Calculation of the Structure Properties of Asymmetrical Nuclear Matter

In this paper the structure properties of asymmetrical nuclear matter has been calculated employing AV18 potential for different values of proton to neutron ratio. These calculations have been also made for the case of symmetrical nuclear matter with UV14, AV14 and AV18 potentials. In our calculations, we use the lowest order constrained variational (LOCV) method to compute the correlation function of the system.Comment: 23 pages, 6 figures, 1 table Research in Astronomy and Astrophysics (2011) accepte

Folding model analysis of 12C−12C ^{12}C- ^{12}C and 16O−16O ^{16}O- ^{16}O elastic scattering using the density-dependent LOCV averaged effective interaction

The averaged effective two-body interaction (\textit{AEI}) which can be generated through the lowest order constrained variational (\textit{LOCV}) method for symmetric nuclear matter (\textit{SNM}) with the input \textit{Reid}68 nucleon-nucleon potential, is used as the effective nucleon-nucleon potential in the folding model to describe the heavy-ion (\textit{HI}) elastic scattering cross sections. The elastic scattering cross sections of $^{12}C-^{12}C$ and $^{16}O-^{16}O$ systems are calculated in the above frameworks. The results are compared with the corresponding calculations coming from the fitting procedures with the input finite range \textit{DDM3Y1-Reid} potential and the available experimental data at different incident energies. It is shown that a reasonable description of the elastic $^{12}C-^{12}C$ and $^{16}O-^{16}O$ scattering data at the low and the medium energies can be obtained by using the above \textit{ LOCV AEI}, without any need to define a parameterize density dependent function in the effective nucleon-nucleon potential, which is formally considered in the typical \textit{DDM3Y1-Reid} interactions

The thermodynamic properties of weakly interacting quark gluon plasma via the one gluon exchange interaction

The thermodynamic properties of the quark gluon plasma($QGP$) as well as its phase diagram are calculated as a function of baryon density (chemical potential) and temperature. The $QGP$ is assumed to be composed of the light quarks only, i.e. the up and the down quarks, which interact weakly and the gluons which are treated as they are free. The interaction between quarks is considered in the framework of the one gluon exchange model which is obtained from the Fermi liquid picture. The bag model is used, with fixed bag pressure (${\cal B}$) for the nonperturbative part and the quantum chromodynamics ($QCD$) coupling is assumed to be constant i.e. no dependence on the temperature or the baryon density. The effect of weakly interacting quarks on the $QGP$ phase diagram are shown and discussed. It is demonstrated that the one gluon exchange interaction for the massless quarks has considerable effect on the $QGP$ phase diagram and it causes the system to reach to the confined phase at the smaller baryon densities and temperatures. The pressure of excluded volume hadron gas model is also used to find the transition phase-diagram. Our results depend on the values of bag pressure and the $QCD$ coupling constant which the latter does not have a dramatic effect on our calculations . Finally, we compare our results with the thermodynamic properties of strange quark matter and the lattice $QCD$ prediction for the $QGP$ transition critical temperature.Comment: 15 pages, 8 figure

LOCV calculation for Beta-stable matter at finite temperature

The method of lowest-order constrained variational, which predicts reasonably the nuclear matter semi-empirical data is used to calculate the equation of state of beta-stable matter at finite temperature. The Reid soft-core with and without the N-$\Delta$ interactions which fits the N-N scattering data as well as the $UV_{14}$ potential plus the three-nucleon interaction are considered in the nuclear many-body Hamiltonian. The electron and muon are treated relativistically in the total Hamiltonian at given temperature, to make the fluid electrically neutral and stable against beta decay. The calculation is performed for a wide range of baryon density and temperature which are of interest in the astrophysics. The free energy, entropy, proton abundance, etc. of nuclear beta-stable matter are calculated. It is shown that by increasing the temperature, the maximum proton abundance is pushed to the lower density while the maximum itself increases as we increase the temperature. The proton fraction is not enough to see any gas-liquid phase transition. Finally we get an overall agreement with other many-body techniques, which are available only at zero temperature.Comment: LaTex, 20 page

Implementation of Symmetric Rank-One Methods for Unconstrained Optimization

The focus of this thesis is on analyzing the theoretical and computational aspects of some quasi-Newton (QN) methods for locating a minimum of a real valued function f over all vectors x 2 Rn. In many practical applications, the Hessian of the objective function may be too expensive to calculate or may even be unavailable in the explicit form. QN methods endeavor to circumvent the deciencies of Newtons method (while retaining the basic structure and thus preserving, as far as possible, its advantages) by constructing approximations for the Hessian iteratively. Among QN updates, symmetric rank-one (SR1) update has been shown to be an e®ective and reliable method of such algorithms. However, SR1 is an awkward method, even though its performance is in general better than well known QN updates. The problem is that the SR1 update may not retain positive deniteness and may become undened because the denominator becomes zero. In recent years considerable attention has been directed towards preserving and ensuring the positive deniteness of SR1 update, but improving the quality of the estimates has rarely been studied in depth. Our purpose in this thesis is to improve the Hessian approximation updates and study the computational performance and convergence property of this update. First, we brie°y give some mathematical background. A review of di®erent minimization methods that can be used to solve unconstrained optimization problems is also given. We consider a modification of secant equation for the SR1 update. In this method, the Hessian approximation is updated based on modifed secant equation, which uses both gradient and function value information in order to get a higher-order accuracy in approximating the second curvature of the objec- tive function. We then examine a new scaled memoryless SR1 method based on modied secant equation for solving large-scale unconstrained optimization problems. We prove that the new method possesses global convergence. The rate of convergence of such algorithms are also discussed. Due to the presence of SR1 deciencies, we introduce a restarting procedure using eigenvalue of the SR1 update. We also introduce a variety of techniques to improve Hessian approximations of the SR1 method for small to large-sized problems, including multi-step, extra updating methods along with the structured method which uses partial information on Hessian. Variants of SR1 update are tested numerically and compared to several other famous minimization methods. Finally, we comment on some achievement in our research. Possible extensions are also given to conclude this thesis