Extraction of nuclear matter properties from nuclear masses by a model of equation of state

The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei. It is shown that the volume energy $a_1$ and the nuclear incompressibility $K_0$ depend essentially on $\mu_n N+\bar{\mu}_p Z-2E_N$, whereas the symmetry energy $J$ and the density symmetry coefficient $L$ as well as symmetry incompressibility $K_s$ depend essentially on $\mu_n-\bar{\mu}_p$, where $\bar{\mu}_p=\mu_p-\partial E_C/\partial Z$, $\mu_n$ and $\mu_p$ are the neutron and proton chemical potentials respectively, $E_N$ the nuclear energy, and $E_C$ the Coulomb energy. The obtained symmetry energy is $J=28.5MeV$, while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.Comment: 12 pages and 7 figure

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess $\delta$. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ($\rho_c, \delta_c$) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of $\delta_c$ is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, $\delta_c$ does not depend sensitively on the choice of the parameter $\gamma$ in Skyrme interaction.Comment: 15 pages, 9 figure

Nuclear matter properties and relativistic mean-field theory

Nuclear matter properties are calculated in the relativistic mean field theory by using a number of different parameter sets. The result shows that the volume energy $a_1$ and the symmetry energy $J$ are around the acceptable values 16MeV and 30MeV respectively; the incompressibility $K_0$ is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry $L$ is around $100MeV$ for most parameter sets, and the symmetry incompressibility $K_s$ has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point $(\rho_c, \delta_c)$, where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm$^{-3}<\rho_c<0.039$fm$^{-3}$ and $0.74<\delta_c\le0.95$; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass $M_{NS}$ of neutron stars is predicted in the range 2.45M$_\odot\leq M_{NS}\leq 3.26$M$_\odot$, the corresponding neutron star radius $R_{NS}$ is in the range 12.2km$\leq R_{NS}\leq 15.1$km.Comment: 10 pages, 5 figure

An Analytic Equation of State for Ising-like Models

Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, $y=f(x)$, that exhibits all desired asymptotic and analyticity properties in the three limits $x\to 0$, $x\to \infty$ and $x\to -1$. The only necessary inputs are the Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N=1, we derive a one-loop equation of state for $2< d<4$ naturally parameterized by a ratio of non-linear scaling fields. For $d=3$ we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure

ALTERATIONS IN GROUND REACTION FORCES DURING TETHERED WALKING

This study examined t h e e f f e c t s of tethering conditions on ground forces while walking a t 2.5 mph. Six males w e r e unweighted 0%, 25%, 50% and 75% of t h e i r BWT while supported i n a Kinney upper body vest by an active traction prototype (Conva-Lift). They walked 10 min. a t each randomly selected unweighting condition in a 12 f t . dia. c i r c l e . Ten right and l e f t s t r i d e impacts w e r e collected a t 1000 Hz with an Ariel APAS system using a K i s t l e r force plate during each condition a t 2.5 mph (27%). Walking velocity was verified by an infra-red timing system. 5 right and l e f t s t r i d e s in which the velocity was closest t o 2.5 mph w e r e selected for analysis. The s t r i d e was delineated into the phases of heelstrike (HS), midfoot support (MFS), and toe-off (TO). The v e r t i c a l forces (F,) a t the 3 phases, the fore-aft forces (Fy) a t HS and TO and the contact time w e r e calculated. A 4x2x5 ANOVA (WtxFtxLeg) with repeated measures on a l l factors was used t o analyze (F,) forces a t HS, MFS, and TO, fore-aft forces (Fy) a t HS, TO, and contact t i m e . The v e r t i c a l forces (Fz) a t HS w e r e 902.0+112.9 Nt(76% BWT), and 389.3276.8 Nt(45% BWT) for the unweighting conditions. The i n i t i a l impact forces w e r e consistent with normal overland walking and the F, forces w e r e significantly reduced when the subject was unweighted a t 50% and 75% of t h e i r BWT. The forea f t forces representing the decelerative forces w e r e 16%, 16%, lo%, and 4% BWT for the weight conditions. Significant differences w e r e found t o exist between the i n i t i a l contact force a t 0% ( f u l l BWT) and 75% unweighting. The MFS v e r t i c a l forces (F,) w e r e 682.7±73.4, 595.7±73.3, 395.9±49.8, and 234.3±28.7 N t for the loading conditions. The midfoot forces represented about a 30% reduction or absorption of the i n i t i a l impact forces, while the 75% condition exhibited only a 18% reduction in the impact force which would suggest that weight bearing mechanism of the arch of the foot functioned differently when unloaded. The F, forces a t TO significantly differed from 869.1±118.5, 76.56±105.4, 537.9±91.8, and 281.4±78.2 f o r t h e conditions. The percentage of reduction of F, forces a t HS and TO for the unweighting conditions, and the v e r t i c a l forces a t TO w e r e decreased more for a similar degree of unweighting. This finding would suggest that t h i s active traction prototype might be beneficial in t h e r e h a b i l i t a t i o n of posterior compartment injuries. When examining the reduction i n the fore-aft accelerative forces a t TO, the % BWT w e r e similar t o the F, forces a t HS for similar unloading conditions. The s t r i d e contact times significantly differed between ,705±03 sec for t h e r i g h t s t r i d e s and ,68±.04 sec for the l e f t s t r i d e s and no differences existed for the weighting condition. Significant time differences w e r e attributable t o the outside leg having t o travel a greater distance in the same t i m e a s t h e inner leg, while walking in a c i r c l e . The Conva-Lift's travel direction is reversible t o prevent any imbalances due t o circular walking. The significant differences in the ground reaction forces in the v e r t i c a l and fore-aft direction as the subjects w e r e unweighted would indicate that the Conva-Lift is a viable means of reducing ground reaction forces while ambulating

Wetting phenomenon in the liquid-vapor phase coexistence of a partially miscible Lennard-Jones binary mixture

We have carried out extensive equilibrium molecular dynamics (MD) simulations to study the structure and the interfacial properties in the liquid-vapor (LV) phase coexistence of partially miscible binary Lennard-Jones (LJ) mixtures. By analyzing the structural properties as a function of the miscibility parameter, $\alpha$, we found that at relatively low temperatures the system separates forming a liquid A-liquid B interface in coexistence with the vapor phase. At higher temperatures and, $0<\alpha\leq 0.5$, we found a temperature range, $T^{*}_{w}(\alpha) \leq T^{*} < T^{*}_{cons}(\alpha)$, where the liquid phases are wet by the vapor phase. Here, $T^{*}_{w}(\alpha)$ represents the wetting transition temperature (WTT) and $T^{*}_{cons}(\alpha)$ is the consolute temperature of the mixture. However, for $0.5< \alpha < 1$, no wetting phenomenon occurs. For the particular value, $\alpha=0.25$, we analyzed quantitatively the $T^{*}$ versus $\rho^{*}$, and $P^{*}$ versus $T^{*}$ phase diagrams and found, $T^{*}_{c}\simeq 1.25$, and $T^{*}_{cons}\simeq1.25$. We also studied quantitatively, as a function of temperature, the surface tension and the adsorption of molecules at the liquid-liquid interface. It was found that the adsorption shows a jump from a finite negative value up to minus infinity, when the vapor wets the liquid phases, suggesting that the wetting transition (WT) is of first order. The calculated phase diagram together with the wetting phenomenon strongly suggest the existence of a tricritical point. These results agree well with some experiments carried out in fluid binary mixtures.Comment: Enlarged version that include results of more extensive simulations. A total of 24 LaTeX pages that include 12 encapsulated poscript figures. To appear in PRE, Vol. 70, issue Sept. 1st (2004