Equations Of Relativistic Dynamics Research Articles

Robust particle methods for relativistic hydrodynamics

In this paper we describe how the equations of relativistic fluid dynamics can be solved numerically using the particle method SPH.

A canonical form for relativistic dynamic equation

In this paper, an elementary proof of representation for Clifford AlgebraCl(3, 0) and some of its applications are given.

Microscopic models for hadronic form factors and vertex functions

We review the status of nucleon (N) and few-nucleon form factors (f.f.'s) from the view-point of a gradual unfolding of successively inner degrees of freedom (d.o.f.) with increase inq 2. To this end we focus attention on the problem of a microscopic formulation of hadronic vertex functions (v.f.) from the point of view of their key role in understanding the physics of a large variety of few-hadron reactions on the one hand, and their practical usefulness in articulating the internal dynamics of hadron and few-hadron systems on the other hand. The criterion of an integrated view from low-energy spectroscopy to high-q 2 amplitudes is employed to emphasize the desirability of formulations in terms of relativistic dynamical equations based on Lorentz and gauge invariance in preference to phenomenological models, which often require additional assumptions beyond their original premises to extend their applicability domains. In this respect, the practical possibilities of the Bethe-Salpeter equation (BSE) in articulating the necessary dynamical ingredients are emphasized on a two-tier basis, the basic constant (3) being pre-determined from the mass spectral data (1st stage) in preparation for the construction of the hadron-quark vertex functions (2nd stage). An explicit construction is outlined for meson-quark and baryon-quark vertex functions as well as of meson-nucleon vertex functions in a stepwise fashion. The role of the latter as basic parameter-free ingredients is discussed for possible use in the more serious treatments in the current literature of quark-meson level (α) and meson-isobar (β) d.o.f. in 2-N and 3-N form factor studies. Since most of these studies are characterized by the use of RGM techniques at the six-quark level, a comparative discussion is also given of several contemporary RGM based models. Finally, the concrete prospects for employing such hardon-quark vertex functions for evaluating pp annihilation amplitudes are briefly indicated, keeping in view the LEAR programme for their studies.

Steady relativistic fluid jets

A numerical simulation is presented of a relativistic jet. Owing to the similar mathematical form of the equations of steady relativistic gas dynamics and steady non-relativistic gas dynamics, the numerical method used to make this calculation can be used to model either type of jet flow. On the basis of simplifying assumptions, the synchrotron emission from the jet is estimated for different viewing angles between it and an observer’s line-of-sight.

Phenomenological formulation of direct interparticle interaction in relativistic theory of gravitation

The general equations of relativistic dynamics of point masses in the post-Newtonian approximation and in the approximation of ultrarelativistic velocities are considered. The consequences of the weak principle of equivalence and its relation with the hypothesis of geodesics is studied. It is shown that, in the above approximations, the equations of motion reduce to the equations of Riemann geodesics.

Relativistic fluid dynamics as a Hamiltonian system

The equations of ideal relativistic fluid dynamics in the laboratory frame form a noncanonical hamiltonian system with the same Poisson bracket as for nonrelativistic fluids, but with dynamical variables and hamiltonian obtained via a regular deformation of their nonrelativistic counterparts.

Relativistic Prandtl- Meyer flow

The exact solution of the equations of relativistic gas dynamics describing plane steady-state flow, depending only on the angular variable, is investigated. The well-known Prandtl-Meyer solution is obtained in the non-relativisitic limit.

Sine-Gordon solitons: Particles obeying relativistic dynamics

We define a dynamical variable associated with the position of a particle representing the sine-Gordon soliton. Simple relativistic dynamic equations for this particle under the influence of forces are derived, including the case of dissipation. The fluctuation-dissipation theorem for this particle is obtained as well as some results on steady-state velocities and slowing of the thermalization time for ultrarelativistic solitions.

Perfect fluids in general relativity

The equations of relativistic fluid dynamics can be completed in several different ways. We discuss and compare three distinct methods for completing these equations. We also discuss variational principles for the different fluid theories.

Effect of a density isomer on high-energy heavy-ion collisions

On the basis of conventional nuclear fluid dynamics, we study the sensitivity of high-energy heavy-ion collisions to a density isomer in the nuclear equation of state, as well as to a variation in the nuclear compressibility coefficient. Our equation of state is a new functional form which has the property that the speed of sound approaches the speed of light in the limit of infinite compression. The equations of relativistic nuclear fluid dynamics are solved numerically in three spatial dimensions by use of a particle-in-cell finite-difference computing method for the reaction $^{20}\mathrm{Ne}$ + $^{238}\mathrm{U}$ at a laboratory bombarding energy per nucleon of 393 MeV. By integrating over the appropriate ranges of impact parameter, we compute the double-differential cross section $\frac{{d}^{2}\ensuremath{\sigma}}{\mathrm{dEd}\ensuremath{\Omega}}$ corresponding both to all impact parameters and to central collisions constituting 15% of the total cross section. To within numerical uncertainties, the results for the various equations of state are very similar to one another except for central collisions at laboratory angle $\ensuremath{\theta}=30\ifmmode^\circ\else\textdegree\fi{}$ and for both central collisions and all impact parameters at $\ensuremath{\theta}=150\ifmmode^\circ\else\textdegree\fi{}$. In these cases, over certain ranges of energy, $\frac{{d}^{2}\ensuremath{\sigma}}{\mathrm{dEd}\ensuremath{\Omega}}$ is larger for the density isomer than for conventional equations of state. The results calculated for all impact parameters are compared with the experimental data of Sandoval et al. for outgoing charged particles.NUCLEAR REACTIONS $^{20}\mathrm{Ne}$ + $^{238}\mathrm{U}$, $\frac{{E}_{\mathrm{bom}}}{20}=393$ MeV; calculated $\frac{{d}^{2}\ensuremath{\sigma}}{\mathrm{dEd}\ensuremath{\Omega}}$ for outgoing charged particles for all impact parameters and for central collisions. High-energy heavy-ion collisions, relativistic nuclear fluid dynamics, nuclear equation of state, density isomer, particle-in-cell finite-difference computing method.

On an exact solution of the equations of relativistic gas dynamics

A particular solution of the equations of relativistic gas dynamics is obtained for one-dimensional adiabatic motions with plane symmetry. The solution is then used to construct an exact discontinuous solution describing a nonsteady motion of gas in the presence of shock waves.

Electromagnetic-plane-wave approach of relativistic particle dynamics

Solely on the basis of the theory of electrodynamics, the basic equations of relativistic particle dynamics are derived, independent of the theory of special relativity, by considering the dynamics of an electron accelerated by an electromagnetic plane wave. The proper time is also shown to be equivalent to the retarded time of the electron with respect to the plane wave.