Excitable regime

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

As known from nuclear physics, a direct extension of quantal mean-field is delicate [36]. Fortunately enough, in the high excitation regime, where semi-classical approximations are likely to become acceptable, Boltzmann-like kinetic equations, offer an efficient alternative. They thus have been extensively used in nuclear physics for describing heavy-ion collisions (VUU,... 

The high sensitivity of this method is related to the fact that we observe a matter-wave interference between the excitation and the condensate, i.e., a heterodyne measurement. Expansion in the inhomogeneous Bogoliubov projection basis confirm this picture [Tozzo 2004] We estimate that this improved sensitivity should give us access to the singly quantized excitation regime. 

Regarding the results discussed above, the interesting aspect of these experiments is that the front velocities took on a constant value. Some data can be seen in Fig. 59. The first three examples show activation fronts in the bistable regime of Fe, Au, and Zn dissolution, respectively the last two curves display examples of pulses in an excitable regime, again for metal dissolution reactions, hi all examples, two stationary electrodes were used to probe the local potential. The velocity of the fronts or pulses were extracted from the time difference at which the transitions were measured at the two probes. In all five examples, the readings of the two probes seem to be just time-shifted versions of each other. This indicates that the structures propagate with constant shape and velocity. 

In the upper row we see the excitable regime. The solid lines represent the nullclines of the system, the dashed line a typical trajectory. Each dash represents a fixed time interval, i.e. where the system moves faster through phase space the dashes become longer. The system possesses one fixed point (intersection of the nullclines) which is stable. Small perturbations decay. A super-threshold perturbation leads to a large response (spike) after which the system returns to the fixed point. After that a new perturbation is possible if the system from outside is brought again over the threshold. 

The results for i p(r) obtained for different values of A, see Fig. 1.11, demonstrate that under a random telegraph signal the coherence of noise-induced excitation is enhanced by an optimal choice of the correlation time. Here, the optimal correlation time Topt decreases as the noise amplitude A increases. Further simulations not shown here, confirm that this phenomenon holds for a wide range of the bifurcation parameter o, covering almost the whole excitable regime. We emphasize that for not well separated time scales, noise-induced excitations are possible even if both cp-... 

This hypothesis was at least partially confirmed by direct observation of v + v ) and (v + v ) fluorescence, which was not observable in the low-excitation regime. The ( i+ 3) emission signal is seen to rise rapidly and decay more rapidly than the normal V-T/R rate, presumably due to nonlinear V-T/R effects, which can occur in the high excitation regime, and/or V-V processes that will affect this signal, since not all of the vibrational manifold is equilibrated on the time scale of the ( + 3) rise time. The second rise rate that is observed may be due to normal filling of ( 1, 4) via processes (20), (21), (23) and (28). 

Figure 3-7. Non-equilibrium vibrational energy distribution functions in diatomie molecular gases strong and intermediate excitation regimes.

Figure 3-16. Influence of a chemical reactionon the vibrational distribution function in the weak excitation regime of non-equilibrium plasma Ty To).

Hyperbolic Plateau Distribution of Vibrationally Excited Molecules. Derive a relationship between the hyperbolic plateau coefficient C (3-133, 3-134) for the vibrational energy distribution function and the ionization degree in non-thermal plasma (Ke/ o)- Take into account that, in the strong vibrational excitation regime, the excitation of lower vibrational levels by electron impact is balanced by resonant non-linear VV exchange between higher vibrationally excited molecules. 

Photoexcitation of luminescence is convenient and allows for flexibility in wavelengths and excitation regimes. Alternative excitation modes of luminescence excitation may be of interest, such as chemiluminescence [80, 81] or electrogenerated chemiluminescence (ECL, see Sect. 7.2) [82]. For example, electrodes may be readily integrated in current lab-on-chip microfluidic systems for biological detection, and both chemiluminescence [83] and ECL [84] have been demonstrated for the detection in microfluidics. Examples of chemical or electrochemical excitation of NIR lanthanide luminescence are rare, but the chemiluminescence of Pr [85] and ECL [86] of Yb have been reported. 

In view of the constantly escalating research efforts put together in the exciting regime of new-generation materials-based catalysts, there is a definite necessity for the development of coherent strategic design principles for the... 

One example will serve to illustrate the use of CML models in this more general context. Suppose we consider the BZ reaction, not in the excitable regime as earlier, but in the oscillatory regime. Certain versions of the BZ... 

In 1931 in her doctoral dissertation supervised by Max Bom, Maria Goppert-Mayer proposed the concept of the simultaneous absorption of two photons by a molecular system in one elementary action,(English translation Ref ). This prediction was based on the principles of the quantmn theory of radiation " as well as the concept of the intermediate energy level. Based on the formalism of summation over all eigenstates of the system, Maria Goppert-Mayer derived an expression for the two-photon absorption probability which, however, occurred to be too low to be experimentally observed in the incoherent light excitation regime. Hence, the unquestionable experimental confirmation took over thirty years. ... 

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