Volume 50, Issue 12

The integer quantum Hall effect (IQHE) and its breakdown (onset of dissipation) reflect general properties of the solutions of the time-dependent Schrödinger equation, where the macroscopic elec­tric field E is properly included. In particular, the dynamics of an electron in a broadened Landau band not only depends on the disorder potential but also on the value of |E|. This leads to an I n ­ dependence of the conductivities σ xx and σ xy , which implies that the IQHE breaks down if |E| is sufficiently high. We show that the general form of the | El-dependence of σ xx and σ xy can lead to jumps in the longitudinal resistance at the breakdown of the IQHE, as observed in recent experiments.

We examined the spatio-temporal behavior of an electrochemical system in the bistable regime, in which the system might take on either a high current density state (active) or a low current density state (passive) at one value of the externally applied voltage. The transition from the passive to the active state is accompanied by accelerating fronts with sharp interfaces, whereas the reverse transition from the active to the passive state exhibits much smoother spatial variations. Also the evolution of the total current density displays qualitative differences in the two cases. Both, the differences of the spatial patterns as well as those of the total current densities are reproduced with a mathemati­cal model, which also reveals the origin of the asymmetry of the transitions: a global coupling, intrinsic in all electrochemical systems, in combination with the specific dependence of the reaction current on the electrode potential.

We investigate the transition from a mono-scroll to a double-scroll attractor observed in the chaotic dynamics of an electronic oscillator. The description in terms of an attractor merging crisis turns out to be successful. The finding is supported by the topological structure of the attractor and the scaling behavior of the mean residence time.

We investigate the dynamics of the Frenkel-Kontorova model with inertia and damping under a uniform driving force. We consider the dependence of the velocity-force characteristic, and the corresponding sliding states on the damping: In the overdamped limit the asymptotic solution with nonzero sliding velocity is unique and periodic. Periodic solutions and their stability can also be calculated for decreasing damping, where the dynamics is dominated by resonance effects of the underlying potential with the phonon modes of the chain. The asymptotic velocity is not unique, leading to hysteresis in the velocity-force characteristic. In addition to periodic sliding states, which lose stability for decreasing damping, quasiperiodic or spatio-temporal chaotic behavior occurs.

The dynamics of the lateral leaflet movement of Desmodium motorium is studied. Simple periodic, quasiperiodic and aperiodic time series are observed. The long-scale dynamics may either be uniform or composed of several prototypic oscillations (one of them reminiscent of homoclinic chaos). Diffusively coupled nonlinear oscillators may account for the variety of ultradian rhythms.

Dweiltime analysis is known to characterize saddles giving rise to chaotic scattering. In the present paper it is used to characterize the dependence on initial conditions of the attractor approached by a trajectory in dissipative systems described by one-dimensional, noninvertible mappings which show symmetry breaking. There may be symmetry-related attractors in these systems, and which attractor is approached may depend sensitively on the initial conditions. Dwell-time analysis is useful in this context because it allows to visualize in another way the repellers on the basin boundary which cause this sensitive dependence.

The concept of generalized Frobenius-Perron operators is applied to multivariante nonlinear dynamical systems, and the associated generalized free energies are investigated. As important applications, diffusion-related free energies obtained from normally and superlinearly diffusive one-dimensional maps are discussed.

We investigate the statics, nucleation, and dynamics of stable kink-antikink pairs (KAP) in a one-dimensional, one-component reaction-diffusion equation with a piecewise linear nonlinearity. The stabilization of the KAP is due to the presence of a strongly nonlocal inhibitor. We find a saddle-node bifurcation of a metastable KAP with a separation proportional to In L, where L is the length of the sample. The KAP becomes globally stable at a characteristic separation proportional to √L. The nucleation of a KAP from the metastable uniform state differs from the case without nonlocality mainly by a change of the activation energy induced by the nonlocality. Furthermore, we investigate the dynamics of the stable KAP in the presence of an external driving force and a diluted density of pointlike impurities; in particular, we derive expressions for the mobility and the average elongation of the KAP.

We investigate the generalized Rössler system introduced by Baier and Saale. They have linearly coupled additional degrees of freedom to the original Rössler system in order to construct a set of equations which shows maximum instability at an arbitrary dimension N, i. e., N - 2 positive Lyapunov exponents. We present a transformation into a mode picture. It enables a qualitative understanding of the mechanism generating the dynamics of this complex system. The advantages of our approach are demonstrated for the exemplary case N = 5.

A macroscopic chemical oscillator involving 3 autocatalytic second-order reactions is simulated microscopically. A deterministic Newtonian simulation involving 1024 particles with a smooth 1/r potential in two dimensions is presented.

Starting from an algorithm for continuous chaos control, a reversible control method based on mutual diffusive coupling of chemical reactors is developed. With sufficient coupling strength, the proposed mutual coupling leads to control even if both reactors are of similar size. The controlling and controlled reactor exchange their roles at a certain size ratio. Insufficient coupling can lead to a more complex dynamics than that of the uncoupled reactors. This method for control via reversible coupling of chemical reactors should be implementable on a purely microscopic level.

We investigate the model of an enzymatic reaction with Michaelis-Menten kinetics and bell-shaped pH-dependence of the reaction rate. In the case of proton consumption the reaction can generate oscillations in a homogeneous reactor and turbulent spatio-temporal patterns in a reaction-diffusion environment. I n s t a b il it i e s in a S im p le E n z y m e R e a c tio n C a u s e d b y p H -D e p e n d e n c e *

The complex conductivity of lithium aluminosilicate based glasses and glass-ceramics (Zerodur from Schott) has been investigated in a broad range of temperatures (200 K < T < 700 K) and frequencies (10 mHz<v<2.5 THz). The data are presented in terms of the conductivity and the electrical modulus formalisms. The width of the modulus loss peak as measured for the ceramic sample is broader than that determined for its precursor glass. This result is shown to be associated with the considerably smaller dc conductivity of this material.

We have observed two radicals in the ESR spectra of γ-irradiated single crystals of acetylcholine picrate and methoxycarbonylcholine picrate hemihydrate. These radicals have been identified as the CH 3 COOH and -CH 2 CH 2 respectively.

Synthetic FeS 2 and RuS 2 single crystals were prepared by the flux method using PbCl 2 , bismut, and tellurium as different solvents. FeS 2 and some RuS 2 samples were doped with elementary vanadium, other RuS 2 crystals with manganese and nickel. The EPR spectra revealed Mn 2+ in the low-spin state and Ni 2+ . The lineshape of the Mn sextet turned out to be asymmetrical. In some RuS 2 samples we detected an isotropic structureless rather narrow signal with a linewidth down to 0.05 mT and attributed it to the conductivity. Its lineshape becomes symmetrical and Lorentzian by grinding the samples to a polycrystalline powder. The EPR parameters of appropriate spin-Hamiltonians were determined. The intensities of the allowed and forbidden lines depended very differently on the microwave power due to different degrees of saturation.

The optical obsorption spectrum of Co(II) ions doped in magnesium thallium sulphate hexahy­ drate is studied at room and liquid nitrogen temperatures. The crystal exhibits characteristic absorption of the Co(II) ion in the visible and near infrared. The observed bands are assigned to transitions from the ground state 4 T 1g (F) to various excited quartet and doublet levels of the Co(II) ion in octahedral symmetry. The splitting of one of the bands at liquid nitrogen temperature is explained to be due to spin-orbit splitting. All band positions have been fitted by the parameters B, C, Dq and ξ.

The behaviour of absorbance, fluorescence and emission anisotropy of linear molecules with one double bond, i.e. 4-amino-4'-nitrostilbene (ANS), 4-dimethylamino-4'-nitrostilbene (DNS) and 4,4'-diphenylstilbene (DPS), was examined in polyvinyl alcohol) (PVA) films at different temperatures (293-423 K). The unusual behaviour of absorption and fluorescence properties of the molecules in­ vestigated, similar to those of linear polyenes in PVA, was, however, less pronounced.

Experimental studies have demonstrated that the absorption and fluorescence spectra of linear molecules with one double bond, i.e. 4-amino-4'-nitrostilbene (ANS), 4-dimethylamino-4'-nitro-stilbene (DNS) and 4,4'-diphenylstilbene (DPS), contained in preheated to 393 K or nonheated polyvinyl chloride) (PVC) films are identical in shape and position, unlike those observed for ANS, DNS and DPS in polyvinyl alcohol) (PVA) films. For polar ANS and DNS molecules in PVC film a decrease in the emission anisotropy with growing wavelength of the fluorescence band was observed. This unusual behaviour of the emission anisotropy is accounted for by the overlap of two close emission bands from different luminescent centres, resulting from different microenvironments of the ANS and DNS molecules in PVC film. The emission anisotropy of nonpolar DPS molecule in PVC does not change within the fluorescence spectrum.

Sixteen new rotational transitions of cyanoacetylene in the ground vibrational state have been measured in the frequency region from 570 GHz to 710 GHz by the Cologne sub-millimeter wave spectrometer. The observed transition frequencies were analyzed together with unpublished millimeter wave data of our group and with the data available in the literature. Precise rota­ tional constant and the quartic and sextic centrifugal distortion constants have been determined; B = 4549.058224(37) MHz, D = 0.544110(19) kHz, and H = 0.0345(21) mHz.

The rotational K-structure (K = 0, ... 6) of the a-type transition (J = 65 - 64) of the symmetric top molecule methylcyanide, CH 3 CN, has been recorded at 1.2 THz employing a newly designed quasi-optical frequency multiplier. A planar Schottky diode is used as non-linear element for producing the harmonic power and is mounted in the focus of an off-axis antenna across a short single ridged waveguide. The 2nd harmonic of the fundamental frequency is filtered with adichroic plate and is focused onto the InSb bolometer after passing an absorption cell. The multiplier is driven by a high power backward wave oscillator with a fundamental frequency near 600 GHz.

We have employed the Cologne terahertz spectrometer [ 1,2] to observe Lamb dip and crossover phenomena in rotational spectra at 572 GHz. Because of the large power output of the backward wave oscillators used in the system, no special means are required to induce this saturation effect; the coincidentally reflected radiation from the bolometer present in our quasi-optical absorption cell is sufficient to saturate the υ z = 0 sub-group. This effect has allowed the observation of the three previously unresolved hyperfine components of the l4 NH 3 A ← S, J K = 1 0 ← 0 0 transition, and was also observed for the analogous 15 NH 3 transition in natural abundance (i. e. 0.366 %). These measurements indicate a possible improvement of molecular transition frequencies in the submillimeter region.

The rotational spectrum of the disulfane isotopomer HS 33 SH has been recorded and assigned between 70 and 300 GHz. In the analysis, rotational constants and 33 S hyperfine parameters are derived, the latter accounting for nuclear electric quadrupole as well as nuclear spin -rotation hyperfine interactions. The quadrupole constants are in qualitative agreement with a published ab-initio calculation. The electric field gradient principal axes are considerably rotated against the principal inertial axes, giving rise to off-diagonal elements in the electric field gradient tensor. In combination with the very small inertial asymmetry of the molecule, this causes the A'-doubling in the lowest rotational levels to be dominated by the hyperfine structure rather than the inertial asymmetry contributions. By diagonalization of the quadrupole tensor, an estimate for the dihedral angle (η≈94°) can be obtained, in good agreement with a previous value.

The distribution of Zn 2+ and Co 2+ cations in ferrite spinels has been determined by applying anomalous X-ray scattering (AXS) near the K absorption edges of Fe, Co and Zn. The energy dependence of the reflection intensities of ZnFe 2 O 4 , detected at the Fe K and Zn K absorption edges, can only be explained when all Zn 2+ being allocated to the tetrahedral site formed by oxygens. On the other hand, the results for CoFe 2 O 4 suggest that 78% of Co 2+ occupy the octahedral site, and that the present CoFe 2 O 4 sample is classified as inverse spinel, although a partial disorder is included. The usefulness of this AXS method coupled with the common Rietveld analysis was well-recognized by determining the cation distribution even in a system with next neighboring elements of the periodic table.

A semi-empirical fitting procedure has been developed and used in analysing the characteristic features of the partial structure factors of binary amorphous alloys. An analytical formula is given to fit the experimental atomic pair correlation function as a sum of Gaussians. The inverse Fourier transform of the fitted terms reproduces all features of the experimental structure function. In addition to the structural parameters, the modelling gives a quantitative explanation for the complex origin of characteristic features in the diffraction pattern such as pre-peak, pre-minimum, and split peaks in the partial structure factor.