Search results for "hypothesis"
showing 10 items of 426 documents
On Riemann’s Ideas on Space and Schwinger’s Treatment of Low-Energy Pion-Nucleon Physics
2020
We begin with a demonstration of how great an influence Riemann’s habilitation essay had on the development of field theory. His ideas about the origin of physical space and the importance of a metric field were clearly outlined as early as 1854, and praised highly by the old C.F. Gauss, who died 1 year later. There is but one formula in Riemann’s article. This formula and its relevance will be explained at the beginning of the present chapter. The basic principle which is omnipresent in Riemann’s entire work is to understand the physical behavior of nature from its smallness. Hence partial differential equations stand at the beginning of any field theory. In our case, it is not the metric …
Numerical 3+1 general relativistic magnetohydrodynamics: a local characteristic approach
2005
We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e. Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jac…
Cosmic censorship conjecture in some matching spherical collapsing metrics
2017
A physically plausible Lema{\^{\i}}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that its {\em intrinsic} energy is, as due, stationary and finite. It is proved for this Lema{\^{\i}}tre-Tolman-Bondi collapse, for some parameter values, that its intrinsic central singularity is globally naked, thus violating the cosmic censorship conjecture with, for each direction, one photon, or perhaps a pencil of photons, leaving the singularity and reaching the null infinity. Our result is discussed in relation to some other cases in the current liter…
An introduction to relativistic hydrodynamics
2007
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, partic…
Precise determination of resonance pole parameters through Pad\'e approximants
2014
In this work, we present a precise and model--independent method to extract resonance pole parameters from phase-shift scattering data. These parameters are defined from the associated poles in the second Riemann sheet, unfolded by the analytic continuation to the complex pole using Pad\'e approximants. Precise theoretical parameterizations of pion-pion scattering phase shifts based on once-- and twice-- subtracted dispersion relations are used as input, whose functional form allows us to show the benefit and accuracy of the method. In particular, we extract from these parametrization the pole positions of the $f_0(500)$ at $\sqrt{s}=(453\pm 15) - i(297 \pm 15)$ MeV, the $\rho(770)$ at $\sq…
Numerical Hydrodynamics in General Relativity
2003
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through lineariz…
Surface effects on phase transitions of modulated phases and at Lifshitz points: A mean field theory of the ANNNI model
1999
The semi-infinite axial next nearest neighbor Ising (ANNNI) model in the disordered phase is treated within the molecular field approximation, as a prototype case for surface effects in systems undergoing transitions to both ferromagnetic and modulated phases. As a first step, a discrete set of layerwise mean field equations for the local order parameter mn in the nth layer parallel to the free surface is derived and solved, allowing for a surface field H1 and for interactions JS in the surface plane which differ from the interactions J0 in the bulk, while only in the z-direction perpendicular to the surface competing nearest neighbor ferromagnetic exchange (J1) and next nearest neighbor an…
Type D vacuum solutions: a new intrinsic approach
2013
We present a new approach to the intrinsic properties of the type D vacuum solutions based on the invariant symmetries that these spacetimes admit. By using tensorial formalism and without explicitly integrating the field equations, we offer a new proof that the upper bound of covariant derivatives of the Riemann tensor required for a Cartan-Karlhede classification is two. Moreover we show that, except for the Ehlers-Kundt's C-metrics, the Riemann derivatives depend on the first order ones, and for the C-metrics they depend on the first order derivatives and on a second order constant invariant. In our analysis the existence of an invariant complex Killing vector plays a central role. It al…
Scattering on Riemannian Symmetric Spaces and Huygens Principle
2018
International audience; The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.
Dynamics of surface enrichment: A theory based on the Kawasaki spin-exchange model in the presence of a wall
1991
A mean-field theory is developed for the description of the dynamics of surface enrichment in binary mixtures, where one component is favored by an impenetrable wall. Assuming a direct exchange (Kawasaki-type) model of interdiffusion, a layerwise molecular-field approximation is formulated in the framework of a lattice model. Also the corresponding continuum theory is considered, paying particular attention to the proper derivation of boundary conditions for the differential equation at the hard wall. As an application, we consider the explicit solutions of the derived equations in the case where nonlinear effects can be neglected, studying the approach of an initially flat (homogeneous) co…