On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

A Robust and Efficient Method for the Computation of Equilibrium Composition in Gaseous Mixtures

This paper presents in detail a robust, efficient and accurate methodology for the computation of equilibrium composition in gaseous mixtures. The methodology is founded on the concept of the chemical basis, which is defined and formalized using a powerful matricial approach. The method is specially designed to be general, thus providing basic thermodynamic data in several areas, such as combustion, plasma chemistry and, more generally speaking, computational fluid dynamics. The performance of the method is given in terms of CPU usage and the computed results are compared with those in the published literature. The method is shown to yield results of very high quality in terms of accuracy and smoothness.     

Thermodynamics of hydrogen-isotope-exchange reactions. Proton solvation inn-hexanol and water

This paper reports our results for the direct experimental determination of the equilibrium constant for the hydrogen-isotope-exchange reaction, 1/2D₂(g)+HCl(hexOH)=1/2H₂(g)+DCl(hexOD), where hexOH isn-hexanol and hexOD isn-hexanol with deuterium substitution in the alcohol function. The reaction was studied in electrochemical double cells without liquid junction for which the net cell reaction is the above isotope-exchange reaction. The experimentally determined value of ε° (296.0°K) for this cell is 4.03±0.95 mV (strong electrolyte standard states, mole-fraction composition scale); the value of the equilibrium constant for the reaction is 1.17±0.05. The contributions of isotope-exchange and transfer effects to the magnitude of the standard Gibbs energy change for the above reaction and for the analogous reaction 1/2D₂(g)+HCl(aq)=DCl(daq)+1/2H₂(g) are considered. Our results support the conclusion of Heinzinger and Weston that the formulation of the solvated proton in water as H₃O⁺, as opposed to H₉O₄ ⁺, is sufficient for the interpretation of the thermodynamics of hydrogen-isotope-exchange reactions in water. We also find that the formulation of the solvated proton inn-hexanol as ROH ₂ ⁺ is sufficient for the interpretation of our results on the thermodynamics of hydrogen-isotope-exchange inn-hexanol.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Influence of Cycle Temperatures on the Thermochemical Heat Storage Densities in the Systems Water/Microporous and Water/Mesoporous Adsorbents

The adsorption equilibrium of water on microporous adsorbents (zeolites of NaA-, NaY- and NaX-type as well as their ion exchanged forms) and on mesoporous adsorbents (different silica gels and composite material i.e. silica gel + salt hydrate) has been studied experimentally and theoretically. Using the Dubinin theory of pore filling the characteristic curves of the adsorption systems and other relevant dependences such as isotherms, isobars, isosteres and the curve of the differential heat of adsorption were calculated. For all systems investigated the adsorption were calculated. A_ads and the desorption potential A_des of the closed heat storage system were estimated. These values define the working range of the adsorption/desorption cycle and allow to calculate the specific heat storage density Δ h_sp. On the basis of Δ h_sp the different adsorbents were compared in order to select the optimal porous storage material for a given application. The presented experimental and theoretical investigations show that the adsorption systems water-zeolite and water-composites are promising working pairs for thermochemical heat storage processes for hot tap water supply and space heating of single family dwellings. The advantage of the water-composite system is the low desorption temperature (solar energy) the main shortcoming the low temperature lift. The advantage of the water zeolite system is the high temperature lift, the shortcoming are the relative high desorption temperatures.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

The Effect of Alkane Chain Length on the Liquid–Liquid Critical Temperatures of Oligostyrene/Linear-Alkane Mixtures

Summary. Upper critical solution temperatures (UCSTs) for liquid–liquid demixing in a set of mixtures of linear alkanes (pentane (N ₁=5) to pentacontane (N ₁=50)) with an oligostyrene (1241amu, N ₂=12) are reported. We find strong correlation between the Hildebrand solubility parameters of the alkanes and the UCST. Correlations are developed which enable predictions concerning the miscibility of mixtures of compounds with longer chains.     

Kinetics of epidermal growth factor/receptor binding on cells measured by total internal reflection/fluorescence recovery after photobleaching

Total internal reflection fluorescence (TIRF) microscopy is used to measure the dissociation kinetic rate of fluorescein-labeled epidermal growth factor from its specific receptors on the surface of intact but mildly fixed A431 human epidermoid cells in culture. Prior applications of TIRF microscopy have been limited to nonreceptor binding or to model membrane systems. The evanescent field excites fluorescence selectively at the surface of the cell proximal to the coverslip. Prismless epiillumination TIR is employed to avoid space limitations and is achieved by passing the excitation laser beam through a high (1.4)-aperture objective so that the light is incident at the glass/water interface beyond the critical angle. Long-term focus is maintained by a special feedback system. Of the possible effects that can influence the time course of the postbleach fluorescence recoveries—the EGF/receptor dissociation ratek ₂, the bulk solution diffusion rate of EGF, and the cell surface motion of the receptors—we infer that the dissociation ratek ₂ dominates. Several fitting schemes are compared and indicate the presence of a multiplicity of values fork ₂, ranging from about 0.05 to 0.004 s^–1, with an average value of about 0.012 s^–1. These results compare well with values previously obtained by radiolabel/washing techniques. The significance of the results in terms of kinetic models and the advantages of the TIRF technique for these sorts of measurements are discussed.     

A highly stereoselective synthesis of the C10–C31 (BCDEF ring) portion of pinnatoxin A

An efficient, highly stereoselective synthesis of the C10–C31 (BCDEF ring) portion of pinnatoxin A has been achieved utilizing tandem double hemiketal formation/intramolecular hetero-Michael addition to construct the 6,5,6-dispiroketal (BCD ring) system and subsequent intramolecular ketalization to form the 5,6-bicycloketal (EF ring) system as key steps.