Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Das Verhalten eines modellmäßig vereinfachten p-n-Gleichrichters bei hohen Durchlaßströmen, d. h. außerhalb des Gültigkeitsbereiches der SHocKLEYschen Theorie, wird untersucht. Es wird wesentlich beherrscht von einem „unbegrenzten“ Anwachsen beider Trägerkonzentrationen mit √i über die Dotierungskonzentration hinaus. Der Spannungsabfall über den Bahngebieten wächst daher nur mit √i, während der Spannungsabfall über dem Raumladungsgebiet erwartungsgemäß den Grenzwert V_D anstrebt. Man erhält daher eine quadratische Strom–Spannungs-Charakteristik: i ~(U—V_D)².

The displacement of the excess charge of the proton in acid solutions is caused by a structure migration of groupings H₅O₂ ⁺ or H₉O₄ ⁺ . The processes which take place during structure migration are discussed on the basis of results gained in IR-investigations. In an electrical field the structure migration is given a preferred direction. The hydrogen bond with the tunneling proton in H₅O₂ ⁺ and the grouping H₃O⁺ in H₅O₂ ⁺ become polarized. Comparison of both polarizabilities demonstrates that, contrary to previous assumptions, the polarization of the hydrogen bond is the field-dependent mechanism. This conclusion is reached upon calculating the polarizability of the hydrogen bond with a symmetrical double minimum potential well. It is shown that the polarizability is extremely large, being approximately two orders of magnitude greater than that of H₃O⁺ . Despite the large polarizability, the shift of the weights of the proton boundary structures is very small for the external fields usually applied in conductivity measurements. It is demonstrated, however, that this slight shift is large enough for the structure diffusion to obtain a preferred direction consistent with the anomalous high proton conductivity.

This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

Bei optischen und strahlungslosen Übergängen zwischen Elektronenzuständen an einem Kristallstörzentrum werden die Ruhelagen der Gitteroszillatoren (d. h. die Nullpunkte der Normalkoordinaten) verschoben. Der Oszillatoranteil der FRANCK-CONDON-Integrale solcher Übergänge wird exakt berechnet, zunächst unter der Annahme, daß die Oszillatorfrequenzen sich bei dem Übergang nicht ändern. Diese Integrale können durch ein Laguerresches Polynom dargestellt werden. Sodann werden FRANCK-CONDON-Integrale behandelt, die auftreten, wenn man die Abhängigkeit der Wellenfunktion des Störstellenelektrons von den Gitterschwingungen in erster Näherung berücksichtigt. Sie können auf die Integrale der nullten Näherung zurückgeführt werden. Schließlich werden noch solche FRANCK-CoNDON-Integrale untersucht, die sich ergeben, wenn man die Änderung der Oszillatoreigenfrequenzen beachtet. Auch sie können exakt berechnet werden, aber man gelangt nicht zu einem expliziten Ausdruck durch ein gebräuchliches Polynom. Abschließend wird am einfachen Beispiel eines optischen Überganges demonstriert, wie die Integrale anzuwenden sind und wie sie durch einfachere Funktionen approximiert werden können.

A new method of approach is proposed for the problem of electronic transitions accompanied by the excitation of molecular or crystal vibrations. The Hamiltonian of the normal vibrations is expressed in terms of the so-called creation and annihilation operators, and the change in the equilibrium nuclear distances and vibrational frequencies are represented by transformations which are also expressed in terms of these operators. Calculations are made for some typical cases.

In the present analysis, we have modeled the governing equations of a two dimensional hyperbolic tangent fluid model. Using the assumption of long wavelength and low Reynolds number, the governing equations of hyperbolic tangent fluid for an asymmetric channel have been solved using the regular perturbation method. The expression for pressure rise has been calculated using numerical integrations. At the end, various physical parameters have been shown pictorially. It is found that the narrow part of the channel requires a large pressure gradient, also in the narrow part the pressure gradient decreases with the increase in Weissenberg number We and channel width d.

The π-electron charge Q_s ^h in alternant conjugated systems with one heteroatom is considered. A complete proof of the law of alternating polarity is presented. The integral expression for Q_s ^h is decomposed into a number of relatively simple terms, which give some insight into the dependence of Q_s ^h, on molecular topology.

Die Ausnutzung gruppentheoretischer Methoden gestattet eine Untersuchung von Bandstrukturen allein auf Grund der Kristallsymmetrie. Diese Methoden werden auf ternäre Halbleiter mit Chalkopyritstruktur angewandt. Dazu werden die Charaktertafeln aller Wellenvektorgruppen zur Raumgruppe D¹² _2d aufgestellt. Aus ihnen werden qualitative Folgerungen für die Bandstruktur mit und ohne Spin gezogen. Sie betreffen die Entartung von Bändern, die mögliche Lage der Bandextrema sowie die Spin—Bahn-Aufspaltung. Die Ergebnisse werden mit den entsprechenden Bandformen der Zinkblendestruktur verglichen.

We investigate experimentally stationary stable states of activator (w) inhibitor (υ) type systems corresponding to the reaction diffusion equation

δ · υ̇ = Δυ + w - υ; ẇ = σ Δw + f(w) - υ; δ, σ = const > 0

with f(w) monotonically increasing for small and decreasing for large |w|. We first describe some general mathematical properties and present qualitative results obtained from numerical calculations. We then investigate experimentally electrical networks described by the spatially discretized version of the above equation. Calculation and experiment are in good agreement. We also interprete a two dimensional-network as an equivalent circuit for a composite material consisting of a linear and a nonlinear layer with an s-shaped current density electric field characteristic. This model is used for a phenomenological description of spatial structures and global current voltage characteristics observed experimentally in pin-diode like and gas discharge devices. The model accounts very well for the experimental results obtained so far. It is concluded that the above equation and the corresponding experimental setup are of great interest for fundamental investigations of self con­trolled processes in nature.