Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Aqueous-phase ion solvation and the selectivity of anion exchange resins for monovalent ions

This research examines and quantifies the influence of ion solvation parameters on the affinity of monovalent anions for strong-base anion resins. A data set comprising resin selectivity coefficients and solvation parameters from the literature is statistically analyzed using correlation and multiple regression techniques. The affinity of monovalent anions for the resin phase correlated well to ionic radii. Solvation parameters such as the hydration number, and entropy, enthalpy and free energy of hydration are also strongly correlated to selectivity. Using the stepwise regression procedure on subsets of independent variables, the entropy of hydration, which characterizes the structure-influencing nature of ions in solution, is incorporated as the sole parameter in the predictive model for resin selectivity. The data are best correlated by the exponential form of the regression equation, and the physical meaning of the correlation is shown to be reasonable. A simple rule for categorizing ions as structure-makers and structure-breakers is proposed, and the results are consistent with conventional classifications.     

An equilibrium and calorimetric investigation of the hydrolysis of L-tryptophan to (indole + pyruvate + ammonia)

Apparent equilibrium constants and calorimetric enthalpies of reaction have been measured for the reaction L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate(aq) + ammonia(aq) which is catalyzed by L-tryptophanase. High-pressure liquid-chromatography and microcalorimetery were used to perform these measurements. The equilibrium measurements were performed as a function of pH, temperature, and ionic strength. The results have been interpreted with a chemical equilibrium model to obtain thermodynamic quantities for the reference reaction: L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate^–(aq) + NH ₄ ⁺ (aq). At T=25°C and I_m=O the results for this reaction are: K^o=(1.05±0.13)×10^–4, G°=(22.71±0.33) kJ-mol^–1, H°=(62.0±2.3) kJ-mol^–1, and S°=(132±8) J-K^–1-mol^–1. These results have been used together with thermodynamic results from the literature to calculate standard Gibbs energies of formation, standard enthalpies of formation, standard molar entropies, standard molar heat capacities, and standard transformed formation properties for the substances participating in this reaction.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

The solubilization of alcohols in micellar solutions

The specific conductivities of dodecyldimethylbenzylammonium bromide (C12BBr) have been determined in aqueous butanol and aqueous benzyl alcohol solutions in the temperature range of 5-40°C. From these data the temperature dependent critical micelle concentration (cmc) was determined. The molar fraction of alcohol in the micelle was estimated using the theory suggested by Motomura et al. for surfactant binary mixtures. The thermal properties such as standard Gibbs free energy, enthalpy and entropy of solubilization of alcohols in the micelles were estimated for the phase separation model. The change in heat capacity upon solubilization of alcohol in the micelle has been estimated form the above properties. This revised version was published online in July 2006 with corrections to the Cover Date.