Stochastic resonance

B. Time Periodic Potentials Resonant Activation and Suprathreshold Stochastic Resonance VII. Conclusions... 

The complete curve x(oo) in Fig. 19 is difficult to describe analytically, but one can have recourse to the adiabatic approximation. This approximation has been used in the context of stochastic resonance by many authors [96,108]. Here... 

It is intuitively obvious that this phenomenon should also exist in systems having steady states (e.g., in a system described by quartic potential that has been intensively studied in the context of stochastic resonance), but it is more natural to investigate the resonant properties of signal-to-noise ratio (SNR) in those cases [113]. 

In conclusion, we note that the practical application of phenomena of resonant activation and suprathreshold stochastic resonance provide an... 

Since the first report of oscillation in 1965 (159), a variety of other nonlinear kinetic phenomena have been observed in this reaction, such as bi-stability, bi-rhythmicity, complex oscillations, quasi-periodicity, stochastic resonance, period-adding and period-doubling to chaos. Recently, the details and sub-systems of the PO reaction were surveyed and a critical assessment of earlier experiments was given by Scheeline and co-workers (160). This reaction is beyond the scope of this chapter and therefore, the mechanistic details will not be discussed here. Nevertheless, it is worthwhile to mention that many studies were designed to explore non-linear autoxidation phenomena in less complicated systems with an ultimate goal of understanding the PO reaction better. 

The main features of the copper catalyzed autoxidation of ascorbic acid were summarized in detail in Section III. Recently, Strizhak and coworkers demonstrated that in a continuously stirred tank reactor (CSTR) as well as in a batch reactor, the reaction shows various non-linear phenomena, such as bi-stability, oscillations and stochastic resonance (161). The results from the batch experiments can be suitably illustrated with a two-dimensional parameter diagram shown in Pig. 5. 

One of the exciting new directions is the control of activated rate processes using external fields. Addition of an external field opens the way for a wide variety of new phenomena such as stochastic resonance, resonance activation, directed transport, control of the hopping distribution in surface diffusion and more. Even the addition of a constant force to the problem leads to interesting additional phenomena such as the locked to running transition, which remains a topic of ongoing research. " Quantum mechanics in the presence of external fields may differ significantly from the classical. 

In Section II.B the fluctuations and fluctuational transitions in an OB system subject to white noise are analyzed. In Section II.C the phenomenon of stochastic resonance in the OB system is discussed in terms of linear response theory and the corresponding experimental results are presented. In Section II.D we discuss theory and experimental results for the new form of optical heterodyning noise-protected with stochastic resonance. Finally, Section II.E contains concluding remarks. 

The onset of this peak is closely related to stochastic resonance, which can occur if a weak periodic signal is added to the input. 

According to several studies [12,13,19,96], the two principal features of stochastic resonance phenomena are that the signal and/or the signal-to-noise ratio R... 

But, as mentioned above in Sec. I, the mechanism of bistable stochastic resonance requires that the frequency of the input signal is much less than reciprocal relaxation time of the system. 

It will be apparent from the above discussion that the double-cavity membrane system is ideally suited to investigations of fluctuations and fluctuational transition phenomena. Stochastic resonance and huge noise-induced amplification of a heterodyne signal have been observed. We would emphasize that noise-protected heterodyning is a general phenomenon that may occur in bistable systems of various sorts, and that it may therefore be of interest for applications in engineering. 

Kashimori, Y., Funakubo, H. and Kambara, T. (1998) Effect of syncytium structure of receptor systems on stochastic resonance by chaotic potential fluctuation. Biophysical Journal 75 1700-1711... 

IV. Magnetic Stochastic Resonance and Related Nonlinear Phenomena... 

B. Magnetic Stochastic Resonance in the Presence of a Bias Field... 

IV. MAGNETIC STOCHASTIC RESONANCE AND RELATED NONLINEAR PHENOMENA... 

The phenomenon called in modern thesaurus the stochastic resonance (SR) by now has shaped up in a general concept appealing to a great many of researchers... 

Stochastic resonance is a kinetic effect universally inherent to bi- or multistable dynamic systems exposed to either white or color noise. Its main manifestation is the appearance of a maximum on the noise intensity dependencies of the signal-to-noise ratio in a system subject to a weak driving force. Essentially, this behavior is due to the presence of an exponential Kramers time x cx exp(AU/3>) of the system switching between energy minima here AU is the effective height of the energy barrier separating the potential wells and 3> is the noise intensity. 

The idea of the magnetic stochastic resonance has emerged in a natural way first as a theoretical issue [25-27] and shortly afterward was supported by some experimental evidence [28,31]. A consistent theoretical treatment of magnetic SR in a superparamagnetic particle in the framework of the linear response theory was developed in Refs. 29 and 30. 

The stochastic resonance is determined by the longitudinal (with respect to n) modes of the relaxational problem (4.90). Since A is not a self-adjoint operator, it produces, together with the spectrum of eigenvalues ,, two sets of eigenfunctions defined as... 

In Section IV.B.4 we have shown that the quadratic dynamic susceptibilities of a superparamagnetic system display temperature maxima that are sharper than those of the linear ones. If the maximum occurs as well at the temperature dependence of the signal-to-noise ratio, this should be called the nonlinear stochastic resonance. However, before discussing this phenomenon, one has to define what should be taken as the signal-to-noise ratio in a nonlinear case. 

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