Band 55, Heft 11-12

We study phase coupled chaotic systems. Using the Kronecker product we derive a recurrence relation for calculating the Ljapunov exponents of the phase coupled system. We investigate whether phase coupling can be used to control dynamical systems with chaotic behaviour.

The thermodynamic functions for the van der Waals equation are investigated at isobaric process. The Gibbs free energy is expressed as the sum of the Helmholtz free energy and PV, and the volume in this case is described as the implicit function of the cubic equation for V in the van der Waals equation. Furthermore, the Gibbs free energy is given as a function of the reduced temperature, pressure and volume, introducing a reduced equation of state. Volume, enthalpy, entropy, heat capacity, thermal expansivity, and isothermal compressibility are given as functions of the reduced temperature, pressure and volume, respectively. Some thermodynamic quantities are calculated numerically and drawn graphically. The heat capacity, thermal expansivity, and isothermal compressibility diverge to infinity at the critical point. This suggests that a second-order phase transition may occur at the critical point.

The self-exchange velocity (SEV) of neighboring unlike ions, has been evaluated by molecular dynamics simulations of molten CsCl, (Li, K)C1 and (Li, K, Cs)Cl at 673 K. From the increase of the SEV's in the same order as the internal mobilities it is conjectured that there is a strong correlation between these two properties. The pair correlation functions, and the self-diffusion coefficients and the SEV's of Li + , K + , and Cs + with reference to Cl - have also been calculated. The results allow to conclude that the self-exchange velocity of the cations become v Cs < v K < v Li at x Cs =0.1 and v Li < v K < v Cs at x Cs > 0.4. The sequence of the self-diffusion coefficients agrees with that of the SEV's. The results enable to conclude that it is possible to enrich Cs at up to x Cs ~ 0.3 - 0.4 in the molten LiCl-KCl eutectic system.

We determine a model of the ionic interactions in RX 3 compounds (where R is a metal in the rare-earth series from La to Lu and X = CI, Br or I) by an analysis of data on the static and dynamic structure of their molecular monomers. The potential energy function that we adopt is patterned after earlier work on Aluminium trichloride [Z. Akdeniz and M. P. Tosi, Z. Naturforsch. 54a, 180 (1999)], but includes as an essential element the electric polarizability of the trivalent metal ion to account for a pyramidal shape of RX 3 molecules. From data referring mostly to trihalides of elements at the ends and in the middle of the rare-earth series (/. e. LaX 3 , GdX 3 and LuX 3 ), we propose systematic variations for the effective valence, ionic radius and electric polarizability of the metal ions across the series. As a first application of our results we predict the structure of the Dy 2 Cl 6 and Dy 2 Br 6 molecular dimers and demonstrate by comparison with electron diffraction data that lanthanide-ion polarizability plays a quantitative role also in this state of tetrahedral-like coordination.

To find nontrivial high dimensional integrable models (especially in (3+1)-dimensions) is one of the most important problems in nonlinear physics. A systematic method to find some nontrivial high dimensional integrable models is established by means of noninvertible deformation relations. Starting from a noninvertible Miura type transformation, we find that the (1+1)-dimensional sinh-Gordon model appearing in many physical fields is a deformation of the (0+1)-dimensional Riccati equation. A high dimensional Miura type deformation (including two different (3+1)-dimensional reductions) of the heat conduction equation is proved to be Painlevé integrable. Some special types of explicit exact solutions, like multi-plane and/or multi-camber soliton solutions, multi-dromion solutions and multiple ring soliton solutions, are obtained.

We have built an electrical impedance tomograph which makes it possible to reconstruct impedance distributions in the interior of a cylinder by means of measurements of currents and potentials on its boundary. The reconstuction algorithm is based on Newton's algorithm for the solution of non-linear integral equations, where the electric fields are calculated by the methods of finite elements and finite integrals. The results can be represented graphically on a PC. The resolution is fine enough to envisage applications in medical diagnostcs.

This study deals with the effect of maturation on the ionic conduction of poorly crystalline synthetic apatite. The tendency of this materials to crystallise during maturation is accompanied by an improvement of its ionic conductivity σ. At room temperature, σ increased by a factor of 300 after 50 days of maturation. The frequency dependence of the ionic conductivity was attenuated gradually during maturation. These results are explained by the short-range organisation of sites with time, and by the fact that the translational movement of the mobile ions becomes less hindered as the material matures.

The EPR spectra of Cu 2+ in zinc saccharin crystalline powder and single crystals have been recorded at room temperature. The angular variation of the spectra indicates the substitution of the host Zn 2+ with Cu 2+ . Two magnetically inequivalent sites for Cu 2+ have been observed. The spectra were fitted with a rhombic spin-Hamiltonian, and the ground state wave function of the complex has been constructed.

Single crystals of pyridinium periodate were grown, and their physical properties were studied. Anomalies of the electric permittivity and birefringence were observed at T C1 = 321 K and T C2 = 211 K. These observations gave evidences for the existence of three phases denoted as I, II, and III. Hysteresis loops were observed both in phase II and III. Pyroelectric measurements showed two anomalies at T C1 and T C2 . The anomaly at T C1 is related to the transition between a para-and ferroelectric phase, and the anomaly at T cl to the transition between two ferroelectric phases.

Phase equilibria of non-mesogenic caesium- and zinc-butyrate mixtures were studied by differential thermal analysis and hot stage polarization microscopy. Smectic liquid crystals were found in some composition range. Their appearance is explained by the latent mesomorphism of caesium butyrate. | 133 Cs NMR spectra and the specific electrical conductivity of the molten mixtures at 155°C were employed to investigate the peculiarities of ionic association and interaction in the melts.

The phase transition temperatures were determined by differential thermal analysis and hot stage polarization microscopy between room temperature and the isotropic liquid region for the binary systems of lead (II) decanoate with zinc (II) or cadmium (II) decanoate. The boundaries of the liquid crystal formation in these systems were found.

2-dimethylamino-9-fluorenol and 2-dimethylamino-9(4'dimethylamino)phenyl-9-fiuorenol in polar solvents in the excited state undergo conformation changes in which two fluorescent isomers are created. The isomers (in the local excited (LE) and charge transfer (CT) configuration) possess separate fluorescence bands, one appearing from the S 1 (LE) state and the second from the intramolecular charge transfer state S 1 (CT) of the neutral, aromatic molecule. Both bands show a solvatochromic effect. Using the method of the solvent induced Stokes shift of the absorption and fluorescence spectra the permanent dipole moment of the excited state of fluorene and its two derivatives have been determined. The dipole moment of the ground state and the Onsager cavity radius of the studied molecules were calculated with the Auestion Model 1 (AM1) program.

With thin wire multimegampere shear flow stabilized fast z-pinch discharges, magnetic fields of hundreds of megagauss can be reached in the vicinity of the discharge channel. Then, if by laser-ablation-propulsion pieces of solid DT are simultaneously shot onto the discharge channel from several sides, the DT is compressed upon impact to high densities, with the magnetic field acting as a cushion to make the compression isentropic. The highly compressed and magnetized DT target can then be ignited at one point by a pulsed laser beam launching a thermonuclear detonation wave propagating along the discharge channel. Estimates indicate thermonuclear gains large in comparison to hohlraum targets.

The local energy is first reviewed and compared with the expected energy. We then present the perturbative local energy method which uses an exactly soluble base problem and a perturbing potential to greatly simplify the expression of the local energy. This is demonstrated with two-electron atoms for which the method gives upper bounds with errors from 18% for He to 4% for Ne 8+ . Finally a call to develop a local energy method for large systems is issued.

By fitting the calculated EPR g i (i = x , y, z) factors to the observed values, the local release factor k l which is introduced to characterize the release (or elongation) effect of impurity-ligand bonds along the rotational axis in the cubic-to-tetragonal phase transition of ABX 3 perovskites, is obtained for the Ni + - II center in RbCaF 3 crystal. The result shows that, similar to the local rotational angle (or order parameter) Φ , the local release factor is unlike that of the host crystal. It suggests that in the doped crystal the impurity can affect the local phase transition behaviour in the vicinity of impurity ions.

The molecular ordering of some biphenyl derivatives like 4-acetyl-2'-nitrobiphenyl (ANBP), 4-nitro-2-biphenylamine (NBPA) and 4-acetyl-3'-chlorobiphenyl (ACBP) has been examined using basic con-cepts of quantum mechanics and intermolecular forces. The CNDO/2 method has been employed to compute the net atomic charge and atomic dipole components at each atomic centre. The modified Ray-leigh-Schrödinger perturbation theory along with the multicentred-multipole expansion method has been employed to evaluate long-range interactions while a '6-exp' potential function has been assumed for short-range interactions. Accuracies upto 0.1 A in translation and 1° in rotation have been achieved. Probability of occurrence of a particular configuration has been calculated using MB-statistics. On the basis of stacking and in-plane interaction energy calculations, all possible geometrical arrangements between molecular pairs have been considered and a most favorable configuration of pairing has been obtained. A comparative picture of molecular parameters like total energy, binding energy, total dipole moment etc. has been given. An attempt has been made to develop a molecular model correlated with the liquid crystalline property exhibited by this class of molecules.

Molecular ordering in a liquid crystal, ethyl 4-(4'-methoxybenzylidene amino) cinnamate (EMBAC) has been studied by intermolecular interaction energy calculations. The CNDO/2 method has been employed to compute the atomic charge and atomic dipole at each atomic centre. The modified Rayleigh-Schrödinger perturbation theory along with the multicentered-multipole expansion method have been employed to evaluate the long-range intermolecular interactions, while a '6-exp' potential function has been assumed for the short-range interactions. On the basis of stacking, in-plane, and terminal interaction energy calculations all possible geometrical arrangements of a molecular pair have been considered, and the most favourable configuration of the pair has been obtained. Molecular parameters like total energy, binding energy and total dipole moment have been given. Results are discussed in the light of those obtained for the nematogens 4-(4'-ethoxyphenylazo) phenyl valerate (EPPV) and 4,4'-di-n-propoxy-azoxybenzene (DPAB). An attempt is made to explain the liquid crystalline behavior of these liquid crystals and thereby develop a molecular model for liquid crystallinity.

A computational analysis of the molecular ordering of 4-(4'-ethoxyphenylazo) phenyl hexanoate (EPPH) has ben carried out on the basis of intermolecular interaction energy calculations. The CNDO/2 method has been employed to evaluate the net atomic charge ad atomic dipole moment components at each atomic centre of the molecule. A modified Rayleigh-Schrödinger perturbation theory alongwith a multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a "6-exp" potential function has been assumed for short-range interactions, and corresponding probabilities have been calculated in a dielectric medium (benzene) using the Maxwell-Boltzmann formula. Further, the flexibility of various configurations has been studied in terms of variations of the probability due to departure from the most probable configuration. All possible geometrical arrangements between molecular pairs have been considered during stacking, in-plane and terminal interactions, and the most favourable configuration of the paring has been obtained. It has been observed that in a dielectric medium the probabilities are redistributed and there is a considerable rise in the prob-ability of interactions although the order of preference remains the same. An attempt has been made to explain the nematogenic behaviour of liquid crystals and thereby develop a molecular model for liquid crystallinity. Results have been discussed in the light of those obtained for other nematogens like EPPV [4-(4'-ethoxyphenylazo) phenyl valerate] and DPAB [4-4'-di-n-propoxy-azoxybenzene],

The phase diagram of 4-cyanobenzyl-5-(4-«-octyloxybenzoyloxy)-2-undecyloxybenzoate (4CNOUB) has been established with differential thermal analysis (DTA). The pressure range for the smectic A phase is limited, resulting in a triple point at 165 MPa and 378.26 K. p, V m , T data have been measured for the smectic and istotropic phases of 4CNOUB between 243 and 383 K and up to 250 MPa. The volume changes accompanying the crystal - smectic and scmectic - isotropic transitions have been deter-mined. The corresponding enthalpy changes have been calculated using the Clausius-Clapeyron equation. The p, V m , T data enable also to estimate the volume entropy for the smectic - isotropic transition and the volume dependence of the clearing temperature.

Using a variational method, a new model of the nonlinear propagation of optical solitons generated from semiconductor lasers through a lossy elliptically low birefringent fiber, is presented within the frame-work of a system of coupled nonlinear Schroedinger (CNLS) equations. This model demonstrates polarized soliton oscillations in a lossy elliptically low birefringent fiber.

AC conductivities at 5 Hz-10 kHz and 78 K up to room temperature of bis- (ethanolammonium) Co 2 X 6 , and bis- (ethanolammonium) Cu 2 X 6 , X=C1 and Br are reported. At high temperatures, band type conduction prevails for all dimers. In the low temperature range T< 200 K the (Co 2 Br 6 ) -2 dimer conducts via small polarons and the other three dimers conduct via quantum mechanical tunneling. The obtained relaxation times for the different dimers were found to be 1.1 • 10 -14 s. The frequency dependence follows the universal power law σ ac (ω) = A ω s . The exponent s and the pre-factor A were found to be very sensitive to the phase transitions, with 5 showing a minimum or maximum at the transition temperature. Changes in the conduction mechanism are reflected by abrupt changes in the variation of the pre-factor A vs 1/T relation. The conduction is found to depend on the type of the halide ion rather than on the transition metal ion. PACS #76, 74.

The linear stability problem for a fluid in a classic Benard configuration is considered. The applied temperature gradient is the sum of a steady component and a time-dependent periodic component. Only infinitesimal disturbances are considered. The time-dependent perturbation is expressed in Fourier series. The shift in critical Rayleigh number is calculated and the modulating effect of the oscillatory temperature gradient on the stability of the fluid layer is examined. Some comparison is made with known results.

A simple model based on the concept of a layered structure near the interface has been used to investigate the surface tension and surface segregation of SnPb and SnZn molten alloys. With increasing concentration of Sn, the surface tension (σ) of SnPb alloys has been found to increase, while a of SnZn alloys decreases, σ of both systems is smaller than the ideal value ΣC i σ i . Our study reveals that both in SnPb and SnZn alloys the heavier atoms segregate towards the surface. The degree of segregation in SnZn alloys is greater than that in SnPb alloys. The Cahn-Hillard phenomenological model for the surface of pure liquids has been extended to binary molten mixtures and applied to the above systems. An attempt has been made to establish a link between the surface tension and the bulk properties such as concentration fluctuations in the long wavelength limit [S cc (0)] and isothermal compressibility (λ T ). The impact of the very sensitive bulk parameter S cc (0) has been examined. Reasonable agreement between our model and the experiment is observed for binary molten alloys such as SnPb in which the segregation is small, while for the SnZn alloys, in which the segregation is quite large, the agreement is not satisfactory.

It was observed that within the Bieri-Dill-Heilbronner-Schmelzer model for the calculation of the ion-ization energies of alkanes C n H 2n+2 , there are exactly n C 2s -electron energy levels lying below the degenerate α-ß manifold. We now show that, indeed, this regularity is obeyed by practically all alkane species. Exceptions do exist, but they must possess a (chemically infeasible) group of more than six mutually connected quaternary carbon atoms.