey the attempts to arrive at a microscopic understanding of this symmetry. In particular, we show that pseudo spin symmetry in nuclei could arise from nucleons moving in a relativistic mean field which has an attractive scalar (Vs) and repulsive vector (Vv) potential nearly equal in magnitude but opposite in sign. We show that the generators of pseudo spin symmetry are the non-relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with Vs 2= -Vv. Furthermore within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials

Study of the equations of a particle in Non- Relativistic Quantum Mechanics

International Nuclear Information System (INIS)

Miltao, Milton Souza Ribeiro; Silva, Vanessa Santos Teles da

2011-01-01

Full text: The study of group theory is relevant to the treatment of physical problems, in which concepts of invariance and symmetry are important. In the field of Non-Relativistic Quantum Mechanics, we can do algebraic considerations taking into account the principles of symmetry, considering the framework of the study of Galileo transformations, which have characteristics of group. Therefore, we discuss the Stern-Gerlach experiment that had the historical importance of demonstrating that the electron has an intrinsic angular momentum. Through discussion of this experiment, we found that the spin appears in Non-Relativistic Quantum Mechanics as a feature of the algebraic structure underlying any physical theory represented by a group. From these studies, we have algebraic considerations for physical systems in non-relativistic domain, which are described by the Schroedinger and Pauli equations, describing the dynamics of particles of spin zero and 1/2 respectively, taking into account the structure of the transformations Galileo. Due to the operatorial, we represent Galileo's transformations by matrices by choosing an appropriate basis of space-time. Using these arrays, we saw group characteristics associated with these transformations, which we call the Galileo Group. We note the invariance of the Schroedinger and Pauli equations after these changes, as well as the physical state associated with it, which is represented by a radius vector in Hilbert space. (author)

Relativistic density matrix in the diagonal momentum representation. Fermi-gas

International Nuclear Information System (INIS)

Makhlin, A.N.; Sinyukov, Yu.M.

1984-01-01

The relativistically invariant theory of ideal Fermi-gas is built in the framework of the quantum field theory. The average occupation numbers and correlation functions of statistical systems are found on the equal-time surfaces of arbitrary inertial frames. The effects of anisotropy in their behaviour are pointed out. The partition function method is developed to calculate the thermodynamic quantities of Fermi-gases moving as a whole

cDNA cloning and primary structure analysis of invariant chain in ...

African Journals Online (AJOL)

cDNA cloning and primary structure analysis of invariant chain in Chinese Pengze crucian carp. X Liu, W Yu, J Li, F Chen, S Liu, C Wu, J Xu. Abstract. Invariant chain (Ii) plays an important role in MHC class II molecules assembly and exogenous peptide presentation in vertebrates. Although mammalian Ii has been ...

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

Holographic stress tensor for non-relativistic theories

International Nuclear Information System (INIS)

Ross, Simon F.; Saremi, Omid

2009-01-01

We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schroedinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schroedinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

Second order gauge invariant measure of a tidally deformed black hole

Energy Technology Data Exchange (ETDEWEB)

Ahmadi, Nahid, E-mail: nahmadi@ut.ac.ir [Department of Physics, University of Tehran, Kargar Avenue North, Tehran 14395-547 (Iran, Islamic Republic of)

2012-08-01

In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory is also discussed. The developments of this paper is a logical continuation of the calculations presented in [1], in which the first order coordinate dependance of the intrinsic and exterinsic geometry of the horizon is examined and the first order gauge invariance of the intrinsic geometry of the horizon is shown. In context of second order perturbation theory, It is shown that the rate of the expansion of the congruence of the horizon generators is invariant under a second order reparametrization; so it can be considered as a measure of tidal perturbation. A generally non-vanishing expression for this observable, which accomodates tidal perturbations and implies nonlinear response of the horizon, is also presented.

Some consequences of the Fourier analysis on the Lorentz group for relativistic quantum mechanics

International Nuclear Information System (INIS)

Mavrodiev, S.Ch.

1974-01-01

On the basis of the analogy between the nonrelativistic and relativistic Fourier analysis the uncertainty relation for rapidity and relativistic relative coordinate is formaly derived. A geometricla interpretation of the behaviour of the elastic scattering differential cross section is given too

Lorentz-invariant Bell's inequality

International Nuclear Information System (INIS)

Kim, Won Tae; Son, Edwin J.

2005-01-01

We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox in the relativistic regime. For this purpose, a relativistically covariant analysis is used in the calculation of the Bell's inequality, which results in the maximally violated Bell's inequality in any reference frame

The evolving Planck mass in classically scale-invariant theories

Energy Technology Data Exchange (ETDEWEB)

Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H. [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia)

2017-04-05

We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

The evolving Planck mass in classically scale-invariant theories

Science.gov (United States)

Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H.

2017-04-01

We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

Curci-Ferrari-type condition in Hamiltonian formalism: A free spinning relativistic particle

Science.gov (United States)

Shukla, A.; Bhanja, T.; Malik, R. P.

2013-03-01

The Curci-Ferrari (CF)-type restriction emerges in the description of a free spinning relativistic particle within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of the horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of the superfield formalism. We show that the above CF condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.

Relativistic hydrodynamics in the presence of puncture black holes

International Nuclear Information System (INIS)

Faber, Joshua A.; Etienne, Zachariah B.; Shapiro, Stuart L.; Taniguchi, Keisuke; Baumgarte, Thomas W.

2007-01-01

Many of the recent numerical simulations of binary black holes in vacuum adopt the moving puncture approach. This successful approach avoids the need to impose numerical excision of the black hole interior and is easy to implement. Here we wish to explore how well the same approach can be applied to moving black hole punctures in the presence of relativistic hydrodynamic matter. First, we evolve single black hole punctures in vacuum to calibrate our Baumgarte-Shapiro-Shibata-Nakamura implementation and to confirm that the numerical solution for the exterior spacetime is invariant to any junk (i.e., constraint-violating) initial data employed in the black hole interior. Then we focus on relativistic Bondi accretion onto a moving puncture Schwarzschild black hole as a numerical test bed for our high-resolution shock-capturing relativistic hydrodynamics scheme. We find that the hydrodynamical equations can be evolved successfully in the interior without imposing numerical excision. These results help motivate the adoption of the moving puncture approach to treat the binary black hole-neutron star problem using conformal thin-sandwich initial data

Asymptotics of pion electromagnetics form factor in scale invariant quark model

International Nuclear Information System (INIS)

Efremov, A.V.; Radyushkin, A.V.

1976-01-01

A consistent relativistic approach is proposed to the investigation of asymptotic behaviour of form factor of a system, composed of two spinor particles, interacting with the vector of (pseudo) scalar neutral field. It is shown that the assumption of finite and small asymptotical value of quark-gluon interaction invariant charge at small distances (g 9 2 9 2 ln(-Q 2 ) 2 values (Q 2 is squared momentum)

On the theory of waves in Chew-Goldberger-Low relativistic magnetohydrodynamics

International Nuclear Information System (INIS)

Shikin, I.S.

1976-01-01

A relativistic invariant form of equations of the Chew-Goldberger-Low magnetic hydrodynamics with longitudinal and transverse pressures has been considered. Fundamental equations, nonlinear riemann waves and ratios on nonremovable discontinuities have been studied. The evolution conditions and the discontinuities ''switching on'' and ''switching off'' the transverse magnetic field have been discussed; a possible presence of jumps is shown after which the transverse pressure decreases

Foldy-Wouthuysen transformations for the classical relativistic electron. Non grassmannian description

International Nuclear Information System (INIS)

Pupasov-Maksimov, Andrey; Deriglazov, Alexei

2012-01-01

Full text: We consider a classical model of the relativistic electron proposed by A. Deriglazov in Phys. Lett. A 376 (2012) 309-313. Though this model contains only bosonic variables, its quantization leads to the Dirac equation and one-particle relativistic quantum mechanics of the electron. There are constraints and gauge symmetries, therefore 18 initial variables of the model {x μ , p μ , ω A , π A }, μ is an element of (0,4), A is an element of (0,5) do not correspond to the observable quantities. There are 10 physical degrees of freedom implying another set of 10 gauge invariant variables which will be interpreted as physically observable quantities. On the other hand, to have a consistent one-particle relativistic quantum mechanics one has to consider only even operators which do not mix quantum states with positive and negative energy states. Such separation can be obtained with the Foldy-Wouthuysen transformation and leads to the Foldy-Wouthuysen representation with new operators for coordinates and spin (so-called Newton-Wigner coordinates). In the present work we match these to pictures by comparing the choice of the gauge invariant classical variables and the transition to the even operators in the quantum mechanics. We study different canonical transformations of this classical model in order to separate the set of observable quantities from variables with ambiguous dynamics. The constraints of the model in the case of free particle can be chosen in such a way that the Dirac brackets coincide with the Poisson brackets. This choice significantly simplify calculations of transformed variables. Moreover, new variables are canonical variables by construction. It is shown that the following generator of an infinitesimal canonical transformation S=1/2J 5j p j A(p 2 ), can be associated with the Foldy-Wouthuysen transformation. Thus we obtain a classical analog of the Foldy- Wouthuysen transformation. Moreover, the gauge invariant variables in the

What's hampering measurement invariance : Detecting non-invariant items using clusterwise simultaneous component analysis

NARCIS (Netherlands)

De Roover, K.; Timmerman, Marieke; De Leersnyder, J.; Mesquita, B.; Ceulemans, Eva

2014-01-01

The issue of measurement invariance is ubiquitous in the behavioral sciences nowadays as more and more studies yield multivariate multigroup data. When measurement invariance cannot be established across groups, this is often due to different loadings on only a few items. Within the multigroup CFA

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

Longitudinal multigroup invariance analysis of the satisfaction with food-related life scale in university students.

Science.gov (United States)

Schnettler, Berta; Miranda, Horacio; Miranda-Zapata, Edgardo; Salinas-Oñate, Natalia; Grunert, Klaus G; Lobos, Germán; Sepúlveda, José; Orellana, Ligia; Hueche, Clementina; Bonilla, Héctor

2017-06-01

This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non-probabilistic longitudinal sampling, 114 university students (65.8% female, mean age: 22.5) completed the SWFL questionnaire three times, over intervals of approximately one year. Confirmatory factor analysis was used to examine longitudinal measurement invariance. Two types of analysis were conducted: first, a longitudinal invariance by time, and second, a multigroup longitudinal invariance by sex, age, socio-economic status and place of residence during the study period. Results showed that the 3-item version of the SWFL exhibited strong longitudinal invariance (equal factor loadings and equal indicator intercepts). Longitudinal multigroup invariance analysis also showed that the 3-item version of the SWFL displays strong invariance by socio-economic status and place of residence during the study period over time. Nevertheless, it was only possible to demonstrate equivalence of the longitudinal factor structure among students of both sexes, and among those older and younger than 22 years. Generally, these findings suggest that the SWFL scale has satisfactory psychometric properties for longitudinal measurement invariance in university students with similar characteristics as the students that participated in this research. It is also possible to suggest that satisfaction with food-related life is associated with sex and age. Copyright © 2017 Elsevier Ltd. All rights reserved.

Do joint CMB and HST data support a scale invariant spectrum?

Energy Technology Data Exchange (ETDEWEB)

Benetti, Micol; Graef, Leila L.; Alcaniz, Jailson S., E-mail: micolbenetti@on.br, E-mail: leilagraef@on.br, E-mail: alcaniz@on.br [Departamento de Astronomia, Observatório Nacional, 20921-400, Rio de Janeiro, RJ (Brazil)

2017-04-01

We combine current measurements of the local expansion rate, H {sub 0}, and Big Bang Nucleosynthesis (BBN) estimates of helium abundance with the latest cosmic microwave background (CMB) data from the Planck Collaboration to discuss the observational viability of the scale invariant Harrison-Zeldovch-Peebles (HZP) spectrum. We also analyze some of its extensions, namely, HZP + Y {sub P} and HZP + N {sub eff}, where Y {sub P} is the primordial helium mass fraction and N {sub eff} is the effective number of relativistic degrees of freedom. We perform a Bayesian analysis and show that the latter model is favored with respect to the standard cosmology for values of N {sub eff} lying in the interval 3.70 ± 0.13 (1σ), which is currently allowed by some independent analyses.

RANKINE-HUGONIOT RELATIONS IN RELATIVISTIC COMBUSTION WAVES

International Nuclear Information System (INIS)

Gao Yang; Law, Chung K.

2012-01-01

As a foundational element describing relativistic reacting waves of relevance to astrophysical phenomena, the Rankine-Hugoniot relations classifying the various propagation modes of detonation and deflagration are analyzed in the relativistic regime, with the results properly degenerating to the non-relativistic and highly relativistic limits. The existence of negative-pressure downstream flows is noted for relativistic shocks, which could be of interest in the understanding of the nature of dark energy. Entropy analysis for relativistic shock waves is also performed for relativistic fluids with different equations of state (EoS), denoting the existence of rarefaction shocks in fluids with adiabatic index Γ < 1 in their EoS. The analysis further shows that weak detonations and strong deflagrations, which are rare phenomena in terrestrial environments, are expected to exist more commonly in astrophysical systems because of the various endothermic reactions present therein. Additional topics of relevance to astrophysical phenomena are also discussed.

Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System

International Nuclear Information System (INIS)

Wang Qi

2010-01-01

In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations. (general)

State vector reduction - 2: Elements of physical reality, nonlocality and stochasticity in relativistic dynamical reduction models

International Nuclear Information System (INIS)

Ghirardi, G.C.; Pearle, P.

1991-02-01

The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical systems and the problem of establishing causal relations between physical events. (author). Refs, 3 figs

Synthesizing Modular Invariants for Synchronous Code

Directory of Open Access Journals (Sweden)

Pierre-Loic Garoche

2014-12-01

Full Text Available In this paper, we explore different techniques to synthesize modular invariants for synchronous code encoded as Horn clauses. Modular invariants are a set of formulas that characterizes the validity of predicates. They are very useful for different aspects of analysis, synthesis, testing and program transformation. We describe two techniques to generate modular invariants for code written in the synchronous dataflow language Lustre. The first technique directly encodes the synchronous code in a modular fashion. While in the second technique, we synthesize modular invariants starting from a monolithic invariant. Both techniques, take advantage of analysis techniques based on property-directed reachability. We also describe a technique to minimize the synthesized invariants.

Selected papers on harmonic analysis, groups, and invariants

CERN Document Server

Nomizu, Katsumi

1997-01-01

This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the Society has chosen to publish them as a volume of selected papers. The papers range over a variety of topics, including representation theory, differential geometry, invariant theory, and complex analysis.

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.)

Proof of the Spin Statistics Connection 2: Relativistic Theory

Science.gov (United States)

Santamato, Enrico; De Martini, Francesco

2017-12-01

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

On the question of symmetries in nonrelativistic diffeomorphism-invariant theories

Science.gov (United States)

Banerjee, Rabin; Gangopadhyay, Sunandan; Mukherjee, Pradip

2017-07-01

A novel algorithm is provided to couple a Galilean-invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields. That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory. The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial nonrelativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.

Beyond the relativistic point particle: A reciprocally invariant system and its generalisation

International Nuclear Information System (INIS)

Pavsic, Matej

2009-01-01

We investigate a reciprocally invariant system proposed by Low and Govaerts et al., whose action contains both the orthogonal and the symplectic forms and is invariant under global O(2,4) intersection Sp(2,4) transformations. We find that the general solution to the classical equations of motion has no linear term in the evolution parameter, τ, but only the oscillatory terms, and therefore cannot represent a particle propagating in spacetime. As a remedy, we consider a generalisation of the action by adopting a procedure similar to that of Bars et al., who introduced the concept of a τ derivative that is covariant under local Sp(2) transformations between the phase space variables x μ (τ) and p μ (τ). This system, in particular, is similar to a rigid particle whose action contains the extrinsic curvature of the world line, which turns out to be helical in spacetime. Another possible generalisation is the introduction of a symplectic potential proposed by Montesinos. We show how the latter approach is related to Kaluza-Klein theories and to the concept of Clifford space, a manifold whose tangent space at any point is Clifford algebra Cl(8), a promising framework for the unification of particles and forces.

Axiomatics of Galileo-invariant quantum field theory

International Nuclear Information System (INIS)

Dadashev, L.A.

1986-01-01

The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms

Schroedinger invariant solutions of type IIB with enhanced supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Imperial College, London (United Kingdom). Theoretical Physics Group; Imperial College, London (United Kingdom). Inst. for Mathematical Sciences

2009-07-15

We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schroedinger algebra. The solutions depend on a five-dimensional Sasaki- Einstein space and it has been shown that they admit two Killing spinors. Here we will show that, for generic Sasaki-Einstein space, there are special subclasses of solutions which admit six Killing spinors and we determine the corresponding superisometry algebra. We also show that for the special case that the Sasaki-Einstein space is the round five-sphere, the number of Killing spinors can be increased to twelve. (orig.)

Relativistic amplitudes in terms of wave functions

International Nuclear Information System (INIS)

Karmanov, V.A.

1978-01-01

In the framework of the invariant diagram technique which arises at the formulation of the fueld theory on the light front the question about conditions at which the relativistic amplitudes may be expressed through the wave functions is investigated. The amplitudes obtained depend on four-vector ω, determining the light front surface. The way is shown to find such values of the four-vector ω, at which the contribution of diagrams not expressed through wave functions is minimal. The investigation carried out is equivalent to the study of the dependence of amplitudes of the old-fashioned perturbation theory in the in the infinite momentum frame on direction of the infinite momentum

Electromagnetic pair production in relativistic heavy-ion collisions

International Nuclear Information System (INIS)

Bottcher, C.; Strayer, M.R.

1988-01-01

We survey the production of electron, muon and tauon pairs in collisions between nuclei at ultra-relativistic energies. Such studies enhance our understanding of the role of the vacuum in field theory, and provide essential input for several experimental programs. A variety of models for the nuclear and nucleon form factors have been considered, revealing some degree of sensitivity to assumptions about sub-nuclear structure. We predict that the cross sections, even at high invariant masses and transverse momenta, are large on hadronic scales, and should act as useful probes of nuclear and nucleon form factors. 21 refs., 5 figs

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

Real-time trajectory analysis using stacked invariance methods

OpenAIRE

Kitts, B.

1998-01-01

Invariance methods are used widely in pattern recognition as a preprocessing stage before algorithms such as neural networks are applied to the problem. A pattern recognition system has to be able to recognise objects invariant to scale, translation, and rotation. Presumably the human eye implements some of these preprocessing transforms in making sense of incoming stimuli, for example, placing signals onto a log scale. This paper surveys many of the commonly used invariance methods, and asse...

Some no-go theorems for string duals of non-relativistic Lifshitz-like theories

International Nuclear Information System (INIS)

Li Wei; Takayanagi, Tadashi; Nishioka, Tatsuma

2009-01-01

We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this.

Canonical formalism for relativistic dynamics

International Nuclear Information System (INIS)

Penafiel-Nava, V.M.

1982-01-01

The possibility of a canonical formalism appropriate for a dynamical theory of isolated relativistic multiparticle systems involving scalar interactions is studied. It is shown that a single time-parameter structure satisfying the requirements of Poincare invariance and simultaneity of the constituents (global tranversality) can not be derived from a homogeneous Lagrangian. The dynamics is deduced initially from a non-homogeneous but singular Lagrangian designed to accommodate the global tranversality constraints with the equaltime plane associated to the total momentum of the system. An equivalent standard Lagrangian is used to generalize the parametrization procedure which is referred to an arbitrary geodesic in Minkowski space. The equations of motion and the definition of center of momentum are invariant with respect to the choice of geodesic and the entire formalism becomes separable. In the original 8N-dimensional phase-space, the symmetries of the Lagrangian give rise to a canonical realization of a fifteen-generator Lie algebra which is projected in the 6N dimensional hypersurface of dynamical motions. The time-component of the total momentum is thus reduced to a neutral element and the canonical Hamiltonian survives as the only generator for time-translations so that the no-interaction theorem becomes inapplicable

A study on relativistic lagrangian field theories with non-topological soliton solutions

International Nuclear Information System (INIS)

Diaz-Alonso, J.; Rubiera-Garcia, D.

2009-01-01

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call 'admissible' models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite

Nonlinear analysis of vehicle control actuations based on controlled invariant sets

Directory of Open Access Journals (Sweden)

Németh Balázs

2016-03-01

Full Text Available In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant sets of the steering and braking control systems at various velocities and road conditions. Illustration examples show that, depending on the environments, different vehicle dynamic regions can be reached and stabilized by these controllers. The results can be applied to the theoretical basis of their interventions into the vehicle control system.

Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

Science.gov (United States)

KlusoÅ, Josef; Oksanen, Markku; Tureanu, Anca

2014-03-01

We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable—a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a three-dimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.

Foliated vector fields, the Godbillon-Vey invariant and the invariant I(F)

International Nuclear Information System (INIS)

Banyaga, A.; Landa, Alain Musesa

2004-03-01

We prove that if the invariant I(F) constructed in 'An invariant of contact structures and transversally oriented foliations', Ann. Global Analysis and Geom. 14(1996) 427-441 (A. Banyaga), through the Lie algebra of infinitesimal automorphisms of transversally oriented foliations F is trivial, then the Godbillon-Vey invariant GV (F) of F is also trivial, but that the converse is not true. For codimension one foliations, the restrictions I τ , (F) of I(F) to the Lie subalgebra of vector fields tangent to the leaves is the Reeb class R(F) of F. We also prove that if there exists a foliated vector field which is everywhere transverse to a codimension one foliation, then the Reeb class R(F) is trivial, hence so is the GV(F) invariant. (author)

A test for ordinal measurement invariance

NARCIS (Netherlands)

Ligtvoet, R.; Millsap, R.E.; Bolt, D.M.; van der Ark, L.A.; Wang, W.-C.

2015-01-01

One problem with the analysis of measurement invariance is the reliance of the analysis on having a parametric model that accurately describes the data. In this paper an ordinal version of the property of measurement invariance is proposed, which relies only on nonparametric restrictions. This

Relativistic interpretation of the nature of the nuclear tensor force

Science.gov (United States)

Zong, Yao-Yao; Sun, Bao-Yuan

2018-02-01

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic Hartree-Fock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the σ-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudo-spin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components, revealing clearly the nature of the tensor force. Supported by National Natural Science Foundation of China (11375076, 11675065) and the Fundamental Research Funds for the Central Universities (lzujbky-2016-30)

A cross-national analysis of measurement invariance of the Satisfaction With Life Scale.

Science.gov (United States)

Whisman, Mark A; Judd, Charles M

2016-02-01

Measurement invariance of the Satisfaction With Life Scale (SWLS) was examined in probability samples of adults 50-79 years of age living in the United States, England, and Japan. Confirmatory factor analysis modeling was used to test for multigroup measurement invariance of a single-factor structure of the SWLS. Results support a single-factor structure of the SWLS across the 3 countries, with tests of measurement invariance of the SWLS supporting its configural invariance and metric invariance. These results suggest that the SWLS may be used as a single-factor measure of life satisfaction in the United States, England, and Japan, and that it is appropriate to compare correlates of the SWLS in middle-aged and older adults across these 3 countries. However, results provided evidence for only partial scalar invariance, with the intercept for SWLS Item 4 varying across countries. Cross-national comparisons of means revealed a lower mean at the latent variable level for the Japanese sample than for the other 2 samples. In addition, over and above the latent mean difference, the Japanese sample also manifested a significantly lower intercept on Item 4. Implications of the findings for research on cross-national comparisons of life satisfaction in European American and East Asian countries are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Longitudinal multigroup invariance analysis of the satisfaction with food-related life scale in university students

DEFF Research Database (Denmark)

Schnettler, Berta; Miranda, Horacio; Miranda-Zapata, Edgardo

2017-01-01

This study examined longitudinal measurement invariance in the Satisfaction with Food-related Life (SWFL) scale using follow-up data from university students. We examined this measure of the SWFL in different groups of students, separated by various characteristics. Through non......-probabilistic longitudinal sampling, 114 university students (65.8% female, mean age: 22.5) completed the SWFL questionnaire three times, over intervals of approximately one year. Confirmatory factor analysis was used to examine longitudinal measurement invariance. Two types of analysis were conducted: first, a longitudinal...... students of both sexes, and among those older and younger than 22 years. Generally, these findings suggest that the SWFL scale has satisfactory psychometric properties for longitudinal measurement invariance in university students with similar characteristics as the students that participated...

Application of an effective gauge-invariant model to nuclear matter in the relativistic Hartree-Fock approximation

Energy Technology Data Exchange (ETDEWEB)

Bernardos, P. [Universidad de Cantabria, Departamento de Matematica Aplicada y Ciencias de la Computacion, 39005, Santander (Spain); Fomenko, V.N. [St Petersburg University for Railway Engineering, Department of Mathematics, 190031, St Petersburg (Russian Federation); Marcos, S.; Niembro, R. [Universidad de Cantabria, Departamento de Fisica Moderna, 39005, Santander (Spain); Lopez-Quelle, M. [Universidad de Cantabria, Departamento de Fisica Aplicada, 39005, Santander (Spain); Savushkin, L.N. [St Petersburg University for Telecommunications, Department of Physics, 191186, St Petersburg (Russian Federation)

2001-02-01

An effective nuclear model describing {omega}-, {rho}- and axial-mesons as gauge fields is applied to nuclear matter in the relativistic Hartree-Fock approximation. The isoscalar two-pion exchange is simulated by a scalar field s similar to that used in the conventional relativistic mean-field approach. Two more scalar fields are essential ingredients of the present treatment: the {sigma}-field, the chiral partner of the pion, and the {sigma}-field, the Higgs field for the {omega}-meson. Two versions of the model are used depending on whether the {sigma}-field is considered as a dynamical variable or 'frozen', by taking its mass as infinite. The model contains four free parameters in the first case and three in the second one which are fitted to the nuclear matter saturation conditions. The nucleon and meson effective masses, compressibility modulus and symmetry energy are calculated. The results prove the reliability of the Dirac-Hartree-Fock approach within the linear realization of the chiral symmetry. (author)

Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

International Nuclear Information System (INIS)

Remler, E.A.

1977-01-01

A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

Pion production in relativistic heavy ion collisions

International Nuclear Information System (INIS)

Norbury, J.W.

1983-01-01

A Lorentz-invariant differential cross section for pion production in peripheral, relativistic, heavy ion collisions is calculated for the collisions of an 16 O projectile onto a 12 C target. The pions are produced via excitations of a Δ(3,3) resonant state in the projectile with simultaneous excitation of an M1 giant resonance in the target. A second order amplitude describing resonance formation and decay is derived within the context of second order, time-dependent perturbation theory and a corresponding transition rate is evaluated. This is then applied to the problem of pion production and a differential cross section is calculated using a simple product-of-states model. The whole theory is then re-formulated within a second quantized particle-hole model which describes the basic process of M1 giant resonance formation as well as the formation and decay of the intermediate Δ(3,3) resonance. Subsequently, a new Lorentz-invariant differential cross section is calculated from the particle-hole amplitude. The theoretical cross section is compared with some experimental data and the agreement is found to be satisfactory given the nature of the data and the assumptions of the theory

Hartree Fock-type equations in relativistic quantum electrodynamics with non-linear gauge fixing

International Nuclear Information System (INIS)

Dietz, K.; Hess, B.A.

1990-08-01

Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electro-magnetic degrees of freedom in certain characteristic non-linear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening, three-body 'forces' etc. can be included already at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'. (orig.)

Relativistic particles coupled to Chern-Simons term-revisited

International Nuclear Information System (INIS)

Chakraborty, B.

1995-01-01

The author considers the model of N relativistic spinless particles coupled to an abelian Chern-Simons term. Rewriting the action in a time reparamaterized form by introducing an arbitary parameter, parameterizing the world line of the particles, the author makes a classical constraint Hamiltonian analysis of the model. Subsequent to gauge fixing by equating the arbitrary parameter with the time the author identifies the Hamiltonian of the system, which agrees with the Hamiltonian obtained by using Banerjee's method of fixing the arbitrary Langrange multiplier by using equations of motion. The author exhibits the Poincare invariance of the model, at the classical level, by constructing spacetime generators using either the canonical or symmetric definition of the energy-momentum tensor. A detailed comparison of the expressions of angular momentum obtained by both methods show that both agree up to a boundary term. In presence of rotationally symmetric vortex configuration this term can be interpreted as an anomalous angular momentum term. The author also heuristically discusses the effect of gauge fixing on the transformation properties. 13 refs

Alterations to the relativistic Love-Franey model and their application to inelastic scattering

International Nuclear Information System (INIS)

Zeile, J.R.

1989-01-01

The fictitious axial-vector and tensor mesons for the real part of the relativistic Love-Franey interaction are removed. In an attempt to make up for this loss, derivative couplings are used for the π and ρ mesons. Such derivative couplings require the introduction of axial-vector and tensor contact term corrections. Meson parameters are then fit to free nucleon-nucleon scattering data. The resulting fits are comparable to those of the relativistic Love-Franey model provided that the contact term corrections are included and the fits are weighted over the physically significant quantity of twice the tensor minus the axial-vector Lorentz invariants. Failure to include contact term corrections leads to poor fits at higher energies. The off-shell behavior of this model is then examined by looking at several applications from inelastic proton-nucleus scattering

Gauge dependence of world lines and invariance of the S-matrix in relativistic classical mechanics

International Nuclear Information System (INIS)

Molotkov, V.V.; Todorov, I.T.

1980-07-01

The notion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend in general (in the presence of interaction) on the choice of the equal-time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a two-particle system and the (classical) S-matrix are indepent of this choice. (author)

Quasilinear analysis of loss-cone driven weakly relativistic electron cyclotron maser instability

International Nuclear Information System (INIS)

Ziebell, L.F.; Yoon, P.H.

1995-01-01

This paper presents a quasilinear analysis of the relativistic electron cyclotron maser instability. Two electron populations are assumed: a low-temperature background component and a more energetic loss-cone population. The dispersion relation is valid for any ratio of the energetic to cold populations, and includes thermal and relativistic effects. The quasilinear analysis is based upon an efficient kinetic moment method, in which various moment equations are derived from the particle kinetic equation. A model time-dependent loss-cone electron distribution function is assumed, which allows one to evaluate the instantaneous linear growth rate as well as the moment kinetic equations. These moment equations along with the wave kinetic equation form a fully self-consistent set of equations which governs the evolution of the particles as well as unstable waves. This set of equations is solved with physical parameters typical of the earth's auroral zone plasma. copyright 1995 American Institute of Physics

What invariant one-particle multiplicity distributions and two-particle correlations are telling us about relativistic heavy-ion collisions

International Nuclear Information System (INIS)

Nix, J.R.; Strottman, D.; Hecke, H.W. van; Schlei, B.R.; Sullivan, J.P.; Murray, M.J.

1998-02-01

The authors have used a nine-parameter expanding source model that includes special relativity, quantum statistics, resonance decays, and freeze-out on a realistic hypersurface in spacetime to analyze in detail invariant π + , K + , and K - one-particle multiplicity distributions and π + and π - two-particle correlations in nearly central collisions of Pb + Pb at p lab /A = 158 GeV/c. These studies confirm an earlier conclusion for nearly central collisions of Si + Au at p lab /A = 14.6 GeV/c that the freeze-out temperature is less than 100 meV and that both the longitudinal and transverse collective velocities -- which are anti-correlated with the temperature -- are substantial. The authors also reconciled their current results with those of previous analyses that yielded a much higher freeze-out temperature of approximately 140 meV for both Pb + Pb collisions at p lab /A = 158 GeV/c and other reactions. One type of analysis was based upon the use of a heuristic equation that neglects relativity to extrapolate slope parameters to zero particle mass. Another type of analysis utilized a thermal model in which there was an accumulation of effects from several approximations. The future should witness the arrival of much new data on invariant one-particle multiplicity distributions and two-particle correlations as functions of bombarding energy and/or size of the colliding nuclei. The proper analysis of these data in terms of a realistic model could yield accurate values for the density, temperature, collective velocity, size, and other properties of the expanding matter as it freezes out into a collection of noninteracting hadrons. A sharp discontinuity in the value of one or more of these properties could conceivably be the long-awaited signal for the formation of a quark-gluon plasma or other new physics

Relativistic quantum mechanics and introduction to field theory

Energy Technology Data Exchange (ETDEWEB)

Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica

1996-12-01

The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.

Relativistic quantum mechanics and introduction to field theory

International Nuclear Information System (INIS)

Yndurain, F.J.

1996-01-01

The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources

Invariance Signatures: Characterizing contours by their departures from invariance

OpenAIRE

Squire, David; Caelli, Terry M.

1997-01-01

In this paper, a new invariant feature of two-dimensional contours is reported: the Invariance Signature. The Invariance Signature is a measure of the degree to which a contour is invariant under a variety of transformations, derived from the theory of Lie transformation groups. It is shown that the Invariance Signature is itself invariant under shift, rotation and scaling of the contour. Since it is derived from local properties of the contour, it is well-suited to a neural network implement...

Photon-photon and photon-hadron processes in relativistic heavy ion collisions

International Nuclear Information System (INIS)

Baron, N.C.

1993-11-01

Photon-photon and photon-hadron interactions in relativistic heavy ion collisions are studied in the framework of the impact parameter dependent equivalent photon approximation. Improvements of this method, like formfactor inclusion and geometrical modifications are developed. In disruptive relativistic heavy ion collisions where the heavy ions overlapp during the collision, electromagnetic processes are an important background to other mechanisms. In peripheral (non-disruptive) relativistic heavy ion collisions where the ions pass each other without strong interactions, the electromagnetic processes can be studied in their pure form. The lepton pair production is an important diagnostic tool in relativistic heavy ion collisions. The coherent γγ lepton pair production is therefore extensively studied in disruptive but also in non-disruptive collisions. The effects of strong interactions on the coherent γγ lepton pair production in disruptive collisions are discussed in terms of a simple stopping model. Coherent γγ dielectron production contributes to the dilepton production in high energy hadron-hadron collisions. As an example, the coherent dielectron production in π - p collisions is studied in terms of the equivalent photon approximation. Peripheral ultrarelativistic heavy ion collisions open up new possibilities for γγ physics. Taking into account γA background reactions, typical γγ processes in the relevant invariant mass ranges are discussed. The extreme high energy part of the equivalent photon spectrum leads to hard photon-parton reactions. As a potential tool to investigate the gluon distribution function of nucleons, thee q anti q production via the γg fusion in ultrarelativistic heavy ion collisions is studied. It is the purpose of this work to investigate how photon-photon and photon-hadron reactions in relativistic heavy ion collisions may contribute to the understanding of QCD and the standard model. (orig.) [de

Relativistic equations

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

Models of non-relativistic quantum gravity: the good, the bad and the healthy

CERN Document Server

Blas, Diego; Sibiryakov, Sergey

2011-01-01

Horava's proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call `khronon'. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Horava's projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.

Relativistic and nonrelativistic annihilation of dark matter: a sanity check using an effective field theory approach

Energy Technology Data Exchange (ETDEWEB)

Cannoni, Mirco [Universidad de Huelva, Departamento de Fisica Aplicada, Facultad de Ciencias Experimentales, Huelva (Spain)

2016-03-15

We find an exact formula for the thermally averaged cross section times the relative velocity left angle σv{sub rel} right angle with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at x = m/T >> 1 directly gives the nonrelativistic limit of left angle σv{sub rel} right angle, which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section σ(s) in powers of the nonrelativistic relative velocity vr. We show the correct invariant procedure that gives the nonrelativistic average left angle σv{sub rel} right angle {sub nr} coinciding with the large x expansion of left angle σv{sub rel} right angle in the comoving frame. We explicitly formulate flux, cross section, thermal average, collision integral of the Boltzmann equation in an invariant way using the true relativistic relative v{sub rel}, showing the uselessness of the Moeller velocity and further elucidating the conceptual and numerical inconsistencies related with its use. (orig.)

Relativistic and nonrelativistic annihilation of dark matter: a sanity check using an effective field theory approach

International Nuclear Information System (INIS)

Cannoni, Mirco

2016-01-01

We find an exact formula for the thermally averaged cross section times the relative velocity left angle σv rel right angle with relativistic Maxwell-Boltzmann statistics. The formula is valid in the effective field theory approach when the masses of the annihilation products can be neglected compared with the dark matter mass and cut-off scale. The expansion at x = m/T >> 1 directly gives the nonrelativistic limit of left angle σv rel right angle, which is usually used to compute the relic abundance for heavy particles that decouple when they are nonrelativistic. We compare this expansion with the one obtained by expanding the total cross section σ(s) in powers of the nonrelativistic relative velocity vr. We show the correct invariant procedure that gives the nonrelativistic average left angle σv rel right angle nr coinciding with the large x expansion of left angle σv rel right angle in the comoving frame. We explicitly formulate flux, cross section, thermal average, collision integral of the Boltzmann equation in an invariant way using the true relativistic relative v rel , showing the uselessness of the Moeller velocity and further elucidating the conceptual and numerical inconsistencies related with its use. (orig.)

Geometrical approach to the dynamics of the relativistic string

International Nuclear Information System (INIS)

Barbashov, B.M.; Koshkarov, A.L.

1979-01-01

The dynamics of the relativistic string is considered from the point of view of the gaussian theory of two-dimensional surfaces in the three-dimensional pseudoeuclidean space-epsilon 3 1 according to which the surface is characterized by its first and second quadratic forms. The geometrical approach possesses an advantage which gives the possibility to solve manifestly additional conditions on the vector describing the coordinates of the string world surface. The equations of motion and boundary conditions are written out for the cases of a string with massive ends and a closed string. The basic equations are formulated for the coefficients of the first and second quadratic forms of the string world surface, which represent the known geometric conditions of integration of Gauss and Weingarten derivation formulas. By means of integration of the derivation formulas the representation is obtained for the form of the string world surface in a certain basis, which satisfies the equations of motion as well as additional conditions. A new relativistic invariant gauge is suggested which fixes the second quadratic form of the surface. This representation can be extended to the case of arbitrary dimensional space

Fully relativistic free-electron laser in a completely filled waveguide

International Nuclear Information System (INIS)

Farokhi, B.; Abdykian, A.

2005-01-01

An analysis of the azimuthally symmetrical, high frequency eigenmodes of a cylindrical metallic waveguide completely filled with a relativistic magnetized plasma is presented. A relativistic nonlinear wave equation is derived in a form which includes the coupling of EH and HE modes due to the finite axial magnetic field. Relativistic equations that permit calculation of the dispersion curves for four families of electromagnetic and electrostatic modes are derived. Numerical analysis is conducted to study the relativistic dispersion curves of various modes as a function of axial magnetic field B 0 . This treatment is shown that the dispersion curves dependent to γ in low frequency which is ignored in previous work. It is found that in drawn figures shown difference between relativistic and non-relativistic cases. The former each figure is treated for two orbit groups. This study is benefiting to facilities the development of devices for generation of high-power electromagnetic radiation, charged particle acceleration, and other applications of plasma waveguide. (author)

Expression of relativistic amplitudes in terms of wave functions

International Nuclear Information System (INIS)

Karmanov, V.A.

1978-01-01

The conditions under which relativistic amplitudes may be expressed in terms of the wave functions are analyzed within the framework of the invariant diagram technique which appears on formulation of field theory on the light front. The amplitudes depend on the 4-vector ω which defines the surface of the light front. A rule is formulated for the determination of those values of the 4-vector ω for which the diagram contribution, which cannot be expressed in terms of the wave functions, is minimum. The present investigation is equivalent to a study of the dependence of the amplitudes of the old fashioned perburbation theory in the infinite momentum depending on the direction of the infinite momentum

A unified treatment of the non-relativistic and relativistic hydrogen atom: Pt. 2

International Nuclear Information System (INIS)

Swainson, R.A.; Drake, G.W.F.

1991-01-01

This is the second in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. In this paper the non-relativistic Green function is examined in detail; new functional forms are presented and a clear mathematical progression is show to link these and most other known forms. A linear transformation of the four radial parts of the relativistic Green function is given which allows for the presentation of this function as a simple generalization of the non-relativistic Green function. Thus, many properties of the non-relativistic Green function are shown to have simple relativistic generalizations. In particular, new recursion relations of the radial parts of both the non-relativistic and relativistic Green functions are presented, along with new expressions for the double Laplace transforms and recursion relations between the radial matrix elements. (author)

Analysis of the EPR-experiment by relativistic quantum logic

International Nuclear Information System (INIS)

Mittelstaedt, P.

1984-01-01

The Einstein-Podolsky-Rosen-experiment is analysed in the framework of an abstract language for relativistic quantum physics, which can be founded on the most general possibilities of physical observations and without any recourse to the Hilbert-space formulation of relativistic quantum theory. -Within this approach one obtains nonlocal correlations between the two EPR-systems in accordance with recent experiments and with quantum theory. These correlations can, however, not be used in order to produce superluminal signals and thus to violate Einstein-causality and special relativity. (author)

Measurement invariance of the strength of motivation for medical school: a multi-group confirmatory factor analysis.

Science.gov (United States)

An, M; Kusurkar, R A; Li, L; Xiao, Y; Zheng, C; Hu, J; Chen, M

2017-07-11

The Strength of Motivation for Medical School-Revised (SMMS-R) questionnaire measures students' motivation for studying medicine. It includes three subscales: 'willingness to sacrifice', 'readiness to start', and 'persistence'. Measurement invariance is a prerequisite for group comparisons. The objectives of this study were to verify the factorial structure of the SMMS-R questionnaire and to investigate it's measurement invariance. A total of 989 medical students were approached, 930 cases were kept for data analysis. Factorial structure of and measurement invariance of the SMMS-R were tested using single and multiple group confirmatory factor analyses with Mplus. Trational Cronbach's α along with McDonald's ω and glb were used to measure internal consistency for each subscale. Internal consistency for subscales and the full instrument were within the acceptable range. A 3-factor structure of the Chinese version of the SMMS-R was supported. Full configural, metric and partial scalar invariance were obtained. The SMMS-R showed measurement invariance across gender and two independent samples. So it can be used for group and cross-cultural comparisons.

Relativistic klystron

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

The study of hadron dynamics in relativistic heavy ion collisions

International Nuclear Information System (INIS)

Venema, L.B.

1994-01-01

In this thesis, pion emission patterns were studied in two reaction systems Ar + Ca and Au + Au at 1 GeV/u, with the aim to improve the understanding of the pion production in relativistic heavy ion collisions. The study of the high energy tail of the π 0 -momentum spectrum was regarded as promising because of its sensitivity to compression since it did not appear in small reaction systems. Experiments were performed with TAPS together with the Forward Wall of the FoPi-collaboration at GSI. The combined measurement of charged particle multiplicities in the Forward Wall and the particles entering TAPS enabled an exclusive study of the pion production. TAPS was tested in separate experiments and its capabilities were demonstrated by measuring different reaction products, like photons, charged particles and neutrons. The data analysis involved new methods to treat the background contamination below the invariant mass peak of the π 0 -meson due to the geometry of the detector and to perform particle identification in a high particle multiplicity environment. (orig.)

Measurement invariance versus selection invariance: Is fair selection possible?

NARCIS (Netherlands)

Borsboom, D.; Romeijn, J.W.; Wicherts, J.M.

2008-01-01

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Measurement invariance versus selection invariance : Is fair selection possible?

NARCIS (Netherlands)

Borsboom, Denny; Romeijn, Jan-Willem; Wicherts, Jelte M.

This article shows that measurement invariance (defined in terms of an invariant measurement model in different groups) is generally inconsistent with selection invariance (defined in terms of equal sensitivity and specificity across groups). In particular, when a unidimensional measurement

Pedagogical systematic derivation of Noether point symmetries in special relativistic field theories and extended gravity cosmology

Science.gov (United States)

Haas, Fernando

2016-11-01

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.

Pedagogical systematic derivation of Noether point symmetries in special relativistic field theories and extended gravity cosmology

International Nuclear Information System (INIS)

Haas, Fernando

2016-01-01

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced. (paper)

Relativistic astrophysics

CERN Document Server

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

Internal-time observable of classical relativistic systems

International Nuclear Information System (INIS)

Ben-Ya'acov, Uri

2006-01-01

The relativistic framework with its symmetries offers a natural definition for the internal time of classical (non-quantum) physical systems as a Lorentz-invariant observable. The internal-time observable, measuring the system's aging or internal evolution, is identified with the proper time of the system derived from its centre-of-mass (CM) coordinate. For its definition as an observable it is required that the system be symmetric not only under Lorentz-Poincare transformations but also under uniform scaling, with the associated existence of a dilatation function D, and yet that D be a varying-not conserved-quantity. Two alternative definitions are discussed, and it is found that in order to maintain simultaneity of the CM time with the events that define it, it is necessary to split the dilatation function into a CM part and an internal part

Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2005-01-01

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

Relativistic analysis of the electromagnetic properties of the deuteron

International Nuclear Information System (INIS)

Hummel, E.

1991-01-01

In this thesis the electromagnetic properties of the deuteron are studied. A relativistic description is constructed starting from a quasi-potential approach of the bethe-Salpeter equation, which treats dynamical and electromagnetical properties in a consistent way. This is applied on elastic as well as inelastic electron-deuteron scattering. In ch. 2 the formalism of electromagnetic scattering in the one-photon exchange approximation is described. The general form of the electromagnetic deuteron current operator and the consequences of current conservation are discussed. The deuteron current operator is constructed in a simple quasipotential approximation model. Ch. 3 discusses elastic electron-deuteron scattering. The ρπγ and ωεγ MEC contributions are taken into account and the results are compared to the experimental data for both the electric and magnetic form factor. In particular, the usual non-relativistic reduction of the two-body current operators is studied. In ch. 4 some improvements are made on the simple approximation model. In this improved model at the same time both elastic and breakup processes can be treated. The differences with the simple model are the treatment of the initial and final states and the propagator structure. The isovector two-body currents are constructed using the OBE-model, where the complications due to the use of strong form factors at the meson-nucleon vertices are accounted for. The results for elastic scattering using the improved model are compared with the results of ch. 3. Finally in ch. 5 the model developed in ch. 4 is used to describe the electro-desintegration of the deuteron. The recent experiments at NIKHEF are discussed in the PWIA approximation also with FSI included. In the analysis of the threshold experiments the π-MEC are included. In both experiments relativistic effects and in the threshold experiment also the controversy about the form factor in the MEC, are discussed. (author). 61 refs.; 40 figs

Relativistic effects and primordial non-Gaussianity in the galaxy bias

International Nuclear Information System (INIS)

Bartolo, Nicola; Matarrese, Sabino; Riotto, Antonio

2011-01-01

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated

Relativistic quantum logic

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 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.

Femtoscopic analysis of baryon correlations in ultra-relativistic heavy-ion collisions registered by ALICE

CERN Document Server

AUTHOR|(INSPIRE)INSPIRE-00361630

Heavy-ion collisions at ultra-relativistic energies give a unique possibility to create and to analyse the Quark-Gluon Plasma predicted by the theory of Quantum Chromodynamics. The research on the properties of such state of matter is crucial for understanding the features of the strongly interacting system. Experimental results reveal the collective behaviour of matter created in the heavy-ion collisions at ultra-relativistic energies. The existence of this effect can be verified by the measurement of the transverse mass dependence of the source size extracted using different particle species. Such characteristics can be determined using the analysis technique called femtoscopy. This method is based on the correlations of particles with small relative momenta which originate from the effects of Quantum Statistics as well as the strong and Coulomb Final State Interactions. A recent analysis of the particle production at the highest available collision energies of heavy-ion collisions reveals the puzzling res...

Object recognition by implicit invariants

Czech Academy of Sciences Publication Activity Database

Flusser, Jan; Kautsky, J.; Šroubek, Filip

2007-01-01

Roč. 2007, č. 4673 (2007), s. 856-863 ISSN 0302-9743. [Computer Analysis of Images and Patterns. Vienna, 27.08.2007-29.08.2007] R&D Projects: GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Invariants * implicit invariants * moments * orthogonal polynomials * nonlinear object deformation Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.402, year: 2005 http:// staff .utia.cas.cz/sroubekf/papers/CAIP_07.pdf

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

Nonlinear analysis of a relativistic beam-plasma cyclotron instability

Science.gov (United States)

Sprangle, P.; Vlahos, L.

1986-01-01

A self-consistent set of nonlinear and relativistic wave-particle equations are derived for a magnetized beam-plasma system interacting with electromagnetic cyclotron waves. In particular, the high-frequency cyclotron mode interacting with a streaming and gyrating electron beam within a background plasma is considered in some detail. This interaction mode may possibly find application as a high-power source of coherent short-wavelength radiation for laboratory devices. The background plasma, although passive, plays a central role in this mechanism by modifying the dielectric properties in which the magnetized electron beam propagates. For a particular choice of the transverse beam velocity (i.e., the speed of light divided by the relativistic mass factor), the interaction frequency equals the nonrelativistic electron cyclotron frequency times the relativistic mass factor. For this choice of transverse beam velocity the detrimental effects of a longitudinal beam velocity spread is virtually removed. Power conversion efficiencies in excess of 18 percent are both analytically calculated and obtained through numerical simulations of the wave-particle equations. The quality of the electron beam, degree of energy and pitch angle spread, and its effect on the beam-plasma cyclotron instability is studied.

Computational invariant theory

CERN Document Server

Derksen, Harm

2015-01-01

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be ...

Invariant submanifold flows

Energy Technology Data Exchange (ETDEWEB)

Olver, Peter J [School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (United States)], E-mail: olver@math.umn.edu

2008-08-29

Given a Lie group acting on a manifold, our aim is to analyze the evolution of differential invariants under invariant submanifold flows. The constructions are based on the equivariant method of moving frames and the induced invariant variational bicomplex. Applications to integrable soliton dynamics, and to the evolution of differential invariant signatures, used in equivalence problems and object recognition and symmetry detection in images, are discussed.

Radiatively driven relativistic spherical winds under relativistic radiative transfer

Science.gov (United States)

Fukue, J.

2018-05-01

We numerically investigate radiatively driven relativistic spherical winds from the central luminous object with mass M and luminosity L* under Newtonian gravity, special relativity, and relativistic radiative transfer. We solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double-iteration processes, to obtain the intensity and velocity fields simultaneously. We found that the momentum-driven winds with scattering are quickly accelerated near the central object to reach the terminal speed. The results of numerical solutions are roughly fitted by a relation of \\dot{m}=0.7(Γ _*-1)\\tau _* β _* β _out^{-2.6}, where \\dot{m} is the mass-loss rate normalized by the critical one, Γ* the central luminosity normalized by the critical one, τ* the typical optical depth, β* the initial flow speed at the central core of radius R*, and βout the terminal speed normalized by the speed of light. This relation is close to the non-relativistic analytical solution, \\dot{m} = 2(Γ _*-1)\\tau _* β _* β _out^{-2}, which can be re-expressed as β _out^2/2 = (Γ _*-1)GM/c^2 R_*. That is, the present solution with small optical depth is similar to that of the radiatively driven free outflow. Furthermore, we found that the normalized luminosity (Eddington parameter) must be larger than unity for the relativistic spherical wind to blow off with intermediate or small optical depth, i.e. Γ _* ≳ \\sqrt{(1+β _out)^3/(1-β _out)}. We briefly investigate and discuss an isothermal wind.

The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation

OpenAIRE

Fedosin, Sergey G.

2018-01-01

For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the...

Relativistic analysis of the LISA long range optical links

International Nuclear Information System (INIS)

Chauvineau, Bertrand; Regimbau, Tania; Vinet, Jean-Yves; Pireaux, Sophie

2005-01-01

The joint ESA/NASA LISA mission consists of three spacecraft on heliocentric orbits, flying in a triangular formation of 5 Mkm each side, linked by infrared optical beams. The aim of the mission is to detect gravitational waves in a low frequency band. For properly processing the scientific data, the propagation delays between spacecraft must be accurately known. We thus analyze the propagation of light between spacecraft in order to systematically derive the relativistic effects due to the static curvature of the Schwarzschild space-time in which the spacecraft are orbiting with time-varying light distances. In particular, our analysis allows us to evaluate rigorously the Sagnac effect, and the gravitational (Einstein) redshift

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.

A relativistic point coupling model for nuclear structure calculations

International Nuclear Information System (INIS)

Buervenich, T.; Maruhn, J.A.; Madland, D.G.; Reinhard, P.G.

2002-01-01

A relativistic point coupling model is discussed focusing on a variety of aspects. In addition to the coupling using various bilinear Dirac invariants, derivative terms are also included to simulate finite-range effects. The formalism is presented for nuclear structure calculations of ground state properties of nuclei in the Hartree and Hartree-Fock approximations. Different fitting strategies for the determination of the parameters have been applied and the quality of the fit obtainable in this model is discussed. The model is then compared more generally to other mean-field approaches both formally and in the context of applications to ground-state properties of known and superheavy nuclei. Perspectives for further extensions such as an exact treatment of the exchange terms using a higher-order Fierz transformation are discussed briefly. (author)

On the geometrical approach to the relativistic string theory

International Nuclear Information System (INIS)

Barbashov, B.M.; Nesterenko, V.V.

1978-01-01

In a geometrical approach to the string theory in the four-dimensional Minkowski space the relativistic invariant gauge proposed earlier for the string moving in three-dimensional space-time is used. In contrast to the results of previous paper the system of equations for the coefficients of the fundamental forms of the string model world sheet can be reduced now to one nonlinear Lionville equation again but for a complex valued function u. It is shown that in the case of space-time with arbitrary dimension there are such string motions which are described by one non-linear equation with a real function u. And as a consequence the soliton solutions investigated earlier take place in a geometrical approach to the string theory in any dimensional space-time

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

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

From Lattice Boltzmann to hydrodynamics in dissipative relativistic fluids

Science.gov (United States)

Gabbana, Alessandro; Mendoza, Miller; Succi, Sauro; Tripiccione, Raffaele

2017-11-01

Relativistic fluid dynamics is currently applied to several fields of modern physics, covering many physical scales, from astrophysics, to atomic scales (e.g. in the study of effective 2D systems such as graphene) and further down to subnuclear scales (e.g. quark-gluon plasmas). This talk focuses on recent progress in the largely debated connection between kinetic transport coefficients and macroscopic hydrodynamic parameters in dissipative relativistic fluid dynamics. We use a new relativistic Lattice Boltzmann method (RLBM), able to handle from ultra-relativistic to almost non-relativistic flows, and obtain strong evidence that the Chapman-Enskog expansion provides the correct pathway from kinetic theory to hydrodynamics. This analysis confirms recently obtained theoretical results, which can be used to obtain accurate calibrations for RLBM methods applied to realistic physics systems in the relativistic regime. Using this calibration methodology, RLBM methods are able to deliver improved physical accuracy in the simulation of the physical systems described above. European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 642069.

Relativistic duality, and relativistic and radiative corrections for heavy-quark systems

International Nuclear Information System (INIS)

Durand, B.; Durand, L.

1982-01-01

We give a JWKB proof of a relativistic duality relation which relates an appropriate energy average of the physical cross section for e + e - →qq-bar bound states→hadrons to the same energy average of the perturbative cross section for e + e - →qq-bar. We show that the duality relation can be used effectively to estimate relativistic and radiative corrections for bound-quark systems to order α/sub s//sup ts2/. We also present a formula which relates the square of the ''large'' 3 S 1 Salpeter-Bethe-Schwinger wave function for zero space-time separation of the quarks to the square of the nonrelativistic Schroedinger wave function at the origin for an effective potential which reproduces the relativistic spectrum. This formula allows one to use the nonrelativistic wave functions obtained in potential models fitted to the psi and UPSILON spectra to calculate relativistic leptonic widths for qq-bar states via a relativistic version of the van Royen--Weisskopf formula

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.

General relativistic radiative transfer code in rotating black hole space-time: ARTIST

Science.gov (United States)

Takahashi, Rohta; Umemura, Masayuki

2017-02-01

We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.

Post-Newtonian reference ellipsoid for relativistic geodesy

Science.gov (United States)

Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena

2016-02-01

We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to

Relativistic electron flux dropout due to field line curvature during the storm on 1 June 2013

Science.gov (United States)

Kang, S. B.; Fok, M. C. H.; Engebretson, M. J.; Li, W.; Glocer, A.

2017-12-01

Significant electron flux depletion over a wide range of L-shell and energy, referred as a dropout, was observed by Van Allen Probes during the storm main phase on June 1, 2013. During the same period, MeV electron precipitation with isotropic pitch-angle distribution was also observed in the evening sector from POES but no EMIC waves were detected from either space- or ground-based magnetometers. Based on Tsyganenko empirical magnetic field model, magnetic field lines are highly non-dipolar and stretched at the night side in the inner magnetosphere. This condition can break the first adiabatic invariant (conservation of magnetic moment) and generate pitch-angle scattering of relativistic electron to the loss cone. To understand the relative roles of different physical mechanisms on this dropout event, we simulate flux and phase space density of relativistic electrons with event specific plasma wave intensities using the Comprehensive Inner Magnetosphere and Ionosphere (CIMI) model, as a global 4-D inner magnetosphere model. We also employ pitch-angle scattering due to field line curvature in the CIMI model. We re-configure magnetic field every minute and update electric field every 20 seconds to capture radial transport. CIMI-simulation with pitch-angle scattering due to field line curvature shows more depletion of relativistic electron fluxes and better agreement to observation than CIMI-simulation with radial transport only. We conclude that pitch-angle scattering due to field line curvature is one of the dominant processes for the relativistic electron flux dropout.

SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION

Energy Technology Data Exchange (ETDEWEB)

Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)

2016-12-20

Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.

Scalewise invariant analysis of the anisotropic Reynolds stress tensor for atmospheric surface layer and canopy sublayer turbulent flows

Science.gov (United States)

Brugger, Peter; Katul, Gabriel G.; De Roo, Frederik; Kröniger, Konstantin; Rotenberg, Eyal; Rohatyn, Shani; Mauder, Matthias

2018-05-01

Anisotropy in the turbulent stress tensor, which forms the basis of invariant analysis, is conducted using velocity time series measurements collected in the canopy sublayer (CSL) and the atmospheric surface layer (ASL). The goal is to assess how thermal stratification and surface roughness conditions simultaneously distort the scalewise relaxation towards isotropic state from large to small scales when referenced to homogeneous turbulence. To achieve this goal, conventional invariant analysis is extended to allow scalewise information about relaxation to isotropy in physical (instead of Fourier) space to be incorporated. The proposed analysis shows that the CSL is more isotropic than its ASL counterpart at large, intermediate, and small (or inertial) scales irrespective of the thermal stratification. Moreover, the small (or inertial) scale anisotropy is more prevalent in the ASL when compared to the CSL, a finding that cannot be fully explained by the intensity of the mean velocity gradient acting on all scales. Implications to the validity of scalewise Rotta and Lumley models for return to isotropy as well as advantages to using barycentric instead of anisotropy invariant maps for such scalewise analysis are discussed.

Dark coupling and gauge invariance

International Nuclear Information System (INIS)

Gavela, M.B.; Honorez, L. Lopez; Mena, O.; Rigolin, S.

2010-01-01

We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data

Dark Coupling and Gauge Invariance

CERN Document Server

Gavela, M B; Mena, O; Rigolin, S

2010-01-01

We study a coupled dark energy-dark matter model in which the energy-momentum exchange is proportional to the Hubble expansion rate. The inclusion of its perturbation is required by gauge invariance. We derive the linear perturbation equations for the gauge invariant energy density contrast and velocity of the coupled fluids, and we determine the initial conditions. The latter turn out to be adiabatic for dark energy, when assuming adiabatic initial conditions for all the standard fluids. We perform a full Monte Carlo Markov Chain likelihood analysis of the model, using WMAP 7-year data.

Loop quasi-invariant chunk detection

DEFF Research Database (Denmark)

Moyen, Jean-Yves; Rubiano, Thomas; Seiller, Thomas

2017-01-01

Several techniques for analysis and transformations are used in compilers. Among them, the peeling of loops for hoisting quasi-invariants can be used to optimize generated code, or simply ease developers’ lives. In this paper, we introduce a new concept of dependency analysis borrowed from the fi...

Recent development of relativistic molecular theory

International Nuclear Information System (INIS)

Takahito, Nakajima; Kimihiko, Hirao

2005-01-01

Today it is common knowledge that relativistic effects are important in the heavy-element chemistry. The continuing development of the relativistic molecular theory is opening up rows of the periodic table that are impossible to treat with the non-relativistic approach. The most straightforward way to treat relativistic effects on heavy-element systems is to use the four-component Dirac-Hartree-Fock approach and its electron-correlation methods based on the Dirac-Coulomb(-Breit) Hamiltonian. The Dirac-Hartree-Fock (DHF) or Dirac-Kohn-Sham (DKS) equation with the four-component spinors composed of the large- and small-components demands severe computational efforts to solve, and its applications to molecules including heavy elements have been limited to small- to medium-size systems. Recently, we have developed a very efficient algorithm for the four-component DHF and DKS approaches. As an alternative approach, several quasi-relativistic approximations have also been proposed instead of explicitly solving the four-component relativistic equation. We have developed the relativistic elimination of small components (RESC) and higher-order Douglas-Kroll (DK) Hamiltonians within the framework of the two-component quasi-relativistic approach. The developing four-component relativistic and approximate quasi-relativistic methods have been implemented into a program suite named REL4D. In this article, we will introduce the efficient relativistic molecular theories to treat heavy-atomic molecular systems accurately via the four-component relativistic and the two-component quasi-relativistic approaches. We will also show several chemical applications including heavy-element systems with our relativistic molecular approaches. (author)

Electromagnetic properties of light and heavy baryons in the relativistic quark model

International Nuclear Information System (INIS)

Nicmorus Marinescu, Diana

2007-01-01

One of the main challenges of nowadays low-energy physics remains the description of the internal structure of hadrons, strongly connected to the electromagnetic properties of matter. In this vein, the success of the relativistic quark model in the analysis of the hadron structure constitutes a solid motivation for the study carried out throughout this work. The relativistic quark model is extended to the investigation of static electromagnetic properties of both heavy and light baryons. The bare contributions to the magnetic moments of the single-, double- and triple-heavy baryons are calculated. Moreover, the relativistic quark model allows the study of the electromagnetic properties of the light baryon octet incorporating meson cloud contributions in a perturbative manner. The long disputed values of the multipole ratios E2/M1 and C2/M1 and the electromagnetic form factors of the N→Δγ transition are successfully reproduced. The relativistic quark model can be viewed as a quantum field theory approach based on a phenomenological Lagrangian coupling light and heavy baryons to their constituent quarks. In our approach the baryon is a composite object of three constituent quarks, at least in leading order. The effective interaction Lagrangian is written in terms of baryon and constituent quark fields. The effective action preserves Lorentz covariance and gauge invariance. The main ingredients of the model are already introduced at the level of the interaction Lagrangian: the three-quark baryon currents, the Gaussian distribution of the constituent quarks inside the baryon and the compositeness condition which sets an upper limit for the baryon-quark vertex. The S-matrix elements are expressed by a set of Feynman quark-diagrams. The model contains only few parameters, namely, the cut-off parameter of the Gaussian quark distribution and the free quark propagator, which are unambiguously determined from the best fit to the data. The heavy quark limit within this

Electromagnetic properties of light and heavy baryons in the relativistic quark model

Energy Technology Data Exchange (ETDEWEB)

Nicmorus Marinescu, Diana

2007-06-14

One of the main challenges of nowadays low-energy physics remains the description of the internal structure of hadrons, strongly connected to the electromagnetic properties of matter. In this vein, the success of the relativistic quark model in the analysis of the hadron structure constitutes a solid motivation for the study carried out throughout this work. The relativistic quark model is extended to the investigation of static electromagnetic properties of both heavy and light baryons. The bare contributions to the magnetic moments of the single-, double- and triple-heavy baryons are calculated. Moreover, the relativistic quark model allows the study of the electromagnetic properties of the light baryon octet incorporating meson cloud contributions in a perturbative manner. The long disputed values of the multipole ratios E2/M1 and C2/M1 and the electromagnetic form factors of the N{yields}{delta}{gamma} transition are successfully reproduced. The relativistic quark model can be viewed as a quantum field theory approach based on a phenomenological Lagrangian coupling light and heavy baryons to their constituent quarks. In our approach the baryon is a composite object of three constituent quarks, at least in leading order. The effective interaction Lagrangian is written in terms of baryon and constituent quark fields. The effective action preserves Lorentz covariance and gauge invariance. The main ingredients of the model are already introduced at the level of the interaction Lagrangian: the three-quark baryon currents, the Gaussian distribution of the constituent quarks inside the baryon and the compositeness condition which sets an upper limit for the baryon-quark vertex. The S-matrix elements are expressed by a set of Feynman quark-diagrams. The model contains only few parameters, namely, the cut-off parameter of the Gaussian quark distribution and the free quark propagator, which are unambiguously determined from the best fit to the data. The heavy quark limit

The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form

International Nuclear Information System (INIS)

Mourad, J.; Sazdjian, H.

1994-01-01

The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs

Invariants for minimal conformal supergravity in six dimensions

Energy Technology Data Exchange (ETDEWEB)

Butter, Daniel [Nikhef Theory Group,Science Park 105, 1098 XG Amsterdam (Netherlands); Kuzenko, Sergei M. [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia); Novak, Joseph; Theisen, Stefan [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, D-14476 Golm (Germany)

2016-12-15

We develop a new off-shell formulation for six-dimensional conformal supergravity obtained by gauging the 6D N=(1,0) superconformal algebra in superspace. This formulation is employed to construct two invariants for 6D N=(1,0) conformal supergravity, which contain C{sup 3} and C◻C terms at the component level. Using a conformal supercurrent analysis, we prove that these exhaust all such invariants in minimal conformal supergravity. Finally, we show how to construct the supersymmetric F◻F invariant in curved superspace.

Invariant and Absolute Invariant Means of Double Sequences

Directory of Open Access Journals (Sweden)

Abdullah Alotaibi

2012-01-01

Full Text Available We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals. We also define the absolute invariant mean through which the space of absolutely σ-convergent double sequences is characterized.

On the linear stability of sheared and magnetized jets without current sheets - relativistic case

Science.gov (United States)

Kim, Jinho; Balsara, Dinshaw S.; Lyutikov, Maxim; Komissarov, Serguei S.

2018-03-01

In our prior series of papers, we studied the non-relativistic and relativistic linear stability analysis of magnetized jets that do not have current sheets. In this paper, we extend our analysis to relativistic jets with a velocity shear and a similar current sheet free structure. The jets that we study are realistic because we include a velocity shear, a current sheet free magnetic structure, a relativistic velocity and a realistic thermal pressure so as to achieve overall pressure balance in the unperturbed jet. In order to parametrize the velocity shear, we apply a parabolic profile to the jets' 4-velocity. We find that the velocity shear significantly improves the stability of relativistic magnetized jets. This fact is completely consistent with our prior stability analysis of non-relativistic, sheared jets. The velocity shear mainly plays a role in stabilizing the short wavelength unstable modes for the pinch as well as the kink instability modes. In addition, it also stabilizes the long wavelength fundamental pinch instability mode. We also visualize the pressure fluctuations of each unstable mode to provide a better physical understanding of the enhanced stabilization by the velocity shear. Our overall conclusion is that combining velocity shear with a strong and realistic magnetic field makes relativistic jets even more stable.

Relativistic centrifugal instability

Science.gov (United States)

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.

Bosonization of non-relativistic fermions and W-infinity algebra

International Nuclear Information System (INIS)

Das, S.R.; Dhar, A.; Mandal, G.; Wadia, S.R.

1992-01-01

In this paper the authors discuss the bosonization of non-relativistic fermions in one-space dimension in terms of bilocal operators which are naturally related to the generators of W-infinity algebra. The resulting system is analogous to the problem of a spin in a magnetic field for the group W-infinity. The new dynamical variables turn out to be W-infinity group elements valued in the coset W-infinity/H where H is a Cartan subalgebra. A classical action with an H gauge invariance is presented. This action is three-dimensional. It turns out to be similar to the action that describes the color degrees of freedom of a Yang-Mills particle in a fixed external field. The authors also discuss the relation of this action with the one recently arrived at in the Euclidean continuation of the theory using different coordinates

Relativistic Kinetic Theory

Science.gov (United States)

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.

Relativistic Linear Restoring Force

Science.gov (United States)

Clark, D.; Franklin, J.; Mann, N.

2012-01-01

We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…

Relativistic decay widths of autoionization processes: The relativistic FanoADC-Stieltjes method

Energy Technology Data Exchange (ETDEWEB)

Fasshauer, Elke, E-mail: Elke.Fasshauer@uit.no [Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø–The Arctic University of Norway, N-9037 Tromsø (Norway); Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany); Kolorenč, Přemysl [Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00 Prague (Czech Republic); Pernpointner, Markus [Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)

2015-04-14

Electronic decay processes of ionized systems are, for example, the Auger decay or the Interatomic/ Intermolecular Coulombic Decay. In both processes, an energetically low lying vacancy is filled by an electron of an energetically higher lying orbital and a secondary electron is instantaneously emitted to the continuum. Whether or not such a process occurs depends both on the energetic accessibility and the corresponding lifetime compared to the lifetime of competing decay mechanisms. We present a realization of the non-relativistically established FanoADC-Stieltjes method for the description of autoionization decay widths including relativistic effects. This procedure, being based on the Algebraic Diagrammatic Construction (ADC), was adapted to the relativistic framework and implemented into the relativistic quantum chemistry program package Dirac. It is, in contrast to other existing relativistic atomic codes, not limited to the description of autoionization lifetimes in spherically symmetric systems, but is instead also applicable to molecules and clusters. We employ this method to the Auger processes following the Kr3d{sup −1}, Xe4d{sup −1}, and Rn5d{sup −1} ionization. Based on the results, we show a pronounced influence of mainly scalar-relativistic effects on the decay widths of autoionization processes.

Pseudospin symmetry in the relativistic Manning-Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term

International Nuclear Information System (INIS)

Wei Gaofeng; Dong Shihai

2010-01-01

Based on the Sturm-Liouville theorem and shape invariance formalism, we study by applying a Pekeris-type approximation to the pseudo-centrifugal term the pseudospin symmetry of a Dirac nucleon subjected to scalar and vector Manning-Rosen potentials including the spin-orbit coupling term. A quartic energy equation and spinor wave functions with arbitrary spin-orbit coupling quantum number k are presented. The bound states are calculated numerically. The relativistic Manning-Rosen potential could not trap a Dirac nucleon in the limit case β→∞.

Relativistic positioning systems: perspectives and prospects

Science.gov (United States)

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).

Electronic structure of FeTiSb using relativistic and scalar-relativistic approaches

Energy Technology Data Exchange (ETDEWEB)

Sahariya, Jagrati [Department of Physics, Manipal University Jaipur, Jaipur-303007, Rajasthan (India); Mund, H. S., E-mail: hmoond@gmail.com [Department of Physics, M. L. Sukhadia University, Udaipur-313001, Rajasthan (India)

2016-05-06

Electronic and magnetic properties of FeTiSb have been reported. The calculations are performed using spin polarized relativistic Korringa-Kohn-Rostoker scheme based on Green’s function method. Within SPR-KKR a fully relativistic and scalar-relativistic approaches have been used to investigate electronic structure of FeTiSb. Energy bands, total and partial density of states, atom specific magnetic moment along with total moment of FeTiSb alloys are presented.

Relativistic entanglement from relativistic quantum mechanics in the rest-frame instant form of dynamics

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.

Quantized gauge invariant periodic TDHF solutions

International Nuclear Information System (INIS)

Kan, K.-K.; Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.

1979-01-01

Time-dependent Hartree-Fock (TDHF) is used to study steady state large amplitude nuclear collective motions, such as vibration and rotation. As is well known the small amplitude TDHF leads to the RPA equation. The analysis of periodicity in TDHF is not trivial because TDHF is a nonlinear theory and it is not known under what circumstances a nonlinear theory can support periodic solutions. It is also unknown whether such periodic solution, if they exist, form a continuous or a discrete set. But, these properties may be important in obtaining the energy spectrum of the collective states from the TDHF description. The periodicity and Gauge Invariant Periodicity of solutions are investigated for that class of models whose TDHF solutions depend on time through two parameters. In such models TDHF supports a continuous family of periodic solutions, but only a discrete subset of these is gauge invariant. These discrete Gauge Invariant Periodic solutions obey the Bohr-Summerfeld quantization rule. The energy spectrum of the Gauge Invariant Periodic solutions is compared with the exact eigenergies in one specific example

Invariant and semi-invariant probabilistic normed spaces

Energy Technology Data Exchange (ETDEWEB)

Ghaemi, M.B. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, B. [Departamento de Estadistica y Matematica Aplicada, Universidad de Almeria, Almeria E-04120 (Spain)], E-mail: blafuerz@ual.es; Saiedinezhad, S. [School of Mathematics Iran, University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: ssaiedinezhad@yahoo.com

2009-10-15

Probabilistic metric spaces were introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . We introduce the concept of semi-invariance among the PN spaces. In this paper we will find a sufficient condition for some PN spaces to be semi-invariant. We will show that PN spaces are normal spaces. Urysohn's lemma, and Tietze extension theorem for them are proved.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

Science.gov (United States)

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.

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)

Relativistic Celestial Mechanics of the Solar System

CERN Document Server

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

Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

International Nuclear Information System (INIS)

Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.

2011-01-01

Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.

Visualizing special relativity: the field of an electric dipole moving at relativistic speed

International Nuclear Information System (INIS)

Smith, Glenn S

2011-01-01

The electromagnetic field is determined for a time-varying electric dipole moving with a constant velocity that is parallel to its moment. Graphics are used to visualize this field in the rest frame of the dipole and in the laboratory frame when the dipole is moving at relativistic speed. Various phenomena from special relativity are clearly illustrated by these graphics and explained with simple calculations; these include the constancy of the speed of light in inertial frames, the Doppler effect, the headlight effect, and the concentration of field lines. In addition, the energy and linear momentum of the radiated field are determined and shown to satisfy the transformation and invariance required by special relativity.

Linear analysis of rotationally invariant, radially variant tomographic imaging systems

International Nuclear Information System (INIS)

Huesmann, R.H.

1990-01-01

This paper describes a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a system are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted least squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix has cubic computational complexity. However, the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared

Rotationally invariant correlation filtering

International Nuclear Information System (INIS)

Schils, G.F.; Sweeney, D.W.

1985-01-01

A method is presented for analyzing and designing optical correlation filters that have tailored rotational invariance properties. The concept of a correlation of an image with a rotation of itself is introduced. A unified theory of rotation-invariant filtering is then formulated. The unified approach describes matched filters (with no rotation invariance) and circular-harmonic filters (with full rotation invariance) as special cases. The continuum of intermediate cases is described in terms of a cyclic convolution operation over angle. The angular filtering approach allows an exact choice for the continuous trade-off between loss of the correlation energy (or specificity regarding the image) and the amount of rotational invariance desired

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)

Properties of invariant modelling and invariant glueing of vector fields

International Nuclear Information System (INIS)

Petukhov, V.R.

1987-01-01

Invariant modelling and invariant glueing of both continuous (rates and accelerations) and descrete vector fields, gradient and divergence cases are considered. The following appendices are discussed: vector fields in crystals, crystal disclinations, topological charges and their fields

On the hierarchy of partially invariant submodels of differential equations

Energy Technology Data Exchange (ETDEWEB)

Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

2008-07-04

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

Science.gov (United States)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

On the hierarchy of partially invariant submodels of differential equations

International Nuclear Information System (INIS)

Golovin, Sergey V

2008-01-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

Energy analysis of four dimensional extended hyperbolic Scarf I plus three dimensional separable trigonometric noncentral potentials using SUSY QM approach

International Nuclear Information System (INIS)

Suparmi, A.; Cari, C.; Deta, U. A.; Handhika, J.

2016-01-01

The non-relativistic energies and wave functions of extended hyperbolic Scarf I plus separable non-central shape invariant potential in four dimensions are investigated using Supersymmetric Quantum Mechanics (SUSY QM) Approach. The three dimensional separable non-central shape invariant angular potential consists of trigonometric Scarf II, Manning Rosen and Poschl-Teller potentials. The four dimensional Schrodinger equation with separable shape invariant non-central potential is reduced into four one dimensional Schrodinger equations through variable separation method. By using SUSY QM, the non-relativistic energies and radial wave functions are obtained from radial Schrodinger equation, the orbital quantum numbers and angular wave functions are obtained from angular Schrodinger equations. The extended potential means there is perturbation terms in potential and cause the decrease in energy spectra of Scarf I potential. (paper)

Statistical analysis of complex systems with nonclassical invariant measures

KAUST Repository

Fratalocchi, Andrea

2011-02-28

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a general formalism based on the Ablowitz-Kaup-Newell-Segur scheme, I demonstrate how to build an invariant measure and, within a one-dimensional phase space, how to develop a suitable thermodynamics. A detailed example is provided with a universal model of wave propagation, with reference to a transparent potential sustaining gray solitons. The system shows a rich thermodynamic scenario, with a free-energy landscape supporting phase transitions and controllable emergent properties. I finally discuss the origin of such behavior, trying to identify common denominators in the area of complex dynamics.

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

Multiwavelength Observations of Relativistic Jets from General Relativistic Magnetohydrodynamic Simulations

Directory of Open Access Journals (Sweden)

Richard Anantua

2018-03-01

Full Text Available This work summarizes a program intended to unify three burgeoning branches of the high-energy astrophysics of relativistic jets: general relativistic magnetohydrodynamic (GRMHD simulations of ever-increasing dynamical range, the microphysical theory of particle acceleration under relativistic conditions, and multiwavelength observations resolving ever-decreasing spatiotemporal scales. The process, which involves converting simulation output into time series of images and polarization maps that can be directly compared to observations, is performed by (1 self-consistently prescribing models for emission, absorption, and particle acceleration and (2 performing time-dependent polarized radiative transfer. M87 serves as an exemplary prototype for this investigation due to its prominent and well-studied jet and the imminent prospect of learning much more from Event Horizon Telescope (EHT observations this year. Synthetic observations can be directly compared with real observations for observational signatures such as jet instabilities, collimation, relativistic beaming, and polarization. The simplest models described adopt the standard equipartition hypothesis; other models calculate emission by relating it to current density or shear. These models are intended for application to the radio jet instead of the higher frequency emission, the disk and the wind, which will be subjects of future investigations.

Integrals of periodic motion and periodic solutions for classical equations of relativistic string with masses at ends. I. Integrals of periodic motion

International Nuclear Information System (INIS)

Barbashov, B.M.

1996-01-01

Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space E 2 1 , there are two invariants of that sort, the curvature K and torsion κ. Curvatures of trajectories of the string ends with masses are always constant, K i =γ/m i (i=1,2), whereas torsions κ i obey a system of differential equations with deviating arguments. For these equations with periodic κ i (τ+nl)=κ(τ), constants of motion are obtained (part 1) and exact solutions are presented (part 2) for periods l and 2l where l is the string length in the plane of parameters τ and σ(σ 1 =0, σ 2 =l). 7 refs

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.

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

Beam analysis spectrometer for relativistic heavy ions

International Nuclear Information System (INIS)

Schimmerling, W.; Subramanian, T.S.; McDonald, W.J.; Kaplan, S.N.; Sadoff, A.; Gabor, G.

1983-01-01

A versatile spectrometer useful for measuring the mass, charge, energy, fluence and angular distribution of primaries and fragments associated with relativistic heavy ion beams is described. The apparatus is designed to provide accurate physical data for biology experiments and medical therapy planning as a function of depth in tissue. The spectrometer can also be used to measure W, the average energy to produce an ion pair, range-energy, dE/dx, and removal cross section data of interest in nuclear physics. (orig.)

CONSERATION LAWS OF RELATIVISTIC VARLABLE MASS SYSTEM%相对论性变质量系统的守恒律

Institute of Scientific and Technical Information of China (English)

方建会

2001-01-01

研究相对论性变质量系统的守恒律. 给出相对论性变质量系统的 d'Alembert-Lagrange原理，利用其在无限小变换下的不变性条件，得到相对论性变质量 系统的守恒律存在的条件和形式，并举例说明结果的应用.%The conservation laws of relativistic variable mass system were studied. The d' Alembert-Lagrange principle of relativistic variable mass system are given. By using invariant condition of The d'Alembert-Lagrange principle under the infin itesimal transformations, the conditions and forms which the conserved quantities of the system do exist were obtained. An example is given to illustrate the ap plication of the result..

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

Relativistic particle in a box

OpenAIRE

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

Effect of an anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions

Science.gov (United States)

Jaiswal, Amaresh; Bhaduri, Partha Pratim

2018-04-01

We study the effect of an anisotropic escape mechanism on elliptic flow in relativistic heavy-ion collisions. We use the Glauber model to generate initial conditions and ignore hydrodynamic expansion in the transverse direction. We employ the Beer-Lambert law to allow for the transmittance of produced hadrons in the medium and calculate the anisotropy generated due to the suppression of particles traversing through the medium. To separate non-flow contribution due to surface bias effects, we ignore hydrodynamic expansion in the transverse direction and consider purely longitudinal boost-invariant expansion. We calculate the transverse momentum dependence of elliptic flow, generated from an anisotropic escape mechanism due to surface bias effects, for various centralities in √{sN N}=200 GeV Au +Au collisions at the Relativistic Heavy Ion Collider and √{sN N}=2.76 TeV Pb +Pb collisions at the Large Hadron Collider. We find that the surface bias effects make a sizable contribution to the total elliptic flow observed in heavy-ion collisions, indicating that the viscosity of the QCD matter extracted from hydrodynamic simulations may be underestimated.

Remarks on the E-invariant and the Casson invariant

International Nuclear Information System (INIS)

Seade, J.

1991-08-01

In this work a framed manifold means a pair (M,F) consisting of a closed C ∞ , stably parallelizable manifold M, together with a trivialization F of its stable tangent bundle. The purpose of this work is to understand and determine in higher dimensions the invariant h(M,F) appearing in connection with the Adams e-invariants. 28 refs

Relativistic hydrodynamics

CERN Document Server

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...

Invariants of generalized Lie algebras

International Nuclear Information System (INIS)

Agrawala, V.K.

1981-01-01

Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants

Study of quantum spin correlations of relativistic electron pairs - Testing nonlocality of relativistic quantum mechanics

International Nuclear Information System (INIS)

Bodek, K.; Rozpędzik, D.; Zejma, J.; Caban, P.; Rembieliński, J.; Włodarczyk, M.; Ciborowski, J.; Enders, J.; Köhler, A.; Kozela, A.

2013-01-01

The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass

Atomic physics using relativistic H- beams

International Nuclear Information System (INIS)

Bryant, H.C.

2005-01-01

Full text: An 8 GeV hydrogen atom can traverse a focused laser beam of width of 1 micron in a time of 353 attoseconds in its rest frame. A design is currently underway at Fermilab for a superconducting linear accelerator that will accelerate H - ions to 8 GeV. This 'Proton Driver' beam is intended to be injected, after stripping down to protons, into the 120 GeV Main Injector for the mass production of neutrinos aimed at a neutrino detector (MINOS) in a mine shaft in Soudan, Minnesota (USA) for the study of neutrino oscillations. It has not passed unnoticed that with some advance planning a few nanoamps from the up-to-250 mA beam could be diverted for atomic physics experiments. Relativistic kinematics enable the creation of extreme conditions for a beam atom. For example, the Doppler shift allows a very large tuning range in the atom's rest frame of a laser beam that is fixed- frequency in the lab. At 8 GeV the rest frame Doppler shift ranges from a factor of 19 in the forward direction to 0.05 backward. The laser intensity is enhanced by the square of the Doppler shift, so that the world's most intense laser beam would be amplified by a factor of 360 in the atom's rest frame. Furthermore, although there are extreme changes in the frequency and intensity in the atom's frame as one changes the intersection angle, the ponderomotive potential remains constant, as it is a relativistic invariant. One of the interesting problems that arises in the planning for this accelerator is the stripping of electrons from the negative ions by photodetachment from Doppler shifted thermal photons. We estimate that, if the transfer lines are kept at 300 K (room temperature), the mean free path at 8 GeV for stripping from collisions with cavity radiation is about 1300 km. The physics of the interactions of such a beam with very thin material foils, again in the attosecond regime, has been treated theoretically, but has not been studied experimentally at such high energies. We will

Invariance as a Tool for Ontology of Information

Directory of Open Access Journals (Sweden)

Marcin J. Schroeder

2016-03-01

Full Text Available Attempts to answer questions regarding the ontological status of information are frequently based on the assumption that information should be placed within an already existing framework of concepts of established ontological statuses related to science, in particular to physics. However, many concepts of physics have undetermined or questionable ontological foundations. We can look for a solution in the recognition of the fundamental role of invariance with respect to a change of reference frame and to other transformations as a criterion for objective existence. The importance of invariance (symmetry as a criterion for a primary ontological status can be identified in the methodology of physics from its beginnings in the work of Galileo, to modern classifications of elementary particles. Thus, the study of the invariance of the theoretical description of information is proposed as the first step towards ontology of information. With the exception of only a few works among publications which set the paradigm of information studies, the issues of invariance were neglected. Orthodox analysis of information lacks conceptual framework for the study of invariance. The present paper shows how invariance can be formalized for the definition of information and, accompanying it, mathematical formalism proposed by the author in his earlier publications.

Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

OpenAIRE

Zhang, Teng; Wu, Kanzhi; Song, Jingwei; Huang, Shoudong; Dissanayake, Gamini

2017-01-01

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation...

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.

Science.gov (United States)

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.

Parity and time invariance violation in mercury

International Nuclear Information System (INIS)

Ginges, J.S.M.; Dzuba, V.A.; Flambaum, V.V.; Kozlov, M.G.

2002-01-01

Full text: In a recent experiment, a stringent upper limit was placed on the atomic electric dipole moment (EDM) of 199 Hg corresponding to the best limit on an atomic EDM to date. This limit can be interpreted in terms of a limit on a parity-and time-invariance violating (P,T-odd) nuclear electric moment, the Schiff moment. This moment can arise in the nucleus due to an intrinsic EDM of an unpaired nucleon or a P,T-odd interaction between nucleons. In previous calculations the electrostatic potential of the Schiff moment was expressed in a singular form which must be treated carefully to avoid divergences in the electronic matrix elements. We have shown that the electric field distribution inside the nucleus arising from the Schiff moment is constant and directed along the nuclear spin. This allows us to express the Schiff moment in a form more convenient for numerical relativistic atomic calculations. We have calculated the atomic EDM induced in Hg due to the Schiff moment (for which no direct calculation has previously been performed) and have placed new limits on the fundamental P,T-odd parameters. These limits strongly constrain competing theories of CP-violation

On density of the Vassiliev invariants

DEFF Research Database (Denmark)

Røgen, Peter

1999-01-01

The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots......The main result is that the Vassiliev invariants are dense in the set of numeric knot invariants if and only if they separate knots.Keywords: Knots, Vassiliev invariants, separation, density, torus knots...

Relativistic Coulomb Fission

Science.gov (United States)

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)

On Integral Invariants for Effective 3-D Motion Trajectory Matching and Recognition.

Science.gov (United States)

Shao, Zhanpeng; Li, Youfu

2016-02-01

Motion trajectories tracked from the motions of human, robots, and moving objects can provide an important clue for motion analysis, classification, and recognition. This paper defines some new integral invariants for a 3-D motion trajectory. Based on two typical kernel functions, we design two integral invariants, the distance and area integral invariants. The area integral invariants are estimated based on the blurred segment of noisy discrete curve to avoid the computation of high-order derivatives. Such integral invariants for a motion trajectory enjoy some desirable properties, such as computational locality, uniqueness of representation, and noise insensitivity. Moreover, our formulation allows the analysis of motion trajectories at a range of scales by varying the scale of kernel function. The features of motion trajectories can thus be perceived at multiscale levels in a coarse-to-fine manner. Finally, we define a distance function to measure the trajectory similarity to find similar trajectories. Through the experiments, we examine the robustness and effectiveness of the proposed integral invariants and find that they can capture the motion cues in trajectory matching and sign recognition satisfactorily.

Statistical characterisation of COSMO Sky-Med X-SAR retrieved precipitation fields by scale-invariance analysis

Science.gov (United States)

Deidda, Roberto; Mascaro, Giuseppe; Hellies, Matteo; Baldini, Luca; Roberto, Nicoletta

2013-04-01

COSMO Sky-Med (CSK) is an important programme of the Italian Space Agency aiming at supporting environmental monitoring and management of exogenous, endogenous and anthropogenic risks through X-band Synthetic Aperture Radar (X-SAR) on board of 4 satellites forming a constellation. Most of typical SAR applications are focused on land or ocean observation. However, X-band SAR can be detect precipitation that results in a specific signature caused by the combination of attenuation of surface returns induced by precipitation and enhancement of backscattering determined by the hydrometeors in the SAR resolution volume. Within CSK programme, we conducted an intercomparison between the statistical properties of precipitation fields derived by CSK SARs and those derived by the CNR Polar 55C (C-band) ground based weather radar located in Rome (Italy). This contribution presents main results of this research which was aimed at the robust characterisation of rainfall statistical properties across different scales by means of scale-invariance analysis and multifractal theory. The analysis was performed on a dataset of more two years of precipitation observations collected by the CNR Polar 55C radar and rainfall fields derived from available images collected by the CSK satellites during intense rainfall events. Scale-invariance laws and multifractal properties were detected on the most intense rainfall events derived from the CNR Polar 55C radar for spatial scales from 4 km to 64 km. The analysis on X-SAR retrieved rainfall fields, although based on few images, leaded to similar results and confirmed the existence of scale-invariance and multifractal properties for scales larger than 4 km. These outcomes encourage investigating SAR methodologies for future development of meteo-hydrological forecasting models based on multifractal theory.

Cosmological measurements with general relativistic galaxy correlations

International Nuclear Information System (INIS)

Raccanelli, Alvise; Montanari, Francesco; Durrer, Ruth; Bertacca, Daniele; Doré, Olivier

2016-01-01

We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called ''relativistic effects'', and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms, especially lensing convergence, introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. The analysis suggests a possible substantial systematic error in cosmological parameter constraints. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.

A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone

Energy Technology Data Exchange (ETDEWEB)

Umeh, Obinna; Jolicoeur, Sheean; Maartens, Roy [Department of Physics and Astronomy, University of the Western Cape, Robert Sobukwe Road, Cape Town 7535 (South Africa); Clarkson, Chris, E-mail: umeobinna@gmail.com, E-mail: beautifulheart369@gmail.com, E-mail: roy.maartens@gmail.com, E-mail: chris.clarkson@gmail.com [School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)

2017-03-01

Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone, as well as from relativistic corrections to the dynamics. As an initial step towards a fully relativistic analysis of the galaxy bispectrum, we compute for the first time the local relativistic lightcone effects on the bispectrum, which come from Doppler and gravitational potential contributions. For the galaxy bispectrum, the problem is much more complex than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the local lightcone projection effects for squeezed shapes at z ∼ 1 mean that the bispectrum can differ from the Newtonian prediction by ∼> 10% when the short modes are k ∼< (50 Mpc){sup −1}. These relativistic projection effects, if ignored in the analysis of observations, could be mistaken for primordial non-Gaussianity. For upcoming surveys which probe equality scales and beyond, all relativistic lightcone effects and relativistic dynamical corrections should be included for an accurate measurement of primordial non-Gaussianity.

Relativistic hydrodynamics, heavy ion reactions and antiproton annihilation

International Nuclear Information System (INIS)

Strottman, D.

1985-01-01

The application of relativistic hydrodynamics to relativistic heavy ions and antiproton annihilation is summarized. Conditions for validity of hydrodynamics are presented. Theoretical results for inclusive particle spectra, pion production and flow analysis are given for medium energy heavy ions. The two-fluid model is introduced and results presented for reactions from 800 MeV per nucleon to 15 GeV on 15 GeV per nucleon. Temperatures and densities attained in antiproton annihilation are given. Finally, signals which might indicate the presence of a quark-gluon plasma are briefly surveyed

Relativistic impulse dynamics.

Science.gov (United States)

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.

Statistical analysis of complex systems with nonclassical invariant measures

KAUST Repository

Fratalocchi, Andrea

2011-01-01

I investigate the problem of finding a statistical description of a complex many-body system whose invariant measure cannot be constructed stemming from classical thermodynamics ensembles. By taking solitons as a reference system and by employing a

Cohomological invariants in Galois cohomology

CERN Document Server

Garibaldi, Skip; Serre, Jean Pierre

2003-01-01

This volume is concerned with algebraic invariants, such as the Stiefel-Whitney classes of quadratic forms (with values in Galois cohomology mod 2) and the trace form of �tale algebras (with values in the Witt ring). The invariants are analogues for Galois cohomology of the characteristic classes of topology. Historically, one of the first examples of cohomological invariants of the type considered here was the Hasse-Witt invariant of quadratic forms. The first part classifies such invariants in several cases. A principal tool is the notion of versal torsor, which is an analogue of the universal bundle in topology. The second part gives Rost's determination of the invariants of G-torsors with values in H^3(\\mathbb{Q}/\\mathbb{Z}(2)), when G is a semisimple, simply connected, linear group. This part gives detailed proofs of the existence and basic properties of the Rost invariant. This is the first time that most of this material appears in print.

The underlying principles of relativistic theory of gravitation

International Nuclear Information System (INIS)

Logunov, A.A.

1989-01-01

The paper deals with the main statements of relativistic theory of gravitation, constructed in result of critical analysis of the general theory of relativity. The principle of geometrization is formulated

Cosmological disformal invariance

Energy Technology Data Exchange (ETDEWEB)

Domènech, Guillem; Sasaki, Misao [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Naruko, Atsushi, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: naruko@th.phys.titech.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp [Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551 (Japan)

2015-10-01

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

Moment invariants for particle beams

International Nuclear Information System (INIS)

Lysenko, W.P.; Overley, M.S.

1988-01-01

The rms emittance is a certain function of second moments in 2-D phase space. It is preserved for linear uncoupled (1-D) motion. In this paper, the authors present new functions of moments that are invariants for coupled motion. These invariants were computed symbolically using a computer algebra system. Possible applications for these invariants are discussed. Also, approximate moment invariants for nonlinear motion are presented

Relativistic finite-temperature Thomas-Fermi model

Science.gov (United States)

Faussurier, Gérald

2017-11-01

We investigate the relativistic finite-temperature Thomas-Fermi model, which has been proposed recently in an astrophysical context. Assuming a constant distribution of protons inside the nucleus of finite size avoids severe divergence of the electron density with respect to a point-like nucleus. A formula for the nuclear radius is chosen to treat any element. The relativistic finite-temperature Thomas-Fermi model matches the two asymptotic regimes, i.e., the non-relativistic and the ultra-relativistic finite-temperature Thomas-Fermi models. The equation of state is considered in detail. For each version of the finite-temperature Thomas-Fermi model, the pressure, the kinetic energy, and the entropy are calculated. The internal energy and free energy are also considered. The thermodynamic consistency of the three models is considered by working from the free energy. The virial question is also studied in the three cases as well as the relationship with the density functional theory. The relativistic finite-temperature Thomas-Fermi model is far more involved than the non-relativistic and ultra-relativistic finite-temperature Thomas-Fermi models that are very close to each other from a mathematical point of view.

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

Fundamental relativistic rotator: Hessian singularity and the issue of the minimal interaction with electromagnetic field

Energy Technology Data Exchange (ETDEWEB)

Bratek, Lukasz, E-mail: lukasz.bratek@ifj.edu.pl [Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskego 152, PL-31342 Krakow (Poland)

2011-05-13

There are two relativistic rotators with Casimir invariants of the Poincare group being fixed parameters. The particular models of spinning particles were studied in the past both at the classical and quantum level. Recently, a minimal interaction with electromagnetic field has been considered. We show that the dynamical systems can be uniquely singled out from among other relativistic rotators by the unphysical requirement that the Hessian referring to the physical degrees of freedom should be singular. Closely related is the fact that the equations of free motion are not independent, making the evolution indeterminate. We show that the Hessian singularity cannot be removed by the minimal interaction with the electromagnetic field. By making use of a nontrivial Hessian null space, we show that a single constraint appears in the external field for consistency of the equations of motion with the Hessian singularity. The constraint imposes unphysical limitation on the initial conditions and admissible motions. We discuss the mechanism of appearance of unique solutions in external fields on an example of motion in the uniform magnetic field. We give a simple model to illustrate that similarly constrained evolution cannot be determinate in arbitrary fields.

Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics

International Nuclear Information System (INIS)

Rose, Harald

2003-01-01

A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles

Relativistic Jahn-Teller effect in tetrahedral systems

International Nuclear Information System (INIS)

Opalka, Daniel; Domcke, Wolfgang; Segado, Mireia; Poluyanov, Leonid V.

2010-01-01

It is shown that orbitally degenerate states in highly symmetric systems are split by Jahn-Teller forces which are of relativistic origin (that is, they arise from the spin-orbit coupling operator). For the example of tetrahedral systems, the relativistic Jahn-Teller Hamiltonians of orbitally degenerate electronic states with spin 1/2 are derived. While both electrostatic and relativistic forces contribute to the Jahn-Teller activity of vibrational modes of E and T 2 symmetry in 2 T 2 states of tetrahedral systems, the electrostatic and relativistic Jahn-Teller couplings are complementary for 2 E states: The E mode is Jahn-Teller active through electrostatic forces, while the T 2 mode is Jahn-Teller active through the relativistic forces. The relativistic Jahn-Teller parameters have been computed with ab initio relativistic electronic-structure methods. It is shown for the example of the tetrahedral cluster cations of the group V elements that the relativistic Jahn-Teller couplings can be of the same order of magnitude as the familiar electrostatic Jahn-Teller couplings for the heavier elements.

The relativistic rocket

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.

Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance

OpenAIRE

Yu Nakayama

2009-01-01

We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeo...

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

An investigation of relativistic microscopic optical potential in terms of relativistic Brueckner-Bethe-Goldstone equation

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

Feedback-Driven Dynamic Invariant Discovery

Science.gov (United States)

Zhang, Lingming; Yang, Guowei; Rungta, Neha S.; Person, Suzette; Khurshid, Sarfraz

2014-01-01

Program invariants can help software developers identify program properties that must be preserved as the software evolves, however, formulating correct invariants can be challenging. In this work, we introduce iDiscovery, a technique which leverages symbolic execution to improve the quality of dynamically discovered invariants computed by Daikon. Candidate invariants generated by Daikon are synthesized into assertions and instrumented onto the program. The instrumented code is executed symbolically to generate new test cases that are fed back to Daikon to help further re ne the set of candidate invariants. This feedback loop is executed until a x-point is reached. To mitigate the cost of symbolic execution, we present optimizations to prune the symbolic state space and to reduce the complexity of the generated path conditions. We also leverage recent advances in constraint solution reuse techniques to avoid computing results for the same constraints across iterations. Experimental results show that iDiscovery converges to a set of higher quality invariants compared to the initial set of candidate invariants in a small number of iterations.

Laser-pulse compression in a collisional plasma under weak-relativistic ponderomotive nonlinearity

International Nuclear Information System (INIS)

Singh, Mamta; Gupta, D. N.

2016-01-01

We present theory and numerical analysis which demonstrate laser-pulse compression in a collisional plasma under the weak-relativistic ponderomotive nonlinearity. Plasma equilibrium density is modified due to the ohmic heating of electrons, the collisions, and the weak relativistic-ponderomotive force during the interaction of a laser pulse with plasmas. First, within one-dimensional analysis, the longitudinal self-compression mechanism is discussed. Three-dimensional analysis (spatiotemporal) of laser pulse propagation is also investigated by coupling the self-compression with the self-focusing. In the regime in which the laser becomes self-focused due to the weak relativistic-ponderomotive nonlinearity, we provide results for enhanced pulse compression. The results show that the matched interplay between self-focusing and self-compression can improve significantly the temporal profile of the compressed pulse. Enhanced pulse compression can be achieved by optimizing and selecting the parameters such as collision frequency, ion-temperature, and laser intensity.

Laser-pulse compression in a collisional plasma under weak-relativistic ponderomotive nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Singh, Mamta; Gupta, D. N., E-mail: dngupta@physics.du.ac.in [Department of Physics and Astrophysics, North Campus, University of Delhi, Delhi 110 007 (India)

2016-05-15

We present theory and numerical analysis which demonstrate laser-pulse compression in a collisional plasma under the weak-relativistic ponderomotive nonlinearity. Plasma equilibrium density is modified due to the ohmic heating of electrons, the collisions, and the weak relativistic-ponderomotive force during the interaction of a laser pulse with plasmas. First, within one-dimensional analysis, the longitudinal self-compression mechanism is discussed. Three-dimensional analysis (spatiotemporal) of laser pulse propagation is also investigated by coupling the self-compression with the self-focusing. In the regime in which the laser becomes self-focused due to the weak relativistic-ponderomotive nonlinearity, we provide results for enhanced pulse compression. The results show that the matched interplay between self-focusing and self-compression can improve significantly the temporal profile of the compressed pulse. Enhanced pulse compression can be achieved by optimizing and selecting the parameters such as collision frequency, ion-temperature, and laser intensity.

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.)

Relating measurement invariance, cross-level invariance, and multilevel reliability

OpenAIRE

Jak, S.; Jorgensen, T.D.

2017-01-01

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across levels, which is needed to give latent variables at the two levels a similar interpretation. Reliabili...

Relativistic Quantum Revivals

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.

Gauge invariance rediscovered

International Nuclear Information System (INIS)

Moriyasu, K.

1978-01-01

A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories

Invariant class operators in the decoherent histories analysis of timeless quantum theories

International Nuclear Information System (INIS)

Halliwell, J. J.; Wallden, P.

2006-01-01

The decoherent histories approach to quantum theory is applied to a class of reparametrization-invariant models whose state is an energy eigenstate. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In nonrelativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization-invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method. The formalism developed here is ultimately aimed at cosmological models described by a Wheeler-DeWitt equation, but the specific features of such models are left to future papers

Gravitational waves from nonlinear couplings of radial and polar nonradial modes in relativistic stars

International Nuclear Information System (INIS)

Passamonti, Andrea; Stergioulas, Nikolaos; Nagar, Alessandro

2007-01-01

The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors

Size-change termination and transition invariants

DEFF Research Database (Denmark)

Heizmann, Matthias; Jones, Neil; Podelski, Andreas

2010-01-01

Two directions of recent work on program termination use the concepts of size-change termination resp. transition invariants. The difference in the setting has as consequence the inherent incomparability of the analysis and verification methods that result from this work. Yet, in order...

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 gas in a Schwarzschild metric

International Nuclear Information System (INIS)

Kremer, Gilberto M

2013-01-01

A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient. (paper)

Relativistic mechanics of two interacting particles and bilocal theory

International Nuclear Information System (INIS)

Takabayasi, Takehiko

1975-01-01

New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical foundation and internal dynamics. As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories. (auth.)

Link invariants from finite Coxeter racks

OpenAIRE

Nelson, Sam; Wieghard, Ryan

2008-01-01

We study Coxeter racks over $\\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.

Fundamental relativistic solution for the rail gun

International Nuclear Information System (INIS)

Liboff, R.L.; Schenter, G.K.

1986-01-01

A fully relativistic analysis is made of the dynamics of a rail gun based on three assumptions: (1) Ohm's law is valid in the rest frame of the plasma, (2) total electron momentum is transferred to the projectile, and (3) motion of the projectile is constrained to one direction. With these assumptions, a relativistic equation for the velocity of the projectile is obtained, whose solution monotonically increases to one of two values depending on field strengths. For B>E, the maximum velocity is cE/B, whereas for E>B it is c, where c is the speed of light, and E and B are applied electric and magnetic fields, respectively (in cgs)

Particle Interferometry for Relativistic Heavy-Ion Collisions

CERN Document Server

Wiedemann, Urs Achim; Wiedemann, Urs Achim; Heinz, Ulrich

1999-01-01

In this report we give a detailed account on Hanbury Brown/Twiss (HBT) particle interferometric methods for relativistic heavy-ion collisions. These exploit identical two-particle correlations to gain access to the space-time geometry and dynamics of the final freeze-out stage. The connection between the measured correlations in momentum space and the phase-space structure of the particle emitter is established, both with and without final state interactions. Suitable Gaussian parametrizations for the two-particle correlation function are derived and the physical interpretation of their parameters is explained. After reviewing various model studies, we show how a combined analysis of single- and two-particle spectra allows to reconstruct the final state of relativistic heavy-ion collisions.

Extended Galilean symmetries of non-relativistic strings

Energy Technology Data Exchange (ETDEWEB)

Batlle, Carles [Departament de Matemàtiques and IOC, Universitat Politècnica de Catalunya, EPSEVG,Av. V. Balaguer 1, E-08808 Vilanova i la Geltrú (Spain); Gomis, Joaquim; Not, Daniel [Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB),Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain)

2017-02-09

We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.

Reparameterization invariance of NRQED self-energy corrections and improved theory for excited D states in hydrogenlike systems

International Nuclear Information System (INIS)

Wundt, Benedikt J.; Jentschura, Ulrich D.

2008-01-01

Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i.e., using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the virtual quanta from the nonrelativistic domain. Here, we calculate the higher-order corrections to the one-photon self-energy calculation with three different overlapping parameters (photon energy, photon mass and dimensional regularization) and demonstrate the reparameterization invariance of nonrelativistic quantum electrodynamics (NRQED) using this particular example. We also present new techniques for the calculation of the low-energy part of this correction, which lead to results for the Lamb shift of highly excited states that are important for high-precision spectroscopy

Reparameterization invariance of NRQED self-energy corrections and improved theory for excited D states in hydrogenlike systems

Energy Technology Data Exchange (ETDEWEB)

Wundt, Benedikt J. [Max-Planck-Institut fuer Kernphysik, Postfach 103980, 69029 Heidelberg (Germany); Jentschura, Ulrich D. [Max-Planck-Institut fuer Kernphysik, Postfach 103980, 69029 Heidelberg (Germany); Institut fuer Theoretische Physik, Philosophenweg 16, 69120 Heidelberg (Germany)], E-mail: ulrich.jentschura@mpi-hd.mpg.de

2008-01-24

Canonically, the quantum electrodynamic radiative corrections in bound systems have been evaluated in photon energy regularization, i.e., using a noncovariant overlapping parameter that separates the high-energy relativistic scales of the virtual quanta from the nonrelativistic domain. Here, we calculate the higher-order corrections to the one-photon self-energy calculation with three different overlapping parameters (photon energy, photon mass and dimensional regularization) and demonstrate the reparameterization invariance of nonrelativistic quantum electrodynamics (NRQED) using this particular example. We also present new techniques for the calculation of the low-energy part of this correction, which lead to results for the Lamb shift of highly excited states that are important for high-precision spectroscopy.

Relativistic generalization of strong plasma turbulence

International Nuclear Information System (INIS)

Chian, A.C.-L.

1982-01-01

Two fundamental electrostatic modes of an unmagnetized plasma, namely, ion acoustic mode and Langumir mode are studied. Previous theories are generalized to include the effect of relativistic mass variations. The existence of relativistic ion acoustic solitons is demonstrated. In addition, it is shown that simple, relativistic Langumir solitons do not exist in a infinite plasma. (L.C.) [pt

The Wigner function in the relativistic quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Kowalski, K., E-mail: kowalski@uni.lodz.pl; Rembieliński, J.

2016-12-15

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.

New relativistic generalization of the Heisenberg commutation relations

International Nuclear Information System (INIS)

Bohm, A.; Loewe, M.; Magnollay, P.; Tarlini, M.; Aldinger, R.R.; Kielanowski, P.

1984-01-01

A relativistic generalization of the Heisenberg commutation relations is suggested which is different from the conventional ones used for the intrinsic coordinates and momenta in the relativistic oscillator model and the relativistic string. This new quantum relativistic oscillator model is determined by the requirement that it gives a unified description of relativistic vibrations and rotations and contracts in the nonrelativistic limit c -1 →0 into the usual nonrelativistic harmonic oscillator

Rotation Invariance Neural Network

OpenAIRE

Li, Shiyuan

2017-01-01

Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap target. Last but not least, this architecture can achieve one-shot learning in some cases using thos...

Permutation-invariant distance between atomic configurations

Science.gov (United States)

Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

2015-09-01

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.

Permutation-invariant distance between atomic configurations

International Nuclear Information System (INIS)

Ferré, Grégoire; Maillet, Jean-Bernard; Stoltz, Gabriel

2015-01-01

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity

N = 2 coset compactifictions with nondiagonal invariants

International Nuclear Information System (INIS)

Aldazabal, G.; Allekotte, I.; Font, A.

1992-01-01

In this paper, the authors consider four-dimensional string models obtained by tensoring N = 2 coset theories with nondiagonal modular invariants. The authors present results from a systematic analysis including moddings by discrete symmetries

Random phase approximation in relativistic approach

International Nuclear Information System (INIS)

Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang

2009-01-01

Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)

The measurement invariance of job diagnostic survey (JDS) across three university student groups

Energy Technology Data Exchange (ETDEWEB)

Martinez-Gomez, M.; Marin-Garcia, J.A.; Girado Omeara, M.

2016-07-01

The main purpose of this study is to apply a multigroup confirmatory analysis to examine the measurement invariance (MI) of the adapted version of the Job Diagnosis Survey (JDS) as a measurement tool that analyses the relationship between the features of teaching methodologies with university students’ motivation and satisfaction across data collected on different degrees and academic years. Design/methodology/approach: Confirmatory factor analysis was carried out using a multigroup structural equation model, using the program EQS 6.1 to test the invariance of the adapted version of JDS in a sample constituted by 535 student of a Spanish public university. The assessment of invariance included the levels of configural, metric, scalar, covariance and latent variables invariance. Several goodness-of-fit measures were assessed... (Author)

Lorentz invariance with an invariant energy scale.

Science.gov (United States)

Magueijo, João; Smolin, Lee

2002-05-13

We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

Analysis of core plasma heating and ignition by relativistic electrons

International Nuclear Information System (INIS)

Nakao, Y.

2002-01-01

Clarification of the pre-compressed plasma heating by fast electrons produced by relativistic laser-plasma interaction is one of the most important issues of the fast ignition scheme in ICF. On the basis of overall calculations including the heating process, both by relativistic hot electrons and alpha-particles, and the hydrodynamic evolution of bulk plasma, we examine the feature of core plasma heating and the possibility of ignition. The deposition of the electron energy via long-range collective mode, i.e. Langmuir wave excitation, is shown to be comparable to that through binary electron-electron collisions; the calculation neglecting the wave excitation considerably underestimates the core plasma heating. The ignition condition is also shown in terms of the intensity I(h) and temperature T(h) of hot electrons. It is found that I(h) required for ignition increases in proportion to T(h). For efficiently achieving the fast ignition, electron beams with relatively 'low' energy (e.g.T(h) below 1 MeV) are desirable. (author)

Inflationary magnetogenesis, derivative couplings and relativistic Van der Waals interactions

CERN Document Server

Giovannini, Massimo

2015-01-01

When the gauge fields have derivative couplings to scalars, like in the case of the relativistic theory of Van der Waals (or Casimir-Polder) interactions, conformal invariance is broken but the magnetic and electric susceptibilities are not bound to coincide. We analyze the formation of large-scale magnetic fields in slow-roll inflation and find that they are generated at the level of a few hundredths of a nG and over typical length scales between few Mpc and $100$ Mpc. Using a new time parametrization that reduces to conformal time but only for coincident susceptibilities, the gauge action is quantized while the evolution equations of the corresponding mode functions are more easily solvable. The power spectra depend on the normalized rates of variation of the two susceptibilities (or of the corresponding gauge couplings) and on the absolute value of their ratio at the beginning of inflation. We pin down explicit regions in the parameter space where all the physical requirements (i.e. the backreaction constr...

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

Quantum gates via relativistic remote control

Energy Technology Data Exchange (ETDEWEB)

Martín-Martínez, Eduardo, E-mail: emartinm@uwaterloo.ca [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Dept. Applied Math., University of Waterloo, Ontario, N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Sutherland, Chris [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)

2014-12-12

We harness relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build 1-qubit quantum gates.

Relativistic BCS-BEC Crossover at Quark Level

Directory of Open Access Journals (Sweden)

Zhuang P.

2010-10-01

Full Text Available The non-relativistic G0G formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The theory recovers the BCS mean field approximation at zero temperature and the non-relativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the non-relativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.

Some studies of the relativistic theories for spin-3/2 particles and its interactions with an uniforme magnetic field

International Nuclear Information System (INIS)

Oliveira, M.A.B. de.

1984-01-01

We present our investigations on the problems of non-causality of propagation, at the c-number level, of four spin 3/2 theories in the Schroedinger form employing the minimum number of eight components, in interaction with a constant magnetic field. Analyzing first the basic formulations of free particle spin 3/2 relativistic wave equations, we deduze, extending to spin 3/2 Dirac's ''spin 1/2 factorization'' of the mas condition, a new eight-component relativistic wave equation in the Schroedinger form for this spin and prove its relativistic invariance. We demostrate explicitly that the entire content of the Rarita-Schwinger (RS) theory for spin 3/2 can be written in the form of two Dirac-Like wave equations. We demonstrate that our wave equation for spin 3/2 cab indeed be deduzed from a modified RS theory wherein both Hamiltonians above referred to are taken hermitian. We also establish, in a transparent maner, the equivalences existing between the formalisms of RS, Belinfante and Hurley-Sudarshan for spin 3/2. We investigate the c-number problem of the stationary state eigevalues of the spin 3/2 Hamiltonians in a constant external magnetic field, in the four theories in the Schoedinger form with eight components, those of Moldauer and Case (deduzed from TS theory), of Weaver, Hammer and Good. (autor) [pt

Consistent resolution of some relativistic quantum paradoxes

International Nuclear Information System (INIS)

Griffiths, Robert B.

2002-01-01

A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics

The Dynamical Invariant of Open Quantum System

OpenAIRE

Wu, S. L.; Zhang, X. Y.; Yi, X. X.

2015-01-01

The dynamical invariant, whose expectation value is constant, is generalized to open quantum system. The evolution equation of dynamical invariant (the dynamical invariant condition) is presented for Markovian dynamics. Different with the dynamical invariant for the closed quantum system, the evolution of the dynamical invariant for the open quantum system is no longer unitary, and the eigenvalues of it are time-dependent. Since any hermitian operator fulfilling dynamical invariant condition ...

Shift-invariant discrete wavelet transform analysis for retinal image classification.

Science.gov (United States)

Khademi, April; Krishnan, Sridhar

2007-12-01

This work involves retinal image classification and a novel analysis system was developed. From the compressed domain, the proposed scheme extracts textural features from wavelet coefficients, which describe the relative homogeneity of localized areas of the retinal images. Since the discrete wavelet transform (DWT) is shift-variant, a shift-invariant DWT was explored to ensure that a robust feature set was extracted. To combat the small database size, linear discriminant analysis classification was used with the leave one out method. 38 normal and 48 abnormal (exudates, large drusens, fine drusens, choroidal neovascularization, central vein and artery occlusion, histoplasmosis, arteriosclerotic retinopathy, hemi-central retinal vein occlusion and more) were used and a specificity of 79% and sensitivity of 85.4% were achieved (the average classification rate is 82.2%). The success of the system can be accounted to the highly robust feature set which included translation, scale and semi-rotational, features. Additionally, this technique is database independent since the features were specifically tuned to the pathologies of the human eye.

Relativistic quantum theory of composite systems

International Nuclear Information System (INIS)

Sogami, I.

1978-01-01

A relativistic quantum theory free from the difficulties of tachyons and ghosts is formulated to describe the scattering processes between composite systems of spinless quarks. To evade the complication brewed by introducing gluon fields or strings, valence quarks are effectively assumed to be in the relative motion of harmonic oscillation correlating with the motion of the composite system as a whole. A quark-antiquark system is represented by a bilocal field describing a sequence of mesons and every meson is identified with the composite system in a definite eigenstate of relative motion. The quantization is performed in the interaction picture, so that the microcausal condition is satisfied by local fields which result from the decomposition of bilocal fields. Imposing a weakened macrocausal condition on the whole motion of the extended system, a causal bilocal propagator is defined and a consistent time ordering among bilocal fields is defined. The invariant S-matrix is obtained and the graphical method for the calculation of its elements is developed in parallel with the conventional local field theory. For the (bilocal field) 3 interaction any malignant divergence does not appear excepting those in the renormalizable local field theory. The theory provides one promising and comprehensive phenomenology of hadrons which is suitable especially to describe the hard structure of hadrons. (author)

An invariant approach to statistical analysis of shapes

CERN Document Server

Lele, Subhash R

2001-01-01

INTRODUCTIONA Brief History of MorphometricsFoundations for the Study of Biological FormsDescription of the data SetsMORPHOMETRIC DATATypes of Morphometric DataLandmark Homology and CorrespondenceCollection of Landmark CoordinatesReliability of Landmark Coordinate DataSummarySTATISTICAL MODELS FOR LANDMARK COORDINATE DATAStatistical Models in GeneralModels for Intra-Group VariabilityEffect of Nuisance ParametersInvariance and Elimination of Nuisance ParametersA Definition of FormCoordinate System Free Representation of FormEst

Test of special relativity theory by means of laser spectroscopy on relativistic 7Li+ ions in the ESR

International Nuclear Information System (INIS)

Botermann, Benjamin

2012-01-01

The invariance under Lorentz transformation of the laws of physics is a fundamental postulate of modern physics and all theories of the fundamental interactions have been stated in a covariant form. Although the theory of Special Relativity (SR) has been tested and confirmed with high accuracy in a large number of experiments, improved tests are of fundamental interest due to the far-reaching relevance of this postulate. Additionally modern attempts of a unified description of the four fundamental interactions point to possible violations of Lorentz invariance. In this context experiments of the Ives-Stilwell type for a test of time dilation play an important role. High resolution laser spectroscopy is applied on relativistic particle beams to investigate the validity of the relativistic Doppler formula - and therefore of the time dilation factor γ. In the course of this thesis an Ives-Stilwell experiment was performed with 7 Li + ions at a velocity of 34 % of the speed of light, which were stored at the experimental storage ring (ESR) of the GSI Helmholtzzentrum fuer Schwerionenforschung. The techniques of Λ- as well as saturation spectroscopy were employed on the 1s2s 3 S 1 →1s2p 3 P 2 transition. By a computer based analysis of the fluorescence detection system and utilization of appropriate edge filters the signal to noise ratio was decisively improved and the application of an additional pump laser allowed for the observation of a saturation signal for the first time. The frequency stability of both laser systems was specified by means of a frequency comb to obtain the highest possible accuracy. The data from the beam times were analyzed in the frameworks of the Robertson-Mansouri-Sexl test theory (RMS) and the Standard Model Extension (SME) and the corresponding upper limits of the relevant test parameters of the assigned theories were calculated. The upper limit of the parameter α was improved by a factor of 4 compared to earlier measurements performed

RELATIVISTIC CYCLOTRON INSTABILITY IN ANISOTROPIC PLASMAS

Energy Technology Data Exchange (ETDEWEB)

López, Rodrigo A.; Moya, Pablo S.; Muñoz, Víctor; Valdivia, J. Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Navarro, Roberto E.; Araneda, Jaime A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Viñas, Adolfo F., E-mail: rlopez186@gmail.com [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, MD 20771 (United States)

2016-11-20

A sufficiently large temperature anisotropy can sometimes drive various types of electromagnetic plasma micro-instabilities, which can play an important role in the dynamics of relativistic pair plasmas in space, astrophysics, and laboratory environments. Here, we provide a detailed description of the cyclotron instability of parallel propagating electromagnetic waves in relativistic pair plasmas on the basis of a relativistic anisotropic distribution function. Using plasma kinetic theory and particle-in-cell simulations, we study the influence of the relativistic temperature and the temperature anisotropy on the collective and noncollective modes of these plasmas. Growth rates and dispersion curves from the linear theory show a good agreement with simulations results.

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

International Nuclear Information System (INIS)

Donker, H.C.; Katsnelson, M.I.; De Raedt, H.; Michielsen, K.

2016-01-01

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.

Differential invariants in nonclassical models of hydrodynamics

Science.gov (United States)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with

Hidden scale invariance of metals

DEFF Research Database (Denmark)

Hummel, Felix; Kresse, Georg; Dyre, Jeppe C.

2015-01-01

Density functional theory (DFT) calculations of 58 liquid elements at their triple point show that most metals exhibit near proportionality between the thermal fluctuations of the virial and the potential energy in the isochoric ensemble. This demonstrates a general “hidden” scale invariance...... of metals making the condensed part of the thermodynamic phase diagram effectively one dimensional with respect to structure and dynamics. DFT computed density scaling exponents, related to the Grüneisen parameter, are in good agreement with experimental values for the 16 elements where reliable data were...... available. Hidden scale invariance is demonstrated in detail for magnesium by showing invariance of structure and dynamics. Computed melting curves of period three metals follow curves with invariance (isomorphs). The experimental structure factor of magnesium is predicted by assuming scale invariant...

Apparent unambiguousness of relativistic time dilation

International Nuclear Information System (INIS)

Strel'tsov, V.N.

1992-01-01

It is indicated on the definite analogy between the dependence of visible sizes of relativistic objects and period of the wave, emitted by the moving source from the observation conditions ('retradition factor'). It is noted that the definition of time for moving extended objects, led to relativistic dilation, corresponds to the definition of the relativistic (radar) length led to the 'elongation formula'. 10 refs

Reducing Lookups for Invariant Checking

DEFF Research Database (Denmark)

Thomsen, Jakob Grauenkjær; Clausen, Christian; Andersen, Kristoffer Just

2013-01-01

This paper helps reduce the cost of invariant checking in cases where access to data is expensive. Assume that a set of variables satisfy a given invariant and a request is received to update a subset of them. We reduce the set of variables to inspect, in order to verify that the invariant is still...

Slowly rotating general relativistic superfluid neutron stars with relativistic entrainment

International Nuclear Information System (INIS)

Comer, G.L.

2004-01-01

Neutron stars that are cold enough should have two or more superfluids or supercondutors in their inner crusts and cores. The implication of superfluidity or superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect; i.e., the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modeling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic σ-ω mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit

Balance equations for a relativistic plasma. Pt. 1

International Nuclear Information System (INIS)

Hebenstreit, H.

1983-01-01

Relativistic power moments of the four-momentum are decomposed according to a macroscopic four-velocity. The thus obtained quantities are identified as relativistic generalization of the nonrelativistic orthogonal moments, e.g. diffusion flow, heat flow, pressure, etc. From the relativistic Boltzmann equation we then derive balance equations for these quantities. Explicit expressions for the relativistic mass conservation, energy balance, pressure balance, heat flow balance are presented. The weak relativistic limit is discussed. The derivation of higher order balance equations is sketched. (orig.)

Loading relativistic Maxwell distributions in particle simulations

Science.gov (United States)

Zenitani, S.

2015-12-01

In order to study energetic plasma phenomena by using particle-in-cell (PIC) and Monte-Carlo simulations, we need to deal with relativistic velocity distributions in these simulations. However, numerical algorithms to deal with relativistic distributions are not well known. In this contribution, we overview basic algorithms to load relativistic Maxwell distributions in PIC and Monte-Carlo simulations. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are newly proposed in a physically transparent manner. Their acceptance efficiencies are 􏰅50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

Machine learning strategies for systems with invariance properties

Science.gov (United States)

Ling, Julia; Jones, Reese; Templeton, Jeremy

2016-08-01

In many scientific fields, empirical models are employed to facilitate computational simulations of engineering systems. For example, in fluid mechanics, empirical Reynolds stress closures enable computationally-efficient Reynolds Averaged Navier Stokes simulations. Likewise, in solid mechanics, constitutive relations between the stress and strain in a material are required in deformation analysis. Traditional methods for developing and tuning empirical models usually combine physical intuition with simple regression techniques on limited data sets. The rise of high performance computing has led to a growing availability of high fidelity simulation data. These data open up the possibility of using machine learning algorithms, such as random forests or neural networks, to develop more accurate and general empirical models. A key question when using data-driven algorithms to develop these empirical models is how domain knowledge should be incorporated into the machine learning process. This paper will specifically address physical systems that possess symmetry or invariance properties. Two different methods for teaching a machine learning model an invariance property are compared. In the first method, a basis of invariant inputs is constructed, and the machine learning model is trained upon this basis, thereby embedding the invariance into the model. In the second method, the algorithm is trained on multiple transformations of the raw input data until the model learns invariance to that transformation. Results are discussed for two case studies: one in turbulence modeling and one in crystal elasticity. It is shown that in both cases embedding the invariance property into the input features yields higher performance at significantly reduced computational training costs.

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)

Algorithms in invariant theory

CERN Document Server

Sturmfels, Bernd

2008-01-01

J. Kung and G.-C. Rota, in their 1984 paper, write: "Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics". The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.

Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

CERN Document Server

Arai, A

2006-01-01

A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral $\\int_{{\\bf R}^3}^\\oplus\\overline{H({\\bf p})}d{\\bf p}$ of a family of self-adjoint operators $\\overline{H({\\bf p})}$ acting in the Hilbert space $\\oplus^4{\\cal F}_{\\rm rad}$, where ${\\cal F}_{\\rm rad}$ is the Hilbert space of the quantum radiation field. The fibre operator $\\overline{H({\\bf p})}$ is called the Hamiltonian of the Dirac polaron with total momentum ${\\bf p} \\in {\\bf R}^3$. The main result of this paper is concerned with the non-relativistic (scaling) limit of $\\overline{H({\\bf p})}$. It is proven that the non-relativistic limit of $\\overline{H({\\bf p})}$ yields a self-adjoint extension of a Hamiltonian of a polaron with spin $1/2$ in non-relativistic quantum electrodynamics.

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Benedetti, Dario; D'Andrea, Francesco; Procaccini, Andrea

2003-01-01

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as an illustrative example for the original proposal (Preprint gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (Preprint hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity and energy-momentum conservation rules in these theories with two relativistic invariants

Relativistic Outflows from ADAFs

Science.gov (United States)

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.

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-04-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map. The question arises as to how the relativistic effects change the nonlinear dynamical behavior described by the classical standard map. The relativistic standard map is a two parameter (K, Β = ω/kc) family of dynamical systems reducing to the standard map when Β → 0. For Β ≠ 0 the relativistic mass increase suppresses the onset of stochasticity. It shown that the speed of light limits the rate of advance of the phase in the relativistic standard map and introduces KAM surfaces persisting in the high momentum region. An intricate structure of mixing in the higher order periodic orbits and chaotic orbits is analyzed using the symmetry properties of the relativistic standard map. The interchange of the stability of the periodic orbits in the relativistic standard map is also observed and is explained by the local linear stability of the orbits. 12 refs., 16 figs

How one can construct a consistent relativistic quantum mechanics on the base of a relativistic wave equation

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)

Two-parameter nonlinear spacetime perturbations: gauge transformations and gauge invariance

International Nuclear Information System (INIS)

Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F

2003-01-01

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Ω), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by λ) are then built on top of the axisymmetric perturbations in Ω. Clearly, any interesting physics requires nonlinear perturbations, as at least terms λΩ need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory

Cartan invariants and event horizon detection

Science.gov (United States)

Brooks, D.; Chavy-Waddy, P. C.; Coley, A. A.; Forget, A.; Gregoris, D.; MacCallum, M. A. H.; McNutt, D. D.

2018-04-01

We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.

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

Mass generation within conformal invariant theories

International Nuclear Information System (INIS)

Flato, M.; Guenin, M.

1981-01-01

The massless Yang-Mills theory is strongly conformally invariant and renormalizable; however, when masses are introduced the theory becomes nonrenormalizable and weakly conformally invariant. Conditions which recover strong conformal invariance are discussed in the letter. (author)

Coordinate-invariant regularization

International Nuclear Information System (INIS)

Halpern, M.B.

1987-01-01

A general phase-space framework for coordinate-invariant regularization is given. The development is geometric, with all regularization contained in regularized DeWitt Superstructures on field deformations. Parallel development of invariant coordinate-space regularization is obtained by regularized functional integration of the momenta. As representative examples of the general formulation, the regularized general non-linear sigma model and regularized quantum gravity are discussed. copyright 1987 Academic Press, Inc

Lorentz invariance violation in the neutrino sector: a joint analysis from big bang nucleosynthesis and the cosmic microwave background

Energy Technology Data Exchange (ETDEWEB)

Dai, Wei-Ming; Cai, Rong-Gen [Chinese Academy of Sciences, CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, P.O. Box 2735, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Guo, Zong-Kuan [Chinese Academy of Sciences, CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, P.O. Box 2735, Beijing (China); University of Chinese Academy of Sciences, School of Astronomy and Space Science, Beijing (China); Zhang, Yuan-Zhong [Chinese Academy of Sciences, CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, P.O. Box 2735, Beijing (China)

2017-06-15

We investigate constraints on Lorentz invariance violation in the neutrino sector from a joint analysis of big bang nucleosynthesis and the cosmic microwave background. The effect of Lorentz invariance violation during the epoch of big bang nucleosynthesis changes the predicted helium-4 abundance, which influences the power spectrum of the cosmic microwave background at the recombination epoch. In combination with the latest measurement of the primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave background anisotropies give a strong constraint on the deformation parameter since adding the primordial helium measurement breaks the degeneracy between the deformation parameter and the physical dark matter density. (orig.)

Lorentz invariance violation in the neutrino sector: a joint analysis from big bang nucleosynthesis and the cosmic microwave background

International Nuclear Information System (INIS)

Dai, Wei-Ming; Cai, Rong-Gen; Guo, Zong-Kuan; Zhang, Yuan-Zhong

2017-01-01

We investigate constraints on Lorentz invariance violation in the neutrino sector from a joint analysis of big bang nucleosynthesis and the cosmic microwave background. The effect of Lorentz invariance violation during the epoch of big bang nucleosynthesis changes the predicted helium-4 abundance, which influences the power spectrum of the cosmic microwave background at the recombination epoch. In combination with the latest measurement of the primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave background anisotropies give a strong constraint on the deformation parameter since adding the primordial helium measurement breaks the degeneracy between the deformation parameter and the physical dark matter density. (orig.)

Lorentz invariance violation in the neutrino sector: a joint analysis from big bang nucleosynthesis and the cosmic microwave background

Science.gov (United States)

Dai, Wei-Ming; Guo, Zong-Kuan; Cai, Rong-Gen; Zhang, Yuan-Zhong

2017-06-01

We investigate constraints on Lorentz invariance violation in the neutrino sector from a joint analysis of big bang nucleosynthesis and the cosmic microwave background. The effect of Lorentz invariance violation during the epoch of big bang nucleosynthesis changes the predicted helium-4 abundance, which influences the power spectrum of the cosmic microwave background at the recombination epoch. In combination with the latest measurement of the primordial helium-4 abundance, the Planck 2015 data of the cosmic microwave background anisotropies give a strong constraint on the deformation parameter since adding the primordial helium measurement breaks the degeneracy between the deformation parameter and the physical dark matter density.

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)

Invariant sets for Windows

CERN Document Server

Morozov, Albert D; Dragunov, Timothy N; Malysheva, Olga V

1999-01-01

This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical

Non-geometrical optics investigation of mode conversion in weakly relativistic inhomogeneous plasmas

International Nuclear Information System (INIS)

Imre, K.

1985-06-01

Electron cyclotron resonance heating of plasmas by waves incident to the fundamental and second harmonic layer is investigated. When the wave propagation is nearly perpendicular to the equilibrium field in a weakly inhomogeneous plasma the standard geometrical optics breaks down and the relativistic corrections become significant at the resonance layer. Unlike the previous studies of this problem, the governing equations are derived from the linearized relativistic Vlasov equation coupled with Maxwell's equations, rather than using the uniform field dispersion relation to construct equations by replacing the refractive index by some spatial differential operations. We employ a boundary layer analysis at the resonance region and match the inner and outer solutions in the usual manner. We obtain not only the full wave solution of the problem, but also the set of physical parameters and their ranges in which the analysis is valid. Although we obtain analytic results for the asymptotic solutions, our analysis usually requires a numerical procedure when the relativistic and/or nonzero parallel refractive index are included

Design and analysis of a radio frequency extractor in an S-band relativistic klystron amplifier

Energy Technology Data Exchange (ETDEWEB)

Zhang Zehai; Zhang Jun; Shu Ting; Qi Zumin [College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073 (China)

2012-09-15

A radio frequency (RF) extractor converts the energy of a strongly modulated intense relativistic electron beam (IREB) into the energy of high power microwave in relativistic klystron amplifier (RKA). In the aim of efficiently extracting the energy of the modulated IREB, a RF extractor with all round coupling structure is proposed. Due to the all round structure, the operating transverse magnetic mode can be established easily and its resonant property can be investigated with an approach of group delay time. Furthermore, the external quality factor can be low enough. The design and analysis of the extractor applied in an S-band RKA are carried out, and the performance of the extractor is validated with three-dimensional (3D) particle-in-cell simulations. The extraction efficiency reaches 27% in the simulation with a totally 3D model of the whole RKA. The primary experiments are also carried out and the results show that the RF extractor with the external quality factor of 7.9 extracted 22% of the beam power and transformed it into the high power microwave. Better results are expected after the parasitic mode between the input and middle cavities is suppressed.

Design and analysis of a radio frequency extractor in an S-band relativistic klystron amplifier

Science.gov (United States)

Zhang, Zehai; Zhang, Jun; Shu, Ting; Qi, Zumin

2012-09-01

A radio frequency (RF) extractor converts the energy of a strongly modulated intense relativistic electron beam (IREB) into the energy of high power microwave in relativistic klystron amplifier (RKA). In the aim of efficiently extracting the energy of the modulated IREB, a RF extractor with all round coupling structure is proposed. Due to the all round structure, the operating transverse magnetic mode can be established easily and its resonant property can be investigated with an approach of group delay time. Furthermore, the external quality factor can be low enough. The design and analysis of the extractor applied in an S-band RKA are carried out, and the performance of the extractor is validated with three-dimensional (3D) particle-in-cell simulations. The extraction efficiency reaches 27% in the simulation with a totally 3D model of the whole RKA. The primary experiments are also carried out and the results show that the RF extractor with the external quality factor of 7.9 extracted 22% of the beam power and transformed it into the high power microwave. Better results are expected after the parasitic mode between the input and middle cavities is suppressed.

Relativistic approach to the near-threshold phenomena in the nucleon-antinucleon interactions

International Nuclear Information System (INIS)

Shapiro, I.S.; Smirnov, A.V.

1997-01-01

It is shown that the strongest (∝r -3 ) singularities at small interparticle distances, arising from the spin-tensor forces in the standard nonrelativistic one-boson-exchange (OBE) potentials, disappear in the relativistic treatment of the NN- and NN-interactions. The partial wave analysis is performed in the framework of a relativistic OBE quasipotential model, and the results are compared with those obtained in the nonrelativistic approximation. (orig.)

Analysis of JET LCHD/ICRH synergy experiments in terms of relativistic current drive theory

Energy Technology Data Exchange (ETDEWEB)

Start, D F.H.; Baranov, Y; Brusati, M; Ekedahl, A; Froissard, P; Gormezano, C; Jacquinot, J; Paquin, L; Rimini, F G [Commission of the European Communities, Abingdon (United Kingdom). JET Joint Undertaking; Cox, M; Gardner, C; O` Brien, M R [UKAEA Culham Lab., Abingdon (United Kingdom); Di Vita, A [Ansaldo SpA, Genoa (Italy)

1994-07-01

The present analysis shows that the observed efficiency of current drive with synergy between LHCD and ICRH is in good agreement with the relativistic theory of Karney and Fisch for Landau damped waves. The predicted power absorption from the fast wave by the electron tail is within 30% of the measured value. In the presence of significant fast electron diffusion within a slowing down time it would be possible to produce central current drive using multiple ICRF resonances even when the LHCD deposition is at half radius, as in an ITER type device. (authors). 4 refs., 6 figs.

Analysis of JET LCHD/ICRH synergy experiments in terms of relativistic current drive theory

International Nuclear Information System (INIS)

Start, D.F.H.; Baranov, Y.; Brusati, M.; Ekedahl, A.; Froissard, P.; Gormezano, C.; Jacquinot, J.; Paquin, L.; Rimini, F.G.; Di Vita, A.

1994-01-01

The present analysis shows that the observed efficiency of current drive with synergy between LHCD and ICRH is in good agreement with the relativistic theory of Karney and Fisch for Landau damped waves. The predicted power absorption from the fast wave by the electron tail is within 30% of the measured value. In the presence of significant fast electron diffusion within a slowing down time it would be possible to produce central current drive using multiple ICRF resonances even when the LHCD deposition is at half radius, as in an ITER type device. (authors). 4 refs., 6 figs

CMBE v05-Implementation of a toy-model for chaos analysis of relativistic nuclear collisions at the present BNL energies

Science.gov (United States)

Grossu, I. V.; Felea, D.; Jipa, Al.; Besliu, C.; Stan, E.; Ristea, O.; Ristea, C.; Calin, M.; Esanu, T.; Bordeianu, C.; Tuturas, N.

2014-11-01

In this paper we present a new version of Chaos Many-Body Engine (CMBE) Grossu et al. (2014) [1]. Inspired by the Mean Free Path concept, we implemented a new parameter, namely the ;Mean Free Time;, which is defined as the mean time between one particle's creation and its stimulated decay. This new parameter should be understood as an effect of the nuclear environment and, as opposed to the particle lifetime, it has the advantage of not being affected by the relativistic dilation. In [2] we presented a toy-model for chaos analysis of relativistic nuclear collisions at 4.5 A GeV/c (the SKM 200 collaboration). In this work, we extended our model to 200 A GeV (the maximum BNL energy).

The infrared problem for the dressed non-relativistic electron in a magnetic field; Le probleme infrarouge pour l'electron habille non relativiste dans un champ magnetique

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)

Manifestation of the relativistic effects and conserving currents in the interference longitudinally-transverse structure function in (e,e'p)-reactions on few-body systems

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)

Symmetries and conservation laws in the single-time Lagrangian form of the Fokker-type relativistic dynamics

International Nuclear Information System (INIS)

Tretyak, V.I.; Gaida, R.P.

1980-01-01

Symmetry properties of the single-time relativistic Lagrangian of an N-particle-system corresponding to the many-time action of the Fokker-type, which are a function of derivatives of particle coordinates with respect to time up to infinite order, are investigated. The conditions for quasi-invariance for such a Lagrangian, with respect to a representation of an arbitrary group in infinite continuation of configuration space of the system, are discussed. Using these conditions a general expression for the Lagrangian, securing Poincare covariance of corresponding equations of motion, is found, and the conservation laws related to this covariance are formulated. In the case of tensor interaction, the expansion of conserved quantities in c -1 up to terms of the order c -4 is performed. (author)

Relativistic ion acceleration by ultraintense laser interactions

International Nuclear Information System (INIS)

Nakajima, K.; Koga, J.K.; Nakagawa, K.

2001-01-01

There has been a great interest in relativistic particle generation by ultraintense laser interactions with matter. We propose the use of relativistically self-focused laser pulses for the acceleration of ions. Two dimensional PIC simulations are performed, which show the formation of a large positive electrostatic field near the front of a relativistically self-focused laser pulse. Several factors contribute to the acceleration including self-focusing distance, pulse depletion, and plasma density. Ultraintense laser-plasma interactions are capable of generating enormous electrostatic fields of ∼3 TV/m for acceleration of protons with relativistic energies exceeding 1 GeV

Measurement Invariance of the "Servant Leadership Questionnaire" across K-12 Principal Gender

Science.gov (United States)

Xu, Lihua; Stewart, Trae; Haber-Curran, Paige

2015-01-01

Measurement invariance of the five-factor "Servant Leadership Questionnaire" between female and male K-12 principals was tested using multi-group confirmatory factor analysis. A sample of 956 principals (56.9% were females and 43.1% were males) was analysed in this study. The hierarchical multi-step measurement invariance test supported…

The Loneliness Questionnaire: Establishing Measurement Invariance Across Ethnic Groups.

Science.gov (United States)

Ritchwood, Tiarney D; Ebesutani, Chad K; Chin, Eu Gene; Young, John

2017-09-01

A state of loneliness describes an individual's perception of having dissatisfying social connections to others. Though it is notable across the life span, it may have particularly deleterious effects in childhood and adolescence, leading to increased risk of emotional impairment. The current study evaluates a widely used test of loneliness, the Loneliness Questionnaire, for measurement invariance across ethnic groups in a large, representative sample of youth in the 2nd to 12th grades ( N = 12,344; 41% African American) in Mississippi. Analyses were conducted using multigroup confirmatory factor analysis following a published, sequential method to examine invariance in form, factor loadings, and item intercepts. Overall, our results indicated that the instrument was invariant across ethnicities, suggesting that youth with equivalent manifest scores can be discerned as having comparable levels of latent loneliness. The loneliness scores also corresponded significantly with depression and anxiety scores for most subsamples, with one exception. These findings are discussed in the context of previous results comparing levels of loneliness across ethnicities. Additionally, the broader context of the need to expand invariance studies in instrumentation work is highlighted.

Stability analysis of spatially invariant systems with event-triggered communication

NARCIS (Netherlands)

Heijmans, S.H.J.; Dolk, V.S.; Borgers, D.P.; Heemels, W.P.M.H.

2016-01-01

In this paper we analyze spatially invariant inter-connections consisting of a (finite) number of subsystems that use packet-based communication networks for the exchange of information. An example of such an interconnected system is the platoon of vehicles that uses cooperative control to drive

Relativistic collective diffusion in one-dimensional systems

Science.gov (United States)

Lin, Gui-Wu; Lam, Yu-Yiu; Zheng, Dong-Qin; Zhong, Wei-Rong

2018-05-01

The relativistic collective diffusion in one-dimensional molecular system is investigated through nonequilibrium molecular dynamics with Monte Carlo methods. We have proposed the relationship among the speed, the temperature, the density distribution and the collective diffusion coefficient of particles in a relativistic moving system. It is found that the relativistic speed of the system has no effect on the temperature, but the collective diffusion coefficient decreases to zero as the velocity of the system approaches to the speed of light. The collective diffusion coefficient is modified as D‧ = D(1 ‑w2 c2 )3 2 for satisfying the relativistic circumstances. The present results may contribute to the understanding of the behavior of the particles transport diffusion in a high speed system, as well as enlighten the study of biological metabolism at relativistic high speed situation.

Exact Relativistic `Antigravity' Propulsion

Science.gov (United States)

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.

Relativistic Boltzmann theory for a plasma

International Nuclear Information System (INIS)

Erkelens, H. van.

1984-01-01

This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)

Relativistic QRPA Calculation of β-Decay Rates of r-process Nuclei

International Nuclear Information System (INIS)

Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.; Ring, P.

2009-01-01

A systematic, fully self-consistent calculation of β-decay rates is presented, based on a microscopic theoretical framework. Analysis is performed on a large number of nuclei from the valley of β stability towards the neutron drip-line. Nuclear ground state is determined using the Relativistic Hartree-Bogoliubov (RHB) model with density-dependent meson-nucleon coupling constants. Transition rates are calculated within the proton-neutron relativistic quasiparticle RPA (pn-RQRPA) using the same interaction that was used in the RHB equations.

Mobius invariant QK spaces

CERN Document Server

Wulan, Hasi

2017-01-01

This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.

The Gaussian formula and spherical aberrations of static and relativistic curved mirrors from Fermat's principle

International Nuclear Information System (INIS)

Sutanto, Sylvia H; Tjiang, Paulus C

2011-01-01

The Gaussian formula and spherical aberrations of static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors. By comparing the results in static and relativistic cases, it is shown that the focal lengths and the spherical aberration relations of the relativistic mirrors obey the Lorentz contraction. Further analysis of the spherical aberrations for both static and relativistic cases have resulted in information about the limits for the paraxial approximation, as well as for the minimum speed of the systems to reduce the spherical aberrations

Improved test of Lorentz invariance in electrodynamics

International Nuclear Information System (INIS)

Wolf, Peter; Bize, Sebastien; Clairon, Andre; Santarelli, Giorgio; Tobar, Michael E.; Luiten, Andre N.

2004-01-01

We report new results of a test of Lorentz invariance based on the comparison of a cryogenic sapphire microwave resonator and a hydrogen-maser. The experimental results are shown together with an extensive analysis of systematic effects. Previously, this experiment has set the most stringent constraint on Kennedy-Thorndike type violations of Lorentz invariance. In this work we present new data and interpret our results in the general Lorentz violating extension of the standard model of particle physics (SME). Within the photon sector of the SME, our experiment is sensitive to seven SME parameters. We marginally improve present limits on four of these, and by a factor seven to ten on the other three

Relativistic effects in the Thomas--Fermi atom

International Nuclear Information System (INIS)

Waber, J.T.; Canfield, J.M.

1975-01-01

Two methods of applying relativistic corrections to the Thomas--Fermi atom are considered, and numerical calculations are discussed. Radial charge distributions calculated from a relativistic Thomas--Fermi equation agree in gross form with those from more complicated self-consistent calculations. Energy eigenvalues for mercury, as determined from the relativistic Thomas--Fermi solution, are compared with other calculated and experimental values

Relativistic klystron research for linear colliders

International Nuclear Information System (INIS)

Allen, M.A.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Hoag, H.A.; Koontz, R.F.; Lavine, T.L.; Lee, T.G.; Loew, G.A.; Miller, R.H.; Morton, P.L.; Palmer, R.B.; Paterson, J.M.; Ruth, R.D.; Schwarz, H.D.; Vlieks, A.E.; Wilson, P.B.

1989-01-01

Relativistic klystrons are being developed as a power source for high gradient accelerator applications which include large linear electron-positron colliders, compact accelerators, and FEL sources. The authors have attained 200 MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. In this paper the authors report on the design of our relativistic klystrons, the results of our experiments so far, and some of our plans for the near future

Relativistic klystron research for linear colliders

International Nuclear Information System (INIS)

Allen, M.A.; Callin, R.S.; Deruyter, H.

1988-09-01

Relativistic klystrons are being developed as a power source for high gradient accelerator applications which include large linear electron-positron colliders, compact accelerators, and FEL sources. We have attained 200 MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. We report here on the design of our relativistic klystrons, the results of our experiments so far, and some of our plans for the near future. 5 refs., 9 figs., 1 tab

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

Impact of Relativistic Electron Beam on Hole Acoustic Instability in Quantum Semiconductor Plasmas

Science.gov (United States)

Siddique, M.; Jamil, M.; Rasheed, A.; Areeb, F.; Javed, Asif; Sumera, P.

2018-01-01

We studied the influence of the classical relativistic beam of electrons on the hole acoustic wave (HAW) instability exciting in the semiconductor quantum plasmas. We conducted this study by using the quantum-hydrodynamic model of dense plasmas, incorporating the quantum effects of semiconductor plasma species which include degeneracy pressure, exchange-correlation potential and Bohm potential. Analysis of the quantum characteristics of semiconductor plasma species along with relativistic effect of beam electrons on the dispersion relation of the HAW is given in detail qualitatively and quantitatively by plotting them numerically. It is worth mentioning that the relativistic electron beam (REB) stabilises the HAWs exciting in semiconductor (GaAs) degenerate plasma.

New models of general relativistic static thick disks

NARCIS (Netherlands)

Vogt, D.; Letelier, P.S.

2005-01-01

New families of exact general relativistic thick disks are constructed using the "displace, cut, fill, and reflect" method. A class of functions used to fill the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the

Modularization of biochemical networks based on classification of Petri net t-invariants.

Science.gov (United States)

Grafahrend-Belau, Eva; Schreiber, Falk; Heiner, Monika; Sackmann, Andrea; Junker, Björn H; Grunwald, Stefanie; Speer, Astrid; Winder, Katja; Koch, Ina

2008-02-08

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find

Modularization of biochemical networks based on classification of Petri net t-invariants

Directory of Open Access Journals (Sweden)

Grunwald Stefanie

2008-02-01

Full Text Available Abstract Background Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior. With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system. Methods Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t

Relativistic heavy-ion physics

CERN Document Server

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.

Invariant density analysis: modeling and analysis of the postural control system using Markov chains.

Science.gov (United States)

Hur, Pilwon; Shorter, K Alex; Mehta, Prashant G; Hsiao-Wecksler, Elizabeth T

2012-04-01

In this paper, a novel analysis technique, invariant density analysis (IDA), is introduced. IDA quantifies steady-state behavior of the postural control system using center of pressure (COP) data collected during quiet standing. IDA relies on the analysis of a reduced-order finite Markov model to characterize stochastic behavior observed during postural sway. Five IDA parameters characterize the model and offer physiological insight into the long-term dynamical behavior of the postural control system. Two studies were performed to demonstrate the efficacy of IDA. Study 1 showed that multiple short trials can be concatenated to create a dataset suitable for IDA. Study 2 demonstrated that IDA was effective at distinguishing age-related differences in postural control behavior between young, middle-aged, and older adults. These results suggest that the postural control system of young adults converges more quickly to their steady-state behavior while maintaining COP nearer an overall centroid than either the middle-aged or older adults. Additionally, larger entropy values for older adults indicate that their COP follows a more stochastic path, while smaller entropy values for young adults indicate a more deterministic path. These results illustrate the potential of IDA as a quantitative tool for the assessment of the quiet-standing postural control system.

Relativistic theories of materials

CERN Document Server

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...

Gauge-invariant cosmological density perturbations

International Nuclear Information System (INIS)

Sasaki, Misao.

1986-06-01

Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)

Relativistic dynamics without conservation laws

OpenAIRE

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.

Common analysis of the relativistic klystron and the standing-wave free-electron laser two-beam accelerator

International Nuclear Information System (INIS)

Wurtele, J.S.; Whittum, D.H.; Sessler, A.M.

1992-07-01

This paper summarizes a new formalism which makes the analysis and understanding of both the relativistic klystron (RK) and the standing-wave free-electron laser (SWFEL) two-beam accelerator (TBA) available to a wide audience of accelerator physicists. A ''coupling impedance'' for both the RK and SWFEL is introduced, which can include realistic cavity features, such as beam and vacuum ports, in a simple manner. The RK and SWFEL macroparticle equations, which govern the energy and phase evolution of successive bunches in the beam, are of identical form, differing only by multiplicative factors. The analysis allows, for the first time, a relative comparison of the RF and SWFEL TBAs

Identification of invariant measures of interacting systems

International Nuclear Information System (INIS)

Chen Jinwen

2004-01-01

In this paper we provide an approach for identifying certain mixture representations of some invariant measures of interacting stochastic systems. This is related to the problem of ergodicity of certain extremal invariant measures that are translation invariant. Corresponding to these, results concerning the existence of invariant measures and certain weak convergence of the systems are also provided

Time Operator in Relativistic Quantum Mechanics

Science.gov (United States)

Khorasani, Sina

2017-07-01

It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

Relativistic klystron research for linear colliders

International Nuclear Information System (INIS)

Allen, M.A.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannesfeldt, W.B.; Higo, T.; Hoag, H.A.; Koontz, R.F.; Lavine, T.L.; Lee, T.G.; Loew, G.A.; Miller, R.H.; Morton, P.L.; Palmer, R.B.; Paterson, J.M.; Ruth, R.D.; Schwarz, H.D.; Takeuchi, Y.; Vlieks, A.E.; Wang, J.W.; Wilson, P.B.; Hopkins, D.B.; Sessler, A.M.; Ryne, R.D.; Westenskow, G.A.; Yu, S.S.

1989-01-01

Relativistic klystrons are being developed as a power source for high gradient accelerator applications which include large linear electron-positron colliders, compact accelerators, and FEL sources. The authors have attained 200MW peak power at 11.4 GHz from a relativistic klystron, and 140 MV/m longitudinal gradient in a short 11.4 GHz accelerator section. They report here on the design of our relativistic klystrons, the results of our experiments so far, and some of our plans for the near future. 5 refs., 9 figs., 1 tab

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.

Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence

Science.gov (United States)

Danish, Mohammad; Meneveau, Charles

2018-04-01

Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Reλ=433 . While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial

Relativistic electromagnetic waves in an electron-ion plasma

Science.gov (United States)

Chian, Abraham C.-L.; Kennel, Charles F.

1987-01-01

High power laser beams can drive plasma particles to relativistic energies. An accurate description of strong waves requires the inclusion of ion dynamics in the analysis. The equations governing the propagation of relativistic electromagnetic waves in a cold electron-ion plasma can be reduced to two equations expressing conservation of energy-momentum of the system. The two conservation constants are functions of the plasma stream velocity, the wave velocity, the wave amplitude, and the electron-ion mass ratio. The dynamic parameter, expressing electron-ion momentum conversation in the laboratory frame, can be regarded as an adjustable quantity, a suitable choice of which will yield self-consistent solutions when other plasma parameters were specified. Circularly polarized electromagnetic waves and electrostatic plasma waves are used as illustrations.

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

Revisiting measurement invariance in intelligence testing in aging research: Evidence for almost complete metric invariance across age groups.

Science.gov (United States)

Sprague, Briana N; Hyun, Jinshil; Molenaar, Peter C M

2017-01-01

Invariance of intelligence across age is often assumed but infrequently explicitly tested. Horn and McArdle (1992) tested measurement invariance of intelligence, providing adequate model fit but might not consider all relevant aspects such as sub-test differences. The goal of the current paper is to explore age-related invariance of the WAIS-R using an alternative model that allows direct tests of age on WAIS-R subtests. Cross-sectional data on 940 participants aged 16-75 from the WAIS-R normative values were used. Subtests examined were information, comprehension, similarities, vocabulary, picture completion, block design, picture arrangement, and object assembly. The two intelligence factors considered were fluid and crystallized intelligence. Self-reported ages were divided into young (16-22, n = 300), adult (29-39, n = 275), middle (40-60, n = 205), and older (61-75, n = 160) adult groups. Results suggested partial metric invariance holds. Although most of the subtests reflected fluid and crystalized intelligence similarly across different ages, invariance did not hold for block design on fluid intelligence and picture arrangement on crystallized intelligence for older adults. Additionally, there was evidence of a correlated residual between information and vocabulary for the young adults only. This partial metric invariance model yielded acceptable model fit compared to previously-proposed invariance models of Horn and McArdle (1992). Almost complete metric invariance holds for a two-factor model of intelligence. Most of the subtests were invariant across age groups, suggesting little evidence for age-related bias in the WAIS-R. However, we did find unique relationships between two subtests and intelligence. Future studies should examine age-related differences in subtests when testing measurement invariance in intelligence.

Relativistic Gas Drag on Dust Grains and Implications

Energy Technology Data Exchange (ETDEWEB)

Hoang, Thiem, E-mail: thiemhoang@kasi.re.kr [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Korea University of Science and Technology, Daejeon, 34113 (Korea, Republic of)

2017-09-20

We study the drag force on grains moving at relativistic velocities through interstellar gas and explore its application. First, we derive a new analytical formula of the drag force at high energies and find that it is significantly reduced compared to the classical model. Second, we apply the obtained drag force to calculate the terminal velocities of interstellar grains by strong radiation sources such as supernovae and active galactic nuclei (AGNs). We find that grains can be accelerated to relativistic velocities by very luminous AGNs. We then quantify the deceleration of relativistic spacecraft proposed by the Breakthrough Starshot initiative due to gas drag on a relativistic lightsail. We find that the spacecraft’s decrease in speed is negligible because of the suppression of gas drag at relativistic velocities, suggesting that the lightsail may be open for communication during its journey to α Centauri without causing a considerable delay. Finally, we show that the damage to relativistic thin lightsails by interstellar dust is a minor effect.

Relativistic and nonrelativistic classical field theory on fivedimensional space-time

International Nuclear Information System (INIS)

Kunzle, H.P.; Duval, C.

1985-07-01

This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form

Constructing Invariant Fairness Measures for Surfaces

DEFF Research Database (Denmark)

Gravesen, Jens; Ungstrup, Michael

1998-01-01

of the size of this vector field is used as the fairness measure on the family.Six basic 3rd order invariants satisfying two quadratic equations are defined. They form a complete set in the sense that any invariant 3rd order function can be written as a function of the six basic invariants together...

On logarithmic extensions of local scale-invariance

International Nuclear Information System (INIS)

Henkel, Malte

2013-01-01

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena

A circuit-level analysis of third order intermodulation mechanisms in CMOS mixers using time-invariant power and Volterra series

NARCIS (Netherlands)

Sakian, P.; Mahmoudi, R.; Roermund, van A.H.M.

2011-01-01

An in-depth analysis is performed on the third-order intermodulation distortions (IMD3) in the switching pair of active CMOS mixers. The nonlinear time-varying switching pair is described by a hypothetical circuit composed of a nonlinear time-invariant circuit cascaded with a linear time-varying

Relativistic electron dropout echoes induced by interplanetary shocks

Science.gov (United States)

Schiller, Q.; Kanekal, S. G.; Boyd, A. J.; Baker, D. N.; Blake, J. B.; Spence, H. E.

2017-12-01

Interplanetary shocks that impact Earth's magnetosphere can produce immediate and dramatic responses in the trapped relativistic electron population. One well-studied response is a prompt injection capable of transporting relativistic electrons deep into the magnetosphere and accelerating them to multi-MeV energies. The converse effect, electron dropout echoes, are observations of a sudden dropout of electron fluxes observed after the interplanetary shock arrival. Like the injection echo signatures, dropout echoes can also show clear energy dispersion signals. They are of particular interest because they have only recently been observed and their causal mechanism is not well understood. In the analysis presented here, we show observations of electron drift echo signatures from the Relativistic Electron-Proton Telescope (REPT) and Magnetic Electron and Ion Sensors (MagEIS) onboard NASA's Van Allen Probes mission, which show simultaneous prompt enhancements and dropouts within minutes of the associated with shock impact. We show that the observations associated with both enhancements and dropouts are explained by the inward motion caused by the electric field impulse induced by the interplanetary shock, and either energization to cause the enhancement, or lack of a seed population to cause the dropout.

Relativistic analysis of nuclear ground state densities at 135 to 200 ...

Indian Academy of Sciences (India)

fitting of differential cross-section and analyzing power, and the appearance of wine-bottle- ... So, the effect of different nuclear density distributions is quite conspicuous in the relativistic ap- proach. Hence, we have analyzed five different nuclear ground state .... The NEG and FNEG densities have been used to see the effect.

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)

Thermodynamic laws and equipartition theorem in relativistic Brownian motion.

Science.gov (United States)

Koide, T; Kodama, T

2011-06-01

We extend the stochastic energetics to a relativistic system. The thermodynamic laws and equipartition theorem are discussed for a relativistic Brownian particle and the first and the second law of thermodynamics in this formalism are derived. The relation between the relativistic equipartition relation and the rate of heat transfer is discussed in the relativistic case together with the nature of the noise term.

Relativistic quantum similarities in atoms in position and momentum spaces

International Nuclear Information System (INIS)

Maldonado, P.; Sarsa, A.; Buendia, E.; Galvez, F.J.

2011-01-01

A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr (Z=1-103). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations. -- Highlights: → Quantum similarity measures and indices in electronic structure of atoms. → Position and momentum electronic densities. → Similarity of relativistic and non-relativistic densities. → Similarity of core and valence regions of different atoms. → Dependence with Z along the Periodic Table.

Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons

Science.gov (United States)

Ayral, Thomas; Kotliar, Gabriel

The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.

Effective interaction for relativistic mean-field theories of nuclear structure

International Nuclear Information System (INIS)

Ai, H.B.; Celenza, L.S.; Harindranath, A.; Shakin, C.M.

1987-01-01

We construct an effective interaction, which when treated in a relativistic Hartree-Fock approximation, reproduces rather accurately the nucleon self-energy in nuclear matter and the Migdal parameters obtained via relativistic Brueckner-Hartree-Fock calculations. This effective interaction is constructed by adding Born terms, describing the exchange of pseudoparticles, to the Born terms of the Dirac-Hartree-Fock analysis. The pseudoparticles have relatively large masses and either real or imaginary coupling constants. (For example, exchange of a pseudo-sigma with an imaginary coupling constant has the effect of reducing the scalar attraction arising from sigma exchange while exchange of a pseudo-omega with an imaginary coupling constant has the effect of reducing the repulsion arising from omega exchange. The terms beyond the Born term in the case of pion exchange are well simulated by pseudo-sigma exchange with a real coupling constant.) The effective interaction constructed here may be used for calculations of the properties of finite nuclei in a relativistic Hartree-Fock approximation

Theoretical study of the relativistic molecular rotational g-tensor

International Nuclear Information System (INIS)

Aucar, I. Agustín; Gomez, Sergio S.; Giribet, Claudia G.; Ruiz de Azúa, Martín C.

2014-01-01

An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH + (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH + systems. Only for the sixth-row Rn atom a significant deviation of this relation is found

Theoretical study of the relativistic molecular rotational g-tensor

Energy Technology Data Exchange (ETDEWEB)

Aucar, I. Agustín, E-mail: agustin.aucar@conicet.gov.ar; Gomez, Sergio S., E-mail: ssgomez@exa.unne.edu.ar [Institute for Modeling and Technological Innovation, IMIT (CONICET-UNNE) and Faculty of Exact and Natural Sciences, Northeastern University of Argentina, Avenida Libertad 5400, W3404AAS Corrientes (Argentina); Giribet, Claudia G.; Ruiz de Azúa, Martín C. [Physics Department, Faculty of Exact and Natural Sciences, University of Buenos Aires and IFIBA CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires (Argentina)

2014-11-21

An original formulation of the relativistic molecular rotational g-tensor valid for heavy atom containing compounds is presented. In such formulation, the relevant terms of a molecular Hamiltonian for non-relativistic nuclei and relativistic electrons in the laboratory system are considered. Terms linear and bilinear in the nuclear rotation angular momentum and an external uniform magnetic field are considered within first and second order (relativistic) perturbation theory to obtain the rotational g-tensor. Relativistic effects are further analyzed by carrying out the linear response within the elimination of the small component expansion. Quantitative results for model systems HX (X=F, Cl, Br, I), XF (X=Cl, Br, I), and YH{sup +} (Y=Ne, Ar, Kr, Xe, Rn) are obtained both at the RPA and density functional theory levels of approximation. Relativistic effects are shown to be small for this molecular property. The relation between the rotational g-tensor and susceptibility tensor which is valid in the non-relativistic theory does not hold within the relativistic framework, and differences between both molecular parameters are analyzed for the model systems under study. It is found that the non-relativistic relation remains valid within 2% even for the heavy HI, IF, and XeH{sup +} systems. Only for the sixth-row Rn atom a significant deviation of this relation is found.

Loading relativistic Maxwell distributions in particle simulations

Energy Technology Data Exchange (ETDEWEB)

Zenitani, Seiji, E-mail: seiji.zenitani@nao.ac.jp [National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588 (Japan)

2015-04-15

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms.

Loading relativistic Maxwell distributions in particle simulations

International Nuclear Information System (INIS)

Zenitani, Seiji

2015-01-01

Numerical algorithms to load relativistic Maxwell distributions in particle-in-cell (PIC) and Monte-Carlo simulations are presented. For stationary relativistic Maxwellian, the inverse transform method and the Sobol algorithm are reviewed. To boost particles to obtain relativistic shifted-Maxwellian, two rejection methods are proposed in a physically transparent manner. Their acceptance efficiencies are ≈50% for generic cases and 100% for symmetric distributions. They can be combined with arbitrary base algorithms

The de Sitter relativistic top theory

International Nuclear Information System (INIS)

Armenta, J.; Nieto, J.A.

2005-01-01

We discuss the relativistic top theory from the point of view of the de Sitter (or anti-de Sitter) group. Our treatment rests on the Hanson-Regge spherical relativistic top Lagrangian formulation. We propose an alternative method for studying spinning objects via Kaluza-Klein theory. In particular, we derive the relativistic top equations of motion starting with the geodesic equation for a point particle in 4+N dimensions. We compare our approach with Fukuyama's formulation of spinning objects, which is also based on Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D dimensional theory

Invariance of Parent Ratings of the ADHD Symptoms in Australian and Malaysian, and North European Australian and Malay Malaysia Children: A Mean and Covariance Structures Analysis Approach

Science.gov (United States)

Gomez, Rapson

2009-01-01

Objective: This study used the mean and covariance structures analysis approach to examine the equality or invariance of ratings of the 18 ADHD symptoms. Method: 783 Australian and 928 Malaysian parents provided ratings for an ADHD rating scale. Invariance was tested across these groups (Comparison 1), and North European Australian (n = 623) and…

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

Dimensionality and measurement invariance in the Satisfaction with Life Scale in Norway.

Science.gov (United States)

Clench-Aas, Jocelyne; Nes, Ragnhild Bang; Dalgard, Odd Steffen; Aarø, Leif Edvard

2011-10-01

Results from previous studies examining the dimensionality and factorial invariance of the Satisfaction with Life Scale (SWLS) are inconsistent and often based on small samples. This study examines the factorial structure and factorial invariance of the SWLS in a Norwegian sample. Confirmatory factor analysis (AMOS) was conducted to explore dimensionality and test for measurement invariance in factor structure, factor loadings, intercepts, and residual variance across gender and four age groups in a large (N = 4,984), nationally representative sample of Norwegian men and women (15-79 years). The data supported a modified unidimensional structure. Factor loadings could be constrained to equality between the sexes, indicating metric invariance between genders. Further testing indicated invariance also at the strong and strict levels, thus allowing analyses involving group means. The SWLS was shown to be sensitive to age, however, at the strong and strict levels of invariance testing. In conclusion, the results in this Norwegian study seem to confirm that a unidimensional structure is acceptable, but that a modified single-factor model with correlations between error terms of items 4 and 5 is preferred. Additionally, comparisons may be made between the genders. Caution must be exerted when comparing age groups.

First spatial isotopic separation of relativistic uranium projectile fragments

International Nuclear Information System (INIS)

Magel, A.; Voss, B.; Armbruster, P.; Aumann, T.; Clerc, H.G.; Czajkowski, S.; Folger, H.; Grewe, A.; Hanelt, E.; Heinz, A.; Irnich, H.; Jong, M. de; Junghans, A.; Nickel, F.; Pfuetzner, M.; Roehl, C.; Scheidenberger, C.; Schmidt, K.H.; Schwab, W.; Steinhaeuser, S.; Suemmerer, K.; Trinder, W.; Wollnik, H.

1994-07-01

Spatial isotopic separation of relativistic uranium projectile fragments has been achieved for the first time. The fragments were produced in peripheral nuclear collisions and spatially separated in-flight with the fragment separator FRS at GSI. A two-fold magnetic-rigidity analysis was applied exploiting the atomic energy loss in specially shaped matter placed in the dispersive central focal plane. Systematic investigations with relativistic projectiles ranging from oxygen up to uranium demonstrate that the FRS is a universal and powerful facility for the production and in-flight separation of monoisotopic, exotic secondary beams of all elements up to Z=92. This achievement has opened a new area in heavy-ion research and applications. (orig.)

Electron correlation within the relativistic no-pair approximation

Energy Technology Data Exchange (ETDEWEB)

Almoukhalalati, Adel; Saue, Trond, E-mail: trond.saue@irsamc.ups-tlse.fr [Laboratoire de Chimie et Physique Quantique, UMR 5626 CNRS — Université Toulouse III-Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse (France); Knecht, Stefan [ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich (Switzerland); Jensen, Hans Jørgen Aa. [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M (Denmark); Dyall, Kenneth G. [Dirac Solutions, 10527 NW Lost Park Drive, Portland, Oregon 97229 (United States)

2016-08-21

This paper addresses the definition of correlation energy within 4-component relativistic atomic and molecular calculations. In the nonrelativistic domain the correlation energy is defined as the difference between the exact eigenvalue of the electronic Hamiltonian and the Hartree-Fock energy. In practice, what is reported is the basis set correlation energy, where the “exact” value is provided by a full Configuration Interaction (CI) calculation with some specified one-particle basis. The extension of this definition to the relativistic domain is not straightforward since the corresponding electronic Hamiltonian, the Dirac-Coulomb Hamiltonian, has no bound solutions. Present-day relativistic calculations are carried out within the no-pair approximation, where the Dirac-Coulomb Hamiltonian is embedded by projectors eliminating the troublesome negative-energy solutions. Hartree-Fock calculations are carried out with the implicit use of such projectors and only positive-energy orbitals are retained at the correlated level, meaning that the Hartree-Fock projectors are frozen at the correlated level. We argue that the projection operators should be optimized also at the correlated level and that this is possible by full Multiconfigurational Self-Consistent Field (MCSCF) calculations, that is, MCSCF calculations using a no-pair full CI expansion, but including orbital relaxation from the negative-energy orbitals. We show by variational perturbation theory that the MCSCF correlation energy is a pure MP2-like correlation expression, whereas the corresponding CI correlation energy contains an additional relaxation term. We explore numerically our theoretical analysis by carrying out variational and perturbative calculations on the two-electron rare gas atoms with specially tailored basis sets. In particular, we show that the correlation energy obtained by the suggested MCSCF procedure is smaller than the no-pair full CI correlation energy, in accordance with the

Analytic invariants of boundary links

OpenAIRE

Garoufalidis, Stavros; Levine, Jerome

2001-01-01

Using basic topology and linear algebra, we define a plethora of invariants of boundary links whose values are power series with noncommuting variables. These turn out to be useful and elementary reformulations of an invariant originally defined by M. Farber.

Status of time reversal invariance

International Nuclear Information System (INIS)

Henley, E.M.

1989-01-01

Time Reversal Invariance is introduced, and theories for its violation are reviewed. The present experimental and theoretical status of Time Reversal Invariance and tests thereof will be presented. Possible future tests will be discussed. 30 refs., 2 figs., 1 tab

Summational invariants

International Nuclear Information System (INIS)

Mackrodt, C.; Reeh, H.

1997-01-01

General summational invariants, i.e., conservation laws acting additively on asymptotic particle states, are investigated within a classical framework for point particles with nontrivial scattering. copyright 1997 American Institute of Physics

Liouville equation of relativistic charged fermion

International Nuclear Information System (INIS)

Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

1991-01-01

As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

Link invariants for flows in higher dimensions

International Nuclear Information System (INIS)

Garcia-Compean, Hugo; Santos-Silva, Roberto

2010-01-01

Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated with n-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure, are computed in the context of quantum field theory. They constitute invariants of smooth dynamical systems (for nonsingular flows) and generalize previous proposals of invariants. In particular, they generalize Arnold's asymptotic Hopf invariant from three to higher dimensions. This invariant is generalized by coupling with a non-Abelian gauge flat connection with nontrivial holonomy. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally, we give a possible interpretation and implementation of these issues in the context of 11-dimensional supergravity and string theory.

An energy principle for two-dimensional collisionless relativistic plasmas

International Nuclear Information System (INIS)

Otto, A.; Schindler, K.

1984-01-01

Using relativistic Vlasov theory an energy principle for two-dimensional plasmas is derived, which provides a sufficient and necessary criterion for the stability of relativistic plasma equilibria. This energy principle includes charge separating effects since the exact Poisson equation was taken into consideration. Applying the variational principle to the case of the relativistic plane plasma sheet, the same marginal wave length is found as in the non-relativistic case. (author)

Dynamical topological invariant after a quantum quench

Science.gov (United States)

Yang, Chao; Li, Linhu; Chen, Shu

2018-02-01

We show how to define a dynamical topological invariant for one-dimensional two-band topological systems after a quantum quench. By analyzing general two-band models of topological insulators, we demonstrate that the reduced momentum-time manifold can be viewed as a series of submanifolds S2, and thus we are able to define a dynamical topological invariant on each of the spheres. We also unveil the intrinsic relation between the dynamical topological invariant and the difference in the topological invariant of the initial and final static Hamiltonian. By considering some concrete examples, we illustrate the calculation of the dynamical topological invariant and its geometrical meaning explicitly.

Frozen reaction fronts in steady flows: A burning-invariant-manifold perspective

Science.gov (United States)

Mahoney, John R.; Li, John; Boyer, Carleen; Solomon, Tom; Mitchell, Kevin A.

2015-12-01

The dynamics of fronts, such as chemical reaction fronts, propagating in two-dimensional fluid flows can be remarkably rich and varied. For time-invariant flows, the front dynamics may simplify, settling in to a steady state in which the reacted domain is static, and the front appears "frozen." Our central result is that these frozen fronts in the two-dimensional fluid are composed of segments of burning invariant manifolds, invariant manifolds of front-element dynamics in x y θ space, where θ is the front orientation. Burning invariant manifolds (BIMs) have been identified previously as important local barriers to front propagation in fluid flows. The relevance of BIMs for frozen fronts rests in their ability, under appropriate conditions, to form global barriers, separating reacted domains from nonreacted domains for all time. The second main result of this paper is an understanding of bifurcations that lead from a nonfrozen state to a frozen state, as well as bifurcations that change the topological structure of the frozen front. Although the primary results of this study apply to general fluid flows, our analysis focuses on a chain of vortices in a channel flow with an imposed wind. For this system, we present both experimental and numerical studies that support the theoretical analysis developed here.

Relativistic neoclassical transport coefficients with momentum correction

International Nuclear Information System (INIS)

Marushchenko, I.; Azarenkov, N.A.

2016-01-01

The parallel momentum correction technique is generalized for relativistic approach. It is required for proper calculation of the parallel neoclassical flows and, in particular, for the bootstrap current at fusion temperatures. It is shown that the obtained system of linear algebraic equations for parallel fluxes can be solved directly without calculation of the distribution function if the relativistic mono-energetic transport coefficients are already known. The first relativistic correction terms for Braginskii matrix coefficients are calculated.

Penetration of relativistic heavy ions through matter

International Nuclear Information System (INIS)

Scheidenberger, C.; Geissel, H.

1997-07-01

New heavy-ion accelerators covering the relativistic and ultra-relativistic energy regime allow to study atomic collisions with bare and few-electron projectiles. High-resolution magnetic spectrometers are used for precise stopping-power and energy-loss straggling measurements. Refined theories beyond the Born approximation have been developed and are confirmed by experiments. This paper summarizes the large progress in the understanding of relativistic heavy-ion penetration through matter, which has been achieved in the last few years. (orig.)

Phenomenology of local scale invariance: from conformal invariance to dynamical scaling

International Nuclear Information System (INIS)

Henkel, Malte

2002-01-01

Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z. For a given value of θ (or z), we construct local scale transformations, which can be viewed as scale transformations with a space-time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ, whereas the second type may describe dynamical scaling with a dynamical exponent z. Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ=1 and Schroedinger invariance for θ=2. The hypothesis of local scale invariance implies that two-point functions of quasi primary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time auto response function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber-Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics

Quantifying Translation-Invariance in Convolutional Neural Networks

OpenAIRE

Kauderer-Abrams, Eric

2017-01-01

A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple ...

Relativistic Kinematics

OpenAIRE

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.

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 klystrons

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

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.

Invariant measures in brain dynamics

International Nuclear Information System (INIS)

Boyarsky, Abraham; Gora, Pawel

2006-01-01

This note concerns brain activity at the level of neural ensembles and uses ideas from ergodic dynamical systems to model and characterize chaotic patterns among these ensembles during conscious mental activity. Central to our model is the definition of a space of neural ensembles and the assumption of discrete time ensemble dynamics. We argue that continuous invariant measures draw the attention of deeper brain processes, engendering emergent properties such as consciousness. Invariant measures supported on a finite set of ensembles reflect periodic behavior, whereas the existence of continuous invariant measures reflect the dynamics of nonrepeating ensemble patterns that elicit the interest of deeper mental processes. We shall consider two different ways to achieve continuous invariant measures on the space of neural ensembles: (1) via quantum jitters, and (2) via sensory input accompanied by inner thought processes which engender a 'folding' property on the space of ensembles

A Primer to Relativistic MOND Theory

NARCIS (Netherlands)

Bekenstein, J.D..; Sanders, R.H.

2005-01-01

Abstract: We first review the nonrelativistic lagrangian theory as a framework for the MOND equation. Obstructions to a relativistic version of it are discussed leading up to TeVeS, a relativistic tensor-vector-scalar field theory which displays both MOND and Newtonian limits. The whys for its

Relativistic Quantum Transport in Graphene Systems

Science.gov (United States)

2015-07-09

dimensional Dirac material systems. 2 List of Publications 1. X. Ni, L. Huang, Y.-C. Lai, and L. M. Pecora, “Effect of chaos on relativistic quantum...development of relativistic quantum devices based on graphene or alternative two-dimensional Dirac material systems. In the project period, we studied

Relativistic astrophysics and theory of gravity

International Nuclear Information System (INIS)

Zel'dovich, Ya.B.

1982-01-01

A brief historical review of the development of astrophysical science in the State Astrophysical Institute named after Shternberg (SAISh) has been given in a popular form. The main directions of the SAISh astrophysical investigations have been presented: relativistic theory of gravity, relativistic astrophysics of interplanetary medium and cosmology

A fundamental special-relativistic theory valid for all real-valued speeds

Directory of Open Access Journals (Sweden)

Vedprakash Sewjathan

1984-01-01

Full Text Available This paper constitutes a fundamental rederivation of special relativity based on the c-invariance postulate but independent of the assumption ds′2=±ds2 (Einstein [1], Kittel et al [2], Recami [3], the equivalence principle, homogeneity of space-time, isotropy of space, group properties and linearity of space-time transformations or the coincidence of the origins of inertial space-time frames. The mathematical formalism is simpler than Einstein's [4] and Recami's [3]. Whilst Einstein's subluminal and Recami's superluminal theories are rederived in this paper by further assuming the equivalence principle and “mathematical inverses” [4,3], this paper derives (independent of these assumptions with physico-mathematical motivation an alternate singularity-free special-relativistic theory which replaces Einstein's factor [1/(1−V2/c2]12 and Recami's extended-relativistic factor [1/(V2/c2−1]12 by [(1−(V2/c2n/(1−V2/c2]12, where n equals the value of (m(V/m02 as |V|→c. In this theory both Newton's and Einstein's subluminal theories are experimentally valid on account of negligible terms. This theory implies that non-zero rest mass luxons will not be detected as ordinary non-zero rest mass bradyons because of spatial collapse, and non-zero rest mass tachyons are undetectable because they exist in another cosmos, resulting in a supercosmos of matter, with the possibility of infinitely many such supercosmoses, all moving forward in time. Furthermore this theory is not based on any assumption giving rise to the twin paradox controversy. The paper concludes with a discussion of the implications of this theory for general relativity.

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

Non-relativistic Bondi-Metzner-Sachs algebra

Science.gov (United States)

Batlle, Carles; Delmastro, Diego; Gomis, Joaquim

2017-09-01

We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein-Gordon field.

Whispering gallery effect in relativistic optics

Science.gov (United States)

Abe, Y.; Law, K. F. F.; Korneev, Ph.; Fujioka, S.; Kojima, S.; Lee, S.-H.; Sakata, S.; Matsuo, K.; Oshima, A.; Morace, A.; Arikawa, Y.; Yogo, A.; Nakai, M.; Norimatsu, T.; d'Humières, E.; Santos, J. J.; Kondo, K.; Sunahara, A.; Gus'kov, S.; Tikhonchuk, V.

2018-03-01

relativistic laser pulse, confined in a cylindrical-like target, under specific conditions may perform multiple scattering along the internal target surface. This results in the confinement of the laser light, leading to a very efficient interaction. The demonstrated propagation of the laser pulse along the curved surface is just yet another example of the "whispering gallery" effect, although nonideal due to laser-plasma coupling. In the relativistic domain its important feature is a gradual intensity decrease, leading to changes in the interaction conditions. The proccess may pronounce itself in plenty of physical phenomena, including very efficient electron acceleration and generation of relativistic magnetized plasma structures.

Relativistic description of the Fermi motion effects on deuterium targets

International Nuclear Information System (INIS)

Kusno, D.

1979-12-01

A comprehensive analysis of the inconsistencies of the conventional, non-relativistic approach, which has been used so far in the extraction of neutron data from deuterium targets, is given. A new approach dealing with the smearing effects, due to the nucleon's Fermi motion inside the deuteron, is developed as an alternative to the conventional one. This new approach is a spin-less, relativistic, simple and consistent approach. A new covariant model of the elastic electromagnetic form factors of the deuteron in the impulse approximation is also presented. The treatment includes spin and allows for a possibility of determining completely the two elastic structure functions

The usage of color invariance in SURF

Science.gov (United States)

Meng, Gang; Jiang, Zhiguo; Zhao, Danpei

2009-10-01

SURF (Scale Invariant Feature Transform) is a robust local invariant feature descriptor. However, SURF is mainly designed for gray images. In order to make use of the information provided by color (mainly RGB channels), this paper presents a novel colored local invariant feature descriptor, CISURF (Color Invariance based SURF). The proposed approach builds the descriptors in a color invariant space, which stems from Kubelka-Munk model and provides more valuable information than the gray space. Compared with the conventional SURF and SIFT descriptors, the experimental results show that descriptors created by CISURF is more robust to the circumstance changes such as the illumination direction, illumination intensity, and the viewpoints, and are more suitable for the deep space background objects.

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...

Effects of relativistic small radial component on atomic photoionization cross sections

International Nuclear Information System (INIS)

Liu Xiaobin; Xing Yongzhong; Sun Xiaowei

2008-01-01

The effects of relativistic small radial component on atomic photoionization cross sections have been studied within relativistic average self-consistent field theory. Relativistic effects are relatively unimportant for low photon energy, along with a review of high-energy photoionization the relativistic effects are quite important. The effects of relativistic small radial component on photoionization process should show breakdown when the nuclear finite-size effects is taken into account. The compression of wavefunction into the space near nucleus is so strong in highly charged ions that the electronic radius greatly decreases, and the effects of relativistic small radial component on photoionization cross sections turn to stronger than ordinary atoms. Since relativistic effects are extremely sensitive to the behavior of small radial component, the results are in good agreement with relativistic effects on photoionization cross section. (authors)

The ionisation equation in a relativistic gas

International Nuclear Information System (INIS)

Kichenassamy, S.; Krikorian, R.A.

1983-01-01

By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 10 9 K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 10 12 K) and also for the ultrarelativistic case (temperatures greater than 10 15 K). (author)

Effectively semi-relativistic Hamiltonians of nonrelativistic form

International Nuclear Information System (INIS)

Lucha, W.; Schoeberl, F.F.; Moser, M.

1993-12-01

We construct effective Hamiltonians which despite their apparently nonrelativistic form incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions. (authors)

Relativistic Astrophysics

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)

Scale invariant Volkov–Akulov supergravity

Energy Technology Data Exchange (ETDEWEB)

Ferrara, S., E-mail: sergio.ferrara@cern.ch [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); INFN – Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy); Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547 (United States); Porrati, M., E-mail: mp9@nyu.edu [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); CCPP, Department of Physics, NYU, 4 Washington Pl., New York, NY 10003 (United States); Sagnotti, A., E-mail: sagnotti@sns.it [Th-Ph Department, CERN, CH-1211 Geneva 23 (Switzerland); Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, 56126 Pisa (Italy)

2015-10-07

A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.

On the invariance principle

Energy Technology Data Exchange (ETDEWEB)

Moller-Nielsen, Thomas [University of Oxford (United Kingdom)

2014-07-01

Physicists and philosophers have long claimed that the symmetries of our physical theories - roughly speaking, those transformations which map solutions of the theory into solutions - can provide us with genuine insight into what the world is really like. According to this 'Invariance Principle', only those quantities which are invariant under a theory's symmetries should be taken to be physically real, while those quantities which vary under its symmetries should not. Physicists and philosophers, however, are generally divided (or, indeed, silent) when it comes to explaining how such a principle is to be justified. In this paper, I spell out some of the problems inherent in other theorists' attempts to justify this principle, and sketch my own proposed general schema for explaining how - and when - the Invariance Principle can indeed be used as a legitimate tool of metaphysical inference.

A functional LMO invariant for Lagrangian cobordisms

DEFF Research Database (Denmark)

Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël

2008-01-01

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...... of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants....

Relativistic description of directly interacting pions and nucleons

International Nuclear Information System (INIS)

Heller, L.

1976-01-01

The expected magnitudes of the leading relativistic effects on an off-energy-shell T matrix element are estimated using the Bakamjian--Thomas formulation of relativistic potential theory. For pion-nucleon scattering at medium energy, the two largest corrections are expected to result from the use of relativistic relative momenta rather than nonrelativistic values. The importance of additional terms depends upon the detailed behavior of the T matrix

Relativistic electron kinetic effects on laser diagnostics in burning plasmas

Science.gov (United States)

Mirnov, V. V.; Den Hartog, D. J.

2018-02-01

Toroidal interferometry/polarimetry (TIP), poloidal polarimetry (PoPola), and Thomson scattering systems (TS) are major optical diagnostics being designed and developed for ITER. Each of them relies upon a sophisticated quantitative understanding of the electron response to laser light propagating through a burning plasma. Review of the theoretical results for two different applications is presented: interferometry/polarimetry (I/P) and polarization of Thomson scattered light, unified by the importance of relativistic (quadratic in vTe/c) electron kinetic effects. For I/P applications, rigorous analytical results are obtained perturbatively by expansion in powers of the small parameter τ = Te/me c2, where Te is electron temperature and me is electron rest mass. Experimental validation of the analytical models has been made by analyzing data of more than 1200 pulses collected from high-Te JET discharges. Based on this validation the relativistic analytical expressions are included in the error analysis and design projects of the ITER TIP and PoPola systems. The polarization properties of incoherent Thomson scattered light are being examined as a method of Te measurement relevant to ITER operational regimes. The theory is based on Stokes vector transformation and Mueller matrices formalism. The general approach is subdivided into frequency-integrated and frequency-resolved cases. For each of them, the exact analytical relativistic solutions are presented in the form of Mueller matrix elements averaged over the relativistic Maxwellian distribution function. New results related to the detailed verification of the frequency-resolved solutions are reported. The precise analytic expressions provide output much more rapidly than relativistic kinetic numerical codes allowing for direct real-time feedback control of ITER device operation.

Theoretical study of relativistic effects in the electronic structure and chemical bonding of UF6

International Nuclear Information System (INIS)

Onoe, Jun; Takeuchi, Kazuo; Sekine, Rika; Nakamatsu, Hirohide; Mukoyama, Takeshi; Adachi, Hirohiko.

1992-01-01

We have performed the relativistic molecular orbital calculation for the ground state of UF 6 , using the discrete-variational Dirac-Slater method (DV-DS), in order to elucidate the relativistic effects in the electronic structure and chemical bonding. Compared with the electronic structure calculated by the non-relativistic Hartree-Fock-Slater (DV-X α )MO method, not only the direct relativistic effects (spin-orbit splitting etc), but also the indirect effect due to the change in screening core potential charge are shown to be important in the MO level structure. From the U-F bond overlap population analysis, we found that the U-F bond formation can be explained only by the DV-DS, not by the DV-X α . The calculated electronic structure in valence energy region (-20-OeV) and excitation energies in UV region are in agreement with experiments. (author)

The measurement invariance of job diagnostic survey (JDS across three university student groups

Directory of Open Access Journals (Sweden)

Monica Martinez-Gomez

2016-02-01

Full Text Available Purpose: The main purpose of this study is to apply a multigroup confirmatory analysis to examine the measurement invariance (MI of the adapted version of the Job Diagnosis Survey (JDS as a measurement tool that analyses the relationship between the features of teaching methodologies with university students’ motivation and satisfaction across data collected on different degrees and academic years. Design/methodology/approach: Confirmatory factor analysis was carried out using a multigroup structural equation model, using the program EQS 6.1 to test the invariance of the adapted version of JDS in a sample constituted by 535 student of a Spanish public university. The assessment of invariance included the levels of configural, metric, scalar, covariance and latent variables invariance. Several goodness-of-fit measures were assessed. Findings: The results show that measurements are equivalent at the configural, metric, covariance and latent factors invariance. Although the hypotheses of scalar invariance is rejected, results suggest that JDS is partial strict invariant and has satisfactory psychometric properties on all samples. Research limitations/implications: The sample is framed in university students aged between 18 and 30 and for a questionnaire on teaching methodology and students' satisfaction in the context of a Spanish university and the generalization to other questionnaire, or population, should be proved with specific data. Furthermore, the sample size is rather small. Originality/value: In the current process of change that is taking place in universities according to the plan developed by the European Space of Higher Education, focused on increasing the student skills, validate instruments as the satisfaction scale of JDS, are necessary to evaluate students’ satisfaction with new active methodologies. These findings are useful for researchers since they add the first sample in which the MI of a student’s satisfaction survey

Relativistic and non-relativistic electronic molecular-structure calculations for dimers of 4p-, 5p-, and 6p-block elements.

Science.gov (United States)

Höfener, Sebastian; Ahlrichs, Reinhart; Knecht, Stefan; Visscher, Lucas

2012-12-07

We report results of non-relativistic and two-component relativistic single-reference coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] treatments for the 4p-block dimers Ga(2) to Br(2) , the 5p-block dimers In(2) to I(2) , and their atoms. Extended basis sets up to pentuple zeta are employed and energies extrapolated to the complete basis-set limit. Relativistic and non-relativistic results for the dissociation energy D(e) are in close agreement with each other and previously published data, provided non-relativistic or scalar-relativistic results are corrected for spin-orbit contributions taken from the literature. An exception is Te(2) where theoretical results scatter by 0.085 eV. By virtue of this agreement it is unexpected that comparison with the experimental D(0) or D(e) dissociation energies (zero-point vibrational effects are negligible in this context) reveal errors larger than 0.1 eV for Ga(2), Ge(2), and Sb(2). Only relativistic treatments are presented for the 6p-block cases Tl(2) to At(2). Sufficient agreement with experimental data is found only for Pb(2) and Bi(2), the deviation of the computed and experimental D(0) values for Po(2) is again larger than 0.1 eV. Deviations of 0.1 eV between the computed and experimental D(0) values are a major reason for concern and call for additional investigations in both fields to clarify the situation. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Continuous Integrated Invariant Inference, Phase I

Data.gov (United States)

National Aeronautics and Space Administration — The proposed project will develop a new technique for invariant inference and embed this and other current invariant inference and checking techniques in an...

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

Test of charge conjugation invariance

International Nuclear Information System (INIS)

Nefkens, B.M.K.; Prakhov, S.; Gaardestig, A.; Clajus, M.; Marusic, A.; McDonald, S.; Phaisangittisakul, N.; Price, J.W.; Starostin, A.; Tippens, W.B.; Allgower, C.E.; Spinka, H.; Bekrenev, V.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lopatin, I.; Briscoe, W.J.; Shafi, A.; Comfort, J.R.

2005-01-01

We report on the first determination of upper limits on the branching ratio (BR) of η decay to π 0 π 0 γ and to π 0 π 0 π 0 γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π 0 π 0 γ) -4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π 0 π 0 π 0 γ) -5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions

Relativistic quantum chaos-An emergent interdisciplinary field.

Science.gov (United States)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Relativistic quantum chaos—An emergent interdisciplinary field

Science.gov (United States)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Relativistic Spacecraft Propelled by Directed Energy

Science.gov (United States)

Kulkarni, Neeraj; Lubin, Philip; Zhang, Qicheng

2018-04-01

Achieving relativistic flight to enable extrasolar exploration is one of the dreams of humanity and the long-term goal of our NASA Starlight program. We derive a relativistic solution for the motion of a spacecraft propelled by radiation pressure from a directed energy (DE) system. Depending on the system parameters, low-mass spacecraft can achieve relativistic speeds, thus enabling interstellar exploration. The diffraction of the DE system plays an important role and limits the maximum speed of the spacecraft. We consider “photon recycling” as a possible method to achieving higher speeds. We also discuss recent claims that our previous work on this topic is incorrect and show that these claims arise from an improper treatment of causality.

Spinning relativistic particles in external fields

International Nuclear Information System (INIS)

Pomeranskii, Andrei A; Sen'kov, Roman A; Khriplovich, Iosif B

2000-01-01

The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. The self-consistent equations of motion are built with the noncovariant description of spin and with the usual, 'naive' definition of the coordinate of a relativistic particle. A simple derivation of the gravitational interaction of first order in spin is presented for a relativistic particle. The approach developed allows one to consider effects of higher order in spin. Concrete calculations are performed for the second order. The gravimagnetic moment is discussed, a special spin effect in general relativity. We also consider the contributions of the spin interactions of first and second order to the gravitational radiation of compact binary stars. (from the current literature)

Scale invariant Volkov–Akulov supergravity

Directory of Open Access Journals (Sweden)

S. Ferrara

2015-10-01

Full Text Available A scale invariant goldstino theory coupled to supergravity is obtained as a standard supergravity dual of a rigidly scale-invariant higher-curvature supergravity with a nilpotent chiral scalar curvature. The bosonic part of this theory describes a massless scalaron and a massive axion in a de Sitter Universe.

Uncertainty dimension and basin entropy in relativistic chaotic scattering

Science.gov (United States)

Bernal, Juan D.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2018-04-01

Chaotic scattering is an important topic in nonlinear dynamics and chaos with applications in several fields in physics and engineering. The study of this phenomenon in relativistic systems has received little attention as compared to the Newtonian case. Here we focus our work on the study of some relevant characteristics of the exit basin topology in the relativistic Hénon-Heiles system: the uncertainty dimension, the Wada property, and the basin entropy. Our main findings for the uncertainty dimension show two different behaviors insofar as we change the relativistic parameter β , in which a crossover behavior is uncovered. This crossover point is related with the disappearance of KAM islands in phase space, which happens for velocity values above the ultrarelativistic limit, v >0.1 c . This result is supported by numerical simulations and by qualitative analysis, which are in good agreement. On the other hand, the computation of the exit basins in the phase space suggests the existence of Wada basins for a range of β relevant in galactic dynamics, and it also has important implications in other topics in physics such as as in the Störmer problem, among others.

New derivation of relativistic dissipative fluid dynamics

International Nuclear Information System (INIS)

Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata

2012-01-01

Relativistic dissipative hydrodynamics has been quite successful in explaining the spectra and azimuthal anisotropy of particles produced in heavy-ion collisions at the RHIC and recently at the LHC. The first-order dissipative fluid dynamics or the relativistic Navier-Stokes (NS) theory involves parabolic differential equations and suffers from a causality and instability. The second-order or Israel-Stewart (IS) theory with its hyperbolic equations restores causality but may not guarantee stability. The correct formulation of relativistic viscous fluid dynamics is far from settled and is under intense investigation

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)

Local density approximations for relativistic exchange energies

International Nuclear Information System (INIS)

MacDonald, A.H.

1986-01-01

The use of local density approximations to approximate exchange interactions in relativistic electron systems is reviewed. Particular attention is paid to the physical content of these exchange energies by discussing results for the uniform relativistic electron gas from a new point of view. Work on applying these local density approximations in atoms and solids is reviewed and it is concluded that good accuracy is usually possible provided self-interaction corrections are applied. The local density approximations necessary for spin-polarized relativistic systems are discussed and some new results are presented

Relativistic astrophysics

CERN Document Server

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.

2D Relativistic MHD simulations of the Kruskal-Schwarzschild instability in a relativistic striped wind

Science.gov (United States)

Gill, Ramandeep; Granot, Jonathan; Lyubarsky, Yuri

2018-03-01

We study the linear and non-linear development of the Kruskal-Schwarzchild instability in a relativisitically expanding striped wind. This instability is the generalization of Rayleigh-Taylor instability in the presence of a magnetic field. It has been suggested to produce a self-sustained acceleration mechanism in strongly magnetized outflows found in active galactic nuclei, gamma-ray bursts, and micro-quasars. The instability leads to magnetic reconnection, but in contrast with steady-state Sweet-Parker reconnection, the dissipation rate is not limited by the current layer's small aspect ratio. We performed two-dimensional (2D) relativistic magnetohydrodynamic (RMHD) simulations featuring two cold and highly magnetized (1 ≤ σ ≤ 103) plasma layers with an anti-parallel magnetic field separated by a thin layer of relativistically hot plasma with a local effective gravity induced by the outflow's acceleration. Our simulations show how the heavier relativistically hot plasma in the reconnecting layer drips out and allows oppositely oriented magnetic field lines to reconnect. The instability's growth rate in the linear regime matches the predictions of linear stability analysis. We find turbulence rather than an ordered bulk flow near the reconnection region, with turbulent velocities up to ˜0.1c, largely independent of model parameters. However, the magnetic energy dissipation rate is found to be much slower, corresponding to an effective ordered bulk velocity inflow into the reconnection region vin = βinc of 10-3 ≲ βin ≲ 5 × 10-3. This occurs due to the slow evacuation of hot plasma from the current layer, largely because of the Kelvin-Helmholtz instability experienced by the dripping plasma. 3D RMHD simulations are needed to further investigate the non-linear regime.

Einstein Never Approved of Relativistic Mass

Science.gov (United States)

Hecht, Eugene

2009-01-01

During much of the 20th century it was widely believed that one of the significant insights of special relativity was "relativistic mass." Today there are two schools on that issue: the traditional view that embraces speed-dependent "relativistic mass," and the more modern position that rejects it, maintaining that there is only one mass and it's…

Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

CERN Document Server

Qin, Hong

2005-01-01

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

On the Origin of the Dark Matter/Energy in the Universe and the Pioneer Anomaly

Directory of Open Access Journals (Sweden)

Abraham A. Ungar

2008-07-01

Full Text Available Einstein's special relativity is a theory rich of paradoxes, one of which is the recently discovered Relativistic Invariant Mass Paradox. According to this Paradox, the relativistic invariant mass of a galaxy of moving stars exceeds the sum of the relativistic invariant masses of the constituent stars owing to their motion relative to each other. This excess of mass is the mass of virtual matter that has no physical properties other than positive relativistic invariant mass and, hence, that reveals its presence by no means other than gravity. As such, this virtual matter is the dark matter that cosmologists believe is necessary in order to supply the missing gravity that keeps galaxies stable. Based on the Relativistic Invariant Mass Paradox we offer in this article a model which quantifies the anomalous acceleration of Pioneer 10 and 11 spacecrafts and other deep space missions, and explains the presence of dark matter and dark energy in the universe. It turns out that the origin of dark matter and dark energy in the Universe lies in the Paradox, and that the origin of the Pioneer anomaly results from neglecting the Paradox. In order to appreciate the physical significance of the Paradox within the frame of Einstein's special theory of relativity, following the presentation of the Paradox we demonstrate that the Paradox is responsible for the extension of the kinetic energy theorem and of the additivity of energy and momentum from classical to relativistic mechanics. Clearly, the claim that the acceleration of Pioneer 10 and 11 spacecrafts is anomalous is incomplete, within the frame of Einstein's special relativity, since those who made the claim did not take into account the presence of the Relativistic Invariant Mass Paradox (which is understandable since the Paradox, published in the author's 2008 book, was discovered by the author only recently. It remains to test how well the Paradox accords with observations.

Lectures on relativistic quantum mechanics and path integration

International Nuclear Information System (INIS)

Gunn, J.M.F.

1989-02-01

The question posed is why bother with relativistic quantum mechanics? Three reasons are given: First that there are many experimental phenomena which cannot be explained in non-relativistic terms. Secondly it would be unsatisfactory if relativity and quantum mechanics could not be united. Thirdly, there are theoretical reasons why new effects can be expected at relativistic velocities. The objectives of the course are to set up relativistic analogues of the Schroedinger equation and to understand their consequences. In doing so there are some questions which are raised and discussed such as can a first order equation be used to describe spin 0 particles and a second order equation be used to describe spin 1/ 2 (author)

Relativistic and Non-Relativistic Electronic Molecular-Structure Calculations for Dimers of 4p-, 5p-, and 6p-Block Elements

NARCIS (Netherlands)

Hoefener, S.; Ahlrichs, R.; Knecht, S.; Visscher, L.

2012-01-01

We report results of non-relativistic and two-component relativistic single-reference coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] treatments for the 4p-block dimers Ga

Recent progress in invariant pattern recognition

Science.gov (United States)

Arsenault, Henri H.; Chang, S.; Gagne, Philippe; Gualdron Gonzalez, Oscar

1996-12-01

We present some recent results in invariant pattern recognition, including methods that are invariant under two or more distortions of position, orientation and scale. There are now a few methods that yield good results under changes of both rotation and scale. Some new methods are introduced. These include locally adaptive nonlinear matched filters, scale-adapted wavelet transforms and invariant filters for disjoint noise. Methods using neural networks will also be discussed, including an optical method that allows simultaneous classification of multiple targets.

Symmetric low-voltage powering system for relativistic electronic devices

International Nuclear Information System (INIS)

Agafonov, A.V.; Lebedev, A.N.; Krastelev, E.G.

2005-01-01

A special driver for double-sided powering of relativistic magnetrons and several methods of localized electron flow forming in the interaction region of relativistic magnetrons are proposed and discussed. Two experimental installations are presented and discussed. One of them is designed for laboratory research and demonstration experiments at a rather low voltage. The other one is a prototype of a full-scale installation for an experimental research at relativistic levels of voltages on the microwave generation in the new integrated system consisting of a relativistic magnetron and symmetrical induction driver

Lagrangian formulation of a consistent relativistic guiding center theory

International Nuclear Information System (INIS)

Wimmel, H.K.

1983-02-01

A new relativistic guiding center mechanics is presented that conserves energy (in time-independent fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in epsilon identical rsub(g)/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived. (orig.)

Finite type invariants and fatgraphs

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Bene, Alex; Meilhan, Jean-Baptiste Odet Thierry

2010-01-01

–Murakami–Ohtsuki of the link invariant of Andersen–Mattes–Reshetikhin computed relative to choices determined by the fatgraph G; this provides a basic connection between 2d geometry and 3d quantum topology. For each fixed G, this invariant is shown to be universal for homology cylinders, i.e., G establishes an isomorphism...

Ermakov–Lewis invariants and Reid systems

Energy Technology Data Exchange (ETDEWEB)

Mancas, Stefan C., E-mail: stefan.mancas@erau.edu [Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, S.L.P. (Mexico)

2014-06-13

Reid's mth-order generalized Ermakov systems of nonlinear coupling constant α are equivalent to an integrable Emden–Fowler equation. The standard Ermakov–Lewis invariant is discussed from this perspective, and a closed formula for the invariant is obtained for the higher-order Reid systems (m≥3). We also discuss the parametric solutions of these systems of equations through the integration of the Emden–Fowler equation and present an example of a dynamical system for which the invariant is equivalent to the total energy. - Highlights: • Reid systems of order m are connected to Emden–Fowler equations. • General expressions for the Ermakov–Lewis invariants both for m=2 and m≥3 are obtained. • Parametric solutions of the Emden–Fowler equations related to Reid systems are obtained.

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

The projective geometry of the spacetime yielded by relativistic positioning systems and relativistic location systems

OpenAIRE

Rubin , Jacques ,

2014-01-01

Version de travail de thèse d'habilitation à diriger des recherches; Preprint; Current positioning systems are not primary, relativistic systems. Nevertheless, genuine, relativistic and primary positioning systems have been proposed recently by Bahder, Coll et al. and Rovelli to remedy such prior defects. These new designs all have in common an equivariant conformal geometry featuring, as the most basic ingredient, the spacetime geometry. We show how this conformal aspect can be the four-dime...

Conformal invariance in the long-range Ising model

Directory of Open Access Journals (Sweden)

Miguel F. Paulos

2016-01-01

Full Text Available We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Conformal Invariance in the Long-Range Ising Model

CERN Document Server

Paulos, Miguel F; van Rees, Balt C; Zan, Bernardo

2016-01-01

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Conformal invariance in the long-range Ising model

Energy Technology Data Exchange (ETDEWEB)

Paulos, Miguel F. [CERN, Theory Group, Geneva (Switzerland); Rychkov, Slava, E-mail: slava.rychkov@lpt.ens.fr [CERN, Theory Group, Geneva (Switzerland); Laboratoire de Physique Théorique de l' École Normale Supérieure (LPTENS), Paris (France); Faculté de Physique, Université Pierre et Marie Curie (UPMC), Paris (France); Rees, Balt C. van [CERN, Theory Group, Geneva (Switzerland); Zan, Bernardo [Institute of Physics, Universiteit van Amsterdam, Amsterdam (Netherlands)

2016-01-15

We consider the question of conformal invariance of the long-range Ising model at the critical point. The continuum description is given in terms of a nonlocal field theory, and the absence of a stress tensor invalidates all of the standard arguments for the enhancement of scale invariance to conformal invariance. We however show that several correlation functions, computed to second order in the epsilon expansion, are nontrivially consistent with conformal invariance. We proceed to give a proof of conformal invariance to all orders in the epsilon expansion, based on the description of the long-range Ising model as a defect theory in an auxiliary higher-dimensional space. A detailed review of conformal invariance in the d-dimensional short-range Ising model is also included and may be of independent interest.

Relativistic transport theory for cosmic-rays

International Nuclear Information System (INIS)

Webb, G.M.

1985-01-01

Various aspects of the transport of cosmic-rays in a relativistically moving magnetized plasma supporting a spectrum of hydromagnetic waves that scatter the cosmic-rays are presented. A local Lorentz frame moving with the waves or turbulence scattering the cosmic-rays is used to specify the individual particle momentum. The comoving frame is in general a noninertial frame in which the observer's volume element is expanding and shearing, geometric energy change terms appear in the cosmic-ray transport equation which consist of the relativistic generalization of the adiabatic deceleration term and a further term involving the acceleration vector of the scatterers. A relativistic version of the pitch angle evolution equation, including the effects of adiabatic focussing, pitch angle scattering, and energy changes is presented

Examining Relativistic Electron Loss in the Outer Radiation Belt

Science.gov (United States)

Green, J. C.; Onsager, T. G.; O'Brien, P.

2003-12-01

Since the discovery of earth's radiation belts researchers have sought to identify the mechanisms that dictate the seemingly erratic relativistic electron flux levels in the outer belt. Contrary to intuition, relativistic electron flux levels do not always increase during geomagnetic storms even though these storms signify enhanced energy input from the solar wind to the magnetosphere [Reeves et al., 2003; O'Brien et al., 2001]. The fickle response of the radiation belt electrons to geomagnetic activity suggests that flux levels are determined by the outcome of a continuous competition between acceleration and loss. Some progress has been made developing and testing acceleration mechanisms but little is known about how relativistic electrons are lost. We examine relativistic electron losses in the outer belt focusing our attention on flux decrease events of the type first described by Onsager et al. [2002]. The study showed a sudden decrease of geosynchronous >2MeV electron flux occurring simultaneously with local stretching of the magnetic field. The decrease was first observed near 15:00 MLT and progressed to all local times after a period of ˜10 hours. Expanding on the work of Onsager et al. [2002], we have identified ˜ 51 such flux decrease events in the GOES and LANL data and present the results of a superposed epoch analysis of solar wind data, geomagnetic activity indicators, and locally measured magnetic field and plasma data. The analysis shows that flux decreases occur after 1-2 days of quiet condition. They begin when either the solar wind dynamic pressure increases or Bz turns southward pushing hot dense plasma earthward to form a partial ring current and stretched magnetic field at dusk. Adiabatic electron motion in response to the stretched magnetic field may explain the initial flux reduction; however, often the flux does not recover with the magnetic field recovery, indicating that true loss from the magnetosphere is occurring. Using Polar and

BRDF invariant stereo using light transport constancy.

Science.gov (United States)

Wang, Liang; Yang, Ruigang; Davis, James E

2007-09-01

Nearly all existing methods for stereo reconstruction assume that scene reflectance is Lambertian and make use of brightness constancy as a matching invariant. We introduce a new invariant for stereo reconstruction called light transport constancy (LTC), which allows completely arbitrary scene reflectance (bidirectional reflectance distribution functions (BRDFs)). This invariant can be used to formulate a rank constraint on multiview stereo matching when the scene is observed by several lighting configurations in which only the lighting intensity varies. In addition, we show that this multiview constraint can be used with as few as two cameras and two lighting configurations. Unlike previous methods for BRDF invariant stereo, LTC does not require precisely configured or calibrated light sources or calibration objects in the scene. Importantly, the new constraint can be used to provide BRDF invariance to any existing stereo method whenever appropriate lighting variation is available.

Gravitationally confined relativistic neutrinos

Science.gov (United States)

Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.

2017-09-01

Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.

Relativistic corrections to molecular dynamic dipole polarizabilities

DEFF Research Database (Denmark)

Kirpekar, Sheela; Oddershede, Jens; Jensen, Hans Jørgen Aagaard

1995-01-01

obtained from the use of the Darwin and mass-velocity operators to first order are included at both levels of approximation. We find that correlation and relativistic contributions are not even approximately additive for the two molecules. The importance of the relativistic corrections is smallest...

Scalar Relativistic Study of the Structure of Rhodium Acetate

Directory of Open Access Journals (Sweden)

Emily E. Edwards

2004-01-01

Full Text Available Abstract: Rhodium acetate, related rhodium carboxylates, and rhodium amide complexes are powerful catalysts for carbene chemistry. They readily promote the decomposition of diazo compounds and transfer the resulting carbene to a variety of substrates. There have been several quantum chemistry studies of these compounds, particularly of the acetate. These have all used non-relativistic methods, and all have shown optimized Rh-Rh bond lengths significantly longer than the experimental value. In this study we have surveyed several scalar relativistic DFT methods using Gaussian, Slater, and numerical basis functions (in DGAUSS, ADF, and DMOL3. Several combinations of exchange-correlation functionals with relativistic and non-relativistic effective core potentials (ECP were investigated, as were non-relativistic and all electron scalar relativistic methods. The combination of the PW91 exchange and PW91 correlation functional with the Christiansen-Ermler ECP gave the best results: 2.3918 Å compared to the experimental value of 2.3855±0.0005 Å.

Holographic Aspects of a Relativistic Nonconformal Theory

Directory of Open Access Journals (Sweden)

Chanyong Park

2013-01-01

Full Text Available We study a general D-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.

On the physics of relativistic double layers

International Nuclear Information System (INIS)

Carlqvist, P.

1982-06-01

A model of a strong, time-independent, and relativistic double layer is studied. Besides double layers having the electric field parallel to the current the model also describes a certain type of oblique double layers. The 'Langmuir condition' (ratio of ion current density to electron current density) as well as an expression for the potential drop of the double layer are derived. Furthermore, the distribution of charged particles, electric field, and potential within the double layer are clarified and discussed. It is found that the properties of relativistic double layers differ substantially from the properties of corresponding non-relativistic double layers. (Author)

Two-dimensional approach to relativistic positioning systems

International Nuclear Information System (INIS)

Coll, Bartolome; Ferrando, Joan Josep; Morales, Juan Antonio

2006-01-01

A relativistic positioning system is a physical realization of a coordinate system consisting in four clocks in arbitrary motion broadcasting their proper times. The basic elements of the relativistic positioning systems are presented in the two-dimensional case. This simplified approach allows to explain and to analyze the properties and interest of these new systems. The positioning system defined by geodesic emitters in flat metric is developed in detail. The information that the data generated by a relativistic positioning system give on the space-time metric interval is analyzed, and the interest of these results in gravimetry is pointed out

A scale invariance criterion for LES parametrizations

Directory of Open Access Journals (Sweden)

Urs Schaefer-Rolffs

2015-01-01

Full Text Available Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change.The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scale-invariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.

Foundations of a spacetime path formalism for relativistic quantum mechanics

International Nuclear Information System (INIS)

Seidewitz, Ed

2006-01-01

Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincare invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, 'off-shell' theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics

An introduction to relativistic processes and the standard model of electroweak interactions

CERN Document Server

Becchi, Carlo Maria

2014-01-01

These lectures are meant to be a reference and handbook for an introductory course in Theoretical Particle Physics, suitable for advanced undergraduates or beginning graduate students. Their purpose is to reconcile theoretical rigour and completeness with a careful analysis of more phenomenological aspects of the physics. They aim at filling the gap between quantum field theory textbooks and purely phenomenological treatments of fundamental interactions. The first part provides an introduction to scattering in relativistic quantum field theory. Thanks to an original approach to relativistic processes, the relevant computational techniques are derived cleanly and simply in the semi-classical approximation. The second part contains a detailed presentation of the gauge theory of electroweak interactions with particular focus to the processes of greatest phenomenological interest. The main novelties of the present second edition are a more complete discussion of relativistic scattering theory and an expansion of ...

Spin-dependent transport in ferromagnet/semiconductor/ferromagnet junctions: a fully relativistic approach

International Nuclear Information System (INIS)

Popescu, Voicu; Ebert, Hubert; Papanikolaou, Nikolaos; Zeller, Rudolf; Dederichs, Peter H

2004-01-01

We present a fully relativistic generalization of the Landauer-Buettiker formalism that has been implemented within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker Green function method. This approach, going beyond the two-current model, supplies a more general description of the electronic transport. It is shown that the relativistic conductance can be split in terms of individual spin-diagonal and spin-off-diagonal (spin-flip) components, which allows a detailed analysis of the influence of spin-orbit-coupling-induced spin-flip processes on the spin-dependent transport. We apply our method to calculate the ballistic conductance in Fe/GaAs/Fe magnetic tunnel junctions. We find that, by removing the spin selection rules, the spin-orbit coupling strongly influences the conductance, not only qualitatively but also quantitatively, especially in the anti-parallel alignment of the magnetization in the two Fe leads

A more general model for testing measurement invariance and differential item functioning.

Science.gov (United States)

Bauer, Daniel J

2017-09-01

The evaluation of measurement invariance is an important step in establishing the validity and comparability of measurements across individuals. Most commonly, measurement invariance has been examined using 1 of 2 primary latent variable modeling approaches: the multiple groups model or the multiple-indicator multiple-cause (MIMIC) model. Both approaches offer opportunities to detect differential item functioning within multi-item scales, and thereby to test measurement invariance, but both approaches also have significant limitations. The multiple groups model allows 1 to examine the invariance of all model parameters but only across levels of a single categorical individual difference variable (e.g., ethnicity). In contrast, the MIMIC model permits both categorical and continuous individual difference variables (e.g., sex and age) but permits only a subset of the model parameters to vary as a function of these characteristics. The current article argues that moderated nonlinear factor analysis (MNLFA) constitutes an alternative, more flexible model for evaluating measurement invariance and differential item functioning. We show that the MNLFA subsumes and combines the strengths of the multiple group and MIMIC models, allowing for a full and simultaneous assessment of measurement invariance and differential item functioning across multiple categorical and/or continuous individual difference variables. The relationships between the MNLFA model and the multiple groups and MIMIC models are shown mathematically and via an empirical demonstration. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Weak Galilean invariance as a selection principle for coarse-grained diffusive models.

Science.gov (United States)

Cairoli, Andrea; Klages, Rainer; Baule, Adrian

2018-05-29

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Dynamics and stability of relativistic gamma-ray-bursts blast waves

Science.gov (United States)

Meliani, Z.; Keppens, R.

2010-09-01

Aims: In gamma-ray-bursts (GRBs), ultra-relativistic blast waves are ejected into the circumburst medium. We analyse in unprecedented detail the deceleration of a self-similar Blandford-McKee blast wave from a Lorentz factor 25 to the nonrelativistic Sedov phase. Our goal is to determine the stability properties of its frontal shock. Methods: We carried out a grid-adaptive relativistic 2D hydro-simulation at extreme resolving power, following the GRB jet during the entire afterglow phase. We investigate the effect of the finite initial jet opening angle on the deceleration of the blast wave, and identify the growth of various instabilities throughout the coasting shock front. Results: We find that during the relativistic phase, the blast wave is subject to pressure-ram pressure instabilities that ripple and fragment the frontal shock. These instabilities manifest themselves in the ultra-relativistic phase alone, remain in full agreement with causality arguments, and decay slowly to finally disappear in the near-Newtonian phase as the shell Lorentz factor drops below 3. From then on, the compression rate decreases to levels predicted to be stable by a linear analysis of the Sedov phase. Our simulations confirm previous findings that the shell also spreads laterally because a rarefaction wave slowly propagates to the jet axis, inducing a clear shell deformation from its initial spherical shape. The blast front becomes meridionally stratified, with decreasing speed from axis to jet edge. In the wings of the jetted flow, Kelvin-Helmholtz instabilities occur, which are of negligible importance from the energetic viewpoint. Conclusions: Relativistic blast waves are subject to hydrodynamical instabilities that can significantly affect their deceleration properties. Future work will quantify their effect on the afterglow light curves.

PSI collapse and relativistic covariance

International Nuclear Information System (INIS)

Costa de Beauregard, Olivier

1980-01-01

We call macrorelativistic a theory invariant under the orthochronous Lorentz group and obeying the 'factlike' principle of retarded causality, and microrelativistic a theory invariant under the full Lorentz group and CPT symmetric. The Einstein correlations either direct (non-separability of measurements issuing from a common preparation) or reversed (non-separability of preparations producing a common measurement) are incompatible with the macro-, but compatible with the microrelativity. We assume that fundamental physics is fully Lorentz and CPT invariant (the transition to macrophysics introducing a 'factlike asymmetry) and consequently define the collapse-and-retrocollapse concept [fr

Relativistic calculations of coalescing binary neutron stars

Indian Academy of Sciences (India)

We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and ...

Deep processes in non-relativistic confining potentials

International Nuclear Information System (INIS)

Fishbane, P.M.; Grisaru, M.T.

1978-01-01

The authors study deep inelastic and hard scattering processes for non-relativistic particles confined in deep potentials. The mechanisms by which the effects of confinement disappear and the particles scatter as if free are useful in understanding the analogous results for a relativistic field theory. (Auth.)

Multiscale Rotation-Invariant Convolutional Neural Networks for Lung Texture Classification.

Science.gov (United States)

Wang, Qiangchang; Zheng, Yuanjie; Yang, Gongping; Jin, Weidong; Chen, Xinjian; Yin, Yilong

2018-01-01

We propose a new multiscale rotation-invariant convolutional neural network (MRCNN) model for classifying various lung tissue types on high-resolution computed tomography. MRCNN employs Gabor-local binary pattern that introduces a good property in image analysis-invariance to image scales and rotations. In addition, we offer an approach to deal with the problems caused by imbalanced number of samples between different classes in most of the existing works, accomplished by changing the overlapping size between the adjacent patches. Experimental results on a public interstitial lung disease database show a superior performance of the proposed method to state of the art.

Isolating relativistic effects in large-scale structure

Science.gov (United States)

Bonvin, Camille

2014-12-01

We present a fully relativistic calculation of the observed galaxy number counts in the linear regime. We show that besides the density fluctuations and redshift-space distortions, various relativistic effects contribute to observations at large scales. These effects all have the same physical origin: they result from the fact that our coordinate system, namely the galaxy redshift and the incoming photons’ direction, is distorted by inhomogeneities in our Universe. We then discuss the impact of the relativistic effects on the angular power spectrum and on the two-point correlation function in configuration space. We show that the latter is very well adapted to isolate the relativistic effects since it naturally makes use of the symmetries of the different contributions. In particular, we discuss how the Doppler effect and the gravitational redshift distortions can be isolated by looking for a dipole in the cross-correlation function between a bright and a faint population of galaxies.

Refitting density dependent relativistic model parameters including Center-of-Mass corrections

International Nuclear Information System (INIS)

Avancini, Sidney S.; Marinelli, Jose R.; Carlson, Brett Vern

2011-01-01

Full text: Relativistic mean field models have become a standard approach for precise nuclear structure calculations. After the seminal work of Serot and Walecka, which introduced a model Lagrangian density where the nucleons interact through the exchange of scalar and vector mesons, several models were obtained through its generalization, including other meson degrees of freedom, non-linear meson interactions, meson-meson interactions, etc. More recently density dependent coupling constants were incorporated into the Walecka-like models, which are then extensively used. In particular, for these models a connection with the density functional theory can be established. Due to the inherent difficulties presented by field theoretical models, only the mean field approximation is used for the solution of these models. In order to calculate finite nuclei properties in the mean field approximation, a reference set has to be fixed and therefore the translational symmetry is violated. It is well known that in such case spurious effects due to the center-of-mass (COM) motion are present, which are more pronounced for light nuclei. In a previous work we have proposed a technique based on the Pierls-Yoccoz projection operator applied to the mean-field relativistic solution, in order to project out spurious COM contributions. In this work we obtain a new fitting for the density dependent parameters of a density dependent hadronic model, taking into account the COM corrections. Our fitting is obtained taking into account the charge radii and binding energies for He 4 , O 16 , Ca 40 , Ca 48 , Ni 56 , Ni 68 , Sn 100 , Sn 132 and Pb 208 . We show that the nuclear observables calculated using our fit are of a quality comparable to others that can be found in the literature, with the advantage that now a translational invariant many-body wave function is at our disposal. (author)

Construction of time-dependent dynamical invariants: A new approach

International Nuclear Information System (INIS)

Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.

2012-01-01

We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.

Wavelet-based moment invariants for pattern recognition

Science.gov (United States)

Chen, Guangyi; Xie, Wenfang

2011-07-01

Moment invariants have received a lot of attention as features for identification and inspection of two-dimensional shapes. In this paper, two sets of novel moments are proposed by using the auto-correlation of wavelet functions and the dual-tree complex wavelet functions. It is well known that the wavelet transform lacks the property of shift invariance. A little shift in the input signal will cause very different output wavelet coefficients. The autocorrelation of wavelet functions and the dual-tree complex wavelet functions, on the other hand, are shift-invariant, which is very important in pattern recognition. Rotation invariance is the major concern in this paper, while translation invariance and scale invariance can be achieved by standard normalization techniques. The Gaussian white noise is added to the noise-free images and the noise levels vary with different signal-to-noise ratios. Experimental results conducted in this paper show that the proposed wavelet-based moments outperform Zernike's moments and the Fourier-wavelet descriptor for pattern recognition under different rotation angles and different noise levels. It can be seen that the proposed wavelet-based moments can do an excellent job even when the noise levels are very high.

Rotation and Noise Invariant Near-Infrared Face Recognition by means of Zernike Moments and Spectral Regression Discriminant Analysis

Czech Academy of Sciences Publication Activity Database

Farokhi, S.; Shamsuddin, S. M.; Flusser, Jan; Sheikh, U. U.; Khansari, M.; Jafari-Khouzani, K.

2013-01-01

Roč. 22, č. 1 (2013), s. 1-11 ISSN 1017-9909 R&D Projects: GA ČR GAP103/11/1552 Keywords : face recognition * infrared imaging * image moments Subject RIV: JD - Computer Applications, Robotics Impact factor: 0.850, year: 2013 http://library.utia.cas.cz/separaty/2013/ZOI/flusser-rotation and noise invariant near-infrared face recognition by means of zernike moments and spectral regression discriminant analysis.pdf

Investigation of relativistic laser-plasmas using nuclear diagnostics

International Nuclear Information System (INIS)

Guenther, Marc M.

2011-01-01

The present work explores with the development of a novel nuclear diagnostic method for the investigation of the electron dynamics in relativistic laser-plasma interactions. An additional aim of this work was the determination of the real laser peak intensity via the interaction of an intense laser short-pulse with a solid target. The nuclear diagnostics is based on a photo-neutron disintegration nuclear activation method. The main constituent of the nuclear diagnostic are novel pseudoalloic activation targets as a kind of calorimeter to measure the high-energy bremsstrahlung produced by relativistic electrons. The targets are composed of several stable isotopes with different (γ,xn)-reaction thresholds. The activated nuclides were identified via the characteristic gamma-ray decay spectrum by using high-resolution gamma spectroscopy after the laser irradiation. Via the gamma spectroscopy the (γ,xn)-reaction yields were determined. The high-energy bremsstrahlung spectrum has been deconvolved using a novel analysis method based on a modified Penfold-Leiss method. This facilitates the reconstruction of the spectrum of bremsstrahlung photons without any anticipated fit procedures. Furthermore, the characterization of the corresponding bremsstrahlung electrons in the interaction zone is accessible immediately. The consolidated findings about the properties of the relativistic electrons were used to determine the real peak intensity at the laser-plasma interaction zone. In the context of this work, experiments were performed at three different laser facilities. First Experiments were carried out at the 100 TW laser facility at Laboratoire pour l'Utilisation des Lasers Intense (LULI) in France and supplementary at the Vulcan laser facility at Rutherford Appleton Laboratory (RAL) in United Kingdom. The main part of the activation experiments were performed at the PHELIX laser facility (Petawatt High Energy Laser for heavy Ion EXperiments) at GSI-Helmholtzzentrum fuer

Novel topological invariants and anomalies

International Nuclear Information System (INIS)

Hirayama, M.; Sugimasa, N.

1987-01-01

It is shown that novel topological invariants are associated with a class of Dirac operators. Trace formulas which are similar to but different from Callias's formula are derived. Implications of these topological invariants to anomalies in quantum field theory are discussed. A new class of anomalies are calculated for two models: one is two dimensional and the other four dimensional

Scaling behaviour of tensor analyzing power (Ayy) in the inelastic scattering of relativistic deuterons

International Nuclear Information System (INIS)

Korovin, P.P.; Malinina, L.V.; Strokovskij, E.A.

1998-01-01

We suggest a new dimensionless relativistic invariant variable R Δm X / ν which may be interpreted as the ratio of the excitation energy to the full transferred energy; therefore this variable measures a 'degree of inelasticity' of the scattering. Existing data on the tensor analyzing power of the p(d polarized, d ' )X and 12 C(d polarized, d ' )X inelastic scattering at momenta from 4.2 to 9 GeV/c are analyzed in terms of this variable. We observe that A yy taken as a function of R does not depend upon the incident energy, the scattering angle (up to the angles of θ cm ∼ 30 deg), and there is no noticeable difference between the proton and nuclear targets as well. It is remarkable that A yy is maximal (of ∼ 0.5) when R ∼ 0.5 - 0.6 and is small in absolute value when R is close to its limiting values of 0 and 1

Wilson loop invariants from WN conformal blocks

Directory of Open Access Journals (Sweden)

Oleg Alekseev

2015-12-01

Full Text Available Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.

Electromagnetic interactions in relativistic infinite component wave equations

International Nuclear Information System (INIS)

Gerry, C.C.

1979-01-01

The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group

Invariants of triangular Lie algebras

International Nuclear Information System (INIS)

Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

2007-01-01

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

Is a Relativistic Thermodynamics possible?; Es posible una Termodinamica Relativista?

Energy Technology Data Exchange (ETDEWEB)

Guemez, J.

2010-07-01

A brief historical review the literature on developing the concept of Thermodynamics Relativistic. We analyze two examples of application of the Galilean and Relativistic Thermodynamics discussed under what circumstances could build a relativistic Thermodynamics Lorentz covariant with physical sense. (Author) 19 refs.

Study of the O-mode in a relativistic degenerate electron plasma

Science.gov (United States)

Azra, Kalsoom; Ali, Muddasir; Hussain, Azhar

2017-03-01

Using the linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. The dispersion relation for the O-mode in a relativistic degenerate electron plasma is investigated by employing the Fermi-Dirac distribution function. The propagation characteristics of the O-mode (cut offs, resonances, propagation regimes, harmonic structure) are examined by using specific values of the density and the magnetic field that correspond to different relativistic dense environments. Further, it is observed that due to the relativistic effects the cut off and the resonance points are shifted to low frequency values, as a result the propagation regime is reduced. The dispersion relations for the non-relativistic and the ultra-relativistic limits are also presented.