The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).     

Influences of tissue composition and structural features of biological media on the ultrasonic nonlinearity parameter

The Acoustic nonlinearity parameter is an important parameter innonlinear acoustics.In this article,the nonlinearity parameter B/A of normaland eight kinds of pathological porcine liver tissues were measured by finiteamplitude insert-substitution method.The mixture law for nonlinearityparameter is used to analyze and predict the volume fractions of the compo-nents in a given tissue.It was found that the nonlinearity parameter is sensitiveto the pathological forms of biological tissues and the values of B/A dependon the tissue composition and structural features.     

Solubility parameters of poly(sulfonyldiphenylene phenylphosphonate) and its miscibility with poly(ethylene terephthalate)

The solubility behaviors of poly(sulfonyldiphenylene phenylphosphonate) (PSPPP), a very efficient flame retardant for poly(ethylene terephthalate) (PET), in more than 50 solvents were examined. Its solubility parameters (δ) were determined by the intrinsic viscosity and turbidic titration methods. The two methods obtained consistent results, δ = 21.0–21.6 J^1/2/cm^3/2 and δ = 21.0 J^1/2/cm^3/2, and the three‐dimensional solubility parameters were δ_d = 18.9 J^1/2/cm^3/2, δ_p = 8.8 J^1/2/cm^3/2, and δ_h = 5.9 J^1/2/cm^3/2. The miscibility of PSPPP with PET was estimated by the calculation of the heats of mixing, which were related to the difference between the solubility parameters of PSPPP and PET. Fourier transform infrared was used to examine the interactions between PSPPP and PET macromolecules, which were the internal factors of polymer–polymer miscibility. The results showed that PSPPP and PET were miscible within a very wide composition range, especially with less than 15 wt % PSPPP, a composition of interest for the preparation of flame‐retardant PET. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2296–2301, 2003     

Markov chain model of mixed surfactant systems

A new model of mixed surfactant systems have been developed in the work presented. It includes two parameters only connected directly with the Gibbs free energy of the surfactant aggregation. They can be determined using both the aggregation equilibrium constant values or the phase composition data. It has been shown also the relation between these new parameters and the same of the regular solution approximation and the alternative models. The possibility to describe the available experimental information about the micelle composition as a function of the singly dispersed surfactant mixture composition better than by the other models has been shown also.     

Non-leptonic weak charmed baryon decays in theSU(4) semidynamical scheme

We study here the Cabibbo enhanced charmed baryon decays in theSU(4) semidynamical model. The weak Hamiltonian 20″ + 15 + 45 + 45* can have the parity violating amplitude for charmed baryon decays. Decay width and α for some modes are also calculated.     

Parametric Statistical Uncertainty Relations and Parametric Statistical Fundamental Equations

Multivariate parametric statistical uncertainty relations are proved to specify multivariate basic parametric statistical models. The relations are expressed by inequalities. They generally show that we cannot exactly determine simultaneously both a function of observation objects and a parametric statistical model in a compound parametric statistical system composed of observations and a model. As special cases of the relations, statistical fundamental equations are presented which are obtained as the conditions of attainment of the equality sign in the relations. Making use of the result, a generalized multivariate exponential family is derived as a family of minimum uncertainty distributions. In the final section, several multivariate distributions are derived as basic multivariate parametric statistical models.     

Line group theory of commensurate and incommensurate modulations

It is shown that the line group formalism proposed is suitable to describe both commensurate and incommensurate modulations. Symmetry groups of modulated crystal lattices can completely be characterized by symmetry transformations existing in real space, without any application of the formalism based on reciprocal space. As typical examples of the method elaborated, the fundamental invariance and symmetry properties of spin density functions and the soliton lattice are determined. Received: 20 July 1997 / Accepted: 25 August 1997     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of fcc metals

New parameters which separately take into account the effects of elastic anisotropy and phonon dispersion on the lattice specific heat in the case of fcc metals have been evaluated. A new graded mesh method which uses 162-direction approximation in (1/16) part of the Brillouin zone has been developed to evaluate the two new parameters.     

Density of stratified ionic melts: Experiment and theory

Densities of phases co-existing in molten ionic systems with partial miscibility out of halides of alkali metals (KBr, KI, RbBr, RbI, CsCl, CsBr, CsI) with lithium fluoride are determined in a broad temperature interval by a method of hydrostatic weighing. A linear decrease in the difference between phase densities with increasing temperature is found for all systems. By studying a molten KBr-LiF mixture, this regularity is traced up to a critical miscibility point. The critical index of the order parameter, calculated from these data happens to equal 1/2 and coincide with results predicted by mid-field theory.     

Permeation of a solvent mixture through an elastomeric membrane—The case of pervaporation

This article presents a model for the permeation of solvent mixtures through an elastomer in the particular case of pervaporation. An analytical expression for each solvent permeation rate is derived, in the limited case of a membrane that undergoes small swelling, without making any assumptions on the solvent diffusion coefficients and their dependence on solvent concentrations. Applying this analytical expression to different situations, we fitted most of the curves previously published on pervaporation experiments. In particular, we correlated the synergy developed by a mixture of two solvents in the permeation process with the sign of their Flory–Huggins interaction parameter χ_AB. This explains why, in most cases (χ_AB > 0), a molecule permeating easily through a membrane is mixed with a molecule permeating much less easily; the latter can see its permeation flux increase by a factor 10 or 100 because the swelling of the polymer induced by the more permeable molecule “opens the meshes of the network” allowing the less permeable molecule to pass through more easily. Within our analysis, the efficiency of the pervaporation process, expressed through the separation factor, is derived very simply as a function of the interaction coefficients and the viscosities of solvents and exhibits an exponential dependence on the volume fraction of either component as seen in most experiments. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 183–193, 2003