A generalized structure of Bell inequalities for bipartite arbitrary dimensional systems

We propose a generalized structure of Bell inequalities for arbitrary d-dimensional bipartite systems, which includes the existing two types of Bell inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)]. We analyze Bell inequalities in terms of correlation functions and joint probabilities, and show that the coefficients of correlation functions and those of joint probabilities are in Fourier transform relations. We finally show that the coefficients in the generalized structure determine the characteristics of quantum violation and tightness.Comment: 6 pages, 1 figur

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\bar\sigma$ of the fundamental $r$-mode is in a good approximation given by $\bar\sigma\approx \kappa_0 \Omega$, where $\bar\sigma$ is defined in the corotating frame at the spatial infinity, and $\Omega$ is the angular frequency of rotation of the star. The proportional coefficient $\kappa_0$ is only weakly dependent on $\Omega$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $\Omega$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.Comment: 22 pages, 8 figures, accepted for publication in Ap

Liquid-Gas Phase Transition in Nuclear Equation of State

A canonical ensemble model is used to describe a caloric curve of nuclear liquid-gas phase transition. Allowing a discontinuity in the freeze out density from one spinodal density to another for a given initial temperature, the nuclear liquid-gas phase transition can be described as first order. Averaging over various freeze out densities of all the possible initial temperatures for a given total reaction energy, the first order characteristics of liquid-gas phase transition is smeared out to a smooth transition. Two experiments, one at low beam energy and one at high beam energy show different caloric behaviors and are discussed.Comment: 12 pages in Revtex including two Postscript figure

Nuclear Incompressibility at Finite Temperature and Entropy

Features of the nuclear isothermal incompressibility $\kappa$ and adiabatic incompressibility $\kappa_Q$ are investigated. The calculations are done at zero and finite temperatures and non zero entropy and for several equations of state. It is shown that $\kappa_Q$ decreases with increasing entropy while the isothermal $\kappa$ increases with increasing $T$. A duality is found between the adiabatic $\kappa_Q$ and the T=0 isothermal $\kappa$. Our isothermal results are compared with a recent lattice Monte Carlo calculation done at finite $T$. The necessity of including correlations is shown if $\kappa$ is to have a peak with increasing $T$ as seen in the Monte Carlo calculations. A peak in $\kappa$ is linked to attractive scattering correlations in two nucleons channel in the virial expansion in our approach which are Pauli blocked at low $T$.Comment: 5 page

Characterization of the residual stresses in spray-formed steels using neutron diffraction

Neutron diffraction was used to characterize the residual stresses in an as-sprayed tube-shaped steel preform. The measured residual stress distributions were compared with those simulated using finite element method by taking into account the effects of the thermal history, porosity and different phases of the sprayed preform. The porosity was measured using X-ray microcomputed tomography. The study revealed for the first time the correlation between the distribution of porosity and residual stress developed in the as-sprayed preform