Showing papers by "University of Stuttgart published in 1979"

Continuous chaos—four prototype equations

Abstract: If oscillation is the typical behavior of 2-dimensional dynamical systems (Euclidean and on manifolds), then chaos, in the same way, characterizes 3-dimensional continuous systems. First a method t o obtain chaos in degenerate (relaxation type) dynamical systems in two variables is outlined whereby five basic flow patterns emerge. Second, following a piecewise linear degenerate equation, four prototypically simple quadratic differential equations in three variables that realize nondegenerate analogs of those five flows are presented. Finally a possible equation for an even higher type of qualitative behavior beyond chaos is proposed.

Time-convolutionless projection operator formalism for elimination of fast variables. Applications to Brownian motion

Abstract: The relation between the time-convolutionless projection operator formalism and the methods developed by Kubo and van Kampen in the context of linear stochastic differential equations is discussed in detail. It is shown how this formalism may be used to develop a systematic procedure for the elimination of “fast variables”. This procedure is applied to the case of a free Brownian particle and to that of a heavily damped Brownian particle in the presence of an external force to obtain a reduced description in terms of the position variable: the results are found to be in complete agreement with the previous works on this problem. The rotational Brownian motion of an asymmetrical top in the presence of an external torque is also considered and an equation for the reduced probability distribution is derived which contains all the previous works on this problem as special cases.

Initiation and propagation of flame fronts in lean CH4-air mixtures by the three modes of the ignition spark

Abstract: The initiation and subsequent propagation of flame fronts by breakdown, are and glow discharge ignition devices have been investigated by time resolved interferometry in CH4-air mixtures (1/Ф=1.0, 1.11, 1.25, 1.4) at 4 bar. Based on size, effective expansion velocity, and radial temperature profiles across the flame fronts as functions of time after spark onset, it is shown that the breakdown controls the inflammation process up to ≈1 ms. The breakdown is far better suited for inflaming combustible mixtures than are or glow discharge due to very high energy transfer efficiency (≈95%), large double sided contact areas with the unburnt mixture, very steep gradients of temperature and particle density, and reignition capabilities at ≈300 μs. Thus extremely lean (1/Φ≈1.6) mixtures ignited at high flow velocities with high inflammation probabilities.

Fluctuations and nonlinear irreversible processes. II

Abstract: This paper forms the second part of a study which reexamines the relationship between fluctuations and nonlinear irreversible processes. The scope of the previous paper is generalized to include macroscopic variables which transform odd under time reversal. The fluxes of some of the variables may be purely reversible so that the diffusion matrix may be singular. The deterministic equations for nonlinear irreversible processes can again be derived from a minimum principle. The fluctuations of the macroscopic variables are treated on the basis of a Fokker-Planck equation which has the form derived from statistical mechanics by one of us. The conditional probability of the fluctuations is constructed as a path integral. The connection between the deterministic and the stochastic descriptions of the macroscopic dynamics is formulated in a covariant way, independent of the frame of coordinates. For that purpose, a metric tensor in the space of state variables is introduced. The form of the metric tensor is particularly simple in frames where the macroscopic variables are sums of molecular variables.

Is quantum mechanics equivalent to a classical stochastic process

Abstract: The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.

Complete automatic analysis of photoelastic fringes: A new method of evaluation of photoelastic-fringe pattern by means of modern image-processing technique is presented in this paper

Abstract: TV technology combined with a modern video-frame store is used to store the complete fringe pattern in digitized form in real time. A minicomputer connected to the store has direct access to any picture point in the store. In this manner, it is possible to evaluate the photoelastic-fringe pattern in the computer by special developed software.

Orthogonal stagnation flow, a framework for steady extensional flow experiments

Abstract: A new framework for viewing steady extensional flow is presented: Steady orthogonal stagnation flow is an ideal which one should strive to reach in an actual experiment. The kinematics and the stress boundary conditions are developed for stagnation flow in general and in two special cases: the impingement of two circular streams and of two planar sheets. Contemplating this ideal clarifies the advantages and disadvantages of current experiments, thereby pointing the way towards new experiments; a number are suggested. Axisymmetric (with\(\dot \varepsilon _x \) > 0) and planar stagnation flow within a lubricated die look particularly promising. Some preliminary experimental results are given for uniaxial extension of a polyacrylamide solution in a water lubricated die.

Ontogeny of Visual Acuity of Rainbow Trout Under Normal Conditions and Light Deprivation

Abstract: The development of visual acuity (minimum separable visual angle) in rainbow trout (Salmo gairdneri) was investigated from hatching to one year old trout by eliciting optomotor reactions in an optokinetic drum. I. The first optomotor responses were found 10 days after hatching with a visual angle of 30° of arc. Then a rapid increase in the visual resolving power occurs leading to a visual angle of about 1° at the end of the larval period. Up to the age of one year the visual angle of rainbow trout improves slightly to final 14' of arc. 2. Light deprivation during rearing causes a severe impairment ot visual acuity during the first 40 days after hatching (best visual angle only 2°05' of arc). 3. The results are discussed with respect to synaptogenetical and biochemical findings in the tectum opticum of rainbow trout under the same rearing conditions.

Pattern Formation and Pattern Recognition — An Attempt at a Synthesis

Abstract: The above sentences by Norbert Wiener form by themselves a pattern. When we look at such a pattern our first impression might be that a pattern is something static. However, when thinking somewhat more about patterns we realize that patterns are intimately connected wi1 processes. First of all, a pattern has been formed. For instance the above pattern was first conceived, then printed etc. On the other hand, when we look at a pattern, it induces processes in our brain leading to the perception of the pattern. Similarly, patterns induce processes in other biological systems or in machines. In this way both pattern formation and pattern recognition are connected with dynamic processes.

Determination of the analytical and the nonanalytical part of the exchange interaction of InP and GaAs from polariton spectra in intermediate magnetic fields

Abstract: The isotropic analytical exchange interaction ${\ensuremath{\Delta}}_{a}$ of GaAs and InP is determined to be 0.02\ifmmode\pm\else\textpm\fi{}0.01 and 0.04\ifmmode\pm\else\textpm\fi{}0.015 meV, respectively, for the two materials from a comparison of theoretically generated and experimentally determined transverse exciton energies and oscillator strengths in magnetic fields up to 20 T. The calculation of the theoretical spectra is based on a recent intermediate-field theory including the analytical and nonanalytical part of the exchange interaction. The experimental values are determined from a two-oscillator line-shape analysis of ${\ensuremath{\sigma}}^{\ensuremath{-}}$,- ${\ensuremath{\sigma}}^{+}$-, and $\ensuremath{\pi}$-polarized magnetoreflection spectra. A newly developed model describing the exciton-free surface layer of a semiconductor by an exponentially decreasing damping of the exciton contribution to the dielectric constant is shown to improve strongly the quality of the line-shape fit. This improvement is achieved without increasing the number of fitting parameters as compared to the older model using a layer of finite thickness with infinite damping. From a similar comparison of theoretical and experimental values of the energies and oscillator strengths of longitudinal-transverse mixed-mode exciton spectra in magnetic fields which are found for the $\ensuremath{\sigma}$ polarization in Voigt configuration ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$) the size of the nonanalytical exchange interaction ${\ensuremath{\Delta}}_{\mathrm{LT}}$ in GaAs is determined to be 0.08\ifmmode\pm\else\textpm\fi{}0.02 meV. For InP an upper limit of ${\ensuremath{\Delta}}_{\mathrm{LT}}l~0.1$ meV is derived.

Flow field and scouring effects of steady and pulsating jets impinging on a movable bed

Abstract: The flow field and erosion pattern of continuous and pulsating impinging jets has been studied experimentally. The mean velocity field as well as turbulent and pulsation components, wall pressure and wall shear stress distributions were investigated in an axisymmetric air jet impinging upon a rough wall. The results show how harmonic velocity pulsations at the nozzle affect both the mean and the turbulent flow field. Corresponding erosion tests with a vertical water jet impinging upon a uniform sand bed exhibited under certain conditions a greatly enhanced erosion rate. The increase in erosion capacity due to pulsation seems to be due to both the changes in the mean flow field and to the greatly increased lateral correlation of the velocity field in the impinging region.

Interstitial migration in iron at 220 K

Abstract: A synopsis is given of recent attempts to clarify the nature of the prominent resistivity recovery stage at 220 K (Stage III) in irradiated high-purity α-iron and of the related magnetic and mechanical relaxation processes. With increasing irradiation dose the height of this stage increases linearly, and its position shifts to lower temperatures according to a second-order reaction. In accord with other experimental results this is taken as evidence for free migration of an elementary point defect in iron at about 220 K. Since vacancy migration can be excluded on the basis of thermal-equilibrium measurements, Stage III is attributed to interstitial migration. Suggestions for the interpretation of the Stage-III relaxation phenomena are presented. Es wird uber neueste Untersuchungen an bestrahltem hochreinem α-Eisen berichtet, die durchgefuhrt wurden, um die Vorgange in der ausgepragten Erholungsstufe des elektrischen Widerstandes bei 220 K (Stufe III) und die in diesem Temperaturbereich auftretenden magnetischen und mechanischen Relaxationsprozesse aufzuklaren. Mit wachsender Bestrahlungsdosis wachst Stufe III linear an und verschiebt sich zu tieferen Temperaturen gemas einer Reaktion zweiter Ordnung. Daraus wird geschlossen, das in Eisen bei ungefahr 220 K eine elementare atomare Fehlstelle frei wandert. Da Leerstellenwanderung aufgrund von Messungen im thermischen Gleichgewicht ausgeschlossen werden kann, wird Stufe III der freien Wanderung von Zwischengitteratomen zugeschrieben. Deutungsmoglichkeiten der Relaxationserscheinungen im Bereich der Stufe III werden vorgeschlagen.

Memory function approach to the dynamics of interacting Brownian particles

Abstract: We investigate some of the dynamic properties of diffusing particles described by a many-body Smoluchowski equation. The dynamic structure factor is expressed in terms of a memory function which is evaluated in the cases of i) weak interaction and ii) low particle density, but arbitrary interaction. A one-dimensional system with a hard-core pair potential is treated explicitly. Furthermore, by including a periodic single-particle potential, a model is obtained which has relevance to superionic conductors. For this case we discuss how the frequency-dependent conductivity is affected by the correlated motion of particles.

Confirmation of the Suess wiggles: 3200–3700 BC

Abstract: USING dendrochronologically dated tree rings de Vries1 showed that the atmospheric 14C concentration has not been entirely constant during the past few hundred years. By extending the North American bristlecone pine tree-ring chronology2 to nearly 8,000 yr ago, several radiocarbon laboratories succeeded in measuring deviations in the 14C concentration from the mid-nineteenth century natural 14C level to a maximum of about 10% around 4000 BC (refs 3–7). Superimposed on this general trend, Suess drew with ‘cosmic schwung’, medium-term variations through his data. These so-called ‘wiggles’ should correspond with variations in the abundance of radiocarbon in atmospheric carbon dioxide on a time scale between one decade and a few centuries. The resulting irregular shape of Suess' calibration curve has been questioned during the past few years8,9. The overall result, however, is that no generally accepted 14C calibration curve is yet available. It would be most convenient to measure 14C concentrations in single tree rings with much higher precision than the usual 4–6‰. For this, however, much larger samples are required than are available from the bristlecone pine tree. An excellent opportunity was presented by the sub-fossil oak trunks discovered in the river valley sediments of southern Germany9; our measurements of these trunks are reported here.

Das anomale Fließverhalten von Polyäthylen hoher Dichte

Abstract: Das anomale Stromungsverhalten von Polyathylen hoher Dichte (HDPE) wird mit Hilfe eines Kapillar-Rheometers am Beispiel der Stromung durch Dusen mit Kreisquerschnitt untersucht. Die Ergebnisse der Untersuchung werden in Form „scheinbarer Flieskurven“ dargestellt. Es wird der Einflus der Temperatur, der Oberflachenbeschaffenheit der Duse, der Duseneinlauf-Geometrie, des Druckniveaus und der Zugabe von Zusatzstoffen (Stabilisator, Holzmehl) auf den Verlauf der „scheinbaren Flieskurve“ untersucht. Es kann gezeigt werden, das die bei diesem Material besonders ausgepragt auftretenden Fliesanomalien nicht wie bei anderen Polymertypen (wie z. B. LDPE, PS, PP) auf Vorgange im Duseneinlauf beruhen, sondern auf eine Anderung der Flieseigenschaften der Kunststoffschmelze im Bereich der Dusenwand zuruckzufuhren sind. Diese Anderung der Flieseigenschaften fuhrt in der Duse zu einem Gleiten bzw. zu Haft-Gleierscheinungen. Visuelle Untersuchungen, bei denen die Lage- und Gestaltanderungen farbig markierter Proben beobachtet werden, bestatigen diese Ergebnisse.

Wing sections for hydrofoils--part 1: symmetrical profiles

Abstract: NACA 16-series wing sections have been extensively applied to U.S. hydrofoil craft. However, this series of wing sections was developed around 1940. Since then new airfoil sections have been continuously investigated both theoretically and experimentally. By means of recently developed methods of calculation for boundary-layer and profile theory, it is possible to determine, in a simple way, profiles with fixed characteristics of pressure distributions and to carry out boundary-layer calculations. Three classes of new wing sections with improved hydrodynamic characteristics in terms of cavitation inception have been successfully developed. It is shown that each series of profiles has its own merit. The choice of a wing section can be made only when the operational requirements of the craft are specified.

Optical and EPR study of the nickel two-electron-trap state in GaP

Abstract: The infrared luminescence and the absorption spectra of the nickel two-electron-trap state, ${\mathrm{Ni}}^{+}$ $3{d}^{9}$, have been observed and analyzed in GaP. The spectra do not exhibit full mirror symmetry relative to the common zero-phonon line (ZPL) at 5 354 ${\mathrm{cm}}^{\ensuremath{-}1}$. Chemical identification of the defect is based on the fine structure of the ZPL which is shown to arise from an isotope effect. The Zeeman splitting of the ZPL in fields up to 5.3 T unambiguously demonstrates that the zero-phonon transition occurs between a cubic ${\ensuremath{\Gamma}}_{8}$ excited and a ${\ensuremath{\Gamma}}_{7}$ ground state, implying that the center is in the ${\mathrm{Ni}}^{+}$ $3{d}^{9}$ charge state. The analysis of the Zeeman data yields $g=\ensuremath{-}0.94$ for the ${\ensuremath{\Gamma}}_{7}$ state and ${g}_{1}=1.45$, $q{g}_{2}=\ensuremath{-}0.23$ for the ${\ensuremath{\Gamma}}_{8}$-state $g$ factors. The ${\mathrm{Ni}}^{+}$ center was also identified in the EPR spectrum of GaP: Ni and the EPR $g$ value is fully consistent with the Zeeman results. Certain details of the optical spectra and the strongly quenched $g$ factors indicate a moderate Jahn-Teller (JT) coupling within the $^{2}T_{2}$, and also a moderate JT coupling within the $^{2}E$ state of ${\mathrm{Ni}}^{+}$. It is shown that static-crystal-field theory is insufficient to account for the data, and a consistent interpretation based on existing JT theories is presented.