Quasi-equilibrium Calculations Research Articles

ANALYTIC APPROXIMATION OF CARBON CONDENSATION ISSUES IN TYPE II SUPERNOVAE

I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56 Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

Modelling of fluidized bed biomass gasification in the quasi-equilibrium regime for preliminary performance studies of energy conversion plants

Thermodynamic equilibrium-based models of gasification process are relatively simple and widely used to predict producer gas characteristics in performance studies of energy conversion plants. However, if an unconstrained calculation of equilibrium is performed, the estimations of product gas yield and heating value are too optimistic. Therefore, reasonable assumptions have to be made in order to correct the results. This paper proposes a model of the process that can be used in case of deficiency of information and unavailability of experimental data. The model is based on free energy minimization, material and energy balances of a single zone reactor. The constraint quasiequilibrium calculations are made using approximated amounts of non-equilibrium products, i.e. solid char, tar, CH4 and C2H4. The yields of these products are attributed to fuel characteristics and estimated using experimental results published in the literature. A genetic algorithm optimization technique is applied to find unknown parameters of the model that lead to the best match between modelled and experimental characteristics of the product gas. Finally, generic correlations are proposed and quality of modelling results is assessed in the aspect of its usefulness for performance studies of power generation plants.

Multilocus models in the infinite island model of population structure

Different methods have been developed to consider the effects of statistical associations among genes that arise in population genetics models: kin selection models deal with associations among genes present in different interacting individuals, while multilocus models deal with associations among genes at different loci. It was pointed out recently that these two types of models are very similar in essence. In this paper, we present a method to construct multilocus models in the infinite island model of population structure (where deme size may be arbitrarily small). This method allows one to compute recursions on allele frequencies, and different types of genetic associations (including associations between different individuals from the same deme), and incorporates selection. Recursions can be simplified using quasi-equilibrium approximations; however, we show that quasi-equilibrium calculations for associations that are different from zero under neutrality must include a term that has not been previously considered. The method is illustrated using simple examples.

Nonequilibrium dilepton production in dropping mass scenarios

We investigate dilepton production in heavy ion collisions for scenarios with dropping vector meson masses within a realtime field theoretical description that includes off-equilibrium effects. Therefore quantum mechanical memory is not neglected as in quasi-equilibrium calculations. We compare these two approaches and thereby determine the importance of memory effects for the regarded scenarios.

Dilepton Yields from Brown-Rho Scaled Vector Mesons Including Memory Effects

Scenarios with dropping vector meson masses, motivated by the work of Brown and Rho, have been strongly discussed after recent NA60 Collaboration data were presented. In this Letter they are investigated within a nonequilibrium field theoretical description that includes quantum mechanical memory. Dimuon yields are calculated by application of a model for the fireball, and strong modifications are found in the comparison to quasiequilibrium calculations, which assume instantaneous adjustment of all meson properties to the surrounding medium. In addition, results for the situation of very broad excitations are presented.

Eccentricity content of binary black hole initial data

Using a post-Newtonian diagnostic tool developed by Mora and Will, we examine numerically generated quasiequilibrium initial data sets that have been used in recently successful numerical evolutions of binary black holes through plunge, merger and ringdown. We show that a small but significant orbital eccentricity is required to match post-Newtonian and quasiequilibrium calculations. If this proves to be a real eccentricity, it could affect the fine details of the subsequent numerical evolutions and the predicted gravitational waveforms.

Exciton formation and stability in semiconductor heterostructures

The formation and stability of excitons in semiconductors is studied on the basis of a microscopic model that includes Coulomb interacting fermionic electrons and holes as well as phonons. Whereas quasiequilibrium calculations predict substantial exciton fractions coexisting with an electron-hole plasma at low temperatures and densities, dynamic calculations reveal that the exciton formation times under these conditions exceed the characteristic lifetimes. At elevated densities, good agreement between dynamical and quasiequilibrium calculations is obtained.

The stability of amino acids at submarine hydrothermal vent temperatures.

It has been postulated that amino acid stability at hydrothermal vent temperatures is controlled by a metastable thermodynamic equilibrium rather than by kinetics. Experiments reported here demonstrate that the amino acids are irreversibly destroyed by heating at 240 degrees C and that quasi-equilibrium calculations give misleading descriptions of the experimental observations. Equilibrium thermodynamic calculations are not applicable to organic compounds under high-temperature submarine vent conditions.

The growth of (100) orientated diamond films

Quasi-equilibrium calculations were performed on the C H and C H O systems to calculate the thermodynamic stability of diamond and graphite phases under CVD conditions. Exclusive diamond growth is dependent, in part, on the increased thermodynamic stability of H-terminated crystallographic surfaces. This feature was included in the methodology by estimating the surface enthalpies by group additivity methods. The lower boundary in the Bachmann ternary diagram which defines the demarcation line between the growth and non-growth regions was calculated. The gradient of the line is a strong function of the degree of stabilization of the H-terminated diamond surfaces. Using mixtures of CH 4 CO H 2 of compositions close to the CO line of the phase diagram, (100) faceted films were grown by microwave assisted CVD at rates of 1.5–2.0 μm h −1.

Thermodynamic properties of fullerenes

Thermochemical quantities for C 60 and C 70 fullerenes including enthalpies of formation, heat capacities, standard molar thermodynamic functions, and vapour pressures are summarized. Simple quasi-equilibrium calculations are tested in order to explain the ratio of experimental yields of C 60 and C 70.

The fragmentation of C 2F 6+

The fragmentation Of C 2F 6 + has been studied by threshold photoelectron—photoion coincidence mass spectrometry and field-ionization mass spectrometry. Four types of data were obtained with the coincidence apparatus: threshold photoelectron spectra, fragmentation breakdown curves, time-dependent breakdown curves and kinetic energy release on fragmentation. The results indicate that the CF 3 + and C 2F 5 + fragments are formed independently, probably from separate electronic states which do not internally convert to the ground electronic state. The field-ionization data show that these fragments are formed in less than 5 × 10 −13 s. Quasi-equilibrium calculations could not reproduce the experimental results.

Deactivation of internally excited H3+ ions: comparison of experimental product distributions of reactions of H3+ ions with CH3NH2, CH3OH and CH3SH with predictions of quasiequilibrium theory calculations

The proton transfer reaction of H3+ ions with CH3NH2, CH3OH and CH3SH produces the excited intermediate complexes [CH3NH3+]★, [CH3,OH2+]★, and [CH3SH2+]★ which subsequently decompose in two ways; by vicinal hydrogen elimination, and by C-X bond scission to give the methyl cation. The condensation reaction of methyl cations with NH3, H2O, and H2S is the reverse of the latter decomposition pathway and proceeds to give the same excited intermediates followed also either by vicinal hydrogen elimination or by back reaction. The H2+ ions formed by reaction of H2+ with H2 are highly excited, and the presence of excess internal energy in the H3+ ion is shown to be a critical factor in the ratio of decomposition products obtained. A detailed analysis of the deactivation of excited H3+ is made. The rate for deactivation of excited H3+ ions by H2 is measured and the internal energy in H3+ obtained as a function of H2 pressure. Quasiequilibrium calculations are applied to the unimolecular decomposition of the excited intermediate complexes formed in the proton transfer and methyl cation condensation reactions. The experimental product distribution as a function of H3+ internal energy is readily reproduced by quasiequilibrium theory. It is shown that barriers of 2.6, 1.1 and < 1.4 eV are required for vicinal hydrogen elimination from [CH3NH3+]★, and [CH3SH2+]★, respectively. These barriers significantly reduce the apparent exothermicities of the CH3+ condensation reactions and, in particular, the apparent exothermicity for the CH3+-H2O reaction is reduced to near zero. In addition, it appears possible that the excess energy may not be completely randomized before dissociation occurs in the complex resulting from the condensation reactions.

Ortho-Effects in Mass Spectra. Alteration of the Molecular-Ion Energy Distribution in Disubstituted Acetanilides

Abstract Simplified quasi-equilibrium calculations performed on the mass spectra of dihalosubstituted phenyl acetates and acetanilides again uncover the same substituent effects on the rise of K with E for the loss of ketene from phenyl acetates as was determined for the monosubstituted phenyl acetates. However, a new effect is found for the disubstituted acetanilides, removal of excitation probability for low-lying energy states of the molecular ion. This effect parallels the removal of transition probability for the lowest excited state of the neutral molecule.