An extended class of minimax generalized Bayes estimators of regression coefficients

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman (2005) to include non-monotone shrinkage functions

Relativistic Effects in Simulations of the Fragmentation Process with the Microscopic Framework

We simulate the fragmentation processes in the \CaCa collisions at the bombarding energy 1.05 GeV/u using the Lorentz covariant RQMD and the non-covariant QMD approaches, incorporated with the statistical decay model. By comparing the results of RQMD with those of QMD, we examine the relativistic effects and find that the multiplicity of the $\alpha$ particle after the statistical decay process is sensitive to the relativistic effects. It is shown that the Lorentz covariant approach is necessary to analyze the fragmentation process even at the energy around \Elab = 1 GeV/u as long as we are concerned with the final observables of the mass distribution, particularly, the light fragments around $A = 3 \sim 4$.Comment: 8pages, Latex is used, 3 Postscript figures are available by request from [email protected]

Liquid-gas mixed phase in nuclear matter at finite temperature

We explore the geometrical structure of Liquid-gas (LG) mixed phase which is relevant to nuclear matter in the crust region of compact stars or supernovae. To get the equation of state (EOS) of the system, the Maxwell construction is found to be applicable to symmetric nuclear matter, where protons and neutrons behave simultaneously. For asymmetric nuclear matter, on the other hand, the phase equilibrium can be obtained by fully solving the Gibbs conditions since the components in the L and G phases are completely different. We also discuss the effects of surface and the Coulomb interaction on the mixed phase.Comment: Contributed talk at the INPC 2010 at Vancouve

On the IMF Multiplicity in Au+Au Reactions

Intermediate mass fragment (IMF) multiplicity has been investigated for Au+Au reactions at incident energies of 100, 250 and 400 MeV/A. From the analysis of the impact-parameter-dependence of the IMF multiplicity using our QMD plus statistical evaporation model, we found that 1) statistical decay process modifies the results greatly, and 2) the Fermi motion plays a role to increase the IMF multiplicity for whole impact-parameter range.Comment: 9pages, Latex is used, 2 Postscript figures are available by request from [email protected]

Internal bores and gravity currents in a two-fluid system

In this paper, a unified theory of internal bores and gravity currents is presented within the framework of the one-dimensional two-layer shallow-water equations. The equations represent four basic physical laws: the theory is developed on the basis of these laws. Though the first three of the four basic laws are apparent, the forth basic law has been uncertain. This paper shows first that this forth basic law can be deduced from the law which is called in this paper the conservation law of circulation. It is then demonstrated that, within the framework of the equations, an internal bore is represented by a shock satisfying the shock conditions that follow from the four basic laws. A gravity current can also be treated within the framework of the equations if the front conditions, i.e. the boundary conditions to be imposed at the front of the current, are known. Basically, the front conditions for a gravity current also follow from the four basic laws. When the gravity current is advancing along a no-slip boundary, however, it is necessary to take into account the influence of the thin boundary layer formed on the boundary; this paper describes how this influence can be evaluated. It is verified that the theory can satisfactorily explain the behaviour of internal bores advancing into two stationary layers of fluid. The theory also provides a formula for the rate of advance of a gravity current along a no-slip lower boundary; this formula proves to be consistent with some empirical formulae. In addition, some well-known theoretical formulae on gravity currents turn out to be obtainable on the basis of the theory.Comment: 47 pages, 5 figure