Excitable systems

Figure A3.14.10. Schematic representation of important features of an excitable system (see the text for details)...

The acronym LASER (Light Amplification via tire Stimulated Emission of Radiation) defines the process of amplification. For all intents and purjDoses tliis metliod was elegantly outlined by Einstein in 1917 [H] wherein he derived a treatment of the dynamic equilibrium of a material in a electromagnetic field absorbing and emitting photons. Key here is tire insight tliat, in addition to absorjDtion and spontaneous emission processes, in an excited system one can stimulate tire emission of a photon by interaction witli tire electromagnetic field. It is tliis stimulated emission process which lays tire conceptual foundation of tire laser. 

Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... 

Rotating armature These have a rotating armature and a static field excitation system. The output from the armature is taken through the sliprings. 

Resonant responses must not coincide with excitation frequencies of rotational shaft speed, especially gear meshing frequency (the speed of a shaft times the number of teeth of the gear on that shaft), or other identi fied system frequencies otherwise, a self-excited system will exist. Lateral response criteria should conform to API 613. 

A typical excitation system includes a voltage regulator, or exciter, protection circuits, and measurements transducers. If the terminal voltage decreases below rated value, the conU ol system increases the rotor cuiTent and thus the magnetic field as shown in Faraday s law, the generated voltage is thus forced up to the desired value. 

The synchronous motor is a constant-speed machine. Unlike the induction motor which inherendy has slip from losses, the synchronous motor uses an excitation system to continually keep the rotor in synchronous speed with current flowing through the stator. Within its designed torque characteristics, it will operate at synchronous speed regardless of load variations. 

The excitation system provides the magnetizing current necessary for the generator to operate at the desired voltage and, when in parallel with other generators, supplies the required amount of reactive current. In modern practice the excitation system can be either brushless or static. 

The deep philosophical significance of the new theory lies precisely at this point, and consists in replacing a somewhat metaphysical concept of the harmonic oscillator (which could never be produced experimentally) by the new concept of a physical oscillator of the limit cycle type, with which we are dealing in the form of electron tube circuits and similar self-excited systems. 

A second simplihcation results from introducing the Born-Oppenheimer separation of electronic and nuclear motions for convenience, the latter is most often considered to be classical. Each excited electronic state of the molecule can then be considered as a distinct molecular species, and the laser-excited system can be viewed as a mixture of them. The local structure of such a system is generally described in terms of atom-atom distribution functions t) [22, 24, 25]. These functions are proportional to the probability of Ending the nuclei p and v at the distance r at time t. Building this information into Eq. (4) and considering the isotropy of a liquid system simplifies the theory considerably. 

The simplest fluorescence measurement is that of intensity of emission, and most on-line detectors are restricted to this capability. Fluorescence, however, has been used to measure a number of molecular properties. Shifts in the fluorescence spectrum may indicate changes in the hydrophobicity of the fluorophore environment. The lifetime of a fluorescent state is often related to the mobility of the fluorophore. If a polarized light source is used, the emitted light may retain some degree of polarization. If the molecular rotation is far faster than the lifetime of the excited state, all polarization will be lost. If rotation is slow, however, some polarization may be retained. The polarization can be related to the rate of macromolecular tumbling, which, in turn, is related to the molecular size. Time-resolved and polarized fluorescence detectors require special excitation systems and highly sensitive detection systems and have not been commonly adapted for on-line use. 

Mueller, P. Rudin, D. O. Tien, H. T. Westcott, W. C., Reconstitution of cell membrane structure in vitro and its transformation into an excitable system, Nature 194, 979-980 (1962). 

A class of kick-excited self-adaptive dynamical systems is formed and proposed. The class is characterized by a nonlinear (inhomogeneous) external periodic excitation (as regards the coordinates of the excited system) and is remarkable for the occurrence of the following objective regularities the phenomenon of discrete oscillation excitation in macro-dynamical systems having multiple branch attractors and strong self-adaptive stability. 

Damgov, V. N. and Popov I. Discrete Oscillations and Multiple Attractors in Kick-Excited Systems. Discrete Dynamics in Nature and Society, Vol. 4, P. 99 (2000)... 

Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

Recognise situations in which the formation of excimers/exciplexes may affect the observed properties of an excited system. 

As an excitation system, TIRF does not specifically refer to the pattern, intensity, or lifetime of the fluorescence emitted from the near-surface molecules which become excited. However, these emission characteristics are somewhat different from those far from a surface, and some of these differences may become experimentally useful. In Section 7.3, the emission pattern of a fluorophore near a dielectric surface (particularly the interface of water with either bare glass or metal-coated glass) is discussed. 

A. Hjelmfelt and J. Ross, Pattern recognition, chaos, and multiplicity in neural networks of excitable systems, Proc. Natl. Acad. Sci. USA, 91, 63-37 (1994). 

J. Rinzel, A formal classification of bursting mechanisms in excitable systems. Lect. Notes Biomath 71, 267-281 (1987). 

After Little s proposal, many researchers have pursued such an exciting system in vain. Even metallic behavior was rarely seen in doped organic polymers, gels, and actuators. As mentioned in Sect. 3.4.4, MCso with linearly polymerized Ceo" exhibited one-dimensional (M = Rb, Cs) or three-dimensional (M = K) metallic behavior [144]. Recently a doped poly aniline was reported to exhibit a metallic temperature dependence for a crystalline polymer chemical oxidation of monomers grew crystallite polyaniline [329] early doping studies on polypyrrole (PFg) and poly(3,4-ethylene-dioxythiophene)X (X = PFg, BF4, and CF3SO3) prepared by electrooxidation at low temperatures also showed a metallic temperature dependence below 10-20 K (Scheme 16) [330, 331]. 

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