The mathematical models of dispersive optical bistability in unidirectional ring cavity yield the transmitted intensity It as a function of the input intensity Iin with additional parameters (mirror reflectivity R and phase shift β). There are two feedback elements in this description: the energy (and, hence, also causal) feedback quantified by R and the purely causal feedback given by dependence of the phase shift on the transmitted power, β=β0+β2It. The apparatus of causal diagrams method is used to represent and analyze phenomena in the ring cavity. The region of physically unstable states is marked by the condition tloop>1, where tloop is the transmission function of the feedback loop ItβIinIt present in the diagram. Besides the critical points defined by tloop=1 (which are linked to the existence of bistability), there are two conditions marked by tloop=0 in which the cavity state is insensitive to the values of R.
Oscillating polar entities, such as protein molecules embedded in the cell's membrane or microtubules in the cell's interior are, as theoretically predicted and empirically demonstrated, sources of electromagnetic fields with frequencies ranging from far infrared to the MHz domain. The preliminary results obtained in our laboratory suggest connection of the characteristics of observed electromagnetic signals with the phases of the mitotic cycle. Such techniques, if adequately developed, could form a basis of new diagnostic methods in cytology. The present contribution examines the influence of temperature changes (within the physiologically acceptable limits) on properties of the oscillator ensembles, in particular on dependences of the occupation numbers versus the energy pumping rate.
Topological structure of the mathematical models of the laser diode amplifier (LDA) can be visualized with the help of a diagrammatic method based on depicting differential relationships of the form (delta) y equals txy(delta) x by the diagram x yields y. The quantity txy is called the transmission function of the oriented line xy. Such atomic diagrams can be combined to more involved schemes to represent systems of mathematic formulas. The approach is demonstrated on the LDA model proposed by Adams. The diagram representing this model is derived and shown to contain two closed oriented paths - feedback loops. The transmission function of these loops are shown to have a controlling influence on the qualitative operation mode of the LDA. In particular, if their sum crosses the unity level in two distinct states, the LDA acts as a bistable element. This condition can be expressed in terms of the numeric values of the characteristics parameters such as the driving electric current, facet reflectivities, resonator length, etc.
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