Analysis Of Thermodynamical Properties Of Asymmetric Nuclear Matter, Structure Of Neutron Stars And Montecarlo Algorithms

This thesis consists of two parts. The first part is the nuclear physics part, which mainlyintroduces the effects of isospin and momentum dependent interactions on thermodynamicalproperties of nuclear matter, the transition density ofβ-equilibrium matter and the structureof neutron stars. The second part is about Montecarlo simulation, which focuses on analysisand applications of Wang-Landau and multicanonical Montecarlo algorithm.In the first part, thermodynamical properties of asymmetric nuclear matter are studiedwithin a self-consistent thermal model using an isospin and momentum dependent interac-tion (MDI) constrained by the isospin diffusion data in heavy-ion collisions, a momentum-independent interaction (MID), and an isoscalar momentum-dependent interaction (eMDYI).In particular, we study the temperature dependence of the isospin-dependent bulk and single-particle properties, the mechanical and chemical instabilities, and liquid-gas phase transitionin hot asymmetric nuclear matter. Our results indicate that the temperature dependence ofthe equation of state and the symmetry energy are not so sensitive to the momentum de-pendence of the interaction. The symmetry energy at fixed density is found to generallydecrease with increasing temperature and for the MDI interaction the decrement is essen-tially due to the potential part. It is further shown that only the low momentum part of thesingle-particle potential and the nucleon effective mass increases significantly with tempera-ture for the momentum-dependent interactions. For the MDI interaction, the low momentumpart of the symmetry potential is significantly reduced with increasing temperature. Forthe mechanical and chemical instabilities as well as the liquid-gas phase transition in hotasymmetric nuclear matter, our results indicate that the boundary of these instabilities andthe phase-coexistence region generally shrink with increasing temperature and is sensitiveto the density dependence of the symmetry energy and the isospin and momentum depen-dence of the nuclear interaction. We analyze the isospin-fractionation, the detailed processof the liquid-gas phase transition and the order of the phase transition under fixed pressureby Maxwell construction. Except for the instability of common nuclear matter, we study the instability and transition density ofβ-equilibrium nuclear matter by dynamical methodand thermodynamical method. We find that the stiffer the symmetry energy is, the lower thetransition density will be. We point out that the dynamical method gives nearly the sameresults as the thermodynamical method if the surface term and Coulomb term are neglected,while large error comes from the parabolic approximation, and the error increases with theincreasing stiffness of the symmetry energy. We analyze the static properties of neutron starby using the results of transition density, such as the mass-radius relation, the moment ofinertia and the properties of the crust. The effects of parabolic approximation are shown, andthe validity of some formulas are checked. With the constraint of the symmetry energy fromthe isospin diffusion data, the transition density, the transition pressure and the mass-radiusrelation are also constrained.In the second part, we have done detailed analysis of multicanonical and Wang-Landaualgorithm. We have compared the advantages and disadvantages of the two algorithms, andmainly focused on the convergence ability and precision. We combined the two algorithmsand developed an efficient one which has the advantages of the two but avoids their disad-vantages. In this paper we take 32×32 Ising model of square lattice as an example, as itsdensity of states is analytically known. Furthermore, by using Wang-Landau algorithm com-bined with analytic method, the density of states of two dimensional XY model on squarelattices of sizes 16×16, 24×24 and 32×32 is accurately calculated. Thermodynamic quan-tities, such as internal energy, free energy, entropy and specific heat are obtained from theresulted density of states by numerical integration. It is found that both the density of statesand the extensive thermodynamic quantities obey the scaling law. From the entropy curvesymptoms of phase transition are observed. A general method of calculation of the densityof states of continuous models by simulation combined with analytical method is proposed.