High-temperature High-density Material, Particle Density, Energy Density And Chemical Potential Calculations

Computational mathematics is a branch of mathematics aiming to solve all kinds of mathematical problems with computer. It covers numerical methods, analysis and applications. As a basic tool, computational mathematics has been comprehensively employing in many research areas, especially, in Physics. The work described in this thesis is an application of the Gauss-Laguerre integration formulas (GLIF) and the Newton Iterative method (NIM) on system of nonlinear equations that belong to computational mathematics, to the High Energy Heavy Ion Collisions (HEHIC), a challengeable research field. Speaking particularly, particle density and energy density of statistic model are calculated by the improved GLF and NIM, and then the baryon chemical potential and strange chemical potential of the particle system in resonance state are further obtained. Using the two mathematics theory methods, it improves the computational precision and computational speed, and we obtain the good results.There are six chapters in the thesis: Chapter 1 presents in detail some basic concepts, research areas and applications of computational mathematics, and then introduces some background knowledges concerning HEHIC. Chapter 2 addresses physical problems on HEHIC and then introduces the physics model of researching the problems-quanta statistic model. Chapter 3 presents in detail what are the GLF method and the infinite series expansion method by which the particle density and the energy density are then calculated. Results of calculations of the two methods are also compared. In Chapter 4 after the net baryon density and the net strangeness density are given, chemical potentials of baryon and strange particle are reversely calculated by NIM. Then relation of chemical potentials is presented. Chapter 5 shows readers subsequent work that has not been finished yetin the current work. Chapter 6 is a summary chapter.HEHIC is a very challengeable research field to help human being to understand matter around us, universe and its evolution. And it is likewise a useful approach to conduct scientific research in Particle Physics and Nuclear Physics. Most of theoretical models that are currently used in HEHIC cannot provide precise results, however, we obtain better approximation results by introducing methods of computational mathematics. So the work is helpful for such problems.