Incompressibility in finite nuclei and nuclear matter

The incompressibility (compression modulus) $K_{\rm 0}$ of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions. We present a comprehensive re-analysis of recent data on GMR energies in even-even $^{\rm 112-124}$Sn and $^{\rm 106,100-116}$Cd and earlier data on 58 $\le$ A $\le$ 208 nuclei. The incompressibility of finite nuclei $K_{\rm A}$ is expressed as a leptodermous expansion with volume, surface, isospin and Coulomb coefficients $K_{\rm vol}$, $K_{\rm surf}$, $K_\tau$ and $K_{\rm coul}$. \textit{Assuming} that the volume coefficient $K_{\rm vol}$ is identified with $K_{\rm 0}$, the $K_{\rm coul}$ = -(5.2 $\pm$ 0.7) MeV and the contribution from the curvature term K$_{\rm curv}$A$^{\rm -2/3}$ in the expansion is neglected, compelling evidence is found for $K_{\rm 0}$ to be in the range 250 $< K_{\rm 0} <$ 315 MeV, the ratio of the surface and volume coefficients $c = K_{\rm surf}/K_{\rm vol}$ to be between -2.4 and -1.6 and $K_{\rm \tau}$ between -840 and -350 MeV. We show that the generally accepted value of $K_{\rm 0}$ = (240 $\pm$ 20) MeV can be obtained from the fits provided $c \sim$ -1, as predicted by the majority of mean-field models. However, the fits are significantly improved if $c$ is allowed to vary, leading to a range of $K_{\rm 0}$, extended to higher values. A self-consistent simple (toy) model has been developed, which shows that the density dependence of the surface diffuseness of a vibrating nucleus plays a major role in determination of the ratio K$_{\rm surf}/K_{\rm vol}$ and yields predictions consistent with our findings.Comment: 26 pages, 13 figures; corrected minor typos in line with the proof in Phys. Rev.

High density matter

The microscopic composition and properties of matter at super-saturation densities have been the subject of intense investigation for decades. The scarcity of experimental and observational data has lead to the necessary reliance on theoretical models. However, there remains great uncertainty in these models, which, of necessity, have to go beyond the over-simple assumption that high density matter consists only of nucleons and leptons. Heavy strange baryons, mesons and quark matter in different forms and phases have to be included to fulfil basic requirements of fundamental laws of physics. In this review the latest developments in construction of the Equation of State (EoS) of high-density matter at zero and finite temperature assuming different composition of the matter are surveyed. Critical comparison of model EoS with available observational data on neutron stars, including gravitational masses, radii and cooling patterns is presented. The effect of changing rotational frequency on the composition of neutron stars during their lifetime is demonstrated. Compatibility of EoS of high-density, low temperature compact objects and low density, high temperature matter created in heavy-ion collisions is discussed.Comment: 10 pages, 6 figures, Invited talk at Nuclei in Cosmos 2012, accepted for publication on PoS. arXiv admin note: text overlap with arXiv:1201.0950 by other author

Selected recollections of my relationship with Leo Breiman

During the period 1962--1964, I had a tenure track Assistant Professorship in Mathematics at Cornell University in Ithaca, New York, where I did research in probability theory, especially on linear diffusion processes. Being somewhat lonely there and not liking the cold winter weather, I decided around the beginning of 1964 to try to get a job in the Mathematics Department at UCLA, in the city in which I was born and raised. At that time, Leo Breiman was an Associate Professor in that department. Presumably, he liked my research on linear diffusion processes and other research as well, since the department offered me a tenure track Assistant Professorship, which I happily accepted. During the Summer of 1965, I worked on various projects with Sidney Port, then at RAND Corporation, especially on random walks and related material. I was promoted to Associate Professor, effective in Fall, 1966, presumably thanks in part to Leo. Early in 1966, I~was surprised to be asked by Leo to participate in a department meeting called to discuss the possible hiring of Sidney. The conclusion was that Sidney was hired as Associate Professor in the department, as of Fall, 1966. Leo communicated to me his view that he thought that Sidney and I worked well together, which is why he had urged the department to hire Sidney. Anyhow, Sidney and I had a very fruitful and enjoyable collaboration in probability and, to a much lesser extent, in theoretical statistics, for a number of years thereafter.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS431 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Vertical Structure of Gas Pressure-Dominated Accretion Disks with Local Dissipation of Turbulence and Radiative Transport

(shortened) We calculate the vertical structure of a local patch of an accretion disk in which heating by dissipation of MRI-driven MHD turbulence is balanced by radiative cooling. Heating, radiative transport, and cooling are computed self-consistently with the structure by solving the equations of radiation MHD in the shearing-box approximation. Using a fully 3-d and energy-conserving code, we compute the structure of this disk segment over a span of more than five cooling times. After a brief relaxation period, a statistically steady-state develops. Measuring height above the midplane in units of the scale-height H predicted by a Shakura-Sunyaev model, we find that the disk atmosphere stretches upward, with the photosphere rising to about 7H, in contrast to the approximately 3H predicted by conventional analytic models. This more extended structure, as well as fluctuations in the height of the photosphere, may lead to departures from Planckian form in the emergent spectra. Dissipation is distributed across the region within roughly 3H of the midplane, but is very weak at greater altitudes. Because fluctuations in the dissipation are particularly strong away from the midplane, the emergent radiation flux can track dissipation fluctuations with a lag that is only 0.1--0.2 times the mean cooling time of the disk. Long timescale asymmetries in the dissipation distribution can also cause significant asymmetry in the flux emerging from the top and bottom surfaces of the disk. Radiative diffusion dominates Poynting flux in the vertical energy flow throughout the disk.Comment: accepted by Ap

On the effects of flight on jet engine exhaust noise

Differences between flight data and predictions of jet engine exhaust noise were reconciled by considering the combined effects of jet mixing noise and internally generated engine exhaust noise. The source strength of the internally generated noise was assumed to be unaffected by flight, as experiments demonstrated. The directivity of the internally generated noise was assumed to be the same statically as that given in the NASA interim prediction method for core engine noise. However, it was assumed that in flight internally generated noise is subject to the convective amplification effect of a simple source. The absolute levels of internally generated noise were obtained from an empirical fit of some typical engine data. The static and flight jet noise were predicted using the above prediction method. It was shown that in many cases much of the flyover noise signature is dominated by internally generated noise

An empirical model for inverted-velocity-profile jet noise prediction

An empirical model for predicting the noise from inverted-velocity-profile coaxial or coannular jets is presented and compared with small-scale static and simulated flight data. The model considered the combined contributions of as many as four uncorrelated constituent sources: the premerged-jet/ambient mixing region, the merged-jet/ambient mixing region, outer-stream shock/turbulence interaction, and inner-stream shock/turbulence interaction. The noise from the merged region occurs at relatively low frequency and is modeled as the contribution of a circular jet at merged conditions and total exhaust area, with the high frequencies attenuated. The noise from the premerged region occurs at high frequency and is modeled as the contribution of an equivalent plug nozzle at outer stream conditions, with the low frequencies attenuated

The $2 bill returns

An abstract for this article is not available.Money