20 research outputs found
Cross section of the processes , , , in the energy region 200 MeV 3 GeV
The cross section for different processes induced by annihilation,
in the kinematical limit
, is
calculated taking into account first order corrections to the amplitudes and
the corrections due to soft emitted photons, with energy in the center of mass of the colliding beams. The results
are given separately for charge--odd and charge--even terms in the final
channels and . In case of pions, form
factors are taken into account. The differential cross sections for the
processes: , , have been calculated and the
corresponding formula are given in the ultrarelativistic limit . For a quantitative evaluation of the
contribution of higher order of the perturbation theory, the production of
, including radiative corrections, is calculated in the approach of
the lepton structure functions. This allows to estimate the precision of the
obtained results as better than 0.5% outside the energy region corresponding to
narrow resonances. A method to integrate the cross section, avoiding the
difficulties which arise from singularities is also described.Comment: 25 pages 3 firgur
Finite difference schemes for the symmetric Keyfitz-Kranzer system
We are concerned with the convergence of numerical schemes for the initial
value problem associated to the Keyfitz-Kranzer system of equations. This
system is a toy model for several important models such as in elasticity
theory, magnetohydrodynamics, and enhanced oil recovery. In this paper we prove
the convergence of three difference schemes. Two of these schemes is shown to
converge to the unique entropy solution. Finally, the convergence is
illustrated by several examples.Comment: 31 page
A theory of -dissipative solvers for scalar conservation laws with discontinuous flux
We propose a general framework for the study of contractive semigroups
of solutions to conservation laws with discontinuous flux. Developing the ideas
of a number of preceding works we claim that the whole admissibility issue is
reduced to the selection of a family of "elementary solutions", which are
certain piecewise constant stationary weak solutions. We refer to such a family
as a "germ". It is well known that (CL) admits many different contractive
semigroups, some of which reflects different physical applications. We revisit
a number of the existing admissibility (or entropy) conditions and identify the
germs that underly these conditions. We devote specific attention to the
anishing viscosity" germ, which is a way to express the "-condition" of
Diehl. For any given germ, we formulate "germ-based" admissibility conditions
in the form of a trace condition on the flux discontinuity line (in the
spirit of Vol'pert) and in the form of a family of global entropy inequalities
(following Kruzhkov and Carrillo). We characterize those germs that lead to the
-contraction property for the associated admissible solutions. Our
approach offers a streamlined and unifying perspective on many of the known
entropy conditions, making it possible to recover earlier uniqueness results
under weaker conditions than before, and to provide new results for other less
studied problems. Several strategies for proving the existence of admissible
solutions are discussed, and existence results are given for fluxes satisfying
some additional conditions. These are based on convergence results either for
the vanishing viscosity method (with standard viscosity or with specific
viscosities "adapted" to the choice of a germ), or for specific germ-adapted
finite volume schemes
Incompatible element-enriched mantle lithosphere beneath kimberlitic pipes in Priazovie, Ukrainian shield: volatile-enriched focused melt flow and connection to mature crust?
The physico-mechanical properties of cellulose nitrates with various degrees of substitution and orientation
A regularizing property of the -eikonal equation
14 pages, 3 figuresInternational audienceWe prove that any -dimensional solution of the eikonal equation has locally Lipschitz gradient except at a locally finite number of vortices