Volume 52, Issue 8-9

We investigate localized periodic solutions (breathers) in a lattice of parametrically driven, nonlinear dissipative oscillators. These breathers are demonstrated to be exponentially localized, with two characteristic localization lengths. The crossover between the two lengths is shown to be related to the transition in the phase of the lattice oscillations.

We establish a straightforward connection between spatially extended systems, the dynamics of which are modeled with the help of partial differential equations and time-delay systems. To this end, we give a linear partial differential equation with a nonlinear boundary condition whose solutions are equivalent to the solutions of a time-delay differential equation. We observe that the phase space of these systems exhibits a pronounced structure. In this paper, we express the structure of the phase space of time-delay systems and the corresponding spatially extended system by distinguishing between a ‘linear subsystem’ and a ‘localized nonlinearity’. We find that the high-dimensional chaotic dynamics observed in time-delay systems is fundamentally different from the spatio-temporal chaos observed in homogeneous spatially extended systems, the dynamics of which is modeled with the help of nonlinear partial differential equations. To this end, we investigate the space-time correlation function and the ‘thermodynamic limit’.

A numerical simulation of a chain of diffusively coupled nonlinear oscillators with a linear parameter gradient exhibits clusters of frequencies. The intention was to investigate the frequency-gradient in the stimulus conduction system of the heart. The phenomenon generalizes earlier findings on “frequency plateaus” described in the 1960's by Nicholas Diamant as a model of small-intestine transport. This “waxing and waining” phenomenon is a version of chaos. Thus, subtle chaos in the heart and waxing and waining type chaos in the intestine may be related.

A new visualization method is found for investigating the complex ray dynamics of whispering gallery orbits inside the Bunimovich stadium. Regarding the whispering gallery as mirror cabinet, a fractal system of virtual images of the mirror walls is found which reflects the sensitive dependence of the dynamic behavior on the initial conditions.

A form of the Verlet-algorithm for the integration of Newton’s equations of motion is derived from Hamilton's principle in discretized space and time. It allows the computation of exactly time-reversible trajectories on a digital computer, offers the possibility of systematically investigating the effects of space discretization, and provides a criterion as to when a trajectory ceases to be physical.

A new application of the theory of Markov processes to the characterization of fractal scaling behavior is presented. We show under which condition distinct stochastic processes of a cascade lead to multifractal scaling behavior. We apply our method to the analysis of the statistical properties of the energy in turbulent fluid flow.

A new synthesis based on microscopic classical thinking is attempted in the spirit of the molecular-dynamics-simulation (MDS) paradigm. Leibniz’s idea that joint scale transformations cancel out is invoked. Boltzmann discovered that a time reversal in the whole universe is undetectable from the inside. As a corollary, objective micro time reversals occur in the interface between a subsystem and the rest of the universe, whenever the former undergoes a time reversal. This is shown to occur in a generic class of Hamiltonian systems. The “microinterface” arrived at generalizes the macro frame of relativity to the micro realm. Micro relativity comprises Bohr’s idea of an observer-relative complementarity and Everett’s idea of an observer-relative state. As in relativity proper, a multiplicity of worlds (cuts) exist. For the inhabitants of an artificial MDS universe, therefore a radically new option is available: world change technology.

By computing the probability distributions of the velocity difference between cars a time-delay τ apart, the scaling properties of traffic flow can be analysed. These data display scaling behaviour thus confirming earlier results that have found 1/ f α -noise in traffic flow. Furthermore, the applicability of the scaling analysis for describing the two-point statistics of traffic flow is demonstrated, leading to an additional test for the dynamical properties of microscopic and macroscopic traffic flow models.

We propose a method of contructing chaotically synchronizing systems and give examples of two control algorithms based on properties of Lipschitz maps. Bifurcation diagrams show the robustness of the method for broad band of control parameters.

The phase transition at T c = 243 K in ammonium chloride is well established to be of the order-disorder type. The ammonium chloride has a CsCl-type cubic structure with hydrogen atoms pointing toward four of the eight chloride ions at the corners of the unit cell. This means that there are two possible orientations of ammonium tetrahedron; a and b. In the ordered phase below the T c temperature all ammonium ions have the same, let it be a, orientation. Above the T c temperature ions are randomly distributed among the two possible orientations a and b. An attempt was made to correlate such structural transition with the second moment of the proton NMR absorption line. This approach was chosen because the second moment is the parameter of the NMR line for which the exact theoretical formula exist, and which is mainly a function of the structure and the reorien-tational state of the studied material. It was found that the NMR second moments calculated for the described above model of the structural transition properly reflect the changes of the experimental NMR second moments measured at temperatures below and above this transition.

The temperature dependence of the 35 Cl nuclear quadrupole resonance (NQR) frequency and spin lattice relaxation time (T 1 ) are studied in crystalline BiCl 3 , in the range 40-300 K. The positive temperature coefficient observed for one of the 35 Cl resonances is explained in terms of the strong intermolecular interactions that exist in this compound. Variation of with temperature is found to be similar at the chemically inequivalent halogen sites. Semiclassical descriptions based on torsional oscillator dynamics are found to be inadequate for explaining the spin lattice relaxation. T 1 (T) data follow an AT 2 + BT 3 type behaviour, indicating that the anharmonic nature of the lattice vibrations plays a significant role in determining the temperature dependence of T 1 at high temperatures.

Charging currents, J-V characteristics and electron conductivity have been measured in triglycine sulphate along three crystallographic directions: a, b and c. The measurements have been taken in a wide temperature range between −196°C and 80 °C. It is found that the charging currents have short relaxation times in the directions: a and c and a long relaxation time along the ferroelec-tric b axis. The J-V characteristics in the direction of the a and c axes have the shapes characteristic for linear dielectrics with space charge limited currents. The J-V characteristic for the b axis depends on the temperature: In the region of the phase transition the Fridkin-Kreher formula (J ∝ V 4/3 ) is satisfied; for low temperatures characteristic agrees with SCLC theory for linear dielectrics with Gaussian traps energy distribution. The d.c. conductivity along the c axis is much higher than along the a and b axes. In the investigated temperature range, the electrical conductivity has an activation character. For −100 °C < T < −193 °C there is: σ ∝ (1/T) exp (− E/kT) . The activation energy depends both on the crystallographic direction and on the temperature-range. For low temperatures, T < −100 °C, the activation energies are very small (of the order of a few hundreds eV).

An alternative approach to log-log plots for defect equilibria in the solid state and ionic equilibria in solution is presented. The method is based on the strictly monotone character of the functional dependence of an externally controlled thermodynamic variable (e.g. the oxygen partial pressure P(O 2 ) for the defect equilibria in a simple oxide, or a total concentration for the ionic equilibria in solution) on a chemically relevant compositional variable (such as the electron concentration n for defect equilibria, or [H 3 O + ] or a free ligand concentration for solution equilibria). This functional dependency can be safely inverted. The concentration of all species and the externally controlled thermodynamic variable can be calculated as a function of the chemically relevant compositional variable. The appropriate plots are then obtained using naively a spreadsheet program. This method gives exact results in many more cases than the traditional approach.

The 1 H spin-lattice and spin-spin relaxation times, and the second moment of the 1 H NMR linewidth of choline Perchlorate, [(CH 3 ) 3 NCH 2 CH 2 OH]ClO 4 , were measured in its highest-temperature solid phase, i. e. above 275 K. X-ray powder patterns taken at ca. 380 K revealed that in this phase the crystal has a CsCl-type cubic structure (a = 6.326(4) Å and Z = 1). From 1 H NMR experiments it was found that the cations in this phase undergo isotropic rotation and translational self-diffusion. From the 1 H T 1 , measurements, the activation energies of the cationic rotation and self-diffusion were evaluated to be 21.4 ± 0.4 and 62 ± 3 kJ mol -1 , respectively.

Resistivity measurements on thin films are very suitable for the study of the kinetics of reactions on metallic surfaces. The oxidation of carbon monoxide on palladium is investigated as an example of great technical relevance, where details of the reaction mechanism and the film structure are well-known from literature. The time dependence of the change in resistivity is quantitatively interpreted with the help of a diffusion model based on a Monte-Carlo simulation of the gas coverage of the surface.

Molten Mn 74 Si 26 and molten Mn 33.5 Si 66.5 were investigated by neutron diffraction. The pair correlation function yielded, together with the X-ray results from a former paper, the partial coordination numbers, atomic distances, and the short range order parameter with the result that the atomic distribution in molten Mn 33.5 Si 66.5 is statistical while the structure factor of molten Mn 74 Si 26 , as obtained with neutrons, shows a strong prepeak which means rather strong compound formation.

The methylene blue - saccharide - NaOH system, the so-called “Blue Bottle” experiment was investigated. When this system is poured into an open petri dish, spatial structures start to generate after an induction period. The induction period increases in the order of xylose < glucose < galactose < arabinose < mannose.

High resolution ultraviolet (UV) and molecular beam Fourier transform microwave (MB FTMW) spectroscopy of the benzonitrile·water (BZNW) cluster were performed to measure cluster structures in the S 0 and S 1 states. The MW experiments provide additional information on the structure and the 14 N-nuclear quadrupole coupling in the ground state So, the UV experiments on the dynamics in Si. The rotationally resolved sub-Doppler UV spectra of BZNW were measured by mass-selective resonance-enhanced two-photon ionization. For the first time this UV technique has been applied to hydrogen-bonded clusters. From the UV spectra the rotational constants are obtained by Correlation Automated Rotational Fitting. The MW spectra were analyzed with the model of a centrifugally distorted rotor including nuclear quadrupole coupling. A r 0 -fit of the water position within the cluster is performed. The water is found to be located with its oxygen nearly in the plane of benzonitrile (BZN). For S 0 (S 1 ), the distance of the oxygen to the ortho hydrogen is r 0 = 2.477(4) Å (2.457(2) Å) and the angle to the ortho carbon-hydrogen bond 143.34(2)° (141.91(3)°). The structure differences in S 1 and S 0 can be explained by the structure changes of the BZN molecule. A line broadening, which points to a faster decay in Si upon clustering with the polar solvent, is observed for the BZNW cluster.

In continuation of earlier work, a set of 90 non-cyclic organic compounds was used to determine atom-in-molecule polarizability increments employing Metzger’s combination of the semiempirical MINDO/3-FP method and a partitioning of the molecular dipole moment. The group contained alcohols, ethers, amines, amides, and carboxylic acids. More than one hundred arbitrarily chosen molecules were then used to evaluate the new set of increments. This set of compounds does not overlap with the one used to derive the increments. The molecular polarizabilities calculated employ-ing the increments were found to correlate nicely with the corresponding “experimental” values determined by means of the Lorenz-Lorentz equation. Thus, the atomic increments together with the correlation equation provide access to polarizabilities which might for example be used to calculate the dispersion-and induction contributions to the lattice energies of organic molecular crystals.

Dielectric spectra (up to 72 GHz) have been measured at 20 °C for mixtures of methanol and one of the following substances: morpholine, N-methyl morpholine, N-cyano morpholine, pyrrolidine and N-cyano pyrrolidine. The composition dependence of the relaxation parameters shows close similarities for the morpholines and, on the other hand, for the pyrrolidines, which indicates that a structure breaking effect on methanol is exerted by the former but not by the latter group of substances.

It is shown that the fundamental quantity v of the inverse transformation does not turn out to be negative.

The crystal structure of the highest-and second highest-temperature solid phases of choline tetrafluoroborate and iodide was determined by X-ray powder diffraction. The structure in the highest-temperature phase of both salts is NaCl-type cubic (a = 10.16(2) Å, Z = 4 for tetrafluorobo-rate; a = 10.08(2) Å, Z = 4 for iodide). The second highest-temperature phase of tetrafluoroborate and iodide is CsCl-type cubic (a = 6.198(6) Å and Z = 1) and tetragonal (a = 8.706(2) Å, c = 6.144(6) Å, and Z = 2), respectively. DSC was carried out for the iodide, where the presence of three solid-solid phase transitions was confirmed. Enthalpy and entropy changes of these transitions were evaluated.