The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Studies of solute self-association by sedimentation equilibrium: allowance for effects of thermodynamic non-ideality beyond the consequences of nearest-neighbor interactions

A sedimentation equilibrium study of a-chymotrypsin self-association in acetate-chloride buffer, pH 4.1 I 0.05, has been used to illustrate determination of a dimerization constant under conditions where thermodynamic non-ideality is manifested beyond the consequences of nearest-neighbor interactions. Because the expressions for the experimentally determinable interaction parameters comprise a mixture of equilibrium constant and excluded volume terms, the assignment of reasonable magnitudes to the relevant virial coefficients describing non-associative cluster formation is essential for the evaluation of a reliable estimate of the dimerization constant. Determination of these excluded volume parameters by numerical integration over the potential-of-mean-force is shown to be preferable to their calculation by approximate analytical solutions of the integral for this relatively small enzyme monomer with high net charge (+ 10) under conditions of low ionic strength (0.05 M). (C) 2001 Elsevier Science B.V. All rights reserved.

A first-principles density-functional calculation of the electronic and vibrational structure of the key melanin monomers

We report first-principles density-functional calculations for hydroquinone (HQ), indolequinone (IQ), and semiquinone (SQ). These molecules are believed to be the basic building blocks of the eumelanins, a class of biomacromolecules with important biological functions (including photoprotection) and with the potential for certain bioengineering applications. We have used the difference of self-consistent fields method to study the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, HL. We show that HL is similar in IQ and SQ, but approximately twice as large in HQ. This may have important implications for our understanding of the observed broadband optical absorption of the eumelanins. The possibility of using this difference in HL to molecularly engineer the electronic properties of eumelanins is discussed. We calculate the infrared and Raman spectra of the three redox forms from first principles. Each of the molecules have significantly different infrared and Raman signatures, and so these spectra could be used in situ to nondestructively identify the monomeric content of macromolecules. It is hoped that this may be a helpful analytical tool in determining the structure of eumelanin macromolecules and hence in helping to determine the structure-property-function relationships that control the behavior of the eumelanins.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Concordance between dispersal and mitochondrial gene flow: isolation by distance in a tropical teleost, Lates calcarifer (Australian barramundi)

Patterns of population subdivision and the relationship between gene flow and geographical distance in the tropical estuarine fish Lares calcarifer (Centropomidae) were investigated using mtDNA control region sequences. Sixty-three putative haplotypes were resolved from a total of 270 individuals from nine localities within three geographical regions spanning the north Australian coastline. Despite a continuous estuarine distribution throughout the sampled range, no haplotypes were shared among regions. However, within regions, common haplotypes were often shared among localities. Both sequence-based (average Phi(ST)=0.328) and haplotype-based (average Phi(ST)=0.182) population subdivision analyses indicated strong geographical structuring. Depending on the method of calculation, geographical distance explained either 79 per cent (sequence-based) or 23 per cent (haplotype-based) of the variation in mitochondrial gene flow. Such relationships suggest that genetic differentiation of L. calcarifer has been generated via isolation-by-distance, possibly in a stepping-stone fashion. This pattern of genetic structure is concordant with expectations based on the life history of L. calcarifer and direct studies of its dispersal patterns. Mitochondrial DNA variation, although generally in agreement with patterns of allozyme variation, detected population subdivision at smaller spatial scales. Our analysis of mtDNA variation in L. calcarifer confirms that population genetic models can detect population structure of not only evolutionary significance but also of demographic significance. Further, it demonstrates the power of inferring such structure from hypervariable markers, which correspond to small effective population sizes.

Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

NMR shim coil design utilising a rapid spherical harmonic calculation method

A rapid spherical harmonic calculation method is used for the design of Nuclear Magnetic Resonance shim coils. The aim is to design each shim such that it generates a field described purely by a single spherical harmonic. By applying simulated annealing techniques, coil arrangements are produced through the optimal positioning of current-carrying circular arc conductors of rectangular cross-section. This involves minimizing the undesirable harmonies in relation to a target harmonic. The design method is flexible enough to be applied for the production of coil arrangements that generate fields consisting significantly of either zonal or tesseral harmonics. Results are presented for several coil designs which generate tesseral harmonics of degree one.

Experimental study of phase equilibria in the "FeO"-ZnO-(CaO+SiO2) system with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron

The pseudoternary sections FeO-ZnO-(CaO + SiO2) with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron have been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surfaces in these pseudoternary sections have been experimentally determined in the composition range from 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2). The sections contain primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (Fu(w)Zn(2-w)SiO(4)), melilite (Ca2ZnuFe1-uSi2O7), willemite (ZnvFe2-vSiO4), dicalcium silicate (Ca2SiO4), pseudowollastonite and wollastonite (CaSiO3), and tridymite (SiO2). The phase equilibria involving the liquid phase and the solid solutions-have also been measured.

Isotopically resolved (B)over-tilde<-(X)over-tilde electronic spectrum of Ag-3 and calculation of its Jahn-Teller effects

Ag-3 was produced by pulsed-nozzle laser vaporisation and jet-cooled in a Ne supersonic expansion. One-color resonant two-photon ionisation (R2PI) spectra of the (B) over tilde(2) E '' <-- (X) over tilde(2) E' transition of Ag-3 were separately measured for all four isotopic combinations. Long vibrational progressions are observed, involving clearly resolved bands at low energy, merging into a dense but resolvable spectrum up to 1000 cm(-1) above the origin. Both the ground (X) over tilde(2) E' and excited (B) over tilde(2) E '' states of Ag-3 are susceptible to Jahn-Teller distortion along the degenerate e' bending coordinate. The Jahn-Teller analysis includes both linear and quadratic terms, simultaneously with the spin-orbit coupling. Following extensive parameter fitting, the absorption spectrum is calculated, and bands assigned. The spin-orbit splitting is quenched below the localization energy, but becomes observable approximate to 300 cm(-1) above the origin.

Sequential asymmetric auctions with endogenous participation

In this paper we suggest a model of sequential auctions with endogenous participation where each bidder conjectures about the number of participants at each round. Then, after learning his value, each bidder decides whether or not to participate in the auction. In the calculation of his expected value, each bidder uses his conjectures about the number of participants for each possible subgroup. In equilibrium, the conjectured probability is compatible with the probability of staying in the auction. In our model, players face participation costs, bidders may buy as many objects as they wish and they are allowed to drop out at any round. Bidders can drop out at any time, but they cannot come back to the auction. In particular we can determine the number of participants and expected prices in equilibrium. We show that for any bidding strategy, there exists such a probability of staying in the auction. For the case of stochastically independent objects, we show that in equilibrium every bidder who decides to continue submits a bid that is equal to his value at each round. When objects are stochastically identical, we are able to show that expected prices are decreasing.

Non-equilibrium energy and momentum accommodation coefficients of Ar atoms scattered from Ni(001) in the thermal regime: A molecular dynamics study

Molecular dynamics simulations are used to study energy and momentum transfer of low-energy Ar atoms scattered from the Ni(001) surface. The investigation concentrates on the dependence of these processes on incident energy, angles of incidence and surface temperature. Energy transfer exhibits a strong dependence on the surface temperature, at incident energies below 500 meV, and incident angles close to specular incidence. Above 500 meV, the surface temperature dependence vanishes, and a limiting value in the amount of energy transferred to the surface is attained. Momentum exchange is investigated in terms of tangential and normal components. Both components exhibit a weak surface temperature dependence, but they have opposite behaviours at all incidence angles. In each component, momentum can be lost or gained following the interaction with the surface. (C) 1997 Elsevier Science B.V.