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Jones, T.W.,Kang, Hyesung Elsevier 2005 Astroparticle physics Vol.24 No.1
<P><B>Abstract</B></P><P>We have developed a new, very efficient numerical scheme to solve the CR diffusion–convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The efficiency of the scheme derives from its use of coarse-grained finite momentum volumes. This approach has enabled us, using ∼10–20 momentum bins spanning nine orders of magnitude in momentum, to carry out simulations that agree well with results from simulations of modified shocks carried out with our conventional finite difference scheme requiring more than an order of magnitude more momentum points. The coarse-grained, CGMV scheme reduces execution times by a factor approximately half the ratio of momentum bins used in the two methods. Depending on the momentum dependence of the diffusion, additional economies in required spatial and time resolution can be utilized in the CGMV scheme, as well. These allow a computational speed-up of at least an order of magnitude in some cases.</P>
Numerical Simulation of Cosmic-Ray Acceleration
JONES T. W. The Korean Astronomical Society 2001 Journal of The Korean Astronomical Society Vol.34 No.4
Cosmic-ray acceleration, although physically important in many astrophysical contexts, is difficult to incorporate into numerical models,. because it involves microphysics that is generally far from thermodynamic equilibrium, and also because the length and time scales for that physics typically range over many orders of magnitude, reflecting the huge range of particle rigidities that must be represented. The most common accelerator models are stochastic in nature and involve nonequilibrium plasma properties that are also often poorly understood. Still, nature clearly finds a way to produce simple, robust and almost scale-free energy distributions for the cosmic-rays. Their importance has inspired a number of approaches to examining the production and transport of cosmic-ray particles in numerical simulations. I offer here a brief comparison of some of the methods that have been introduced.
The Development of the European Union : Lessons for Northeast Asia?
Jones, Robert A. Center for the Reconstruction of Human Socity, Kyu 2001 OUGHTOPIA Vol.16 No.1
[T]he focus of this paper is upon regional integration, with particular reference to the European Union and Northeast Asia. The central question it seeks to answer is whether a study of the development of the European Union(EU) holds lessons in integration for the Northeast Asian region. The search for the answer to this question leads to an examination of further questions, relating for example to the value of the EU as potential model for regional integration projucts; the problem of defining 'regional integration'; the nature of the EU; and the principal differences between the European Union and Northeast Asia with regard to regional integration. It also outlines and examines some specific potential lessons of the EU's development for other regions, in particular for Northeast Asia.