Volume 48, Issue 5-6

A variety of surprising effects arise from the nonlinear light-matter interaction of circularly polarized laser light propagating through sodium vapor. We present experimental evidence for an asymmetry in the absorption of left hand and right hand circularly polarized light as well as for the creation of a collimated light beam of apposite polarization within the light-matter interaction region. Both effects are not yet explained by common theories.

During low-temperature impact ionization breakdown in extrinsic germanium, spontaneous current and voltage oscillations can be observed. The onset of periodic oscillatory behavior is governed by a saddle-node bifurcation on a limit cycle. Besides the well-known square-root law of control parameter dependence, we find a different scaling in the vicinity of the bifurcation point. Such anomalous behavior is reproduced by a simple model approach.

The usefulness of the Ott-Grebogi-Yorke control method is demonstrated by stabilizing a chaotic NMR-laser system around an unstable period-one orbit. We have used a six-dimensional delay-coordinate embedding technique in order to fully determine the stability properties of the orbit controlled. Our analysis yields small time-dependent perturbations of the system quality factor capable to perform real-time control.

The methods of stabilization of unstable periodic and aperiodic orbits of a strange attractor with the help of a small time-continuous perturbation are discussed. The perturbation is applied to the system in such a way that the desired periopdic or aperiodic orbits remain unperturbed. An experimental application of the methods can be carried out by a purely analogous technique without use of any computer.

We observe the phenomenon of stochastic resonance in a semiconductor experiment. Originally, such an effect was predicted for bistable dynamical systems that are influenced by a periodic modulation as well as a random perturbation. In that case, a "resonance" peak can be observed in the power spectrum. The phenomenon investigated is the low-temperature impact ionization breakdown. There, bistability results from the competing states of low and high conductance.

We derive the nucleation rate of a localized structure of a one-dimensional, nonlocal, bistable reaction diffusion equation near instability of the uniform state.

The electric avalanche breakdown in semiconductors exhibits many features of a phase transition. In this paper, we introduce time-resolved measurements performed during the transition from a low to a high conducting state as reaction to a sudden change of the control parameter (i.e., the voltage bias).

The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the scaling of an ensemble with non-Gaussian fluctuations evolves for certain values of the external parameter.

A three-cell model of an enzymatic electrocatalytic experiment is introduced. Inhibition of a Michaelis-Menten type of reaction leads to bistability and oscillations under potentiostatic conditions.

An interpretation of a recently proposed generic model for fractal basin boundaries in terms of a cascade-like model for turbulence is presented. Intermittency effects are shown by the analysis of structure functions and non-Gaussian probability density functions.

Various measures of the physical complexity of a dynamical system are considered. Without question, these measures introduce a new quality in the description of nonlinear complex systems, but we think that their advantages have not yet been demonstrated in a convincing manner. We show that the estimation of the complexity of a given system is related to the extraction of models from real-world data.

Two well-known bifurcation routes to chaos of two-dimensional coupled logistic maps are embedded in a two-parameter plane of a canonical nonlinear oscillator which contains a non-analytic analogon to the Mandelbrot set.

By means of the linear response of the cat map to a constant perturbation, it is illustrated how relaxation to equilibrium occurs in chaotic hamiltonian systems.

Coupling a one-dimensional chaotic forcing to a stable fixed point in the plane may generate different fractal attractors embedded in three dimensions. The system with real eigenvalues of the fixed point gives rise to simple chaotic attractors with three different types of fractal structures. We show that the competition of local exponents provides a generic criterion for the classification of the fractal structures in dynamical systems.

The fractal basin boundary of a two-dimensional discrete dynamical system modelling a chaotic forcing applied to bistability is shown to be identical to the graph of an infinite series F(x,t)= of weighted iterates of an ergodic unimodal interval function f. In the special case, when f is the logistic map in "full chaos", i.e. ƒ: x ↦ 4x(1 - x), F is a nowhere differentiable function of x for each t > exp(-λ f ) (even equal to the Weierstrass function), where λ f >0 is denoting the Lyapunov exponent of f. For further chaotic functions f, nowhere-differentiability is shown to be obvious from computer simulations.

A 3-D invertible map generating a 4-loop solenoid attractor is presented. The attractor of the "standard" 4-solenoid turns out to be "fat" - that is, fractal dimensionality exceeds topological dimensionality by more than unity. If a fourth variable that is weakly damped is added to this 3-variable map, a new type of attractor is generated. In a cross section it is a continuous nowhere-differentiable function over a 2-D domain which is a 2-D Cantor set. Such an object can be called a "singular-continuous 2-D Weierstrass function". The latter can be "superfat" (dimension gap larger than 2). Realistic systems possessing attractors of this new type are possible.

A new base for three-dimensional divergence-free vector fields in Hilbert space (Galerkin method) is proposed. The base fields have vanishing boundary conditions for their curl and are useful to solve the incompressible Navier-Stokes equation. The base vector potentials are obtained as the eigensolutions of the squared Laplace operator. We first derive the operator in a simply connected domain and then study Couette flow in the small gap approximation. The method yields a rapidly converging critical Taylor number and in lowest approximation a three mode model for the Taylor vortices, similar to the Lorenz model. It represents the first bifurcation of the flow very well.

The band origin of the A 1 mode v 2 , which represents the symmetrical stretching vibration of the two C = N bonds of furazan, has been determined from the high-resolution FT-IR band as v 2 0 = 1418.4724± 0.0001 cm -1 . The rotational parameters of this excited state, as determined in a preceding DRM microwave study, have been confirmed and their precision was raised through the combined fit of microwave data and of some 2500 rovibrational transitions. The use of conjugate low-J Q-branch lines for the determination of the origin of a B-type IR band of an asymmetric rotor is illustrated.

The electric field gradients (EFG) in SCl 2 have been computed with both self-consistent-field (SCF) and configuration-interaction (Cl) methods. The predicted EFG, along with the nuclear quadrupole moment Q N of 35 Cl and 37 Cl from other sources, allows us to compare theoretical quadrupole coupling constants with new experimental results. The best values obtained agree with the experiment within 3%. It has been found that the principal axis of the coupling tensor does not coincide with the S-Cl internuclear axis, and the tilt angle has been predicted close to that from experiment.

The stability problem of a stationary circular flow of an ideal fluid between two coaxial cylinders is considered. It is shown that Rayleigh's circulation criterion is necessary and sufficient for the total kinetic energy of an axisymmetric disturbance to be bounded in time.

Differential thermal analysis has been performed on cyanocyclohexane (CCH), 1,2,3,4-tetrahydro-5,6-dimethyl-1,4-methanonaphthalene (TDMN), and 2-methyl-2-propanol (t-butanol) up to 300 MPa. The latter compound was also investigated dielectrically. CCH displays an ODIC phase that transforms only reluctantly to the low-temperature stable phase II. Annealing under pressure can appreciably accelerate this transformation. For all three compounds the phase diagrams were established. For CCH and TDMN also the pressure dependence of the glass transition has been determined.

The correlation of the solvatochromic fluorescence properties of 8-(phenylamino)-1-naphthalene-ammoniumsulfonate (8,1 ANS) in 1,4-dioxane/water mixtures with E τ (30) and Δƒ values of the respective solvents shows that besides the polarity the nature of the solvent mixture determines the fluorescence intensity I and the Stokes shift Δv̅. Different amounts of hydrogen-bonding are suggested to be responsible for the different slopes of the correlation line plots. Key words: Solvatochromic fluorescence 8-(phenylamino)-1-naphthalene-ammoniumsulfonate (8,1 ANS); Semi-empiric polarity parameters 1,4-dioxane/water mixtures.

A model for the spin lattice relaxation time of the protons of dimethylammonium in the Redfield limit and common spin temperature approximation is developed. The three fold reorientations of the methyl groups, the rotation of the whole molecular group around its two fold symmetric axis and possible correlations among these motions are considered. The effect of these processes on the dipolar interactions among the protons within the same molecular group is taken into account. The resulting relaxation rate is powder averaged and used to explain the experimental data in literature on [NH 2 (CH 3 ) 2 ] 3 Sb 2 Br 9 . The analysis shows that dynamically inequivalent groups exist in this compound and that the effect of proposed correlation among the different motions on the final results is negligible.

We investigated l-type doublet transitions of 15 N 2 0 in the first excited state of the degenerate bending vibration v 2 with 14 < J < 34. From analysis of the J-dependence of the line center frequencies, the doubling constant q (0) was obtained together with the first and second order centrifugal distortion constants q (1) and q (2) respectively. For the lines in the J-band (4 to 8.2 GHz) and K-band (18 to 26.5 GHz) we have also investigated the pressure broadening due to self-collisions with use of the transient emission technique. The experimental results for the pressure broadening parameter Γ p are compared with predictions from binary collision theory, based on the modified Murphy-Boggs perturbative treatment.

A bridge type microwave Fourier transform spectrometer, equipped with flat oversized Stark cells and an operational range from 8 GHz to 40 GHz is described. As application we report the experimental determination of the vibronic ground state dipole moment and of the anisotropy in the static polarizability of 1,1-dideuteroallene. Our experimental values are: μ a = 0.0053(2) D for the dipole moment, and (α ∥ - α ⊥ ) = 4.26(6) • 10 -24 cm 3 , for the polarizability anisotropy.

The rotational spectra of the 32 S-, 34 S- and 33 S-isotopomers of thiophene have been studied in their natural abundances using microwave Fourier transform spectroscopy. For the 32 S-isotopomer the rotational and centrifugal distortion constants were found to be A' = 8041.59407(46) MHz, B' = 5418.26219(17) MHz, C' = 3235.78061(16) MHz, D' J = 0.6967(96) kHz, D' JK = 0.530(14) kHz, D' K = 1.789(49) kHz, δ' K = 0.3067(21) kHz, R' 6 = - 0.0738(12) kHz. For the 34 S-isotopomer A' = 8041.7055(84) MHz, B'= 5274.1837(23) MHz, C' = 3183.8432(23) MHz, and for the 33 S-isotopomer A'= 8041.651 (10) MHz, B' = 5344.2988(15) MHz, C' = 3209.25777(66) MHz with almost the same centrifugal distortion constants were obtained. The 33 S-quadrupole coupling constants of the 33 S-thiophene are χ aa = 6.8610(64) MHz and χ bb - χ cc = -48.766(11) MHz.

The design and performance of an automatic scan wave-guide microwave Fourier transform spectrometer is described, which is of great help in assigning microwave spectra.

Using metallic zinc from BDH Chemicals, the conversion of water into hydrogen was investigated by measuring the D/H ratio of the latter. It was found that 8 μl of water, 3.0 g of zinc, and a reaction time of 30 minutes at 480 °C are the optimal conditions for the conversion reaction.

Infrared reflectance spectroscopy has been used for the identification of the different modifications of silica and for the determination of their crystallinity.