Beta-equilibrium

The central quantity which determines neutron star properties is the EoS, at T = 0 specified by the energy density e(p). For densities above, say, p = 0.1 fm-3 one assumes a charge neutral uniform matter consisting of protons, neutrons, electrons and muons the conditions imposed are charge neutrality, Pp = Pe + PfM, and beta equilibrium, pn pp + pe with pe = p/t. ... 

In order to study the effects of different TBF on neutron star structure, we have to calculate the composition and the EOS of cold, catalyzed matter. We require that the neutron star contains charge neutral matter consisting of neutrons, protons, and leptons (e, p ) in beta equilibrium. Using the various TBF discussed above, we compute the proton fraction and the EOS for charge neutral and beta-stable matter in the following standard way [23, 24] The Brueckner calculation yields the energy density of lepton/baryon matter as a function of the different partial densities,... 

Beta equilibrium, neutrino trapping, charge and color neutrality. The stellar matter in equilibrium has to obey the constraints of /3-equilibrium (d — u + e + ve,u + e — d + ve), expressed as... 

Gr. aktis, aktinos, beam or ray). Discovered by Andre Debierne in 1899 and independently by F. Giesel in 1902. Occurs naturally in association with uranium minerals. Actinium-227, a decay product of uranium-235, is a beta emitter with a 21.6-year half-life. Its principal decay products are thorium-227 (18.5-day half-life), radium-223 (11.4-day half-life), and a number of short-lived products including radon, bismuth, polonium, and lead isotopes. In equilibrium with its decay products, it is a powerful source of alpha rays. Actinium metal has been prepared by the reduction of actinium fluoride with lithium vapor at about 1100 to 1300-degrees G. The chemical behavior of actinium is similar to that of the rare earths, particularly lanthanum. Purified actinium comes into equilibrium with its decay products at the end of 185 days, and then decays according to its 21.6-year half-life. It is about 150 times as active as radium, making it of value in the production of neutrons. 

Because beta-scission is mono-molecular and cracking is endothermic, the cracking rate is favored by high temperatures and is not equilibrium-limited. 

Richard, J. P. Amyes, T. L. Bei, L. Stubblefield, V. The effect of beta-fluorine substituents on the rate and equilibrium-constants for the reactions of alpha-substituted 4-methoxybenzyl carbocations and on the reactivity of a simple quinone methide. J. Am. Chem. Soc. 1990, 112, 9513-9519. 

Degradation and evaporation seem to be the major pathways for acrolein loss in water smaller amounts are lost through absorption and uptake by aquatic organisms and sediments (USEPA 1980 Reinert and Rodgers 1987). The half-time persistence of acrolein in freshwater is 38 h at pH 8.6 and 50 h at pH 6.6 degradation is more rapid when initial acrolein concentrations are less than 3000 pg/L (Bowmer and Higgins 1976). Nordone et al. (1998) show a half-time persistence of 2.9 to 11.3 h at initial nominal concentrations of 20 pg/L, and 27.1 to 27.8 h at 101 pg/L. At pH 5, acrolein reacts by reversible hydrolysis to produce an equilibrium mixture with 92% beta-hydroxy-... 

Where concentrated solutions are desired, as they are in special applications, the rather slow rate of solution of dextrose is encountered. This is due to the fact that a saturated solution of dextrose consists of an equilibrium mixture of the alpha and beta isomers and the attainment of this equilibrium at room temperature is slow if crystalline alpha dextrose is the starting material. If, on the other hand, beta dextrose or a mixture rich in this isomer is used, the rate of solution is very rapid.18... 

However, a more realistic model for the phase transition between baryonic and quark phase inside the star is the Glendenning construction [16], which determines the range of baryon density where both phases coexist. The essential point of this procedure is that both the hadron and the quark phase are allowed to be separately charged, still preserving the total charge neutrality. This implies that neutron star matter can be treated as a two-component system, and therefore can be parametrized by two chemical potentials like electron and baryon chemical potentials [if. and iin. The pressure is the same in the two phases to ensure mechanical stability, while the chemical potentials of the different species are related to each other satisfying chemical and beta stability. The Gibbs condition for mechanical and chemical equilibrium at zero temperature between both phases reads... 

Figure 5. Isotherms of hydrogen gas (pressure p atm) in equilibrium with absorbed hydrogen in LaNi5 (concentration H atoms/LaNi5). Notice the alpha-region is where hydrogen is in solid solution, the (alpha+beta)-region is made-up of both solid solution hydrogen and hydrides, and the beta-region is...

In order to compare the performance of various adsorbent and desorbent systems for the same feedstock on must use the selectivity beta ratio. Equation (8.1) depicts the selectivity beta ratio of an adsorbent/desorbent pair is defined as the ratio of the two components in the adsorbed phase divided by the ratio of the same two components in the unabsorbed phase at equilibrium conditions. 

ZSM-5 propylene and higher alkene selectivities are typically higher and ethylene selectivity is typically lower compared to SAPO-34 [97]. Over Beta light alkene breakdown is closer to thermodynamic equilibrium compared with ZSM-5 and SAPO-34 [97]. While the SAPO-34 pore opening is not large enough to let aromatics and branched alkanes out, di- and trimethylbenzenes and even some tetra-methylbenzenes are observed over ZSM-5 as products in the effluent and hexamethylbenzenes are observed over Beta as products in the effluent [98, 99]. 

An alternative mechanism for the formation of a two hosts-two guests complex has been suggested. From equilibrium studies of the concentration-dependence of the absorption spectra and excimer fluorescence intensities of naphthalene in the presence of beta cyclodextrin, Hamai ° concluded that the excimer fluorescence is due to a two hosts-two guests complex, formed by the association of two 1 1 beta cyclodextrin-naphthalene complexes. Thus, the mechanism can be described as follows. 

An interesting equilibrium study was performed by Kasatani and coworkers on the interaction of a series of cyanine dyes with beta and gamma cyclodextrin, using u.v.-visible spectrophotometric measurements. The results were consistent with the enhancement of dimer formation by inclusion of the dye molecules within the cyclodextrin. As expected from the work of others, such geometrical factors " as the size of the aromatic groups and the lengths of the central methine chains strongly influence the occurrence of dimer formation within the cyclodextrin cavity. 

The probable configuration of isosucrose was systematically discussed by Georg,who thought that the yield was much greater when the beta anomer, rather than the equilibrium mixture or the alpha anomer, of 2,3,4,6-tetraacetyl-D-glucose was used in the condensation. Analogy with tetraacetyl-D-fructopyranosyl chloride, which yielded the acetylated... 

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