Volume 53, Issue 5

The general structure of thermodynamic equilibrium states for a class of quantum mechanical (multi-lattice) systems is elaborated, combining quantum statistical and thermodynamical methods. The quantum statistical formulation is performed in terms of recent operator algebraic concepts emphasizing the role of the permutation symmetry due to homogeneous coarse graining and employing the internal symmetries. The variational principle of the free energy functional is derived, which determines together with the symmetries the general form of the limiting Gibbs states in terms of their central decomposition. The limiting minimal free energy density and its possible equilibrium states are analyzed on various levels of the description by means of convex analysis, where the Fenchel transforms of the free energies provide entropy like potentials. On the thermodynamic level a modified entropy surface is obtained, which specifies only in combination with its concave envelope the regions of pure and mixed phase states. The symmetry properties of a certain model allow to specify the (non-) differentiability of the minimal free energy density. A characterization and classification of phase transitions in terms of quantum statistical equilibrium states is proposed, and the connection to the Landau theory is established demonstrating that the latter implies a (continuous) deformation of the sets of equilibrium states along a canonically given curve.

Molecular dynamics simulations have been performed with and without three-body corrections at an average temperature of 240 K using a flexible ammonia model. The system consists of one calcium ion and 215 ammonia molecules. The calcium(II)-ammonia interactions were newly developed, based on ab initio calculations with a basis set of double zeta quality. The role of three-body interactions on the structural and dynamical properties of the solution has been investigated. The presence of three-body corrections leads to the reduction of the first shell coordination number of Ca(II) in liquid ammonia from 9 to 8, the increase of the size of the solvation shell by 0.33 A and the disappearance of the sec-ond solvation shell.

The method of multiple scales is used to analyse the nonlinear propagation of waves on the interface between two superposed dielectric fluids with uniform depths in the presence of a normal electric field, taking into account the interfacial surface charges. The evolution of the amplitude for travelling waves is governed by a nonlinear Schrödinger equation which gives the criterion for modulational instability. Numerical results are given in graphical form, and some limiting cases are recovered. Three cases, in the pure hydrodynamical case, depending on whether the depth of the lower fluid is equal to or greater than or smaller than the one of the upper fluid are considered, and the effect of the electric field on the stability regions is determined. It is found that the effect of the electric field is the same in all the cases for small values of the field, and there is a value of the electric field after which the effect differs from case to case. It is also found that the effect of the electric field is stronger in the case where the depth of the lower fluid is larger than the one of the upper fluid. On the other hand, the evolution of the am-plitude for standing waves near the cut-off wavenumber is governed by another type of nonlinear Schrödinger equation with the roles of time and space are interchanged. This equation makes it possible to determine the nonlinear dispersion relation, and the nonlinear effect on the cut-off wavenumber.

P, V m , T data were established for 4'-n-hexyl-biphenyl-4-carbonitrile (6CB) and 4'-n-heptyl-biphenyl-4-carbonitrile (7CB) between 300 and 370 K up to 300 MPa, and specific volumes were determined for the liquid crystalline, isotropic, and also partly for the crystal phases. Volume and enthalpy changes at the phase transitions are also presented. In the case of 6CB, a new crystal phase has been detected, corresponding to a triple point at 338 K and 196 MPa. The p, V m , T data enabled us to separate the entropy change into a volume-dependent part and configurational part. From the molar volumes along the nematic-isotropic phase transition T Nl (p), the molecular field parameter γ=∂lnT NI /∂lnV NI was determined.

The reaction between hematite and aluminum in presence of allumina as diluent activated by Ball Milling powder mixtures in different energetic conditions has been investigated. To this purpose, the powders at different milling times have been characterized by X-ray Diffraction and Mössbauer Spectroscopy. A self-substained combustion reaction was observed when the strongest energetic conditions of milling were adopted. The intermediate products of the reaction also depend on the energetic conditions: the formation of hercynite is favoured by the use of strong energetic conditions while the formation of an Fe-Al alloy was observed when a low energy per single hit is transferred to the powders.

Electron Paramagnetic Resonance (EPR) studies of Cr 3+ in single crystals of tris(guanidinium) hexafluoroaluminate, [C(NH 2 ) 3 ] 3 AlF 6 , have been carried out in the X-band region. A temperature dependent study of the zero-field splitting parameter D in the range 77-398 K shows the presence of a phase transition, which is supported by Differential Thermal Analysis. In addition, 19 F superhyperfine struc-ture has been observed in the 9.3% naturally abundant 53 Cr isotope hyperfine structure. D shows a large decrease with increasing temperature. The phase transition brings about a chemical inequivalence in the two chemically equivalent but magnetically inequivalent room temperature (CrF 6 ) 3- species. Compar-ison is made with the alums AlCl 3 • 6H 2 0, as well as other guanidinium aluminum salts.

To study a nonlinear partial differential equation (PDE), the Painleve expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painleve analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is used for many nonlinear integrable and nonintegrable PDEs such as the Burgers, Korteweg de-Vries (KdV), Kadomtsev-Petviashvli (KP), Caudrey-Dodd-Gibbon-Sawada-Kortera (CDGSK), Nonlinear Schrödinger (NLS), Davey-Stewartson (DS), Broer-Kaup (BK), KdV-Burgers (KdVB), λf 4 , sine-Gordon (sG) etc.

In this paper the results of X-ray diffraction experiments of Ln-Si-Al-O-N (Ln = La, Gd, Yb) glasses are presented. Total structure factors and pair correlation functions allow the determination of the first coordination sphere of Ln atoms. The bond lengths observed correspond to the ionic radii of the Ln-ions surrounded by oxygen and nitrogen atoms. The presence of non-bridging nitrogen is discussed together with results of neutron diffraction, NMR-experiments and XPS-studies of other authors.

An experimentally discovered inverted spiral-type chaotic attractor is reproduced by a model equation. Does there exist a simple equation for the attractor re-cently found both in an electronic and a hydrodynamical system [1]? After a first, unpublished attempt by Sven Sahle to mirror a classical spiral-type attractor using a tube put into the middle, which yielded "messy" equa-tions, a fairly simple ordinary differential equation (ODE) was found and will be presented in the following. An experimental result is reproduced in Figure 1. It Deviation Fig. 1. Experimental attractor obtained with a hydrodynami-cal system, cf. [1]