Lattice gases and exactly solvable models

We detail the construction of a family of lattice gas automata based on a model of 't Hooft, proceeding by use of symmetry principles to define first the kinematics of the model and then the dynamics. A spurious conserved quantity appears; we use it to effect a radical transformation of the model into one whose spacetime configurations are equivalent to the two-dimensional states of an exactly solvable statistical mechanics model, the symmetric eight-vertex model with parameters restricted to a disorder variety. We comment on the implications of this identification for the original lattice gas.     

Statistical-thermodynamic approach to a chaotic dynamical system: Exactly solvable examples

The static and dynamic properties of a chaotic attractor of a two-dimensional map are studied, which belongs to a particular class of piecewise continuous invertible maps. Coverings of a natural size to cover the attractor are introduced, so that the microscopic information of the attractor is written on each box composing the cover. The statistical thermodynamics of the scaling indices and the size indices of the boxes is formulated. Analytic forms of the free energy functions of the scaling indices and the size indices of the boxes are obtained for examples of a hyperbolic and a nonhyperbolic chaotic attractor. The statistical thermodynamics of local Lyapunov exponents is also studied and a relation between the thermodynamics of scaling indices and of local Lyapunov exponents is invetigated. For the nonhyperbolic example, the free energy and entropy functions of local Lyapunov exponents are obtained in analytic forms. These results display the existence of phase transitions. A phase transition is seen in the thermodynamics of scaling indices also.     

Thermodynamic description of sorption processes in swelling systems

The thermodynamics of sorptive moistening of various types of swelling sorbents have been analyzed. The energy and entropy characteristics of the sorbed substance have been calculated.Institute of Physical Chemistry, Russian Academy of Sciences, Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 29–33, January, 1992.     

Evidence of ionic adsorption on C12E6 non-ionic micellar solutions

Summary In this paper we present conductivity measurements on different concentrations of C₁₂E₆ non-ionic surfactant solutions as a function of temperature and buffer ionic strength. The experimental data were analysed by means of Looyenga equation. The isothermal slopes of the linearized Looyenga equation depend on the ionic strength, showing saturation effect. Our results indicate that one of the basic hypotheses of the mixture equations is not fulfilled. Adsorption of light ions at micellar interface is necessary to justify the experimental data. Then for non-ionic surfactant solutions the ion adsorption prevents any explicit computation of the micellar hydrated volume. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

A multisymplectic framework for classical field theory and the calculus of variations II: space + time decomposition

In a previous paper I laid the foundations of a covariant Hamiltonian framework for the calculus of variations in general. The purpose of the present work is to demonstrate, in the context of classical field theory, how this covariant Hamiltonian formalism may be space + time decomposed. It turns out that the resulting “instantaneous” Hamiltonian formalism is an infinite- dimensional version of Ostrogradski 's theory and leads to the standard symplectic formulation of the initial value problem. The salient features of the analysis are: (i) the instantaneous Hamiltonian formalism does not depend upon the choice of Lepagean equivalent; (ii) the space + time decomposition can be performed either before or after the covariant Legendre transformation has been carried out, with equivalent results; (iii) the instantaneous Hamiltonian can be recovered in natural way from the multisymplectic structure inherent in the theory; and (iv) the space + time split symplectic structure lives on the space of Cauchy data for the evolution equations, as opposed to the space of solutions thereof.     

Auxiliary ghost fields in statistical dynamics

The path integral formulation of statistical dynamics involves a functional determinant whose role within the theory has remained somewhat unclear. This has occasionally led to incorrect generalizations of the formalism to the case of multiplicative random forces. We present a hidden symmetry of the theory and show how it can be used to clarify these issues. Important further applications are also pointed out.     

Simple inequality for the free energy of disordered systems

It is proved that the free energy of a disordered system described by a quadratic form in Bose or Fermi operators with random coefficients, calculated in the simplest approximation for the associated eigenvalue problem, gives the upper (Bose case) and lower (Fermi case) bounds for the exact free energy.     

Complexation of CH3Hg+ with chloride,sulfate and carbonate in NaClO4: construction of thermodynamic models

The complexation of CH₃Hg⁺ with major ions present in sea and estuary waters (Cl^?, SO₄^2? and CO₃^2?) was studied potentiometrically in an NaClO₄ medium in the ionic strength range 0.1–3.0 mol dm^?3 at 25 °C. The potentiometric data, treated with non‐linear least squares computer programs, led us to establish the formation of the species CH₃HgCl in equilibrium with chloride, CH₃Hg(SO₄)^? species with sulfate and no complex with carbonate. The stoichiometric stability constants obtained at the different ionic strengths were correlated by means of the modified Bromley methodology (MBM) to determine the corresponding thermodynamic constants and interaction parameters. This study is the second of a series designed to simulate, using the MBM thermodynamic model, the behaviour of methylmercury in different conditions of sea and estuary waters. In the first study of the series, the hydrolysis equilibria of methylmercury in NaClO₄ ionic media were established. Copyright © 2002 John Wiley & Sons, Ltd.     

Zustandsbarogramm und thermodynamische Daten für das System Germanium – Tellur

Barogram and Thermodynamic Data of the System Germanium—Tellurium The barogram Ge? Te is constructed by total pressure measurements. From the temperature function of the pressure of GeTe follows the thermodynamic data of sclid and gaseous GeTe and gaseous GeTe₂. The data are proved by chemical transport experiments of Ge with Tellurium.     

Stabilities and Thermodynamic Properties of Ethylenediamine-di(o-Hydroxyphenylacetic Acid) Chelates of Tripositive Lanthanide Ions

The interaction between ethylenediamine-di(o-hydroxyphenylacetic acid) (EDDHA, H₄Z) and tripositive lanthanide ions has been investigated. The formation constants of the protonated chelates (LnHZ) and those of the normal chelates (LnZ^?) have been evaluated at various temperatures and at a constant ionic strength of 0.1(KNO₁). For LnHZ, the pH-titrimetric technique, and for LnZ^?, the mercury indicator electrode method were used. The enthalpy and entropy changes characterizing the formation of LnZ^? have been calculated at 25° and, these functions have been compared with the corresponding values of other lanthanide chelates with related chelating agents.