Approximate relativistic corrections to atomic radial wave functions

International Nuclear Information System (INIS)

Cowan, R.D.; Griffin, D.C.

1976-01-01

The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations

Calculation of deuteron wave functions with relativistic interactions

International Nuclear Information System (INIS)

Buck, W.W. III.

1976-01-01

Deuteron wave functions with a repulsive core are obtained numerically from a fully relativistic wave equation introduced by Gross. The numerical technique enables analytic solutions for classes of interactions composed of the relativistic exchanges of a single pion and a single phenomenological meson, sigma. The pion is chosen to interact as a mixture of pseudoscalar and pseudovector. The amount of mixture is determined by a free mixing parameter, lambda, ranging between 1 (pure pseudoscalar) and (pure pseudovector). Each value of lambda corresponds, then, to a different interaction. Solutions are found for lambda = 1, .9, .8, .6, and 0. The wave functions for each interaction come in a group of four. Of the four wave functions, two are the usual S and D state wave functions, while the remaining two, arising out of the relativistic prescription, are identified as 3 P 1 and 1 P 1 wave functions (P state wave functions). For the interactions solved for, the D state probabilities ranged between 5.1 percent and 6.3 percent, while the total P state probabilities ranged between 0.7 percent and 2.7 percent. The method of obtaining solutions was to adjust the sigma meson parameters to give the correct binding energy and a good quadrupole moment. All wave functions obtained are applied to relativistic N-d scattering in the backward direction where the effect of the P states is quite measurable

Electron trapping in the electrosound solitary wave for propagation of high intensity laser in a relativistic plasma

International Nuclear Information System (INIS)

Heidari, E; Aslaninejad, M; Eshraghi, H

2010-01-01

Using a set of relativistic equations for plasmas with warm electrons and cold ions, we have investigated the effects of trapped electrons in the propagation of an electrosound wave and discussed the possibility of the formation of electromagnetic solitons in a plasma. The effective potential energy and deviations of the electron and ion number densities in this relativistic model have been found. We have obtained the governing equations for the amplitude of the HF field with relativistic corrections. In order to show the destructive impact of the trapped electrons on the solitary wave, a relativistic effective potential and the governing equation have been found. It is shown that for certain values of the parameters the condition of localization of the HF amplitude is violated. In addition, it is shown that as the flow velocity of the plasma changes, the shape of the solitary wave shows two opposing behaviours, depending on whether the solitary wave velocity is larger than the flow velocity or smaller. Also, the existence of stationary solitary waves which are prohibited for nonrelativistic plasma has been predicted. Finally, we have obtained the Korteweg-de Vries equation showing the relativistic, trapping and nonlinearity effects.

Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

International Nuclear Information System (INIS)

Krolikowski, W.

1983-01-01

A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

The influence of ion temperature on solitary waves in collisionless weak relativistic plasma

International Nuclear Information System (INIS)

Cerepaniuc, Adina

2004-01-01

Korteweg-de Vries equation is used to study the influence of the ion temperature, on the ion acoustic waves in the frame of collisionless plasma's weak relativistic effect. In the literature it is discussed the influence of ion temperature on the ion acoustic wave in a relativistic plasma for a ratio of the ion flow velocity to the light velocity between 0 and 1. In this paper, the dependence of the phase velocity on the relativistic effect for different values of the ratio of the ion temperature to the electron temperature is studied. In case of weak relativistic effect (ratio of the ion flow velocity to the light velocity is 10 -6 and the step of the representation is 10 -6 ) we noticed the occurrence of an antisoliton within soliton amplitude graphical representation as function of the relativistic effect and the temperature ratio. The novelty of this article consists in the fact that a much smaller interval is considered for velocity ratio (size) and we studied the influence of ion temperature on ion acoustic wave in a collisionless relativistic plasma. We performed the numerical calculation of equations and we plotted the phase velocity and the amplitude of soliton wave as a function of velocity ratio and the temperature ratio. We considered the step of velocity ratio variation equal with 10 -6 and the step of temperature ratio variation 10 -2 . The observation made in this paper refines the results of other authors who studied these equations for velocity ratio variation of 10 -1 . In herein chosen interval we observed new phenomena that were not noticed in the case of choosing larger intervals. (author)

Closed form solutions of two time fractional nonlinear wave equations

Directory of Open Access Journals (Sweden)

M. Ali Akbar

2018-06-01

Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation

Relativistic bound state wave functions

International Nuclear Information System (INIS)

Micu, L.

2005-01-01

A particular method of writing the bound state wave functions in relativistic form is applied to the solutions of the Dirac equation with confining potentials in order to obtain a relativistic description of a quark antiquark bound system representing a given meson. Concerning the role of the effective constituent in the present approach we first observe that without this additional constituent we couldn't expand the bound state wave function in terms of products of free states. Indeed, we notice that if the wave function depends on the relative coordinates only, all the expansion coefficients would be infinite. Secondly we remark that the effective constituent enabled us to give a Lorentz covariant meaning to the potential energy of the bound system which is now seen as the 4th component of a 4-momentum. On the other side, by relating the effective constituent to the quantum fluctuations of the background field which generate the binding, we provided a justification for the existence of some spatial degrees of freedom accompanying the interaction potential. These ones, which are quite unusual in quantum mechanics, in our model are the natural consequence of the the independence of the quarks and can be seen as the effect of the imperfect cancellation of the vector momenta during the quantum fluctuations. Related with all these we remark that the adequate representation for the relativistic description of a bound system is the momentum representation, because of the transparent and easy way of writing the conservation laws and the transformation properties of the wave functions. The only condition to be fulfilled is to find a suitable way to take into account the potential energy of the bound system. A particular feature of the present approach is that the confining forces are due to a kind of glue where both quarks are embedded. This recalls other bound state models where the wave function is factorized in terms of constituent wave functions and the confinement is

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

Vlasov simulation of the relativistic effect on the breaking of large amplitude plasma waves

International Nuclear Information System (INIS)

Xu Hui; Sheng Zhengming; Zhang Jie

2007-01-01

The influence of relativistic and thermal effects on plasma wave breaking has been studied by solving the coupled Vlasov-Poisson equations. When the relativistic effect is not considered, the wave breaking will not occur, provided the initial perturbation is less than certain value as predicted previously, and the largest amplitude of the plasma wave will decrease with the increase of the initial temperature. When the relativistic effect is considered, wave breaking always occurs during the time evolution, irrespective of the initial perturbation amplitude. Yet the smaller the initial perturbation amplitude is, the longer is the time for wave breaking to occur. With large initial perturbations, wave breaking can always occur with the without the relativistic effect. However, the results are significantly different in the two cases. The thermal effects of electrons decrease the threshold value to initial amplitude for wave breaking and large phase velocity makes the nonlinear phenomenon occur more easily. (authors)

Resonant Scattering of Relativistic Outer Zone Electrons by Plasmaspheric Plume Electromagnetic Ion Cyclotron Waves

International Nuclear Information System (INIS)

Zhen-Peng, Su; Hui-Nan, Zheng

2009-01-01

The bounce-averaged Fokker–Planck equation is solved to study the relativistic electron phase space density (PSD) evolution in the outer radiation belt due to resonant interactions with plasmaspheric plume electromagnetic ion cyclotron (EMIC) waves. It is found that the PSDs of relativistic electrons can be depleted by 1–3 orders of magnitude in 5h, supporting the previous finding that resonant interactions with EMIC waves may account for the frequently observed relativistic electron flux dropouts in the outer radiation belt during the main phase of a storm. The significant precipitation loss of ∼MeV electrons is primarily induced by the EMIC waves in H + and He + bands. The rapid remove of highly relativistic electrons (> 5 MeV) is mainly driven by the EMIC waves in O + band at lower pitch-angles, as well as the EMIC waves in H + and He + bands at larger pitch-angles. Moreover, a stronger depletion of relativistic electrons is found to occur over a wider pitch angle range when EMIC waves are centering relatively higher in the band

Quantum ion-acoustic solitary waves in weak relativistic plasma

Indian Academy of Sciences (India)

Abstract. Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive ...

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.)

A wave equation interpolating between classical and quantum mechanics

Science.gov (United States)

Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

2015-10-01

We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

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)

Closed form solutions of two time fractional nonlinear wave equations

Science.gov (United States)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

International Nuclear Information System (INIS)

Linares, Jesus; Nistal, Maria C.

2009-01-01

A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.

Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field

International Nuclear Information System (INIS)

Colavita, E.; Hacyan, S.

2014-01-01

We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded. -- Highlights: •We study a relativistic electron in a particular electromagnetic field configuration. •New exact solutions of the Klein–Gordon and Dirac equations are obtained. •Coherent and displaced number states can describe a relativistic particle

Contribution of Higher-Order Dispersion to Nonlinear Electron-Acoustic Solitary Waves in a Relativistic Electron Beam Plasma System

International Nuclear Information System (INIS)

Zahran, M.A.; El-Shewy, E.K.

2008-01-01

The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg--de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained

Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves.

Science.gov (United States)

Chesler, Paul M; Loeb, Abraham

2017-07-21

In the weak-field limit of general relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of general relativity are supported by the observation of ultrahigh-energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of modified Newtonian dynamics, namely, the generalized Einstein-aether theory and bimetric modified Newtonian dynamics, display fatal inconsistencies with these observations.

Three dimensional electrostatic solitary waves in a dense magnetoplasma with relativistically degenerate electrons

Energy Technology Data Exchange (ETDEWEB)

Ata-ur-Rahman,; Qamar, A. [Institute of Physics and Electronics, University of Peshawar, Peshawar 25000 (Pakistan); National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Masood, W. [National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); COMSATS, Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); Eliasson, B. [Physics Department, University of Strathclyde, Glasgow G4 0NG, Scotland (United Kingdom)

2013-09-15

In this paper, small but finite amplitude electrostatic solitary waves in a relativistic degenerate magnetoplasma, consisting of relativistically degenerate electrons and non-degenerate cold ions, are investigated. The Zakharov-Kuznetsov equation is derived employing the reductive perturbation technique and its solitary wave solution is analyzed. It is shown that only compressive electrostatic solitary structures can propagate in such a degenerate plasma system. The effects of plasma number density, ion cyclotron frequency, and direction cosines on the profiles of ion acoustic solitary waves are investigated and discussed at length. The relevance of the present investigation vis-a-vis pulsating white dwarfs is also pointed out.

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

Dynamics of the relativistic acceleration of charged particles in space plasma while surfing the package electromagnetic waves

International Nuclear Information System (INIS)

Erokhin, N.S.; Zol'nikova, N.N.; Kuznetsov, E.A.; Mikhajlovskaya, L.A.

2010-01-01

Based on numerical calculations considered the relativistic acceleration of charged particles in space plasma when surfing on the spatially localized package of electromagnetic waves. The problem is reduced to the study of unsteady, nonlinear equation for the wave phase at the carrier frequency at the location of the accelerated charge, which is solved numerically. We study the temporal dynamics of the relativistic factor, the component of momentum and velocity of the particle, its trajectory is given gyro-rotation in an external magnetic field after the departure of the effective potential well. Dependence of the dynamics of a particle interacting with the wave of the sign of the velocity of the charge along the wave front. We formulate the optimal conditions of the relativistic particle acceleration wave packet, indicate the possibility of again (after a number gyro-turnover) charge trapping wave with an additional relativistic acceleration.

Electromagnetic wave propagation in relativistic magnetized plasmas

International Nuclear Information System (INIS)

Weiss, I.

1985-01-01

An improved mathematical technique and a new code for deriving the conductivity tensor for collisionless plasmas have been developed. The method is applicable to a very general case, including both hot (relativistic) and cold magnetized plasmas, with only isotropic equilibrium distributions being considered here. The usual derivation starts from the relativistic Vlasov equation and leads to an integration over an infinite sum of Bessel functions which has to be done numerically. In the new solution the integration is carried out over a product of two Bessel functions only. This reduces the computing time very significantly. An added advantage over existing codes is our capability to perform the computations for waves propagating obliquely to the magnetic field. Both improvements greatly facilitate investigations of properties of the plasma under conditions hitherto unexplored

Self-focusing of nonlinear waves in a relativistic plasma with positive and negative ions

International Nuclear Information System (INIS)

Mukherjee, Joydeep; Chowdhury, A.R.

1994-01-01

The phenomenon of self-focusing of nonlinear waves was analysed in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. The effect of the inertia of the relativistic electron is also considered by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schroedinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing. 10 refs., 2 figs

Relativistic three-particle dynamical equations: I. Theoretical development

International Nuclear Information System (INIS)

Adhikari, S.K.; Tomio, L.; Frederico, T.

1993-11-01

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

Influence of a relativistic kinematics on s-wave KN phase shifts in a quark model

International Nuclear Information System (INIS)

Lemaire, S.; Labarsouque, J.; Silvestre-Brac, B.

2001-01-01

The I = 1 and I = 0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid Hamiltonian method. The results have been compared to the non-relativistic ones. For each isospin channel the phase shifts obtained are not so far from the non-relativistic results. (author)

Fully nonlinear heavy ion-acoustic solitary waves in astrophysical degenerate relativistic quantum plasmas

Science.gov (United States)

Sultana, S.; Schlickeiser, R.

2018-05-01

Fully nonlinear features of heavy ion-acoustic solitary waves (HIASWs) have been investigated in an astrophysical degenerate relativistic quantum plasma (ADRQP) containing relativistically degenerate electrons and non-relativistically degenerate light ion species, and non-degenerate heavy ion species. The pseudo-energy balance equation is derived from the fluid dynamical equations by adopting the well-known Sagdeev-potential approach, and the properties of arbitrary amplitude HIASWs are examined. The small amplitude limit for the propagation of HIASWs is also recovered. The basic features (width, amplitude, polarity, critical Mach number, speed, etc.) of HIASWs are found to be significantly modified by the relativistic effect of the electron species, and also by the variation of the number density of electron, light ion, and heavy ion species. The basic properties of HIASWs, that may propagated in some realistic astrophysical plasma systems (e.g., in white dwarfs), are briefly discussed.

The incompressible non-relativistic Navier-Stokes equation from gravity

International Nuclear Information System (INIS)

Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

2009-01-01

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation

International Nuclear Information System (INIS)

Znojil, Miloslav

2004-01-01

Witten's the non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations

Parametric decay of an extraordinary electromagnetic wave in relativistic plasma

Energy Technology Data Exchange (ETDEWEB)

Dorofeenko, V. G. [Institute for Advanced Studies (Austria); Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Peoples’ Friendship University of Russia (Russian Federation)

2015-03-15

Parametric instability of an extraordinary electromagnetic wave in plasma preheated to a relativistic temperature is considered. A set of self-similar nonlinear differential equations taking into account the electron “thermal” mass is derived and investigated. Small perturbations of the parameters of the heated plasma are analyzed in the linear approximation by using the dispersion relation determining the phase velocities of the fast and slow extraordinary waves. In contrast to cold plasma, the evanescence zone in the frequency range above the electron upper hybrid frequency vanishes and the asymptotes of both branches converge. Theoretical analysis of the set of nonlinear equations shows that the growth rate of decay instability increases with increasing initial temperature of plasma electrons. This result is qualitatively confirmed by numerical simulations of plasma heating by a laser pulse injected from vacuum.

Non-relativistic and relativistic quantum kinetic equations in nuclear physics

International Nuclear Information System (INIS)

Botermans, W.M.M.

1989-01-01

In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes

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.

Quaternion wave equations in curved space-time

Science.gov (United States)

Edmonds, J. D., Jr.

1974-01-01

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

Science.gov (United States)

Gamayunov, K. V.; Khazanov, G. V.

2006-01-01

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we

Relativistic transport equation for a discontinuity wave of multiplicity one

Energy Technology Data Exchange (ETDEWEB)

Giambo, S; Palumbo, A [Istituto di Matematica, Universita degli Studi, Messina (Italy)

1980-04-14

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering Based on the Newly Developed Self-consistent RC/EMIC Waves Model by Khazanov et al. [2006

Science.gov (United States)

Khazanov, G. V.; Gallagher, D. L.; Gamayunov, K.

2007-01-01

It is well known that the effects of EMIC waves on RC ion and RB electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. Therefore, realistic characteristics of EMIC waves should be properly determined by modeling the RC-EMIC waves evolution self-consistently. Such a selfconsistent model progressively has been developing by Khaznnov et al. [2002-2006]. It solves a system of two coupled kinetic equations: one equation describes the RC ion dynamics and another equation describes the energy density evolution of EMIC waves. Using this model, we present the effectiveness of relativistic electron scattering and compare our results with previous work in this area of research.

Asymmetric systems described by a pair of local covariant wave equations

Energy Technology Data Exchange (ETDEWEB)

Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

1979-07-16

A class of asymmetric solutions of the integrability conditions for systems obeying the Leutwyler-Stern pair of covariant wave equations is obtained. The class of unequal-mass systems described by these solutions does not embed the particle-antiparticle system behaving as a relativistic harmonic oscillator.

Supergroup extensions: from central charges to quantization through relativistic wave equations

International Nuclear Information System (INIS)

Aldaya, V.; Azcarraga, J.A. de.

1982-07-01

We give in this paper the finite group law of a family of supergroups including the U(1)-extended N=2 super-Poincare group. From this family of supergroups, and by means of a canonical procedure, we are able to derive the Klein-Gordon and Dirac equations for the fields contained in the superfield. In the process, the physical content of the central charge as the mass parameter and the role of covariant derivatives are shown to come out canonically from the group structure, and the U(1)-extended supersymmetry is seen as necessary for the geometric quantization of the relativistic elementary systems. (author)

Relativistic quantum vorticity of the quadratic form of the Dirac equation

International Nuclear Information System (INIS)

Asenjo, Felipe A; Mahajan, Swadesh M

2015-01-01

We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

Science.gov (United States)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Relativistic actions for bound-states and applications in the meson spectroscopy

International Nuclear Information System (INIS)

Silva Carvalho, Hendly da.

1991-08-01

We study relativistic equations for bound states of two-body systems using Dirac's constraint formalism and supersymmetry. The two-body system can be of spinless particles, one of them spinning and the other one spinless, or both of them spinning. The interaction is described by scalar, timelike four-vector and spacelike four-vector potentials under Lorentz transformations. As an application we use the relativistic wave equation for two scalar particles and calculate the mass spectra of the mesons treating them as spinless quark-antiquark bound states. The interaction potential in this case is a convenient adaptation of the potential employed in non-relativistic calculations. Finally, we compare our results with more recent experimental data and with theoretical results obtained with the same potential used by us but with a non-relativistic wave equation. We also compare our results with results obtained with the relativistic wave equation but with a different interaction potential. (author). 38 refs, 9 figs, 8 tabs

Nonlinear Waveforms for Ion-Acoustic Waves in Weakly Relativistic Plasma of Warm Ion-Fluid and Isothermal Electrons

Directory of Open Access Journals (Sweden)

S. A. El-Wakil

2012-01-01

Full Text Available The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.

Equations of motion in relativistic gravity

CERN Document Server

Lämmerzahl, Claus; Schutz, Bernard

2015-01-01

 The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...

Relativistic simulation of the Vlasov equation for plasma expansion into vacuum

Directory of Open Access Journals (Sweden)

H Abbasi

2012-12-01

Full Text Available   In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.

Relativistic effects on large amplitude nonlinear Langmuir waves in a two-fluid plasma

International Nuclear Information System (INIS)

Nejoh, Yasunori

1994-07-01

Large amplitude relativistic nonlinear Langmuir waves are analyzed by the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two-fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ion mass to electron mass ratio. The constant energy is determined by the specific range of the relativistic effect. In the non-relativistic limit, large amplitude relativistic Langmuir waves do not exist. The present investigation predicts new findings of large amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important. (author)

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.)

Compression-amplified EMIC waves and their effects on relativistic electrons

Energy Technology Data Exchange (ETDEWEB)

Li, L. Y., E-mail: lyli-ssri@buaa.edu.cn; Yu, J.; Cao, J. B. [School of Space and Environment, Beihang University, Beijing (China); Yuan, Z. G. [School of Electronic Information, Wuhan University, Wuhan (China)

2016-06-15

During enhancement of solar wind dynamic pressure, we observe the periodic emissions of electromagnetic ion cyclotron (EMIC) waves near the nightside geosynchronous orbit (6.6R{sub E}). In the hydrogen and helium bands, the different polarized EMIC waves have different influences on relativistic electrons (>0.8 MeV). The flux of relativistic electrons is relatively stable if there are only the linearly polarized EMIC waves, but their flux decreases if the left-hand polarized (L-mode) EMIC waves are sufficiently amplified (power spectral density (PSD) ≥ 1 nT{sup 2}/Hz). The larger-amplitude L-mode waves can cause more electron losses. In contrast, the R-mode EMIC waves are very weak (PSD < 1 nT{sup 2}/Hz) during the electron flux dropouts; thus, their influence may be ignored here. During the electron flux dropouts, the relativistic electron precipitation is observed by POES satellite near the foot point (∼850 km) of the wave emission region. The quasi-linear simulation of wave-particle interactions indicates that the L-mode EMIC waves can cause the rapid precipitation loss of relativistic electrons, especially when the initial resonant electrons have a butterfly-like pitch angle distribution.

Compression-amplified EMIC waves and their effects on relativistic electrons

International Nuclear Information System (INIS)

Li, L. Y.; Yu, J.; Cao, J. B.; Yuan, Z. G.

2016-01-01

During enhancement of solar wind dynamic pressure, we observe the periodic emissions of electromagnetic ion cyclotron (EMIC) waves near the nightside geosynchronous orbit (6.6R E ). In the hydrogen and helium bands, the different polarized EMIC waves have different influences on relativistic electrons (>0.8 MeV). The flux of relativistic electrons is relatively stable if there are only the linearly polarized EMIC waves, but their flux decreases if the left-hand polarized (L-mode) EMIC waves are sufficiently amplified (power spectral density (PSD) ≥ 1 nT 2 /Hz). The larger-amplitude L-mode waves can cause more electron losses. In contrast, the R-mode EMIC waves are very weak (PSD < 1 nT 2 /Hz) during the electron flux dropouts; thus, their influence may be ignored here. During the electron flux dropouts, the relativistic electron precipitation is observed by POES satellite near the foot point (∼850 km) of the wave emission region. The quasi-linear simulation of wave-particle interactions indicates that the L-mode EMIC waves can cause the rapid precipitation loss of relativistic electrons, especially when the initial resonant electrons have a butterfly-like pitch angle distribution.

Relativistic deuteron wave function on light front

International Nuclear Information System (INIS)

Karmanov, V.A.

1980-01-01

In the framework of the one boson exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. WF depends on extra variable having the form of a unit vector and is determined by six functions instead of two ones (S-and D-waves) in the nonrelativistic case. At moderate momenta the WF is matched with WF in the Reid model. It is emphasized the importance of indication of the qualitative observed phenomena associated with change of parametrization and spin structure of relativistic deuteron WF

The interaction between a relativistic electron beam and a slow electromagnetic wave in a waveguide that is partially filled with a dielectric

Energy Technology Data Exchange (ETDEWEB)

Ivanov, S.T.; Nikolov, N.A.

1979-01-01

The problem of the excitation of microwaves during the propagation of a relativistic electron beam through a waveguide which is partially filled with a dielectric is solved using Maxwell equations and relativistic magnetic hydrodynamics. Two cases are found in which the beam-excited wave has a single mode (it is coherent). For one of the coherent waves, the saturation amplitude and the efficiency of converting the beam energy into electomagnetic field energy are determined.

Development of a 2 MW relativistic backward wave oscillator

Indian Academy of Sciences (India)

In this paper, a high power relativistic backward wave oscillator (BWO) experiment is reported. A 230 keV, 2 kA, 150 ns relativistic electron beam is generated using a Marx generator. The beam is then injected into a hollow rippled wall metallic cylindrical tube that forms a slow wave structure. The beam is guided using an ...

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

International Nuclear Information System (INIS)

Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.

2010-01-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.

On completeness and orthogonality of solutions of relativistic wave equations on zero plane

International Nuclear Information System (INIS)

Gitman, D.M.; Shakhmatov, V.M.; Shvartsman, Sh.M.

1975-01-01

The work considers the possible redeterminations of the scalar product for the relativistic wave fields, such as the Klein-Gordon and Dirac ones. It has been shown that a whole class of new exact solutions, for which the usual scalar product on the plane x 0 =const. could not be previously determinated, allows a correct scalar product on the zero plane x 0 -x 3 =const. The relations of orthogonality and completeness with respect to the above scalar product have been proved. Possible applications of the obtained results are discussed

Dispersion formulae for waves in a magneto-active relativistic plasma

International Nuclear Information System (INIS)

Misra, P.; Mohanty, J.N.

1980-01-01

Dispersion formulae are derived for the transverse waves propagating through a collisionless magneto-active plasma in the direction of the magnetic field valid for relativistic as well as non-relativistic temperatures. Wave propagation under various limiting conditions of temperatures and magnetic field are discussed. (author)

Dispersion formulae for waves in a magneto-active relativistic plasma

Energy Technology Data Exchange (ETDEWEB)

Misra, P. (Ravenshaw Coll., Cuttack (India)); Mohanty, J.N. (F.M. College, Balasore (India). Dept. of Physics)

1980-12-01

Dispersion formulae are derived for the transverse waves propagating through a collisionless magneto-active plasma in the direction of the magnetic field valid for relativistic as well as non-relativistic temperatures. Wave propagation under various limiting conditions of temperatures and magnetic field are discussed.

Global existence proof for relativistic Boltzmann equation

International Nuclear Information System (INIS)

Dudynski, M.; Ekiel-Jezewska, M.L.

1992-01-01

The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions

Well-posedness for Semi-relativistic Hartree Equations of Critical Type

International Nuclear Information System (INIS)

Lenzmann, Enno

2007-01-01

We prove local and global well-posedness for semi-relativistic, nonlinear Schroedinger equations with initial data in H s (R 3 ). Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2 -norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class

Ion temperature effect on the propagation of ion acoustic solitary waves in a relativistic magnetoplasma

International Nuclear Information System (INIS)

Salahuddin, M.

1990-01-01

Using the reductive perturbation technique the Korteweg-de Vries (KdV) equation is derived for ion acoustic waves, in the presence of weak relativistic effects and warm ions, in a magnetized plasma. The influence of non ideal effects on the amplitude and width of the ion acoustic solitary waves is also discussed. The results are depicted in the figures. It is shown that the simultaneous presence of ion streaming and magnetic field stops the tendency of soliton breaking. (author)

Integral representations of solutions of the wave equation based on relativistic wavelets

International Nuclear Information System (INIS)

Perel, Maria; Gorodnitskiy, Evgeny

2012-01-01

A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)

The Poisson equation at second order in relativistic cosmology

International Nuclear Information System (INIS)

Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.

2013-01-01

We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field

Relativistic particle in a box: Klein-Gordon versus Dirac equations

Science.gov (United States)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

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

Relativistic wave functions of two spin 1/2 quarks in a model with QCD interaction

International Nuclear Information System (INIS)

Skachkov, N.B.; Solovtsov, I.L.

1981-01-01

Within the hamiltonian formulation of quantum field theory an equation is obtained for the vertex and wave functions of a composite system of two spin 1/2 quarks. Exact solutions are found for the relativistic potential having in the momentum representation the ''asymptotically-free'' behaviour at large values of momentum transfer Q 2 . It is shown that within the given model the π-meson wave function has zero at a finite distance corresponding to the point of discontinuity of the effective potential [ru

Spreading of a relativistic wave packet

International Nuclear Information System (INIS)

Almeida, C.; Jabs, A.

1983-01-01

A simple general proof that the spreading velocity of a relativistic free wave packet of the Broglie waves is limited is presented. For a wide class of packets it is confirmed that the limit is the velocity of light, and it is shown how this limit is approached when the width Δp of the wave packet in momentum space tends to infinity and the minimum width σ(t=o) in ordinary space tends to zero. (Author) [pt

Relativistic two-fermion equations with form factors and anomalous magnetic moment interactions

International Nuclear Information System (INIS)

Ahmed, S.

1977-04-01

Relativistic equations for two-fermion systems are derived from quantum field theory taking into account the form factors of the particles. When the q 2 dependence of the form factors is disregarded, in the static approximation, the two-fermion equations with Coulomb and anomalous magnetic moment interactions are obtained. Separating the angular variables, a sixteen-component relativistic radial equation are finally given

Statistical investigation of the efficiency of EMIC waves in precipitating relativistic electrons

Science.gov (United States)

Hudson, M. K.; Qin, M.; Millan, R. M.; Woodger, L. A.; Shekhar, S.

2017-12-01

Electromagnetic ion cyclotron (EMIC) waves have been proposed as an effective way to scatter relativistic electrons into the atmospheric loss cone. In our study, however, among the total 399 coincidence events when NOAA satellites goes through the region of EMIC wave activity, only 103 are associated with Relativistic Electron Precipitation (REP) events, which indicates that the link between EMIC waves and relativistic electrons is much weaker than expected. Most of the studies so far have been focused on the He+ band EMIC waves, and H+ band EMIC waves have been regarded as less important to the precipitation of electrons. In our study, we demonstrate that among the 103 EMIC wave events detected by Van Allen Probes that are in close conjunction with relativistic electron precipitation observed by POES satellites, the occurrence rate of H+ and He+ band EMIC waves coincident with REP is comparable, suggesting closer examination of the range of ΔL and ΔMLT used to determine coincidence between Van Allen Probes EMIC waves and POES precipitation observation.

Workshop on gravitational waves and relativistic astrophysics

Indian Academy of Sciences (India)

Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been ...

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.

From Fermat principle to wave equation - quantization of 'particle mechanics of light'

International Nuclear Information System (INIS)

Ogawa, Naohisa

2004-01-01

The Fermat principle states that light chooses the temporally shortest path. The action for this 'motion' is the observed time, and it has no Lorentz invariance. In this Letter we show how this action can be obtained from a relativistic action of massive particle, and how the classical wave equation of light can be obtained from this action

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

On the relativistic transport equation for a discontinuity wave of multiplicity one

International Nuclear Information System (INIS)

Giambo, Sebastiano; Palumbo, Annunziata

1980-01-01

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity [fr

Relativistic equation of the orbit of a particle in a arbitrary central force field

International Nuclear Information System (INIS)

Aaron, Francisc D.

2005-01-01

The equation of the orbit of a relativistic particle moving in an arbitrary central force field is derived. Straightforward generalizations of well-known first and second order differential equations are given. It is pointed out that the relativistic equation of the orbit has the same form as in the non-relativistic case, the only changes consisting in the appearance of additional terms proportional to 1/c 2 in both potential and total energies. (author)

Relativistic equations of state at finite temperature

International Nuclear Information System (INIS)

Santos, A.M.S.; Menezes, D.P.

2004-01-01

In this work we study the effects of temperature on the equations of state obtained within a relativistic model with and without β equilibrium, over a wide range of densities. We integrate the TOV equations. We also compare the results of the equation of state, effective mass and strangeness fraction from the TM1, NL3 and GL sets of parameters, as well as investigating the importance of antiparticles in the treatment. The have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars. (author)

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.

Relativistic hydrodynamics with QHD-I equation of state

International Nuclear Information System (INIS)

Menezes, D.P.

1993-04-01

We derive the equation of state of the QHD-I lagrangian in a classical approach. The obtained equation of state is then used as input in a relativistic hydrodynamical numerical routine. Rapidity and transverse momentum distributions are calculated and compared with experimental data on heavy ion collisions obtained at BNL-AGS and CERN-SPS. (orig.). 7 figs

Electron acoustic waves and parametric instabilities in a 4-component relativistic quantum plasma with Thomas-Fermi distributed electrons

Science.gov (United States)

Ikramullah, Ahmad, Rashid; Sharif, Saqib; Khattak, Fida Younus

2018-01-01

The interaction of Circularly Polarized Electro-Magnetic (CPEM) waves with a 4-component relativistic quantum plasma is studied. The plasma constituents are: relativistic-degenerate electrons and positrons, dynamic degenerate ions, and Thomas-Fermi distributed electrons in the background. We have employed the Klein-Gordon equations for the electrons as well as for the positrons, while the ions are represented by the Schrödinger equation. The Maxwell and Poisson equations are used for electromagnetic waves. Three modes are observed: one of the modes is associated with the electron acoustic wave, a second mode at frequencies greater than the electron acoustic wave mode could be associated with the positrons, and the third one at the lowest frequencies could be associated with the ions. Furthermore, Stimulated Raman Scattering (SRS), Modulational, and Stimulated Brillouin Scattering (SBS) instabilities are studied. It is observed that the growth rates of both the SRS and SBS instabilities decrease with increase in the quantum parameter of the plasma. It is also observed that the scattering spectra in both the SRS and SBS get restricted to very small wavenumber regions. It is shown that for low amplitude CPEM wave interaction with the quantum plasma, the positron concentration has no effect on the SRS and SBS spectra. In the case of large amplitude CPEM wave interaction, however, one observes spectral changes with varying positron concentrations. An increase in the positron concentration also enhances the scattering instability growth rates. Moreover, the growth rate first increases and then decreases with increasing intensity of the CPEM wave, indicating an optimum value of the CPEM wave intensity for the growth of these scattering instabilities. The modulational instability also shows dependence on the quantum parameter as well as on the positron concentration.

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.

Newtonian hydrodynamic equations with relativistic pressure and velocity

Energy Technology Data Exchange (ETDEWEB)

Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)

2016-07-01

We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Relativistic theory of electron-impact ionization

International Nuclear Information System (INIS)

Rosenberg, Leonard

2010-01-01

A relativistic version of an earlier, non-relativistic, formulation of the theory of ionization of an atomic system by electron impact is presented. With a time-independent resolvent operator taken as the basis for the dynamics, a wave equation is derived for a system with open channels consisting of two positive-energy electrons in an external field generated by the residual ion. Virtual intermediate states can be accounted for by the effective Hamiltonian that appears in the wave equation and which in principle may be constructed perturbatively. The asymptotic form of the wavefunction, modified by the effects of the long-range Coulomb interactions of the two electrons in the external field, is derived. These electrons are constrained, by projection operators which appear naturally in the theory, to propagate in positive-energy states only. The long-range Coulomb effects take the form of phase factors similar to those that are found in the non-relativistic version of the theory. With the boundary conditions established, an integral identity for the ionization amplitude is derived, and used to set up a distorted-wave Born expansion for the transition amplitude involving Coulomb-modified propagating waves.

Relativistic Tsiolkovsky equation -- a case study in special relativity

Science.gov (United States)

Redd, Jeremy; Panin, Alexander

2011-10-01

A possibility of using antimatter in future space propulsion systems is seriously discussed in scientific literature. Annihilation of matter and antimatter is not only the energy source of ultimate density 9x10^16 J/kg (provided that antimatter fuel is available on board or can be collected along the journey) but also potentially allows to reach ultimate exhaust speed -- speed of light c. Using relativistic rocket equation we discuss the feasibility of achieving relativistic velocities with annihilation powered photon engine, as well as the advantages and disadvantages of interstellar travel with relativistic and ultrarelativistic velocities.

Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

International Nuclear Information System (INIS)

Rizzato, F.B.

1985-01-01

Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

Beyond the relativistic mean-field approximation. II. Configuration mixing of mean-field wave functions projected on angular momentum and particle number

International Nuclear Information System (INIS)

Niksic, T.; Vretenar, D.; Ring, P.

2006-01-01

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions

Fundamental laws of relativistic classical dynamics revisited

International Nuclear Information System (INIS)

Blaquiere, Augustin

1977-01-01

By stating that a linear differential form, whose coefficients are the components of the momentum and the energy of a particle, has an antiderivative, the basic equations of the dynamics of points are obtained, in the relativistic case. From the point of view of optimization theory, a connection between our condition and the Bellman-Isaacs equation of dynamic programming is discussed, with a view to extending the theory to relativistic wave mechanics [fr

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

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)

Relativistic point dynamics general equations, constant proper masses, interactions between electric charges, variable proper masses, collisions

CERN Document Server

Arzeliès, Henri

1972-01-01

Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma

Energy Technology Data Exchange (ETDEWEB)

McKerr, M.; Kourakis, I. [Centre for Plasma Physics, School of Mathematics and Physics, Queen' s University Belfast, BT7 1NN Belfast, Northern Ireland (United Kingdom); Haas, F. [Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, Porto Alegre, RS (Brazil)

2016-05-15

A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case—in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.

Electromagnetic wave in a relativistic magnetized plasma

International Nuclear Information System (INIS)

Krasovitskiy, V. B.

2009-01-01

Results are presented from a theoretical investigation of the dispersion properties of a relativistic plasma in which an electromagnetic wave propagates along an external magnetic field. The dielectric tensor in integral form is simplified by separating its imaginary and real parts. A dispersion relation for an electromagnetic wave is obtained that makes it possible to analyze the dispersion and collisionless damping of electromagnetic perturbations over a broad parameter range for both nonrelativistic and ultrarelativistic plasmas.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

Science.gov (United States)

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

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

General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation

Energy Technology Data Exchange (ETDEWEB)

H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)

2007-05-15

An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.

General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation

International Nuclear Information System (INIS)

H, Jorge A Rueda; Nunez, L A

2007-01-01

An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure

General relativistic Boltzmann equation, II: Manifestly covariant treatment

NARCIS (Netherlands)

Debbasch, F.; van Leeuwen, W.A.

2009-01-01

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics

International Nuclear Information System (INIS)

Le Bourdiec, S.

2007-03-01

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

The cosmic-ray shock structure problem for relativistic shocks

Science.gov (United States)

Webb, G. M.

1985-01-01

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Relativistic three-particle dynamical equations: II. Application to the trinucleon system

International Nuclear Information System (INIS)

Adhikari, S.K.; Tomio, L.

1993-11-01

The contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy is calculated employing five sets tri nucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (author)

Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

Energy Technology Data Exchange (ETDEWEB)

Suparmi, A., E-mail: suparmiuns@gmail.com; Cari, C., E-mail: suparmiuns@gmail.com [Physics Department, Post Graduate Study, Sebelas Maret University (Indonesia); Angraini, L. M. [Physics Department, Mataram University (Indonesia)

2014-09-30

The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

Three-dimensional formulation of the relativistic two-body problem in terms of rapidities

International Nuclear Information System (INIS)

Amirkhanov, I.V.; Grusha, G.V.; Mir-Kasimov, R.M.

1976-01-01

The scheme, based on the three-dimensional relativistic equation of the quasi-potential type is developed. As a basic variable rapidity, canonically conjugated to the relativistic relative distance is adopted. The free Green function has a simple pole in the complex rapidity plane, ensuring the fulfillment of the elastic unitarity for real potentials. In the local potential case the corresponding partial wave equation in configurational r-representation is a differential second-order equation. The problem of boundary conditions, which is a non-trivial one in the relativistic r-space, is studied. The exact solutions of the equation in simple cases have been found

Relativistic actions for bound-states and applications in the meson spectroscopy; Acoes relativisticas para estados ligados e aplicacoes na espectroscopia de mesons

Energy Technology Data Exchange (ETDEWEB)

Silva Carvalho, Hendly da

1991-08-01

We study relativistic equations for bound states of two-body systems using Dirac`s constraint formalism and supersymmetry. The two-body system can be of spinless particles, one of them spinning and the other one spinless, or both of them spinning. The interaction is described by scalar, timelike four-vector and spacelike four-vector potentials under Lorentz transformations. As an application we use the relativistic wave equation for two scalar particles and calculate the mass spectra of the mesons treating them as spinless quark-antiquark bound states. The interaction potential in this case is a convenient adaptation of the potential employed in non-relativistic calculations. Finally, we compare our results with more recent experimental data and with theoretical results obtained with the same potential used by us but with a non-relativistic wave equation. We also compare our results with results obtained with the relativistic wave equation but with a different interaction potential. (author). 38 refs, 9 figs, 8 tabs.

Wave Equation Inversion of Skeletonized SurfaceWaves

KAUST Repository

Zhang, Zhendong

2015-08-19

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.

Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

International Nuclear Information System (INIS)

Sharp, W.M.; Yu, S.S.; Lee, E.P.

1987-01-01

A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

Relativistic theory of vector mesons in laser fields

Energy Technology Data Exchange (ETDEWEB)

Becker, W; Mitter, H [Tuebingen Univ. (F.R. Germany). Inst. fuer Theoretische Physik

1975-01-01

The relativistic wave equation for a particle with spin 1 and an anomalous magnetic moment ..mu.. in an external wave field is reduced to a set of coupled ordinary differential equations for three amplitudes, which multiply the exponential known from the spin 0 case. These amplitudes are constant for ..mu..=1 (and not ..mu..=0). Exact solutions are given for a linear polarized laser wave of finite pulse shape and for an infinitely extended plane wave with circular polarization. In contrast to the situation in a constant magnetic field there are no internal inconsistencies.

Proton relativistic model

International Nuclear Information System (INIS)

Araujo, Wilson Roberto Barbosa de

1995-01-01

In this dissertation, we present a model for the nucleon, which is composed by three relativistic quarks interacting through a contract force. The nucleon wave-function was obtained from the Faddeev equation in the null-plane. The covariance of the model under kinematical null-plane boots is discussed. The electric proton form-factor, calculated from the Faddeev wave-function, was in agreement with the data for low-momentum transfers and described qualitatively the asymptotic region for momentum transfers around 2 GeV. (author)

The Dirac equation and its solutions

CERN Document Server

Bagrov, Vladislav G

2014-01-01

Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

The Dirac equation and its solutions

International Nuclear Information System (INIS)

Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk

2013-01-01

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Studies on the propagation of relativistic plasma waves in high density plasmas produced by hypersonic ionizing shock waves

International Nuclear Information System (INIS)

Williams, R.L.; Johnson, J.A. III

1993-01-01

The feasibility of using an ionizing shock wave to produce high density plasmas suitable for the propagation large amplitude relativistic plasma waves is being investigated. A 20 kv arc driven shock tube of coaxial geometry produces a hypersonic shock wave (10 p > 10 17 cm -3 ). The shock can be made to reflect off the end of the tube, collide with its wake, and thus increase the plasma density further. After reflecting, the plasma is at rest. The shock speed is measured using piezoelectric pressure probes and the ion density is measured using laser induced fluorescence (LIF) techniques on argon 488.0 nm and 422.8 nm lines. The future plans are to excite large amplitude relativistic plasma waves in this plasma by either injecting a short pulse laser (Laser Wake Field Scheme), two beating lasers (Plasma Beat Wave Scheme), or a short bunch of relativistic electrons (Plasma Wake Field Scheme). Results of recent computational and theoretical studies, as well as initial experimental measurements on the plasma using LIF, are reported. Implications for the application of high density plasmas produced in this way to such novel schemes as the plasma wave accelerator, photon accelerator, plasma wave undulator, and also plasma lens, are discussed. The effect of plasma turbulence is also discussed

Relativistic phenomenological equations and transformation laws of relative coefficients

Directory of Open Access Journals (Sweden)

Patrizia Rogolino

2017-06-01

Full Text Available The aim of this paper is to derive the phenomenological equations in the context of special relativistic non-equilibrium thermodynamics with internal variables. In particular, after introducing some results developed in our previous paper, by means of classical non-equilibrium thermodynamic procedure and under suitable assumptions on the entropy density production, the phenomenological equations and transformation laws of phenomenological coefficients are derived. Finally, some symmetries of aforementioned coefficients are obtained.

The investigation of relativistic microscopic optical potential based on RBBG equation

International Nuclear Information System (INIS)

Chen Baoqiu; Ma Zhongyu

1992-01-01

The relativistic microscopic optical potential is derived from the RBBG equation. The nucleon complex effective mass is determined phenomenologically by a fit to 200 MeV proton-nucleus scattering data. Then the relativistic microscopic optical potentials of proton scattered from different targets: 16 O, 40 Ca, 90 Zr and 208 Pb in the energies range from 160 to 800 MeV have been got. The relativistic microscopic optical potentials have been used to study proton- 40 Ca scattering at 200 MeV. Theoretical predictions for cross section and spin observables are compared with experimental data and phenomenological Dirac optical potential

Relativistic magnetohydrodynamics

Energy Technology Data Exchange (ETDEWEB)

Hernandez, Juan; Kovtun, Pavel [Department of Physics and Astronomy, University of Victoria,Victoria, BC, V8P 5C2 (Canada)

2017-05-02

We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the “conventional” magnetohydrodynamics (formulated using Maxwell’s equations in matter) to those in the “dual” version of magnetohydrodynamics (formulated using the conserved magnetic flux).

Waves and discontinuities in relativistic and anisotropic magnetohydrodynamics

International Nuclear Information System (INIS)

Cissoko, Mahdy

1975-01-01

This work is devoted to the relativistic study of a non-dissipative anisotropic fluid diagram of infinite conductivity. Such a fluid diagram is constructed in part one. Starting from a macroscopic viewpoint a hydrothermodynamic study of the fluid diagram considered is carried out and the fundamental differential system of anisotropic magnetohydrodynamics is deduced. Part two concerns the study of characteristic varieties and propagation of waves for a polytropic anisotropic fluid diagram. Three types of characteristic varieties are revealed: entropy waves (or material waves), magnetosonic waves and Alfven waves. The propagation rates of Alfven and magnetosonic waves are situated with respect to each other. The study of wave cones showed up on the one hand certain special features of wave propagation in anisotropic magnetohydrodynamics and on the other hand the hyperbolic nature of differential operators associated with the various waves [fr

Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation

Directory of Open Access Journals (Sweden)

A. A. Deriglazov

2011-01-01

Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.

General relativistic continuum mechanics and the post-Newtonian equations of motion

International Nuclear Information System (INIS)

Morrill, T.H.

1991-01-01

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

The Dirac equation and its solutions

Energy Technology Data Exchange (ETDEWEB)

Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics

2013-07-01

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

A relativistic solitary wave in electron positron plasma

International Nuclear Information System (INIS)

Berezhiani, V.I.; Skarka, V.; Mahajan, S.

1993-09-01

The relativistic solitary wave propagation is studied in cold electron-positron plasma embedded in an external arbitrary strong magnetic field. The exact, analytical soliton-like solution corresponding to a localized, purely electromagnetic pulse with arbitrary big amplitude is found. (author). 7 refs, 1 fig

Planar and nonplanar ion acoustic shock waves in relativistic degenerate astrophysical electron-positron-ion plasmas

Energy Technology Data Exchange (ETDEWEB)

Ata-ur-Rahman,; Qamar, A. [Institute of Physics and Electronics, University of Peshawar, Peshawar 25000 (Pakistan); National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan)

2013-04-15

We have studied the propagation of ion acoustic shock waves involving planar and non-planar geometries in an unmagnetized plasma, whose constituents are non-degenerate ultra-cold ions, relativistically degenerate electrons, and positrons. By using the reductive perturbation technique, Korteweg-deVries Burger and modified Korteweg-deVries Burger equations are derived. It is shown that only compressive shock waves can propagate in such a plasma system. The effects of geometry, the ion kinematic viscosity, and the positron concentration are examined on the ion acoustic shock potential and electric field profiles. It is found that the properties of ion acoustic shock waves in a non-planar geometry significantly differ from those in planar geometry. The present study has relevance to the dense plasmas, produced in laboratory (e.g., super-intense laser-dense matter experiments) and in dense astrophysical objects.

Approximative analytic study of fermions in magnetar's crust; ultra-relativistic plane waves, Heun and Mathieu solutions and beyond

Science.gov (United States)

Dariescu, Marina-Aura; Dariescu, Ciprian

2012-10-01

Working with a magnetic field periodic along Oz and decaying in time, we deal with the Dirac-type equation characterizing the fermions evolving in magnetar's crust. For ultra-relativistic particles, one can employ the perturbative approach, to compute the conserved current density components. If the magnetic field is frozen and the magnetar is treated as a stationary object, the fermion's wave function is expressed in terms of the Heun's Confluent functions. Finally, we are extending some previous investigations on the linearly independent fermionic modes solutions to the Mathieu's equation and we discuss the energy spectrum and the Mathieu Characteristic Exponent.

Nonlinear dynamics in the relativistic field equation

International Nuclear Information System (INIS)

Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An

2007-01-01

We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory

Plasma waves in hot relativistic beam-plasma systems: Pt. 1

International Nuclear Information System (INIS)

Magneville, A.

1990-01-01

Dispersion relations of plasma waves in a beam-plasma system are computed in the general case where the plasma and beam temperatures, and the velocity of the beam, may be relativistic. The two asymptotic temperature cases, and different contributions of plasma or beam particles to wave dispersion are considered. (author)

Relativistic Bosons in Time-Harmonic Electric Fields

Science.gov (United States)

Buhucianu, Ovidiu; Dariescu, Marina-Aura; Dariescu, Ciprian

2012-02-01

In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample's plane. The Klein-Gordon equation describing the relativistic bosons leads to a Mathieu's type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing

2016-09-06

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

International Nuclear Information System (INIS)

Malenfant, J.

1988-01-01

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

Two-body Dirac equation and its wave function at the origin

International Nuclear Information System (INIS)

Ito, Hitoshi

1998-01-01

We propose a relativistic bound state equation for the Dirac particles interacting through an Abelian gauge field. It reduces to the (one body) Dirac equation in the infinite limit of one of the masses and is invariant under the PCT transformation. This invariance is a consequence of a modification of the Stueckelberg-Feynman boundary condition for propagation of the negative-energy two-body states, by which the some effect of the crossed diagram is taken in the lowest ladder equation. We can correct back the modification in perturbative calculations of the weak-coupling theory by adding a counter correction term in the interaction kernel. The equation can be used for the phenomenology of the heavy flavored mesons. We get good behavior of the wave function at the origin (WFO), with which the annihilation amplitude of the pseudoscalar meson becomes finite. Some comments are mentioned for the application in the heavy quark effective theory. The talk was based on a preprint

Shock waves in relativistic nuclear matter, I

International Nuclear Information System (INIS)

Gleeson, A.M.; Raha, S.

1979-02-01

The relativistic Rankine-Hugoniot relations are developed for a 3-dimensional plane shock and a 3-dimensional oblique shock. Using these discontinuity relations together with various equations of state for nuclear matter, the temperatures and the compressibilities attainable by shock compression for a wide range of laboratory kinetic energy of the projectile are calculated. 12 references

Electromagnetic surface waves at the interface of a relativistic electron beam with vacuum

International Nuclear Information System (INIS)

Shoucri, M.M.; Gagne, R.R.J.

1977-01-01

The dispersion relation for electromagnetic surface waves propagating at the interface between a relativistic electron beam and vacuum is derived. The excitation of surface modes in a plasma at rest by a relativistic electron beam is discussed

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

Energy Technology Data Exchange (ETDEWEB)

Le Bourdiec, S

2007-03-15

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

Electromagnetic solitons in degenerate relativistic electron–positron plasma

International Nuclear Information System (INIS)

Berezhiani, V I; Shatashvili, N L; Tsintsadze, N L

2015-01-01

The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron–positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For a circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown. (invited comment)

A relativistic extended Fermi-Thomas-like equation for a self-gravitating system of fermions

International Nuclear Information System (INIS)

Merloni, A.; Ruffini, R.; Torroni, V.

1998-01-01

The authors extend previous results of a Fermi-Thomas model, describing self-gravitating fermions in their ground state, to a relativistic gravitational theory in Minkowski space. In such a theory the source term of the gravitational potential depends both on the pressure and the density of the fluid. It is shown that, in correspondence of this relativistic treatment, still a Fermi-Thomas-like equation can be derived for the self-gravitating system, though the non-linearities are much more complex. No Fermi-Thomas-like equation can be obtained in the General Relativistic treatment. The canonical results for neutron stars and white dwarfs are recovered and also some erroneous statements in the scientific literature are corrected

Existence condition of the relativistic ion-acoustic soliton in plasma

International Nuclear Information System (INIS)

Chian, A.C.-L.

1981-07-01

Stationary solutions which descrite longitudinal waves in a hot ion-electron plasma, taking in account the relativistic effect of the particle dynamics, are investigated. The solution of the problem can be reduced to two equations related with energy-momentum conservation of the system. Particular attention to the existence condition of the solitary wave solution is given. It is shown that the Langmuir mode (Te=Ti) only admits infinite train-like wave solutions, the existence of solitary-like wave solutions being not possible. On the other hand, in the case of hot electrons and cold ions, an appropriate choice of the boundary conditions produces localized wave solutions, which describe relativistic ion-acoustic solitons. (L.C.) [pt

The birth of wave mechanics (1923-1926)

Science.gov (United States)

Aspect, Alain; Villain, Jacques

2017-11-01

In 1923, in three articles published in the Comptes Rendus of the Académie des Sciences, Louis de Broglie proposed the concept of wave-particle duality. Physicists from many countries seized upon this idea. In particular, Schrödinger developed de Broglie's qualitative idea by writing down the equation that the wave must satisfy in the non-relativistic approximation. A relativistic version of this equation was proposed in 1926 by several scientists, and other ones found a solution to the Schrödinger equation as an expansion in powers of the Planck constant.

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

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

Relativistic electron precipitation in the auroral zone

International Nuclear Information System (INIS)

Simons, D.J.

1975-01-01

The energy spectra and pitch angle distributions of electrons in the energy range 50 keV to 2 MeV have been determined by a solid state electron energy spectrometer during the Relativistic Electron Precipitation (REP) event of 31 May 1972. The experiment was carried aboard a Nike-Cajun sounding rocket as the University of Maryland component of a joint American-Norwegian (NASA-NDRE) ionospheric investigation. The difficulty of determining the expected electron flux prior to the experiment required an instrument with a large dynamic range. The design and theoretical modeling of this instrument is described in great detail. The electron pitch angle distributions are determined from a knowledge of the rocket aspect and the direction in space of the Earth's magnetic field. The electron fluxes during the REP event were highly variable demonstrating correlated energy, flux and pitch angle pulsations with time periods less than one second. Increases in flux were accompanied by marked filling of the loss cone at lower energies (near 50 keV). Drawing upon the quasilinear equations of plasma wave-electron interactions, a theoretical model for the production of relativistic electrons is proposed. A self consistent set of fully relativistic equations for the evolution of the electron distribution function due to the interaction of the electrons with parallel propagating whistler waves is derived in the Appendix. An examination of these equations leads to the conclusion that at comparatively low background electron densities, the anomalous Doppler resonance leads to the acceleration of near relativistic particles. The results of a computer solution of the five coupled integrodifferential quasilinear equations confirms this conclusion

Simulating satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds

OpenAIRE

M. Füllekrug; C. Hanuise; M. Parrot

2010-01-01

Relativistic electron beams above thunderclouds emit 100 kHz radio waves which illuminate the Earth's atmosphere and near-Earth space. This contribution aims to clarify the physical processes which are relevant for the spatial spreading of the radio wave energy below and above the ionosphere and thereby enables simulating satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds. The simulation uses the DEMETER satellite which observes 100 kHz ...

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.

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.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

Science.gov (United States)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Magnetohydrodynamic waves with relativistic electrons and positrons in degenerate spin-1/2 astrophysical plasmas

Science.gov (United States)

Maroof, R.; Ali, S.; Mushtaq, A.; Qamar, A.

2015-11-01

Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.

Magnetohydrodynamic waves with relativistic electrons and positrons in degenerate spin-1/2 astrophysical plasmas

Energy Technology Data Exchange (ETDEWEB)

Maroof, R. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Mushtaq, A. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Qamar, A. [Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan)

2015-11-15

Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.

Wave Equation Inversion of Skeletonized SurfaceWaves

KAUST Repository

Zhang, Zhendong; Liu, Yike; Schuster, Gerard T.

2015-01-01

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve

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.

Chaotic behavior in a relativistic electron beam interacting with a transverse slow electromagnetic wave

International Nuclear Information System (INIS)

Serbeto, A.; Alves, M.V.

1993-01-01

Using a nonlinear set of equations which describes the excitation of a purely transverse slow electromagnetic wave by a relativistic electron beam, it is shown that the system runs from chaotic behavior to a regular stable state due to crisis phenomenon and from stabilized soliton and repeated stabilized explosive solutions to a temporal chaos. These behaviors suggest that the primary mechanism for the saturation of the explosive instability is not only the cubic nonlinear frequency shift as pointed out by many authors until now. The inclusion of the velocity perturbation in the beam charge initial equilibrium state leads the system to these strange behaviors. (author)

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)

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

Relativistic effects in decay of S-wave quarkoniums

International Nuclear Information System (INIS)

Martynenko, A.P.; Saleev, V.A.

1995-01-01

The width of S-wave quarkonium decays η c ,η b → γγ and J/ψ, Y → e + e - are calculated using the quasipotential approach. The nontrivial dependence of decay amplitude on relative quark momentum is considered. It is shown that relativistic corrections reach values of 30-50% in the processes studied

Comparison of two forms of Vlasov-type relativistic kinetic equations in hadrodynamics

International Nuclear Information System (INIS)

Mashnik, S.G.; Maino, G.

1996-01-01

A comparison of two methods in the relativistic kinetic theory of the Fermi systems is carried out assuming, as an example, the simplest σω-version of quantum hadrodynamics with allowance for strong mean meson fields. It is shown that the Vlasov-type relativistic kinetic equation (VRKE) obtained by means of the procedure of squaring at an intermediate step is responsible for unphysical features. A direct method of derivation of kinetic equations is proposed. This method does not contain such drawback and gives rise to VRKE in hydrodynamics of a non-contradictory form in which both spin degrees of freedom and states with positive and negative energies are taken into account. 17 refs

Linear relativistic gyrokinetic equation in general magnetically confined plasmas

International Nuclear Information System (INIS)

Tsai, S.T.; Van Dam, J.W.; Chen, L.

1983-08-01

The gyrokinetic formalism for linear electromagnetic waves of arbitrary frequency in general magnetic-field configurations is extended to include full relativistic effects. The derivation employs the small adiabaticity parameter rho/L 0 where rho is the Larmor radius and L 0 the equilibrium scale length. The effects of the plasma and magnetic field inhomogeneities and finite Larmor-radii effects are also contained

Wave-equation Qs Inversion of Skeletonized Surface Waves

KAUST Repository

Li, Jing

2017-02-08

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

Skeletonized wave-equation Qs tomography using surface waves

KAUST Repository

Li, Jing

2017-08-17

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.

Wave-equation Qs Inversion of Skeletonized Surface Waves

KAUST Repository

Li, Jing; Dutta, Gaurav; Schuster, Gerard T.

2017-01-01

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

How well can gravitational wave observations of coalescing binaries involving neutron stars constrain the neutron star equation of state?

International Nuclear Information System (INIS)

Bose, Sukanta

2015-01-01

The Advanced LIGO detectors began observation runs a few weeks ago. This has afforded relativists and astronomers the opportunity to use gravitational waves to improve our understanding of a variety of astronomical objects and phenomena. In this talk I will examine how well gravitational wave observations of coalescing binaries involving neutron stars might constrain the neutron star (NS) equation of state. These astrophysical constraints can improve our understanding of nuclear interactions in ways that complement the knowledge acquired from terrestrial labs. I will study the effects of different NS equations of states in both NS-NS and NS-Black Hole systems, with and without spin, on these constraint. (author)

Precursor Wave Emission Enhanced by Weibel Instability in Relativistic Shocks

Science.gov (United States)

Iwamoto, Masanori; Amano, Takanobu; Hoshino, Masahiro; Matsumoto, Yosuke

2018-05-01

We investigated the precursor wave emission efficiency in magnetized purely perpendicular relativistic shocks in pair plasmas. We extended our previous study to include the dependence of upstream magnetic field orientations. We performed two-dimensional particle-in-cell simulations and focused on two magnetic field orientations: the magnetic field in the simulation plane (i.e., in-plane configuration) and that perpendicular to the simulation plane (i.e., out-of-plane configuration). Our simulations in the in-plane configuration demonstrated that not only extraordinary but also ordinary mode waves are excited. We quantified the emission efficiency as a function of the magnetization parameter σ e and found that the large-amplitude precursor waves are emitted for a wide range of σ e . We found that especially at low σ e , the magnetic field generated by Weibel instability amplifies the ordinary mode wave power. The amplitude is large enough to perturb the upstream plasma, and transverse density filaments are generated as in the case of the out-of-plane configuration investigated in the previous study. We confirmed that our previous conclusion holds regardless of upstream magnetic field orientations with respect to the two-dimensional simulation plane. We discuss the precursor wave emission in three dimensions and the feasibility of wakefield acceleration in relativistic shocks based on our results.

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing; Schuster, Gerard T.

2016-01-01

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

Equation with the many fathers

DEFF Research Database (Denmark)

Kragh, Helge

1984-01-01

In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...

Nonlinear Korteweg-de Vries-Burger equation for ion-acoustic shock waves in the presence of kappa distributed electrons and positrons

International Nuclear Information System (INIS)

Shah, Asif; Saeed, R

2011-01-01

The ion-acoustic shock waves are studied in electron-positron-ion plasma. The plasma system is composed of three components, specifically relativistic adiabatic ions, kappa distributed electrons and positrons. The Korteweg-de Vries-Burger equation is derived, solved analytically. The effects of plasma parameters on the shock strength and steepness are investigated. The numerical results are presented graphically for illustration. The results may have importance in non-thermal and relativistic plasmas of pulsar magnetosphere (Arons 2009 Astrophys. Space Sci. Library 357 373; Blasi and Amato arXiv:1007.4745V1 [astro-Ph.HE]).

Relativistic Photoionization Computations with the Time Dependent Dirac Equation

Science.gov (United States)

2016-10-12

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser

Covariant two-particle wave functions for model quasipotential allowing exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1982-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Relativistic plasma dispersion functions

International Nuclear Information System (INIS)

Robinson, P.A.

1986-01-01

The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived

Covariant two-particle wave functions for model quasipotentials admitting exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1983-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Two-spinor description of massive particles and relativistic spin projection operators

Science.gov (United States)

Isaev, A. P.; Podoinitsyn, M. A.

2018-04-01

On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.

Relativistic Energy Analysis of Five-Dimensional q-Deformed Radial Rosen-Morse Potential Combined with q-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

International Nuclear Information System (INIS)

Pramono, Subur; Suparmi, A.; Cari, Cari

2016-01-01

We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separable q-deformed quantum potentials. The q-deformed hyperbolic Rosen-Morse potential is perturbed by q-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equation l_D_-_1 have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum number n causes the increase of bound state relativistic energy level in both dimensions D=5 and D=3. The bound state relativistic energy level decreases with increasing of both deformation parameter q and orbital quantum number n_l.

Three-parameter relativistic dynamics. 1. Equation of motion, energy conservation

International Nuclear Information System (INIS)

Rogachevskii, A.G.

1995-01-01

A formally geometric analog of the relativistic dynamics of a point charged particle is constructed. Time as a function of the spatial coordinates is taken as the trajectory equation, i.e., the trajectory is a hypersurface in Minkowski space. The dynamics is presented. The law of open-quotes energyclose quotes conservation is examined

Nonlinear wave equation with intrinsic wave particle dualism

International Nuclear Information System (INIS)

Klein, J.J.

1976-01-01

A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

Science.gov (United States)

Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.

2018-03-01

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

Relativistic reversal of the ponderomotive force in a standing laser wave

International Nuclear Information System (INIS)

Pokrovsky, A.L.; Kaplan, A.E.

2005-01-01

Effect of relativistic reversal of the ponderomotive force (PF), reported earlier for a collinear configuration of electron and laser standing wave [A. E. Kaplan and A. L. Pokrovsky, Phys. Rev. Lett., 95, 053601 (2005)], is studied here theoretically for various types of polarizations of the laser beam. We demonstrated that the collinear configuration, in which the laser wave is linearly polarized with electric field E-vector parallel to the initial electron momentum p-vector 0 , is the optimal configuration for the relativistic reversal. In that case, the transverse PF reverses its direction when the incident momentum is p 0 =mc. The reversal effect vanishes in the cases of circular and linear with E-vector perpendicular p-vector 0 polarizations. We have discovered, however, that the counter-rotating circularly polarized standing waves develop attraction and repulsion areas along the axis of laser, in the laser field whose intensity is homogeneous in that axis, i.e., has no field gradient

Fundamental problem in the relativistic approach to atomic structure theory

International Nuclear Information System (INIS)

Kagawa, Takashi

1987-01-01

It is known that the relativistic atomic structure theory contains a serious fundamental problem, so-called the Brown-Ravenhall (BR) problem or variational collapse. This problem arises from the fact that the energy spectrum of the relativistic Hamiltonian for many-electron systems is not bounded from below because the negative-energy solutions as well as the positive-energy ones are obtained from the relativistic equation. This report outlines two methods to avoid the BR problem in the relativistic calculation, that is, the projection operator method and the general variation method. The former method is described first. The use of a modified Hamiltonian containing a projection operator which projects the positive-energy solutions in the relativistic wave equation has been proposed to remove the BR difficulty. The problem in the use of the projection operator method is that the projection operator for the system cannot be determined uniquely. The final part of this report outlines the general variation method. This method can be applied to any system, such as relativistic ones whose Hamiltonian is not bounded from below. (Nogami, K.)

Parsimonious wave-equation travel-time inversion for refraction waves

KAUST Repository

Fu, Lei

2017-02-14

We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

Relativistic jet with shock waves like model of superluminal radio source. Jet relativista con ondas de choque como modelo de radio fuentes superluminales

Energy Technology Data Exchange (ETDEWEB)

Alberdi, A.; Gomez, J.L.; Marcaide, J.M.

1993-01-01

The structure of the compact radio sources at milliarcsecond angular resolution can be explained in terms of shock waves propagating along bent jets. These jets consist of narrow-angle cones of plasma flowing at bulk relativistic velocities, within tangled magnetic fields, emitting synchrotron radiation. We have developed a numerical code which solves the synchrotron radiation transfer equations to compute the total and polarized emission of bent shocked relativistic jets, and we have applied it to reproduce the compact structure, kenimatic evolution and time flux density evolution of the superluminal radio source 4C 39.25 and to obtain its jet physical parameters. (Author) 23 ref.

Auroral kilometric radiation - An example of relativistic wave-particle interaction in geoplasma

International Nuclear Information System (INIS)

Pritchett, P.L.

1990-01-01

The earth's auroral kilometric radiation (AKR) is believed to be produced by the electron-cyclotron maser instability. This instability is the result of a wave-particle interaction in which relativistic effects are crucial. An explanation is given as to how these relativistic effects alter the shape of the resonance curve in velocity space and modify the R - X mode wave dispersion near the electron cyclotron frequency compared to the results obtained in the nonrelativistic limit and from cold-plasma theory. The properties of the cyclotron maser instability in a driven system are illustrated using two-dimensional electromagnetic particle simulations which incorporate a continual flow of primary energetic electrons along the magnetic field. 31 refs

Solving the relativistic inverse stellar problem through gravitational waves observation of binary neutron stars

Science.gov (United States)

Abdelsalhin, Tiziano; Maselli, Andrea; Ferrari, Valeria

2018-04-01

The LIGO/Virgo Collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e., to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.

Two-spinor description of massive particles and relativistic spin projection operators

Directory of Open Access Journals (Sweden)

A.P. Isaev

2018-04-01

Full Text Available On the basis of the Wigner unitary representations of the covering group ISL(2,C of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac–Pauli–Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends–Fronsdal projection operators. With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends–Fronsdal projection operators and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends–Fronsdal projection operators for arbitrary space–time dimensions D>2.

Scalar potentials and the Dirac equation

International Nuclear Information System (INIS)

Bergerhoff, B.; Soff, G.

1994-01-01

The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1/r-potential as well as for a mixed scalar and Coulomb 1/r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement. (orig.)

An integral transform of the Salpeter equation

International Nuclear Information System (INIS)

Krolikowski, W.

1980-03-01

We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)

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.

Experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds

OpenAIRE

Fullekrug, Martin; Hanuise, C; Parrot, M

2011-01-01

Relativistic electron beams above thunderclouds emit 100 kHz radio waves which illuminate the Earth's atmosphere and near-Earth space. This contribution aims to clarify the physical processes which are relevant for the spatial spreading of the radio wave energy below and above the ionosphere and thereby enables an experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds. The simulation uses the DEMETER satellite which...

Truncated Painleve expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

International Nuclear Information System (INIS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-01-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painleve expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model

Semi-analytical wave functions in relativistic average atom model for high-temperature plasmas

International Nuclear Information System (INIS)

Guo Yonghui; Duan Yaoyong; Kuai Bin

2007-01-01

The semi-analytical method is utilized for solving a relativistic average atom model for high-temperature plasmas. Semi-analytical wave function and the corresponding energy eigenvalue, containing only a numerical factor, are obtained by fitting the potential function in the average atom into hydrogen-like one. The full equations for the model are enumerated, and more attentions are paid upon the detailed procedures including the numerical techniques and computer code design. When the temperature of plasmas is comparatively high, the semi-analytical results agree quite well with those obtained by using a full numerical method for the same model and with those calculated by just a little different physical models, and the result's accuracy and computation efficiency are worthy of note. The drawbacks for this model are also analyzed. (authors)

Nonlinear wave equations

CERN Document Server

Li, Tatsien

2017-01-01

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

Plasma simulation by macroscale, electromagnetic particle code and its application to current-drive by relativistic electron beam injection

International Nuclear Information System (INIS)

Tanaka, M.; Sato, T.

1985-01-01

A new implicit macroscale electromagnetic particle simulation code (MARC) which allows a large scale length and a time step in multi-dimensions is described. Finite mass electrons and ions are used with relativistic version of the equation of motion. The electromagnetic fields are solved by using a complete set of Maxwell equations. For time integration of the field equations, a decentered (backward) finite differencing scheme is employed with the predictor - corrector method for small noise and super-stability. It is shown both in analytical and numerical ways that the present scheme efficiently suppresses high frequency electrostatic and electromagnetic waves in a plasma, and that it accurately reproduces low frequency waves such as ion acoustic waves, Alfven waves and fast magnetosonic waves. The present numerical scheme has currently been coded in three dimensions for application to a new tokamak current-drive method by means of relativistic electron beam injection. Some remarks of the proper macroscale code application is presented in this paper

Linear waves in two-fluid relativistic gasdynamics

International Nuclear Information System (INIS)

Gavrikov, M.B.; Solov'ev, L.S.

1988-01-01

This paper is devoted to the development of a theory of waves propagating in a two-component gaseous medium. In all cases considered the authors use only the method of two-fluid relativistic electromagnetic gasdynamics in the framework of the special relativity theory. They pay special attention to the problem of the interaction in a mixture of both neutral and charged gases when they move relative to one another. This interaction is for charged gases responsible for the appearance of ohmic resistance to an electrical current

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

Maxwell's equations, quantum physics and the quantum graviton

International Nuclear Information System (INIS)

Gersten, Alexander; Moalem, Amnon

2011-01-01

Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of 'relativistic quaternions'. Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

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

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Causal electromagnetic interaction equations

International Nuclear Information System (INIS)

Zinoviev, Yury M.

2011-01-01

For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.

On plane-wave relativistic electrodynamics in plasmas and in vacuum

International Nuclear Information System (INIS)

Fiore, Gaetano

2014-01-01

We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. In response to this penetration, the electrons are pulled back by the electric force exerted by the ions and the other displaced electrons and may leave the plasma with high energy in the direction opposite to that of propagation of the pulse ‘slingshot effect’ (Fiore G et al 2013 arXiv:1309.1400). (paper)

Benney's long wave equations

International Nuclear Information System (INIS)

Lebedev, D.R.

1979-01-01

Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

Longitudinal waves and a beam instability in a relativistic anisotropic plasma

International Nuclear Information System (INIS)

Onishchenko, O.G.

1981-01-01

Dispersion relations are derived for longitudinal waves in a relativistic plasma with an arbitrary anisotropic particle distribution function. Longitudinal waves with phase velocity lower than the speed of light are shown to exist in such a plasma. The damping rate of longitudinal waves due to the Cerenkov interaction with plasma particles is derived for such a plasma. The instability of a beam of high-energy particles in such a plasma is studied. As the anisotropy of an ultrarelativistic plasma becomes less pronounced, the maximum hydrodynamic growth rate decreases

Meson spectra from two-body dirac equations with minimal interactions

International Nuclear Information System (INIS)

Crater, H.W.; Becker, R.L.; Wong, C.Y.

1991-01-01

Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?

International Nuclear Information System (INIS)

Dvoeglazov, V. V.

2009-01-01

We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can give the introduction of non-commutativity. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.

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.)

Relativistic hydrodynamic theory of heavy-ion collisions

International Nuclear Information System (INIS)

Amsden, A.A.; Bertsch, G.F.; Harlow, F.H.; Nix, J.R.

1975-01-01

By use of finite-difference methods the classical relativistic equations of motion for the head-on collision of two heavy nuclei are solved. For 16 O projectiles incident onto various targets at laboratory bombarding energies per nucleon less than or equal to2.1 GeV, curved shock waves develop. The target and projectile are deformed and compressed into crescents of revolution. This is followed by rarefaction waves and an overall expansion of the matter into a moderately wide distribution of angles

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Relativistic shock waves and the excitation of plerions

Energy Technology Data Exchange (ETDEWEB)

Arons, J. (California Univ., Berkeley, CA (USA)); Gallant, Y.A. (California Univ., Berkeley, CA (USA). Dept. of Physics); Hoshino, Masahiro; Max, C.E. (California Univ., Livermore, CA (USA). Inst. of Geophysics and Planetary Physics); Langdon, A.B. (Lawrence Livermore National Lab., CA (USA))

1991-01-07

The shock termination of a relativistic magnetohydrodynamic wind from a pulsar is the most interesting and viable model for the excitation of the synchrotron sources observed in plerionic supernova remnants. We have studied the structure of relativistic magnetosonic shock waves in plasmas composed purely of electrons and positrons, as well as those whose composition includes heavy ions as a minority constituent by number. We find that relativistic shocks in symmetric pair plasmas create fully thermalized distributions of particles and fields downstream. Therefore, such shocks are not good candidates for the mechanism which converts rotational energy lost from a pulsar into the nonthermal synchrotron emission observed in plerions. However, when the upstream wind contains heavy ions which are minority constituent by number density, but carry the bulk of the energy density, much of the energy of the shock goes into a downstream, nonthermal power law distribution of positrons with energy distribution N(E)dE {proportional to}E{sup {minus}s}. In a specific model presented in some detail, s = 3. These characteristics are close to those assumed for the pairs in macroscopic MHD wind models of plerion excitation. The essential mechanism is collective synchrotron emission of left-handed extraordinary modes by the ions in the shock front at high harmonics of the ion cyclotron frequency, with the downstream positrons preferentially absorbing almost all of this radiation, mostly at their fundamental (relativistic) cyclotron frequencies. Possible applications to models of plerions and to constraints on theories of energy loss from pulsars are briefly outlines. 27 refs., 5 figs.

Relativistic transport equation for a multiple discontinuity wave

Energy Technology Data Exchange (ETDEWEB)

Giambo, S [Istituto di Matematica, Universita degli Studi, Messina (Italy)

1980-09-29

The theory of singular hypersurfaces is combined with the ray theory to study propagation of weak discontinuities of solutions of a quasi-linear hyperbolic system in the context of special relativity. The case of a multiple wave is considered.

Relativistic dissipative hydrodynamics and the nuclear equation of state

International Nuclear Information System (INIS)

Olson, T.S.; Hiscock, W.A.

1989-01-01

The theory of dissipative, relativistic fluids due to Israel and Stewart is used to constrain the form of the nuclear equation of state. In the Israel-Stewart theory, there are conditions on the equation of state and other thermodynamic properties (the ''second-order'' coefficients) of a fluid which, if satisfied, guarantee that equilibria are stable and that fluid perturbations propagate causally and obey hyperbolic equations. The second-order coefficients in the Israel-Stewart theory, which are relaxation times for the dissipative degrees of freedom and coupling constants between different forms of dissipation, are derived for a free, degenerate Fermi gas. It is shown rigorously that the free, degenerate Fermi gas is stable (and hence causal) at all temperatures in this theory. These values for the second-order coefficients are then used in the stability conditions to constrain various proposed expressions for the nuclear ground-state energy. The stability conditions are found to provide significantly more stringent constraints on the proposed equations of state than the usual simple restriction that the adiabatic sound speed be less than the speed of light

Spatial evolution equation of wind wave growth

Institute of Scientific and Technical Information of China (English)

WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)

2003-01-01

Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.

Second harmonic generation by a relativistic annular electron beam propagating through a cylindrical waveguide

International Nuclear Information System (INIS)

Yasumoto, Kiyotoshi; Abe, Hiroshi

1983-01-01

The second harmonic generated by a relativistic annular electron beam propagating through a cylindrical waveguide immersed in a strong axial magnetic field is investigated on the basis of the relativistic hydrodynamic equations for cold electrons. The efficiency of second harmonic generation is calculated separately for the pump by the TM electromagnetic wave and for the pump by the slow space-charge wave, by assuming that the electron beam is thin and of low density and the pump wave is azimuthally symmetric. It is shown that, in the case of slow space-charge wave pump, an appreciably large efficiency of second harmonic generation is achieved in the high frequency region, whereas the efficiency by the TM electromagnetic wave pump is relatively small over the whole frequency range.(author)

Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions

International Nuclear Information System (INIS)

Ishikawa, Y.; Quiney, H.M.

1993-01-01

A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence

Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

International Nuclear Information System (INIS)

Randrüüt, Merle; Braun, Manfred

2013-01-01

The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech 2 type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

Energy Technology Data Exchange (ETDEWEB)

Randrüüt, Merle, E-mail: merler@cens.ioc.ee [Tallinn University of Technology, Faculty of Mechanical Engineering, Department of Mechatronics, Ehitajate tee 5, 19086 Tallinn (Estonia); Braun, Manfred [University of Duisburg–Essen, Chair of Mechanics and Robotics, Lotharstraße 1, 47057 Duisburg (Germany)

2013-10-30

The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech{sup 2} type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

Probabilistic solutions of generalized birth and death equations and application to non-relativistic electrodynamics

International Nuclear Information System (INIS)

Serva, M.

1986-01-01

In this paper we give probabilistic solutions to the equations describing non-relativistic quantum electrodynamical systems. These solutions involve, besides the usual diffusion processes, also birth and death processes corresponding to the 'photons number' variables. We state some inequalities and in particular we establish bounds to the ground state energy of systems composed by a non relativistic particle interacting with a field. The result is general and it is applied as an example to the polaron problem. (orig.)

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions

Energy Technology Data Exchange (ETDEWEB)

Kalita, B. C., E-mail: bckalita123@gmail.com [Gauhati University, Department of Mathematics (India); Choudhury, M., E-mail: choudhurymamani@gmail.com [Handique Girls’ College, Department of Mathematics (India)

2016-10-15

Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z{sub d} and ion-to-dust mass ratio Q’ = m{sub i}/m{sub d} are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N{sub d} to yield rarefactive relativistic solitons of maximum amplitude.

Separate P‐ and SV‐wave equations for VTI media

KAUST Repository

Pestana, Reynam C.; Ursin, Bjø rn; Stoffa, Paul L.

2011-01-01

In isotropic media we use the scalar acoustic wave equation to perform reverse time migration RTM of the recorded pressure wavefleld data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic VTI media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where ε - δ is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method REM to propagate the waveflelds in time. © 2011 Society of Exploration Geophysicists.

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

Relativistic wave equations for particles in electromagnetic fields

International Nuclear Information System (INIS)

Good, R.H. Jr.

1989-01-01

A new type of generalization of the Dirac equation of higher spin particles and antiparticles is given, in case only the terms proportional to the external fields need to be retained. copyright 1989 Academic Press, Inc

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)

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

Stimulated scattering of space-charge waves in a relativistic electron beam by the ion acoustic wave of a plasma waveguide

International Nuclear Information System (INIS)

Balakirev, V.A.; Buts, V.A.

1982-01-01

The interaction of a relativistic electron beam with a plasma waveguide whose density is modulated by an ion acoustic wave leads to the emission of electromagnetic radiation. The wavelength of the radiation is 2#betta# 2 times shorter than the ion acoustic wavelength. The emission is accompanied by the amplification of the ion acoustic wave. The maximum amplitudes of the excited waves are found

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

Institute of Scientific and Technical Information of China (English)

孙国华; 董世海

2012-01-01

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.

Analytic properties of the relativistic Thomas-Fermi equation and the total energy of atomic ions

International Nuclear Information System (INIS)

March, N.H.; Senatore, G.

1985-06-01

The analytic properties of solutions of the relativistic Thomas-Fermi equation which tend to zero at infinity are first examined, the neutral atom solution being a member of this class. A new length is shown to enter the theory, proportional to the square root of the fine structure constant. This information is used to develop a perturbation expansion around the neutral atom solution, corresponding to positive atomic ions with finite but large radii. The limiting law relating ionic radius to the degree of ionization is thereby displayed in functional form, and solved explicitly to lowest order in the fine structure constant. To embrace this knowledge of heavy positive ions, as well as results from the one-electron Dirac equation, a proposal is then advanced as to the analytic form of the relativistic total energy E(Z,N) of an atomic ion with nuclear charge Ze and total number of electrons N. The fact that, for N>1, the nucleus is known only to bind Z+n electrons, where n is 1 or 2, indicates non-analyticity in the complex Z plane, represented by a circle of radius Z approx.= N. Such non-analyticity is also a property of the non-relativistic energy derived from the many-electron Schroedinger equation. The relativistic theory, however, must also embody a second type of non-analyticity associated with the known property for N=1 that the Dirac equation predicts electron-positron pair production when the electronic binding energy becomes equal to twice the electron rest mass energy. This corresponds to a second circle of non-analyticity in E(Z,N), and hence to a Taylor-Laurent expansion of this quantity in the atomic number Z. The relation of this expansion to the Layzer-Bahcall series is finally discussed. (author)

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

On the influence of electromagnetic wave and relativistic electron beam on a plasma

International Nuclear Information System (INIS)

El Ashry, M.Y.; Berezhiani, V.I.; Javakhishvili, J.L.

1993-08-01

The dynamics of nonlinear wave in plasma under the influence of high-frequency electromagnetic pump and relativistic electron beam is considered. It is shown that the electrons of the beam play the role of the heavy plasma component, the matter which creates a possibility of formation of wave of a soliton type in a pure electron plasma. The wave structure is investigated and the characteristic parameters of the soliton are obtained. (author). 8 refs

Dispersion relation and Landau damping of waves in high-energy density plasmas

International Nuclear Information System (INIS)

Zhu Jun; Ji Peiyong

2012-01-01

We present a theoretical investigation on the propagation of electromagnetic waves and electron plasma waves in high energy density plasmas using the covariant Wigner function approach. Based on the covariant Wigner function and Dirac equation, a relativistic quantum kinetic model is established to describe the physical processes in high-energy density plasmas. With the zero-temperature Fermi–Dirac distribution, the dispersion relation and Landau damping of waves containing the relativistic quantum corrected terms are derived. The relativistic quantum corrections to the dispersion relation and Landau damping are analyzed by comparing our results with those obtained in classical and non-relativistic quantum plasmas. We provide a detailed discussion on the Landau damping obtained in classical plasmas, non-relativistic Fermi plasmas and relativistic Fermi plasmas. The contributions of the Bohm potential, the Fermi statistics pressure and relativistic effects to the dispersion relation and Landau damping of waves are quantitatively calculated with real plasma parameters. (paper)

Resonant generation of electromagnetic surface wave by inhomogeneous relativistic electron stream

Energy Technology Data Exchange (ETDEWEB)

Cadez, V.M.; Vukovic, S. (Belgrade Univ. (Yugoslavia). Inst. za Fiziku); Frolov, V.V.; Kyrie, A.Y. (AN SSSR, Moscow. Fizicheskij Inst.)

1981-12-01

Generation of electromagnetic surface waves by relativistic inhomogeneous particle flows is investigated for plane and cylindrical geometries. The basic excitation mechanisms are shown to be the induced anomalous Doppler effect and the hydrodynamic Cerenkov effect. The relevant maximal growth rates may differ significantly from those derived for monoenergetic beams.

Relativistic corrections to the form factors of Bc into P-wave orbitally excited charmonium

Science.gov (United States)

Zhu, Ruilin

2018-06-01

We investigated the form factors of the Bc meson into P-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were obtained, and the asymptotic expressions were studied in the infinite bottom quark mass limit. Employing the general form factors, we discussed the exclusive decays of the Bc meson into P-wave orbitally excited charmonium and a light meson. We found that the relativistic corrections lead to a large correction for the form factors, which makes the branching ratios of the decay channels B (Bc ± →χcJ (hc) +π± (K±)) larger. These results are useful for the phenomenological analysis of the Bc meson decays into P-wave charmonium, which shall be tested in the LHCb experiments.

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

Nonlinear interaction of a parallel-flow relativistic electron beam with a plasma

International Nuclear Information System (INIS)

Jungwirth, K.; Koerbel, S.; Simon, P.; Vrba, P.

1975-01-01

Nonlinear evolution of single-mode high-frequency instabilities (ω approximately ksub(parallel)vsub(b)) excited by a parallel-flow high-current relativistic electron beam in a magnetized plasma is investigated. Fairly general dimensionless equations are derived. They describe both the temporal and the spatial evolution of amplitude and phase of the fundamental wave. Numerically, the special case of excitation of the linearly most unstable mode is solved in detail assuming that the wave energy dissipation is negligible. Then the strength of interaction and the relativistic properties of the beam are fully respected by a single parameter lambda. The value of lambda ensuring the optimum efficiency of the wave excitation as well as the efficiency of the self-acceleration of some beam electrons at higher values of lambda>1 are determined in the case of a fully compensated relativistic beam. Finally, the effect of the return current dissipation is also included (phenomenologically) into the theoretical model, its role for the beam-plasma interaction being checked numerically. (J.U.)

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

Energy Technology Data Exchange (ETDEWEB)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com [Physics Department, Faculty of Mathematics and Science, Sebelas Maret University, Jl. Ir. Sutami 36A Kentingan Surakarta 57126 (Indonesia); Deta, U. A. [Physics Department, Faculty of Science and Mathematics Education and Teacher Training, Surabaya State University, Surabaya (Indonesia)

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy. The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.

Form factor of relativistic two-particle system and covariant hamiltonian formulation of quantum field theory

International Nuclear Information System (INIS)

Skachkov, N.; Solovtsov, I.

1979-01-01

Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential

Cooling rates and intensity limitations for laser-cooled ions at relativistic energies

Science.gov (United States)

Eidam, Lewin; Boine-Frankenheim, Oliver; Winters, Danyal

2018-04-01

The ability of laser cooling for relativistic ion beams is investigated. For this purpose, the excitation of relativistic ions with a continuous wave and a pulsed laser is analyzed, utilizing the optical Bloch equations. The laser cooling force is derived in detail and its scaling with the relativistic factor γ is discussed. The cooling processes with a continuous wave and a pulsed laser system are investigated. Optimized cooling scenarios and times are obtained in order to determine the required properties of the laser and the ion beam for the planed experiments. The impact of beam intensity effects, like intrabeam scattering and space charge are analyzed. Predictions from simplified models are compared to particle-in-cell simulations and are found to be in good agreement. Finally two realistic example cases of Carbon ions in the ESR and relativistic Titanium ions in SIS100 are compared in order to discuss prospects for future laser cooling experiments.

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

Resonant generation of electromagnetic surface wave by inhomogeneous relativistic electron stream

International Nuclear Information System (INIS)

Cadez, V.M.; Vukovic, S.; Frolov, V.V.; Kyrie, A.Y.

1981-01-01

Generation of electromagnetic surface waves by relativistic inhomogeneous particle flows is investigated for plane and cylindrical geometries. The basic excitation mechanisms are shown to be the induced anomalous Doppler effect and the hydrodynamic Cerenkov effect. The relevant maximal growth rates may differ significantly from those derived for monoenergetic beams. (author)

On analytic solutions of (1+3)D relativistic ideal hydrodynamic equations

International Nuclear Information System (INIS)

Lin Shu; Liao Jinfeng

2010-01-01

In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and power law ansatz for the remaining longitudinal velocity field will be found. Going beyond the power law ansatz, we further find a few solutions with transverse 2D Hubble embedding and nontrivial longitudinal velocity field. Finally we investigate general scaling flows with each component of the velocity fields scaling independently, for which we also find all possible solutions.

Blowing-up Semilinear Wave Equation with Exponential ...

Indian Academy of Sciences (India)

Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue

Proton relativistic model; Modelo relativistico do proton

Energy Technology Data Exchange (ETDEWEB)

Araujo, Wilson Roberto Barbosa de

1996-12-31

In this dissertation, we present a model for the nucleon, which is composed by three relativistic quarks interacting through a contract force. The nucleon wave-function was obtained from the Faddeev equation in the null-plane. The covariance of the model under kinematical null-plane boots is discussed. The electric proton form-factor, calculated from the Faddeev wave-function, was in agreement with the data for low-momentum transfers and described qualitatively the asymptotic region for momentum transfers around 2 GeV. (author) 42 refs., 22 figs., 1 tab.

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

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2007-01-01

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and

Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions

International Nuclear Information System (INIS)

Zamolodchikov, A.B.

1981-01-01

The quantum S-matrix theory of straight-strings (infinite one-dimensioanl objects like straight domain walls) in 2 + 1-dimensions is considered. The S-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-string S-matrix, which apparently satisfies this tetrahedron equation, is proposed. (orig.)

Modulational instability of coupled waves

International Nuclear Information System (INIS)

McKinstrie, C.J.; Bingham, R.

1989-01-01

The collinear propagation of an arbitrary number of finite-amplitude waves is modeled by a system of coupled nonlinear Schroedinger equations; one equation for each complex wave amplitude. In general, the waves are modulationally unstable with a maximal growth rate larger than the modulational growth rate of any wave alone. Moreover, waves that are modulationally stable by themselves can be driven unstable by the nonlinear coupling. The general theory is then applied to the relativistic modulational instability of two laser beams in a beat-wave accelerator. For parameters typical of a proposed beat-wave accelerator, this instability can seriously distort the incident laser pulse shapes on the particle-acceleration time scale, with detrimental consequences for particle acceleration

Relativistic generalization and extension to the non-Abelian gauge theory of Feynman's proof of the Maxwell equations

International Nuclear Information System (INIS)

Tanimura, Shogo

1992-01-01

R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs

Orbital stability of solitary waves for Kundu equation

Science.gov (United States)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

Some Mathematical Structures Including Simplified Non-Relativistic Quantum Teleportation Equations and Special Relativity

International Nuclear Information System (INIS)

Woesler, Richard

2007-01-01

The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future

An approach to rogue waves through the cnoidal equation

Science.gov (United States)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

Production of high energy neutrinos in relativistic supernova shock waves

International Nuclear Information System (INIS)

Weaver, T.A.

1979-01-01

The possibility of producing high-energy neutrinos (> approx. 10 GeV) in relativistic supernova shock waves is considered. It is shown that, even if the dissipation in such shocks is due to hard hadron--hadron collisions, the resulting flux of neutrinos is too small to be observed by currently envisioned detectors. The associated burst of hard γ-rays, however, may be detectable. 3 tables

Relativistic solitary waves modulating long laser pulses in plasmas

International Nuclear Information System (INIS)

Sanchez-Arriaga, G; Siminos, E; Lefebvre, E

2011-01-01

This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency ω, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V-ω plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.

Travelling wave solutions for a surface wave equation in fluid mechanics

Directory of Open Access Journals (Sweden)

Tian Yi

2016-01-01

Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

Nonlinear extraordinary wave in dense plasma

Energy Technology Data Exchange (ETDEWEB)

Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.

Wave equations in higher dimensions

CERN Document Server

Dong, Shi-Hai

2011-01-01

Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

Science.gov (United States)

Tsai, Hung-Ming; Poirier, Bill

2016-03-01

In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

Energy Technology Data Exchange (ETDEWEB)

Milant' ev, V. P., E-mail: vmilantiev@sci.pfu.edu.ru; Castillo, A. J., E-mail: vmilant@mail.ru [Peoples' Friendship University of Russia (Russian Federation)

2013-04-15

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive force in the cases of circularly and linearly polarized waves has been confirmed.

Relativistic quarkonium dynamics

International Nuclear Information System (INIS)

Sazdjian, H.

1985-06-01

We present, in the framework of relativistic quantum mechanics of two interacting particles, a general model for quarkonium systems satisfying the following four requirements: confinement, spontaneous breakdown of chiral symmetry, soft explicit chiral symmetry breaking, short distance interactions of the vector type. The model is characterized by two arbitrary scalar functions entering in the large and short distance interaction potentials, respectively. Using relationships with corresponding quantities of the Bethe-Salpeter equation, we also present the normalization condition of the wave functions, as well as the expressions of the meson decay coupling constants. The quark masses appear in this model as free parameters

Local U(2,2) Symmetry in Relativistic Quantum Mechanics

OpenAIRE

Finster, Felix

1997-01-01

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

Local U(2,2) symmetry in relativistic quantum mechanics

Science.gov (United States)

Finster, Felix

1998-12-01

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

Travelling wave solutions to the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Nickel, J.

2007-01-01

Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by Schuermann to find physical (real and bounded) solutions and to discriminate between periodic and solitary wave solutions are used. The method is shown in detail by evaluating new solutions of the Kuramoto-Sivashinsky equation

Wave-equation Q tomography

KAUST Repository

Dutta, Gaurav

2016-10-12

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

Wave-equation Q tomography

KAUST Repository

Dutta, Gaurav; Schuster, Gerard T.

2016-01-01

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

Comparison of a noncausal with a causal relativistic wave-packet evolution

International Nuclear Information System (INIS)

Castro, A.N. de; Jabs, A.

1991-01-01

In order to study causality violation in more detail we contrast the Klein-Gordon wave packet of Rosenstein und Usher with the Dirac wave packet of Bakke and Wergeland. Both packets are initially localized with exponentially bounded tails but just outside the condition of the general Hegerfeldt theorem for causality violation. It turns out that the wave packet of Bakke and Wergeland exhibits all the features investigated by Rosenstein and Usher, except that it never violates relativistic causality. Thus none of those features, in particular the back- and forerunners emerging from the light cone, can be held responsible for causality violation, and the Ruijsenaars integral is not necessarily a measure of the amount of causality violation. (orig.)

Rogue periodic waves of the modified KdV equation

Science.gov (United States)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Traveling wave behavior for a generalized fisher equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2008-01-01

There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation

Parsimonious wave-equation travel-time inversion for refraction waves

KAUST Repository

Fu, Lei; Hanafy, Sherif M.; Schuster, Gerard T.

2017-01-01

We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

Science.gov (United States)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

Science.gov (United States)

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation

International Nuclear Information System (INIS)

Durand, B.; Durand, L.

1983-01-01

We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly

General-relativistic celestial mechanics. II. Translational equations of motion

International Nuclear Information System (INIS)

Damour, T.; Soffel, M.; Xu, C.

1992-01-01

The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) 4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies

Wave-equation reflection traveltime inversion

KAUST Repository

Zhang, Sanzong

2011-01-01

The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

Electron non-linearities in Langmuir waves with application to beat-wave experiments

International Nuclear Information System (INIS)

Bell, A.R.; Gibbon, P.

1988-01-01

Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

Science.gov (United States)

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Rarefaction wave in relativistic steady magnetohydrodynamic flows

Energy Technology Data Exchange (ETDEWEB)

Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)

2014-07-15

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.

Particle Dynamics under Quasi-linear Interaction with Electromagnetic Waves

Energy Technology Data Exchange (ETDEWEB)

Castejon, F.; Eguilior, S.

2003-07-01

Langevin equations for quasi-linear wave particle interaction are obtained taking advantage of the unique vocal equivalence between Fokker-Plank equation and the former ones. Langevin equations are solved numerically and, hence, the evolution of a single particle embedded in an electromagnetic field in momentum space is obtained. The equations are relativistic and valid for any wave. It is also shown that the stochastic part of the equations is negligible in comparison with the deterministic term, except for the momentum to the resonance condition for the main parallel refractive index. (Author) 24 refs.

Particle Dynamics under Quasi-linear Interaction with Electromagnetic Waves

International Nuclear Information System (INIS)

Castejon, F.; Eguilior, S.

2003-01-01

Langevin equations for quasi-linear wave particle interaction are obtained taking advantage of the unique vocal equivalence between Fokker-Plank equation and the former ones. Langevin equations are solved numerically and, hence, the evolution of a single particle embedded in an electromagnetic field in momentum space is obtained. The equations are relativistic and valid for any wave. It is also shown that the stochastic part of the equations is negligible in comparison with the deterministic term, except for the momentum to the resonance condition for the main parallel refractive index. (Author) 24 refs

Paraxial WKB solution of a scalar wave equation

International Nuclear Information System (INIS)

Pereverzev, G.V.

1993-04-01

An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

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.

Relativistic invariance of dispersion-relations and their associated wave-operators and Green-functions

International Nuclear Information System (INIS)

Censor, Dan

2010-01-01

Identifying invariance properties helps in simplifying calculations and consolidating concepts. Presently the Special Relativistic invariance of dispersion relations and their associated scalar wave operators is investigated for general dispersive homogeneous linear media. Invariance properties of the four-dimensional Fourier-transform integrals is demonstrated, from which the invariance of the scalar Green-function is inferred. Dispersion relations and the associated group velocities feature in Hamiltonian ray tracing theory. The derivation of group velocities for moving media from the dispersion relation for these media at rest is discussed. It is verified that the group velocity concept satisfies the relativistic velocity-addition formula. In this respect it is considered to be 'real', i.e., substantial, physically measurable, and not merely a mathematical artifact. Conversely, if we assume the group velocity to be substantial, it follows that the dispersion relation must be a relativistic invariant. (orig.)

Traveling waves of the regularized short pulse equation

International Nuclear Information System (INIS)

Shen, Y; Horikis, T P; Kevrekidis, P G; Frantzeskakis, D J

2014-01-01

The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by a finite sum of hyperbolic secants powers. The dependence of the soliton's parameters (height, width, etc) to the parameters of the equation is also investigated. Second, by developing a multiple scale reduction of the RSPE to the nonlinear Schrödinger equation, we are able to construct (both standing and traveling) envelope wave breather type solutions of the former, based on the solitary wave structures of the latter. Both the regular and the breathing traveling wave solutions identified are found to be robust and should thus be amenable to observations in the form of few optical cycle pulses. (paper)

Perturbed Coulomb Potentials in the Klein-Gordon Equation: Quasi-Exact Solution

Science.gov (United States)

Baradaran, M.; Panahi, H.

2018-05-01

Using the Lie algebraic approach, we present the quasi-exact solutions of the relativistic Klein-Gordon equation for perturbed Coulomb potentials namely the Cornell potential, the Kratzer potential and the Killingbeck potential. We calculate the general exact expressions for the energies, corresponding wave functions and the allowed values of the parameters of the potential within the representation space of sl(2) Lie algebra. In addition, we show that the considered equations can be transformed into the Heun's differential equations and then we reproduce the results using the associated special functions. Also, we study the special case of the Coulomb potential and show that in the non-relativistic limit, the solution of the Klein-Gordon equation converges to that of Schrödinger equation.

An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

Energy Technology Data Exchange (ETDEWEB)

Peysson, Y. [Association Euratom-CEA, CEA Grenoble, 38 (France). Dept. de Recherches sur la Fusion Controlee; Choucri, M. [Centre Canadien de Fusion Magnetique, Varennes, PQ (Canada)

1997-09-01

A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2{sub D}) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author) 21 refs.

An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver

International Nuclear Information System (INIS)

Peysson, Y.

1997-09-01

A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2 D ) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author)

General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies

Science.gov (United States)

Kopeikin, Sergei

2003-01-01

The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.

Some aspects of transformation of the nonlinear plasma equations to the space-independent frame

International Nuclear Information System (INIS)

Paul, S.N.; Chakraborty, B.

1982-01-01

Relativistically correct transformation of nonlinear plasma equations are derived in a space-independent frame. This transformation is useful in many ways because in place of partial differential equations one obtains a set of ordinary differential equations in a single independent variable. Equations of Akhiezer and Polovin (1956) for nonlinear plasma oscillations have been generalized and the results of Arons and Max (1974), and others for wave number shift and precessional rotation of electromagnetic wave are recovered in a space-independent frame. (author)

Wave-equation dispersion inversion

KAUST Repository

Li, Jing; Feng, Zongcai; Schuster, Gerard T.

2016-01-01

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

Temperature waves and the Boltzmann kinetic equation for phonons

International Nuclear Information System (INIS)

Urushev, D.; Borisov, M.; Vavrek, A.

1988-01-01

The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

Properties of the DKP [Duffin-Kemmer-Petiau] equation

International Nuclear Information System (INIS)

Nieto, M.M.

1988-01-01

After recalling the development of relativistic quantum mechanics, I elucidating the properties of the Duffin-Kemmer-Petiau first-order wave equation for spin-0 and -1 mesons. The DKP equation is formally compared to the Dirac equation, and physically compared to the Klein-Gordon second-order equation for mesons. I point out where the DKP and KG equations predict the same results, and where their predictions are different. I conclude with an example of where these differences might interest people studying quark models of nuclei. 9 refs

Nonlinear relativistic plasma resonance: Renormalization group approach

Energy Technology Data Exchange (ETDEWEB)

Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

2017-02-15

An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.

An overmoded relativistic backward wave oscillator with efficient dual-mode operation

International Nuclear Information System (INIS)

Xiao, Renzhen; Li, Jiawei; Bai, Xianchen; Song, Zhimin; Teng, Yan; Ye, Hu; Li, Xiaoze; Sun, Jun; Chen, Changhua; Zhang, Xiaowei

2014-01-01

A dual-mode operation mechanism in an overmoded relativistic backward wave oscillator is presented. The electron beam interacts with the −1st space harmonic of TM 01 mode synchronously in the slow wave structure. Then the backward propagating TM 01 mode is converted to the forward propagating TM 02 mode. As the phase velocity of the volume harmonic of TM 02 mode is about twice that of the surface harmonic of TM 01 mode, the TM 02 mode also plays an important role in the high-power microwave generation. Particle-in-cell simulation shows that an efficiency of 48% and a significant improvement of the power capacity have been obtained

Sine-Gordon Equation in (1+2 and (1+3 dimensions: Existence and Classification of Traveling-Wave Solutions.

Directory of Open Access Journals (Sweden)

Yair Zarmi

Full Text Available The (1+1-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2- and (1+3-dimensional equations for all N ≥ 1 are presented. In (1+2 dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2-dimensional solutions, or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2 and (1+3 dimensions.

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge

2010-10-17

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

Planar channeled relativistic electrons and positrons in the field of resonant hypersonic wave

International Nuclear Information System (INIS)

Grigoryan, L.Sh.; Mkrtchyan, A.H.; Khachatryan, H.F.; Tonoyan, V.U.; Wagner, W.

2003-01-01

The wave function of a planar channeled relativistic particle (electron, positron) in a single crystal excited by longitudinal hypersonic vibrations (HVs) is determined. The obtained expression is valid for periodic (not necessarily harmonic) HV of desired profile and single crystals with an arbitrary periodic continuous potential. A revised formula for the wave number of HV that exert resonance influence on the state of a channeled particle was deduced to allow for non-linear effects due to the influence of HV

Solitons in a relativistic plasma with negative ions--

International Nuclear Information System (INIS)

Das, G.C.; Karmakar, B.; Ibohanbi Singh, KH.

1990-01-01

The interaction of the nonlinearity and the dispersiveness causing the solitary waves are studied in a relativistic plasma with negative ions through the derivation of a nonlinear partial differential equation known as the Korteweg-Devries (K-DV) equation. The negative ions play a salient feature on the existence and behavior of the solitons and could be of interest in laboratory plasmas. First, the observations are made in a nonisothermal plasma, and later the reduction to the nonisothermality of the plasma shows entirely different characteristics as compared to the solitons in the isothermal plasmas. A comparison with the various solutions has been emphasized

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

Energy Technology Data Exchange (ETDEWEB)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

Compact toroidal energy storage device with relativistically densified electrons through the use of travelling magnetic waves

International Nuclear Information System (INIS)

Peter, W.; Faehl, R.J.

1983-01-01

A new concept for a small compact multimegajoule energy storage device utilizing relativistically densified electron beam circulating in a torus is presented. The electron cloud is produced through inductive charge injection by a travelling magnetic wave circulating the torus. Parameters are given for two representative toroidal energy storage devices, consisting of 1 m and 32 m in radius respectively, which could store more than 4 x 10 17 electrons and 30' MJ in energy. The concept utilizes the idea that large electric and magnetic fields can be produced by a partially space-charge neutralized intense relativistic electron beam which could become many orders of magnitude greater than the externally applied field confining the beam. In the present approach, the electron cloud densification can be achieved gradually by permitting multiple traversals of the magnetic wave around the torus. The magnetic mirror force acts on the orbital magnetic electron dipole moment and completely penetrates the entire electron cloud. As the electrons gain relativistic energies, the beam can be continuously densified at the front of the travelling wave, where the magnetic field is rising with time. The use of travelling magnetic wave to accelerate an electron cloud and the use of large electric field at the thusly accelerated cloud form the basis for a high beam intensity and hence high energy storage. Technical considerations and several potential applications, which include the driving of a powerful gyrotron, are discussed

Low-lying qq(qq)-bar states in a relativistic model based on the Bethe-Salpeter equation

International Nuclear Information System (INIS)

Ram, B.; Kriss, V.

1985-01-01

Low-lying qq(qq)-bar states are analysed in a previously given relativistic model based on the Bethe-Salpeter equation. It is not got M-diquonia, P-mesonia, or meson molecules, but it is got T-diquonia

Gabor Wave Packet Method to Solve Plasma Wave Equations

International Nuclear Information System (INIS)

Pletzer, A.; Phillips, C.K.; Smithe, D.N.

2003-01-01

A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

Relativistic acceleration of captured particles by a longitudinal wave in a slightly inhomogeneous plasma

International Nuclear Information System (INIS)

Erokhin, N.S.; Zol'nikova, N.N.; Mikhajlovskaya, L.A.

1991-01-01

Relativistic acceleration of charged particles, captured by a longitudinal wave in a slightly inhomogeneous plasma without an external magnetic field is considered numerically and analytically. It is shown that with the growth of the plasma inhomogeneity parameter the maximum energy of accelerated captured particles exponentially increases. Attention is paid to the possibility of 'eternal' confinement and, respectively, unlimited acceleration of captured particles by an undamped longitudinal wave in a plasma without a magnetic field

Diffusion phenomenon for linear dissipative wave equations

KAUST Repository

Said-Houari, Belkacem

2012-01-01

In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

Nonlinear Electrostatic Wave Equations for Magnetized Plasmas

DEFF Research Database (Denmark)

Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans

1984-01-01

The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....

Distortions of the distribution function of collisionless particles by high-frequency gravitational waves

International Nuclear Information System (INIS)

Vainer, B.V.; Nasel'skii, P.D.

1983-01-01

Equations for the correlation functions of fluctuations in the spectra of relativistic collisionless particles are obtained from the combined system of Einstein's equations and the Vlasov equation. It is shown that the interaction of high-frequency gravitational waves with collisionless particles leads to diffusion of their spectrum in the momentum space. The distortions in the spectrum of the microwave background radiation in a cosmological model with high-frequency gravitational waves are discussed. Bounds are obtained on the spectral characteristics of background gravitational waves

Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function

International Nuclear Information System (INIS)

Mao, G.; Li, Z.; Zhuo, Y.

1996-01-01

We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society

Wave function of free electron in a strong laser plasma

International Nuclear Information System (INIS)

Zhu Shitong; Shen Wenda; Guo Qizhi

1993-01-01

The wave function of free electron in a strong laser plasma is obtained by solving exactly the Dirac equation in a curved space-time with optical metric for the laser plasma. When the laser field is diminished to zero, the wave function is naturally reduced to relativistic wave function of free electron. The possible application of the wave function is discussed

Bifurcations of traveling wave solutions for an integrable equation

International Nuclear Information System (INIS)

Li Jibin; Qiao Zhijun

2010-01-01

This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.

Traveling waves in a free-electron laser with an electromagnetic wiggler

International Nuclear Information System (INIS)

Olumi, Mohsen; Maraghechi, B; Rouhani, M H

2011-01-01

The propagation of electromagnetic traveling wave in a free-electron laser (FEL) with an electromagnetic wiggler is investigated using the relativistic fluid-Maxwell formulation. By adapting the traveling-wave ansatz, three coupled, nonlinear ordinary differential equations are obtained describing the nonlinear propagation of the coupled wave. These equations may be used to study saturation in FELs. By linearizing the nonlinear equations dispersion relations for the traveling wave are obtained. Numerical solution of the small-signal traveling dispersion relation reveals the coupling of radiation to both slow and fast space-charge waves. It is shown that the traveling wave, which is not a normal mode in a laboratory frame, becomes a normal mode in terms of a transformed variable.

Capillary-gravity waves and the Navier-Stokes equation

International Nuclear Information System (INIS)

Behroozi, F.; Podolefsky, N.

2001-01-01

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

Modelling properties of hard x-rays generated by the interaction between relativistic electrons and very intense laser beams

International Nuclear Information System (INIS)

Popa, Alexandru

2009-01-01

In a previous paper we presented a calculation model for high harmonic generation by relativistic Thomson scattering of the electromagnetic radiation by free electrons. In this paper we present a similar model for the calculation of the energies of hard x-rays (20- 200 keV) resulted from the interaction between relativistic electrons (20-100 MeV) and very intense laser beams. Starting from the relativistic equations of motion of an electron in the electromagnetic field we show that the Lienard-Wiechert equation leads to electromagnetic waves whose frequencies are in the domain of hard x-rays. When the relativistic parameter of the laser beam is greater than unity, the model predicts the existence of harmonics of the above frequencies. Our theoretical values are in good agreement with experimental values of the x-ray energies from the literature and predict accurately their angular distribution.

A new iterative solver for the time-harmonic wave equation

NARCIS (Netherlands)

Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.

2006-01-01

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can

Nonlinear interaction of waves in an inhomogeneous plasma

International Nuclear Information System (INIS)

Istomin, Ya.N.

1988-01-01

Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered

Covariant spectator theory of $np$ scattering:\\\\ Effective range expansions and relativistic deuteron wave functions

Energy Technology Data Exchange (ETDEWEB)

Franz Gross, Alfred Stadler

2010-09-01

We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.

An acoustic wave equation for pure P wave in 2D TTI media

KAUST Repository

Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

2011-01-01

In this paper, a pure P wave equation for an acoustic 2D TTI media is derived. Compared with conventional TTI coupled equations, the resulting equation is unconditionally stable due to the complete isolation of the SV wave mode. To avoid numerical dispersion and produce high quality images, the rapid expansion method REM is employed for numerical implementation. Synthetic results validate the proposed equation and show that it is a stable algorithm for modeling and reverse time migration RTM in a TTI media for any anisotropic parameter values. © 2011 Society of Exploration Geophysicists.

Point form relativistic quantum mechanics and relativistic SU(6)

Science.gov (United States)

Klink, W. H.

1993-01-01

The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

Science.gov (United States)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

Waves in magnetized quark matter

Science.gov (United States)

Fogaça, D. A.; Sanches, S. M.; Navarra, F. S.

2018-05-01

We study wave propagation in a non-relativistic cold quark-gluon plasma immersed in a constant magnetic field. Starting from the Euler equation we derive linear wave equations and investigate their stability and causality. We use a generic form for the equation of state, the EOS derived from the MIT bag model and also a variant of the this model which includes gluon degrees of freedom. The results of this analysis may be relevant for perturbations propagating through the quark matter phase in the core of compact stars and also for perturbations propagating in the low temperature quark-gluon plasma formed in low energy heavy ion collisions, to be carried out at FAIR and NICA.

Concluding Remarks: Connecting Relativistic Heavy Ion Collisions and Neutron Star Mergers by the Equation of State of Dense Hadron- and Quark Matter as signalled by Gravitational Waves

Science.gov (United States)

Hanauske, Matthias; Steinheimer, Jan; Bovard, Luke; Mukherjee, Ayon; Schramm, Stefan; Takami, Kentaro; Papenfort, Jens; Wechselberger, Natascha; Rezzolla, Luciano; Stöcker, Horst

2017-07-01

The underlying open questions in the fields of general relativistic astrophysics and elementary particle and nuclear physics are strongly connected and their results are interdependent. Although the physical systems are quite different, the 4D-simulation of a merger of a binary system of two neutron stars and the properties of the hot and dense matter created in high energy heavy ion collisions, strongly depend on the equation of state of fundamental elementary matter. Neutron star mergers represent optimal astrophysical laboratories to investigate the QCD phase structure using a spectrogram of the post-merger phase of the emitted gravitational waves. These studies can be supplemented by observations from heavy ion collisions to possibly reach a conclusive picture on the QCD phase structure at high density and temperature. As gravitational waves (GWs) emitted from merging neutron star binaries are on the verge of their first detection, it is important to understand the main characteristics of the underlying merging system in order to predict the expected GW signal. Based on numerical-relativity simulations of merging neutron star binaries, the emitted GW and the interior structure of the generated hypermassive neutron stars (HMNS) have been analyzed in detail. This article will focus on the internal and rotational HMNS properties and their connection with the emitted GW signal. Especially, the appearance of the hadon-quark phase transition in the interior region of the HMNS and its conjunction with the spectral properties of the emitted GW will be addressed and confronted with the simulation results of high energy heavy ion collisions.

Relativistic Killingbeck energy states under external magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Eshghi, M. [Islamic Azad University, Researchers and Elite Club, Central Tehran Branch, Tehran (Iran, Islamic Republic of); Mehraban, H. [Semnan University, Faculty of Physics, Semnan (Iran, Islamic Republic of); Ikhdair, S.M. [An-Najah National University, Department of Physics, Faculty of Science, Nablus, West Bank, Palestine (Country Unknown); Near East University, Department of Electrical Engineering, Nicosia, Northern Cyprus (Turkey)

2016-07-15

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun's differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states. (orig.)

Relativistic Killingbeck energy states under external magnetic fields

International Nuclear Information System (INIS)

Eshghi, M.; Mehraban, H.; Ikhdair, S.M.

2016-01-01

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun's differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states. (orig.)

Anisotropic wave-equation traveltime and waveform inversion

KAUST Repository

Feng, Shihang

2016-09-06

The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave

Directory of Open Access Journals (Sweden)

Arbab A. I.

2009-04-01

Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.

Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

Science.gov (United States)

Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.

2018-05-01

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.

Solution of the relativistic 2-D Fokker-Planck equation for LH current drive

International Nuclear Information System (INIS)

Hizanidis, K.; Hewett, D.W.; Bers, A.

1984-03-01

We solve numerically the steady-state two-dimensional relativistic Fokker-Planck equation with strong rf diffusion using spectra relevant to recent experiments in ALCATOR-C. The results (current generated, power dissipated, and the distribution of energetic electrons) are sensitive to the location of the spectrum in momentum space. Relativistic effects play an important role, especially for wide spectra. The dependence on the ionic charge number Z/sub i/ is also investigated. Particular attention is paid to the perpendicular temperature inside the resonant region and beyond, as well as to the angular energetic particle-temperature distribution, T/sub μ/, a function of the pitch angle parameter μ. The dependence of the perpendicular temperature on the location of the spectrum is also investigated analytically with a model based on the method of moments and the results compared with those found numerically

Ultra Deep Wave Equation Imaging and Illumination

Energy Technology Data Exchange (ETDEWEB)

Alexander M. Popovici; Sergey Fomel; Paul Sava; Sean Crawley; Yining Li; Cristian Lupascu

2006-09-30

In this project we developed and tested a novel technology, designed to enhance seismic resolution and imaging of ultra-deep complex geologic structures by using state-of-the-art wave-equation depth migration and wave-equation velocity model building technology for deeper data penetration and recovery, steeper dip and ultra-deep structure imaging, accurate velocity estimation for imaging and pore pressure prediction and accurate illumination and amplitude processing for extending the AVO prediction window. Ultra-deep wave-equation imaging provides greater resolution and accuracy under complex geologic structures where energy multipathing occurs, than what can be accomplished today with standard imaging technology. The objective of the research effort was to examine the feasibility of imaging ultra-deep structures onshore and offshore, by using (1) wave-equation migration, (2) angle-gathers velocity model building, and (3) wave-equation illumination and amplitude compensation. The effort consisted of answering critical technical questions that determine the feasibility of the proposed methodology, testing the theory on synthetic data, and finally applying the technology for imaging ultra-deep real data. Some of the questions answered by this research addressed: (1) the handling of true amplitudes in the downward continuation and imaging algorithm and the preservation of the amplitude with offset or amplitude with angle information required for AVO studies, (2) the effect of several imaging conditions on amplitudes, (3) non-elastic attenuation and approaches for recovering the amplitude and frequency, (4) the effect of aperture and illumination on imaging steep dips and on discriminating the velocities in the ultra-deep structures. All these effects were incorporated in the final imaging step of a real data set acquired specifically to address ultra-deep imaging issues, with large offsets (12,500 m) and long recording time (20 s).

Wave equations for pulse propagation

International Nuclear Information System (INIS)

Shore, B.W.

1987-01-01

Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

Science.gov (United States)

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

Local energy decay for linear wave equations with variable coefficients

Science.gov (United States)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

On the relativistic transport equation for a multiple discontinuity wave

International Nuclear Information System (INIS)

Giambo, Sebastiano

1980-01-01

The theory of singular hypersurfaces is combined with the ray theory to study propagation of weak discontinuities of solutions of quasi-linear hyperbolic system in the context of special relativity. The case of a multiple wave is considered [fr

On the H particle stability in the non relativistic quark model

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Carbonell, J.; Gignoux, C.

1987-05-01

The H particle with quark content (uuddss) is presented as a good candidate to be stable with respect to strong interactions. In the framework of a non relativistic potential model, the binding energy is calculated by a full dynamical approach using a resonating group trial wave function. The center of mass motion and the Pauli principle are correctly treated. Sophisticated baryon wave functions are employed and the equation of motion is solved with six coupled channels including radial excited baryon states. The effect of breaking SU(3) flavour symmetry is discussed in detail

Intertwining solutions for magnetic relativistic Hartree type equations

Science.gov (United States)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Nonlinear propagation of ion-acoustic solitary waves in relativistic ion-beam plasma with negative ions

International Nuclear Information System (INIS)

Singh, Kh.I.; Das, G.C.

1993-01-01

Soliton propagations are studied in a relativistic multicomponent ion-beam plasma through the derivation of Korteweg-deVries (K-dV) and modified K-dV (mK-dV) equations. A generalization of the mK-dV equation involving higher order nonlinearities gives a transitive link between the K-dV and mK-dV equations for isothermal plasma, and the validity of this generalized equation throughout the whole range of negative ion concentrations is investigated through the derivation of Sagdeev potential. Parallel discussion of various K-dV solitons enlightening the experimental implications is also made. (author). 22 refs

Topological horseshoes in travelling waves of discretized nonlinear wave equations

International Nuclear Information System (INIS)

Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming

2014-01-01

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes

Topological horseshoes in travelling waves of discretized nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

2014-04-15

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

Axial motion of collector plasma in a relativistic backward wave oscillator

Energy Technology Data Exchange (ETDEWEB)

Xiao, Renzhen; Chen, Changhua; Deng, Yuqun; Cao, Yibing; Sun, Jun; Li, Jiawei [Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi' an 710024 (China)

2016-06-15

In this paper, it is proposed that plasma formed at the collector may drift back to the cathode and cause pulse shortening of the relativistic backward wave oscillator. Theoretical analysis shows that the axial drift velocity of plasma ions can be up to 5 mm/ns due to the presence of space charge potential provided by an intense relativistic electron beam. Particle-in-cell simulations indicate that the plasma electrons are initially trapped around the collector surface. With the accumulation of the plasma ions, a large electrostatic field forms and drives the plasma electrons to overcome the space charge potential and enter the beam-wave interaction region along the magnetic field lines. As a result, the beam current modulation is disturbed and the output microwave power falls rapidly. The plasma ions move in the beam-wave interaction region with an average axial velocity of 5–8 mm/ns. After the plasma ions reach the diode region, the emitted current at the cathode rises due to the charge neutralizations by the ions. The impedance collapse leads to further decrease of the microwave power. In experiments, when the diode voltage and beam current were 850 kV and 9.2 kA, and the collector radius was 2.15 cm, the output microwave power was 2.4 GW with a pulse width of less than 20 ns. The ion drift velocity was estimated to be about 5 mm/ns. After an improved collector with 3.35 cm radius was adopted, the pulse width was prolonged to more than 30 ns.

Relativistic theory of tidal Love numbers

International Nuclear Information System (INIS)

Binnington, Taylor; Poisson, Eric

2009-01-01

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

Relativistic harmonic content of nonlinear electromagnetic waves in underdense plasmas

International Nuclear Information System (INIS)

Mori, W.B.; Decker, C.D.; Leemans, W.P.

1993-01-01

The relativistic harmonic content of large amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w p /w o ) much-lt 1 and critical density (w p /w o ) ≅ 1 limits. For weak nonlinearities, eE o /mcw o p /w o . Arguments are given for extending these results for arbitrary wave amplitudes. The authors also show that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

Skeletonized wave-equation inversion for Q

KAUST Repository

Dutta, Gaurav

2016-09-06

A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

Skeletonized wave-equation inversion for Q

KAUST Repository

Dutta, Gaurav; Schuster, Gerard T.

2016-01-01

A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

A novel quantum-mechanical interpretation of the Dirac equation

Science.gov (United States)

K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

2016-04-01

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

Periodic and solitary-wave solutions of the Degasperis-Procesi equation

International Nuclear Information System (INIS)

Vakhnenko, V.O.; Parkes, E.J.

2004-01-01

Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered

A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

International Nuclear Information System (INIS)

Hamzavi, M.; Ikhdair, S.M.; Rajabi, A.A.

2013-01-01

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for an arbitrary l-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schroedinger-Woods-Saxon problem for an arbitrary l-state and the exact s-wave (l=0). (authors)

DKE: a fast numerical solver for the 3-D relativistic bounce-averaged electron drift kinetic equation

Energy Technology Data Exchange (ETDEWEB)

Decker, J.; Peysson, Y

2004-12-01

A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)

DKE: a fast numerical solver for the 3-D relativistic bounce-averaged electron drift kinetic equation

International Nuclear Information System (INIS)

Decker, J.; Peysson, Y.

2004-12-01

A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high β p plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)

New exact travelling wave solutions of bidirectional wave equations

Indian Academy of Sciences (India)

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.

A nonlinear wave equation in nonadiabatic flame propagation

International Nuclear Information System (INIS)

Booty, M.R.; Matalon, M.; Matkowsky, B.J.

1988-01-01

The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time

Exact solution of the relativistic Coulomb problem for two-particle bound states in the quasipotential approach

International Nuclear Information System (INIS)

Kapshay, V.N.; Skachkov, N.B.

1979-01-01

A composite system of two relativistic particles is studied on the basis of the Kadyshevsky quasipotential equation, in which the ''Coulomb'' potential is taken in the form of a propagator of the massless-scalar-particle exchange. The obtained exact solutions to this equation are shown to be a geometrical generalization of nonrelativistic Coulomb wave functions in the sense of change of the Euclidean geometry of momentum space to the Lobachevsky geometry

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

Science.gov (United States)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

Relativistic dissipative hydrodynamic equations at the second order for multi-component systems with multiple conserved currents

International Nuclear Information System (INIS)

Monnai, Akihiko; Hirano, Tetsufumi

2010-01-01

We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.

Causal wave propagation for relativistic massive particles: physical asymptotics in action

International Nuclear Information System (INIS)

Berry, M V

2012-01-01

Wavepackets representing relativistic quantum particles injected into a half-space, from a source that is switched on at a definite time, are represented by superpositions of plane waves that must include negative frequencies. Propagation is causal: it is a consequence of analyticity that at time t no part of the wave has travelled farther than ct, corresponding to the front of the signal. Nevertheless, interference fringes behind the front travel superluminally. For Klein-Gordon and Dirac wavepackets, the spatially integrated density increases because current is injected at the boundary. Even in the simplest causal model, understanding the shape of the wave after long times is an instructive exercise in the asymptotics of integrals, illustrating several techniques at a level suitable for graduate students; different spatial features involve contributions from a pole and from two saddle points, the uniform asymptotics for the pole close to a saddle, and the coalescence of two saddles into the Sommerfeld precursor immediately behind the front. (paper)

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

New traveling wave solutions to AKNS and SKdV equations

International Nuclear Information System (INIS)

Ozer, Teoman

2009-01-01

We analyze the traveling wave solutions of Ablowitz-Kaup-Newell-Segur (AKNS) and Schwarz-Korteweg-de Vries (SKdV) equations. As the solution method for differential equations we consider the improved tanh approach. This approach provides to transform the partial differential equation into the ordinary differential equation and then obtain the new families of exact solutions based on the solutions of the Riccati equation. The different values of the coefficients of the Riccati equation allow us to obtain new type of traveling wave solutions to AKNS and SKdV equations.

The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

Hot QCD equations of state and relativistic heavy ion collisions

Science.gov (United States)

Chandra, Vinod; Kumar, Ravindra; Ravishankar, V.

2007-11-01

We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of O(g5). The second EOS is an improvement over the first, with contributions up to O[g6ln(1/g)]; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.

Experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds

Directory of Open Access Journals (Sweden)

M. Füllekrug

2011-01-01

Full Text Available Relativistic electron beams above thunderclouds emit 100 kHz radio waves which illuminate the Earth's atmosphere and near-Earth space. This contribution aims to clarify the physical processes which are relevant for the spatial spreading of the radio wave energy below and above the ionosphere and thereby enables an experimental simulation of satellite observations of 100 kHz radio waves from relativistic electron beams above thunderclouds. The simulation uses the DEMETER satellite which observes 100 kHz radio waves from fifty terrestrial Long Range Aid to Navigation (LORAN transmitters. Their mean luminosity patch in the plasmasphere is a circular area with a radius of 300 km and a power density of 22 μW/Hz as observed at 660 km height above the ground. The luminosity patches exhibit a southward displacement of 450 km with respect to the locations of the LORAN transmitters. The displacement is reduced to 150 km when an upward propagation of the radio waves along the geomagnetic field line is assumed. This residual displacement indicates that the radio waves undergo 150 km sub-ionospheric propagation prior to entering a magnetospheric duct and escaping into near-Earth space. The residual displacement at low (L < 2.14 and high (L > 2.14 geomagnetic latitudes ranges from 100 km to 200 km which suggests that the smaller inclination of the geomagnetic field lines at low latitudes helps to trap the radio waves and to keep them in the magnetospheric duct. Diffuse luminosity areas are observed northward of the magnetic conjugate locations of LORAN transmitters at extremely low geomagnetic latitudes (L < 1.36 in Southeast Asia. This result suggests that the propagation along the geomagnetic field lines results in a spatial spreading of the radio wave energy over distances of 1 Mm. The summative assessment of the electric field intensities measured in space show that nadir observations of terrestrial 100 kHz radio waves, e.g., from

The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

International Nuclear Information System (INIS)

Scully, M O

2008-01-01

The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

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.)

Dynamic equations for gauge-invariant wave functions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

1984-01-01

The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

Similarity flows in relativistic hydrodynamics

International Nuclear Information System (INIS)

Blaizot, J.P.; Ollitrault, J.Y.

1986-01-01

In ultra-relativistic heavy ion collisions, one expects in particular to observe a deconfinement transition leading to a formation of quark gluon plasma. In the framework of the hydrodynamic model, experimental signatures of such a plasma may be looked for as observable consequences of a first order transition on the evolution of the system. In most of the possible scenario, the phase transition is accompanied with discontinuities in the hydrodynamic flow, such as shock waves. The method presented in this paper has been developed to treat without too much numerical effort such discontinuous flow. It relies heavily on the use of similarity solutions of the hydrodynamic equations

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. )

Optimization of relativistic backward wave oscillator with non-uniform slow wave structure and a resonant reflector

International Nuclear Information System (INIS)

Chen, Zaigao; Wang, Jianguo; Wang, Yue

2015-01-01

This letter optimizes synchronously 18 parameters of a relativistic backward wave oscillator with non-uniform slow wave structure (SWS) and a resonant reflector by using the parallel genetic algorithms and particle-in-cell simulation. The optimization results show that the generation efficiency of microwave from the electron beam has increased 32% compared to that of the original device. After optimization, the electromagnetic mode propagating in the resonant changes from the original TM 020 mode of reflector to higher-order TM 021 mode, which has a high reflection coefficient in a broader frequency range than that of the former. The modulation of current inside the optimized device is much deeper than that in the original one. The product of the electric field and current is defined. Observing this product, it is found that the interaction of the electron beam with the electromagnetic wave in the optimized device is much stronger than that in the original device, and at the rear part of SWS of the optimized device, the electron beam dominantly gives out the energy to the electromagnetic wave, leading to the higher generation efficiency of microwave than that of the original device

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

Science.gov (United States)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Relativistic quarkonium model with retardation effect, 1

International Nuclear Information System (INIS)

Ito, Hitoshi

1990-01-01

A new relativistic two-body equation is proposed which has the charge-conjugation symmetry. The renormalization of the wave function at the origin (WFO) is done by incorporating the corresponding vertex equation. By using this model, the heavy-quarkonium phenomenology is developed putting emphasis on the short-distance interaction. The typical scale of the distance restricting the applicability of the ladder model for the mass spectra is found to be 0.13 fm: By assuming the equivalent high-momentum cutoff for the gluonic correction, good results are obtained for the charmonium masses. The improved fine-splittings of the bb-bar states are obtained by inclusion of the retardation. Leptonic decay rates are predicted by assuming the renormalized WFO reduced by another high-momentum cutoff. (author)

The propagation of travelling waves for stochastic generalized KPP equations

International Nuclear Information System (INIS)

Elworthy, K.D.; Zhao, H.Z.

1993-09-01

We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs

Newton-Hooke spacetimes, Hpp-waves and the cosmological constant

International Nuclear Information System (INIS)

Gibbons, G W; Patricot, C E

2003-01-01

We show explicitly how the Newton-Hooke groups N ± 10 act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes M ± 4 and show how these may be obtained from a null reduction of five-dimensional homogeneous pp-wave Lorentzian spacetimes M ± 5 . This allows us to realize the Newton-Hooke groups and their Bargmann-type central extensions as subgroups of the isometry groups of M ± 5 . The extended Schroedinger-type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model

Current status of relativistic core collapse simulations

Energy Technology Data Exchange (ETDEWEB)

Font, Jose A [Departamento de Astronomia y Astrofisica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)

2007-05-15

With the first generation of ground-based gravitational wave laser interferometers already taking data, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (albeit for models with simplified input physics), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of Einstein's equations. In this paper, the current status of relativistic core collapse simulations is discussed, with the emphasis given to the modelling of the collapse dynamics and to the computation of the gravitational radiation in the existing numerical approaches. Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein's equations is reported, as well as extensions of this approximation (CFC+) and investigations within the framework of the so-called BSSN formulation of the 3+1 gravitational field equations (with no approximation for the spacetime dynamics). On the other hand, the incorporation of magnetic fields and the MHD equations in numerical codes to improve the realism of core collapse simulations in general relativity, is currently an emerging field where significant progress is bound to be soon achieved. The paper also contains a brief discussion of magneto-rotational simulations of core collapse, aiming at addressing the effects of magnetic fields on the collapse dynamics and on the gravitational waveforms.

Current status of relativistic core collapse simulations

International Nuclear Information System (INIS)

Font, Jose A

2007-01-01

With the first generation of ground-based gravitational wave laser interferometers already taking data, the availability of reliable waveform templates from astrophysical sources, which may help extract the signal from the anticipated noisy data, is urgently required. Gravitational stellar core collapse supernova has traditionally been considered among the most important astrophysical sources of potentially detectable gravitational radiation. Only very recently the first multidimensional simulations of relativistic rotational core collapse have been possible (albeit for models with simplified input physics), thanks to the use of conservative formulations of the hydrodynamics equations and advanced numerical methodology, as well as stable formulations of Einstein's equations. In this paper, the current status of relativistic core collapse simulations is discussed, with the emphasis given to the modelling of the collapse dynamics and to the computation of the gravitational radiation in the existing numerical approaches. Work employing the conformally-flat approximation (CFC) of the 3+1 Einstein's equations is reported, as well as extensions of this approximation (CFC+) and investigations within the framework of the so-called BSSN formulation of the 3+1 gravitational field equations (with no approximation for the spacetime dynamics). On the other hand, the incorporation of magnetic fields and the MHD equations in numerical codes to improve the realism of core collapse simulations in general relativity, is currently an emerging field where significant progress is bound to be soon achieved. The paper also contains a brief discussion of magneto-rotational simulations of core collapse, aiming at addressing the effects of magnetic fields on the collapse dynamics and on the gravitational waveforms

An optimization method of relativistic backward wave oscillator using particle simulation and genetic algorithms

Energy Technology Data Exchange (ETDEWEB)

Chen, Zaigao; Wang, Jianguo [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Wang, Yue; Qiao, Hailiang; Zhang, Dianhui [Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Guo, Weijie [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2013-11-15

Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.

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.

Solving the relativistic inverse scattering problem on the basis of n/d equations and application of the resulting solution to analysis of pion-nucleon interaction at low and intermediate energies

International Nuclear Information System (INIS)

Safronov, A.N.

2007-01-01

Full text: The pion-nucleon dynamics is one of the most fundamental problems in nuclear and particle physics. It is now widely believed that QCD is fundamental theory of strong interactions. On this basis all hadron-hadron interactions are completely determined by the underlying quark-gluon dynamics. However, due to the formidable mathematical problems raised by the non-perturbative character of QCD at low and intermediate energies, we are still far from a quantitative understanding hadron-hadron interactions from this point of view. Recently the relativistic approaches to constructing effective interaction operators between strongly interacting composite particles has been proposed on the basis of analytic S-matrix theory and methods for solving the inverse quantum scattering problem. The kernel of Marchenko equation in theory of inverse scattering problem can be expressed in terms of the discontinuity of the partial wave amplitude on dynamic cut in the complex s=k 2 plane, k being the relative momentum of colliding particles. The discontinuities of partial-wave amplitudes are determined by model-independent quantities (renormalized vertex constants and amplitudes of sub-processes involving on-mass-shell particles off physical region) and can be calculated by methods of relativistic quantum field theory within various dynamical approaches. In particular, effective field theory can be used to calculate the discontinuities across dynamical cuts closest to physical region. In present work a new manifestly Poincare-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. With the help of N/D-equations it was earlier shown that solution of a scattering problem in case of nonzero angular momentum does not exist for arbitrary discontinuity of partial-wave amplitude. The method is elaborated allowing to determine contributions of

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier

Energy Technology Data Exchange (ETDEWEB)

Wu, Y. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Science and Technology on High Power Microwave Laboratory, Mianyang 621900 (China); Xu, Z.; Li, Z. H. [Institute of Applied Electronics, China Academy of Engineering Physics, Mianyang 621900 (China); Tang, C. X. [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China)

2012-07-15

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier

Science.gov (United States)

Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.

2012-07-01

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

Energy Technology Data Exchange (ETDEWEB)

Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

1997-05-27

Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

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.

Nonlinear electrostatic wave equations for magnetized plasmas - II

DEFF Research Database (Denmark)

Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.

1985-01-01

For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....

On the convexity of relativistic hydrodynamics

International Nuclear Information System (INIS)

Ibáñez, José M; Martí, José M; Cordero-Carrión, Isabel; Miralles, Juan A

2013-01-01

The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 Relativistic Fluids and Magneto-Fluids (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla (note)

Relativistic fluid model of the resistive hose instability

International Nuclear Information System (INIS)

Siambis, J.G.

1992-01-01

A systematic analysis of the hose instability using the relativistic fluid formulation is reported. In its basic nature, the hose instability is a macroscopic, low-frequency instability, hence a fluid model should, in principle, give an accurate account of the hose instability. It has been found that for zeroth-order beam displacements, giving rise to rigid beam displacements, the fluid wave equation and resulting dispersion relation are identical to the spread-mass model and the energy-group model results. When first-order fluid displacements are included as well, giving rise to compressible, nonfrozen displacements in the axial direction and beam cross-section distortion in the radial direction, then there is obtained a wave equation similar, but not identical to the multicomponent model. The dispersion relation is solved for numerically. The hose instability growth rate is found to be similar to the multicomponent model result, over part of the beam frame, real hose frequency range

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB

Science.gov (United States)

Khazanov, G. V.; Gamayunov, K. V.

2007-01-01

We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.

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.

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)

Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

International Nuclear Information System (INIS)

Arum Sari, Resita; Suparmi, A; Cari, C

2016-01-01

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number n r causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. (paper)

A NUMERICAL SCHEME FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER EQUATION

Energy Technology Data Exchange (ETDEWEB)

Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)

2016-02-20

We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.

Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

International Nuclear Information System (INIS)

Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.

2009-01-01

A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.

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.

Conserving relativistic many-body approach: Equation of state, spectral function, and occupation probabilities of nuclear matter

International Nuclear Information System (INIS)

de Jong, F.; Malfliet, R.

1991-01-01

Starting from a relativistic Lagrangian we derive a ''conserving'' approximation for the description of nuclear matter. We show this to be a nontrivial extension over the relativistic Dirac-Brueckner scheme. The saturation point of the equation of state calculated agrees very well with the empirical saturation point. The conserving character of the approach is tested by means of the Hugenholtz--van Hove theorem. We find the theorem fulfilled very well around saturation. A new value for compression modulus is derived, K=310 MeV. Also we calculate the occupation probabilities at normal nuclear matter densities by means of the spectral function. The average depletion κ of the Fermi sea is found to be κ∼0.11

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)

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

Science.gov (United States)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

Some aspects of gravitational waves in an isotropic background universe

International Nuclear Information System (INIS)

Pandey, S.N.

1981-06-01

Gravitational waves are an inescapable consequence of the relativistic theory of gravitation. They are meaningfully comparable with electromagnetic waves. However, they are not conformally invariant. So, to investigate this property for gravitational waves, modified field equations are obtained of which the underlying Lagrangian is based on gravitation only. It gives, if helicity is preserved, amplitude modification, and the wave is represented by Bessel function of zero order. Some aspects of this theory are discussed with reference to gravitational waves only. (author)

Quasistationary model of high-current relativistic electron beam. 1. Exact solution of Poisson equations

International Nuclear Information System (INIS)

Brenner, S.E.; Gandyl', E.M.; Podkopaev, A.P.

1995-01-01

The dynamics of high-current relativistic electron beam moving trough the cylindrical drift space has been modelled by the large particles, the shape of which allows to solve the Poisson equations exactly, and in such a way to avoid the linearization being usually used in those problems. The expressions for the components of own electric field of electron beam passing through the cylindrical drift space have been obtained. (author). 11 refs., 1 fig

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.

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Directory of Open Access Journals (Sweden)

Claudio Cremaschini

2017-07-01

Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

International Nuclear Information System (INIS)

Greenspan, D.

2006-01-01

An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

Unified formulation of radiation conditions for the wave equation

DEFF Research Database (Denmark)

Krenk, Steen

2002-01-01

A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second......-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms...