### TABLE I DYNAMIC AND EQUILIBRIUM PROPERTIES

2005

Cited by 2

### Table 7. Equilibrium properties of dimers Ga1As1,As2, and Ga2. d is the equilibrium separation of the atoms, Eb is the binding energy per atom, and ! is the vibrational frequency.

1997

### Table 1 Properties of six equilibrium states calculated from the methane equation of state12 at 185 K

"... In PAGE 3: ... apos;, Because the equation is non-cubic, the Helmholtz energy behaviour inside the two-phase region resembles that depicted in Fig. 3, and it therefore produces six equilibrium states, the relevant properties of which are shown in Table1 . All of these states satisfy the three basic thermody- A ~ V Fig.... In PAGE 3: ... 3 Schematic Helmholtz energy isotherm in the two-phase region for non-cubic equations of state namic equalities of T, p and p for each respective pair of phases and all can be found using the iterative scheme of the area method (vide infra). The values of A in Table1 were calculated along the 0.096 dm3 mol-I isochore, which lies between the equilibrium volumes of all six states.... In PAGE 3: ...83426 kJ mol- apos;. For a system at constant tem- perature and volume, the stable phase configuration is the one with the minimum Helmholtz energy, state 1 in Table1 . As this state also has the maximum value of 9, the correspon- dence between minimum A and maximum F holds.... In PAGE 3: ... As this state also has the maximum value of 9, the correspon- dence between minimum A and maximum F holds. Further insight into the question of stability may be gained from the values of the second derivatives of the area method objective function in columns 6-8 of Table1 . For state 6, the matrix of the second derivatives is negative definite and state 6 is therefore a minimum of the objective function F.... In PAGE 12: ...534 08 Table 19 Consistency with the Gibbs phase rule NP F E U U-E 12 1 13 0 22 2 23 1 24 0 25 -1 32 3 33 2 34 1 44 2 46 0 N P N-P+2 2 3 1 4 4 0 2 4 2 4 5 1 6 6 0 8 7 -1 3 6 3 6 8 2 9 10 1 12 14 2 20 20 0 N(P - 1) P(N - 1) + 2 N - P + 2 fluid case. Finally, from Table1 9, it is clear that when the number of equations and the number of phases are the same, then the number of degrees of freedom and also (U - E) is two. This can be seen for N = 2, 3 and 4.... ..."

### Table 8 Star properties for matter in beta equilibrium at nite entropy using relativistic models.

"... In PAGE 22: ... This model is referred to as the GM model. Table8 shows the basic properties of stars in beta equilibrium for the MRHA model with various values of r=M and for the GM model. The structural changes at nite entropy compared to the zero entropy case are qualitatively similar to those given by the BPAL potential model in the previous section.... In PAGE 22: ...urves in the upper panel of Fig. 7 for r=M=1.25. The temperature is a maximum at the center of the star (here the density ratio is 7 for a maximum mass star, see Table8 ) and decreases with decreasing density, the fall o being particularly marked at low density. The density of a neutron star is approximately constant in the interior and drops to zero over a radial distance R=R 0:1.... In PAGE 25: ... The softening introduced in the MRHA EOS by hyperons is evident in the maximum masses in Table 11. These are about 0:4 ? 0:9M , smaller than the results of Table8 , for which only nucleons are allowed in matter. Notice that in some cases, the maximum mass falls below 1:44M , and the pressure support of nite entropy is not adequate to raise the maximum mass above 1:44M .... In PAGE 37: ... In Table 14, we give the stellar properties for the neutrino-free and neutrino-trapped cases. Comparison of the neutrino-free results with Table8 shows rather small e ects, except for the largest magnitudes for the parameter a3ms. It is only for these cases that the central densities signi cantly exceed the critical densities (Table 13) and allow a size-... ..."

### Table 4 Star properties for matter in beta equilibrium at nite entropy in the BPAL potential model.

"... In PAGE 17: ... Further, Pkin, Ppot, and P0 = Pkin + Ppot are the kinetic, potential, and the total pressures at zero temperature and include the contributions from both neutrons and protons. Quantitative results for the physical attributes of the maximum mass star are summa- rized in Table4 for the di erent BPAL EOSs which have varying sti nesses and di erent density dependence of the symmetry energy, the latter determining the proton and lepton... In PAGE 18: ... This is re ected in the limiting masses obtained with neutrino trapped matter (see Table 6), which are lower than those without neutrinos (cf. Table4 ). Results for the maximum mass stars are summarized in Table 6 for the BPAL models with di erent sti nesses.... ..."

### Table 5 Star properties for matter in beta equilibrium at nite entropy in the SL potential model.

### Table 11 Star properties for matter, including hyperons, in beta equilibrium at nite entropy using relativistic models.

"... In PAGE 25: ... 12 shows that the baryons carry most of the entropy, since the lepton populations remain low at high density, due to the magnitude of the electron chemical potential. Table11 summarizes the gross features of the maximum mass star populated with hy- perons. Compared to the case in which only nucleons are present, the addition of hyperons causes the central temperatures to be reduced.... In PAGE 25: ...om and the top panels in Fig. 7. This gure also shows that with hyperons present the temperature changes rather little with density until u lt; 2, so that a constant temperature would be achieved over much of the star. The softening introduced in the MRHA EOS by hyperons is evident in the maximum masses in Table11 . These are about 0:4 ? 0:9M , smaller than the results of Table 8, for which only nucleons are allowed in matter.... In PAGE 26: ... The changes due to entropy alone are small and not always in the direction of increasing the maximum mass. Notice, however, that for each entropy shown, the maximum masses are all about 0:2M larger than those in Table11 for neutrino free stars. Since the star has to cool down from an S 1 con guration, with neutrinos trapped, to a con guration of S 0 without neutrinos, the maximum stable mass decreases.... ..."