Incompressibility Coefficient Research Articles

“Doughnut” nuclear shapes in head-on heavy ion collisions

Based on the hydrodynamic approach, the formation of exotic structures in head-on heavy ion collisions at 60 MeV/nucleon is explained. The physical explanation of the different structures' formation with dependence on the incompressibility coefficient is suggested. Within the developed approach the Rayleigh-Plateau mechanism is confirmed to be the origin of the fragments in the case of ``stiff'' equation of state of nuclear matter (with an incompressibility of 380 MeV). The cold breakdown of the system is suggested to be caused by the presence of the Coulomb force. The obtained results are compared with the existing Boltzmann-like theory calculations and the experimental data for the ``doughnut'' -like geometries.

Hartree-Fock-Bogoliubov nuclear mass model with 0.50 MeV accuracy based on standard forms of Skyrme and pairing functionals

We present a new Hartree-Fock-Bogoliubov nuclear mass model based on standard forms of Skyrme and pairing functionals, which corresponds to the most accurate mass model we ever achieved within the framework of the nuclear energy density functional theory. Our new mass model is characterized by a model standard deviation ${\ensuremath{\sigma}}_{\mathrm{mod}}=0.500$ MeV with respect to essentially all the 2353 available mass data for nuclei with neutron and proton numbers larger than 8. At the same time, the underlying Skyrme functional yields a realistic description of infinite homogeneous nuclear matter properties, as determined by realistic calculations and by experiments; these include in particular the incompressibility coefficient, the pressure in charge-symmetric nuclear matter, the neutron-proton effective mass splitting, the stability against spin and spin-isospin fluctuations, as well as the neutron-matter equation of state.

Determination of the nucleon-nucleon interaction in the ImQMD model by nuclear reactions at the Fermi energy region

The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic (ImQMD) model with three sets of parameters IQ1, IQ2 and IQ3, in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for 238U+197Au at 15 A MeV and the charge distributions for 129Xe+120Sn at 32 and 45 A MeV, and 197Au+197Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that: 1) The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2) The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.

Giant Resonances in 40Ca and 48Ca

We present results of fully self-consistent Hartree-Fock based random phase approximation calculations of the centroid energies ECEN of isoscalar (T = 0) and isovector (T = 1) giant resonances of multipolarities L = 0 – 3 in 40Ca and 48Ca, using a wide range of commonly employed Skyrme type nucleon-nucleon effective interactions. We determined the sensitivities of ECEN and of the isotopic differences ECEN(48Ca) – ECEN(40Ca) to physical quantities, such as nuclear matter incompressibility coefficient, symmetry energy density and effective mass, associated with the Skyrme interactions. We compare the results with the available experimental data, in particular, with the recent data indicating that the ISGMR centroid energy in 48Ca is somewhat higher than in 40Ca.

Giant resonances in40Ca and48Ca

We present results of fully self-consistent Hartree-Fock-based random phase approximation calculations of the strength functions $S$($E$) and centroid energies ${E}_{\mathrm{CEN}}$ of isoscalar ($T=0$) and isovector ($T=1$) giant resonances of multipolarities $L=$ 0--3 in ${}^{40}$Ca and ${}^{48}$Ca, using a wide range of commonly employed 18 Skyrme-type nucleon-nucleon effective interactions. We determined the sensitivities of ${E}_{\mathrm{CEN}}$ and of the isotopic differences ${E}_{\mathrm{CEN}}$(${}^{48}$Ca) -- ${E}_{\mathrm{CEN}}$(${}^{40}$Ca) to physical quantities, such as nuclear matter incompressibility coefficient, symmetry energy density, and effective mass, associated with the Skyrme interactions and compare the results with the available experimental data.

An Investigation of Reynolds Lapse Rate for Highly Loaded Low Pressure Turbine Airfoils With Forward and Aft Loading

This paper presents an experimental and computational study of the midspan low Reynolds number loss behavior for two highly loaded low pressure turbine airfoils, designated L2F and L2A, which are forward and aft loaded, respectively. Both airfoils were designed with incompressible Zweifel loading coefficients of 1.59. Computational predictions are provided using two codes, Fluent (with k-kl-ω model) and AFRL’s Turbine Design and Analysis System (TDAAS), each with a different eddy-viscosity RANS based turbulence model with transition capability. Experiments were conducted in a low speed wind tunnel to provide transition models for computational comparisons. The Reynolds number range based on axial chord and inlet velocity was 20,000 < Re < 100,000 with an inlet turbulence intensity of 3.1%. Predictions using TDAAS agreed well with the measured Reynolds lapse rate. Computations using Fluent however, predicted stall to occur at significantly higher Reynolds numbers as compared to experiment. Based on triple sensor hot-film measurements, Fluent’s premature stall behavior is likely the result of the eddy-viscosity hypothesis inadequately capturing anisotropic freestream turbulence effects. Furthermore, rapid distortion theory is considered as a possible analytical tool for studying freestream turbulence that influences transition near the suction surface of LPT airfoils. Comparisons with triple sensor hot-film measurements indicate that the technique is promising but more research is required to confirm its utility.

Dynamical nucleus-nucleus potential and incompressibility of nuclear matter

The dynamical nucleus-nucleus potentials for some fusion reactions are investigated by using the improved quantum molecular dynamics (ImQMD) model with different sets of parameters in which the corresponding incompressibility coefficient of nuclear matter is different. Two new sets of parameters SKP* and IQ3 for the ImQMD model are proposed with the incompressibility coefficient of 195 and 225 MeV, respectively. The measured fusion excitation function for 16O+208Pb and the charge distribution of fragments for Ca+Ca and Au+Au in multi-fragmentation process can be reasonably well reproduced. Simultaneously, the influence of the nuclear matter incompressibility and the range of nucleon-nucleon interaction on the nucleus-nucleus dynamic potential is investigated.

Temperature and density dependence of asymmetric nuclear matter and protoneutron star properties within an extended relativistic mean field model

The effect of temperature and density dependence of the asymmetric nuclear matter properties is studied within the extended relativistic mean field (ERMF) model, which includes the contribution from the self and mixed interaction terms by using different parametrizations obtained by varying the neutron skin thickness $\Delta$r and $\omega$-meson self-coupling ($\zeta$). We observed that the symmetry energy and its slope and incompressibility coefficients decrease with increasing temperatures up to saturation densities. The ERMF parametrizations were employed to obtain a new set of equations of state (EOS) of the protoneutron star (PNS) with and without inclusion of hyperons. In our calculations, in comparison with cold compact stars, we obtained that the gravitational mass of the protoneutron star with and without hyperons increased by $\sim 0.4M_{\odot}$ and its radius increased by $\sim 3$km. Whereas in case of the rotating PNS, the mass shedding limit decreased with increasing temperature, and this suggested that the keplerian frequency of the PNS, at T = 10 MeV should be smaller by $14-20%$ for the EOS with hyperon, as compared to the keplerian frequency of a cold compact star.

On the moment of inertia of a proto neutron star

The influences of σ* and Φ mesons, temperature and coupling constants of nucleons on the moment of inertia of the proto neutron star (PNS) are examined in the framework of relativistic mean field theory for the baryon octet {n, p, Λ, Σ−, Σ0, Σ+, Ξ−, Ξ0} system. It is found that, compared with that without considering σ* and Φ mesons, the moment of inertia decreases. It is also found that the higher the temperature, the larger the incompressibility and symmetry energy coefficient, and the larger the moment of inertia of a PNS. The influence of temperature and coupling constants of the nucleons on the moment of inertia of a PNS is larger than that of the σ* and Φ mesons.

Modern energy density functional for nuclei and the nuclear matter equation of state

We discuss a method of determining a modern energy density functional (EDF) in nuclei. We adopt a Skyrme type EDF and fit the Skyrme parameters to an extensive set of experimental data on the ground-state binding energies, radii, and the breathing mode energies of a wide range of nuclei. We further constrain the values of the Skyrme parameters by requiring positive values for the slope of the symmetry energy S, the enhancement factor κ, associated with the isovector giant dipole resonance, and the Landau parameter G0′. This is done within the approaches of Hartree-Fock (HF) and HF with the inclusion of correlation effects, using a simulated-annealing based algorithm forminimizing χ2.We also present results of HF based random phase approximation for the excitation strength function of the breathing mode and discuss the current status of the nuclear matter incompressibility coefficient.

10.1007/s11496-008-2005-2

Accurate assessment of the value of the incompressibility coefficient, K ∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K ∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K ∞ from experimental data is highlighted.

Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models

We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfvén theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.

Incompressibility of neutron-rich matter

The saturation properties of neutron-rich matter are investigated in a relativistic mean-field formalism using two accurately calibrated models: NL3 and FSUGold. The saturation properties\char22{}density, binding energy per nucleon, and incompressibility coefficient\char22{}are calculated as a function of the neutron-proton asymmetry $\ensuremath{\alpha}\ensuremath{\equiv}(N\ensuremath{-}Z)/A$ to all orders in $\ensuremath{\alpha}$. Good agreement (at the 10% level or better) is found between these numerical calculations and analytic expansions that are given in terms of a handful of bulk parameters determined at saturation density. Using insights developed from the analytic approach and a general expression for the incompressibility coefficient of infinite neutron-rich matter, i.e., ${K}_{0}(\ensuremath{\alpha})={K}_{0}+{K}_{\ensuremath{\tau}}{\ensuremath{\alpha}}^{2}+\dots{}$, we construct a hybrid model with values for ${K}_{0}$ and ${K}_{\ensuremath{\tau}}$ as suggested by recent experimental findings. Whereas the hybrid model provides a better description of the measured distribution of isoscalar monopole strength in the Sn isotopes relative to both NL3 and FSUGold, it significantly underestimates the distribution of strength in $^{208}\mathrm{Pb}$. Thus, we conclude that the incompressibility coefficient of neutron-rich matter remains an important open problem.

Experimental investigation on mass flow characteristics of electronic expansion valves with R22, R410A and R407C

A novel model depicting mass flow characteristics of electronic expansion valves (EEVs) is developed based on Bernoulli equation. Different from some conventional models using the two-phase outlet pressure and corrected flow coefficient, the new model considers metastable phenomenon caused by rapid depressurization and employs the pressure at throat of EEVs and the single-phase incompressible flow coefficient. Based on experimental data, a set of empirical correlations for the pressure calculation are developed for R22 and its substitutes, R407C and R410A. The relative deviations of mass flow rate predicted by the present model to the measured data are ranged from −6.12% to +7.50% for R22, and from −9.56% to +9.94% for R410A, and from −13.19% to +16.75% for R407C. The theoretical analyses and predicting results for flow characteristics of EEVs show that the new model is better than other conventional models.

A new model of mass flow characteristics in electronic expansion valves considering metastability

This paper presents an experimental study on the mass flow characteristics of electronic expansion valves in a wide operating condition range. It was found that flow choking always occurs under common operating conditions in refrigeration systems. Based on metastability in EEVs, a new model predicting mass flow rate was proposed under flow choking conditions. Different from the conventional models using Bernoulli equation which employed downstream pressure at the EEV exit and a corrected mass flow coefficient, the present model considered metastable liquid flow caused by rapid depressurization, and employed single-phase incompressible flow coefficient and metastable pressure at the throat. An empirical correlation of the metastable pressure, based on the experimental data for R22 and its substitutes, R407C and R410A, was developed in a power law form of dimensionless parameters including upstream operating parameters and refrigerant thermophysical properties and throat area. The predictions of the present model were found to be in good agreement with the measured data, and approximately 95% of the measured data fall within a relative deviation of ±7.0%. The comparison with a prior model shows that, in terms of flashing mechanism application and predicting accuracy, the present model is better than the conventional model without considering metastability.

The compression modes in atomic nuclei and their relevance for the nuclear equation of state

Accurate assessment of the value of the incompressibility coefficient, K∞, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K∞ as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei by employing the microscopic theory based on the Random Phase Approximation (RPA). The importance of full self-consistent calculations is emphasized. In recent years, a comparision between RPA calculations based on either non-relativistic effective interactions or relativistic Lagrangians has been pursued in great detail. It has been pointed out that these two types of models embed different ansatz for the density dependence of the symmetry energy. This fact has consequences on the extraction of the nuclear incompressibility, as it is discussed. The comparison with other ways of extracting K∞ from experimental data is highlighted.

Nonrotating and rotating neutron stars in the extended field theoretical model

We study the properties of nonrotating and rotating neutron stars for a new set of equations of state (EOSs) with different high-density behavior obtained using the extended field theoretical model. The high-density behavior for these EOSs are varied by varying the {omega}-meson self-coupling and hyperon-meson couplings in such a way that the quality of fit to the bulk nuclear observables, nuclear matter incompressibility coefficient, and hyperon-nucleon potential depths remain practically unaffected. We find that the largest value for maximum mass for the nonrotating neutron star is 2.1M{sub {center_dot}}. The radius for a neutron star with canonical mass is 12.8-14.1 km, provided only those EOSs are considered for which the maximum mass is larger than 1.6M{sub {center_dot}}, the lower bound on the maximum mass measured so far. Our results for the very recently discovered fastest rotating neutron star indicate that this star is supramassive with mass 1.7M{sub {center_dot}}-2.7M{sub {center_dot}} and circumferential equatorial radius 12-19 km.

NUCLEAR MATTER PROPERTIES FROM COLLECTIVE MODES IN NUCLEI

Bulk properties of nuclear matter associated with the equation of state, the nuclear matter incompressibility coefficient, Knm, in particular, are very important physical quantities required in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. Here we review the current status of Knm and the experimental and theoretical methods used to determine the value of Knm from the excitation cross-sections and the transition strength distributions of compression modes in nuclei, mainly the the isoscalar giant monopole resonance and the isoscalar giant dipole resonance.

Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes

Accurate assessment of the value of the incompressibility coefficient, K, of symmetric nuclear matter, which is directly related to the curvature of the equation of state (EOS), is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on isoscalar giant monopole and dipole resonances (compression modes) in nuclei, by employing the microscopic theory based on the random-phase approximation (RPA).

Current status of equation of state of nuclear matter

The equation of state (EOS) of symmetric nuclear matter (SNM) is a very important ingredient in the study of various phenomena of interest in nuclear physics and astrophysics. Accurate assessment of the value of the SNM incompressibility coefficient, K, which is directly related to the curvature of the EOS, is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on compression modes in nuclei using the mean-field-based random-phase approximation.