Stochastic switching

Ramachandran GK, Hopson TJ, Rawlett AM, Nagahara LA, Primak A, Lindsay SM (2003) A bond-fluctuation mechanism for stochastic switching in wired molecules. Science 300 1413-1416... 

If we input a small periodic forcing term to the particle, stochastic switching and jumping occurs between the potential wells and the switching may become synchronized with the input. This stochastic synchronization happens if the mean waiting time satisfies the time-scale matching requirement (Gammaitoni et al, 1998)... 

Bryan MT, Porter NA, Claydon JS, Bashir MA, Burnell G, Marrows CH, Schrefl T, Allwood DA (2012) Stochastic switching asymmetry in magnetoresistive stacks due to adjacent nanowire stray field. Appl Phys Lett 101 262404... 

When hok was placed under the invertible fimA promoter (which randomly switches to constitutive expression by virtue of the fimB and fimE regulators) a stochastic killing was observed, and the population of viable cells in the culture slowly decreased. Unfortunately, the fimA promoter only works in E. coli, and therefore would be of little utility in actual bioremediation scenarios. 

In the work by Willemsen and co-authors [84] the three Stokes polarization parameters were studied during polarization switches in a vertical-cavity semiconductor laser. It was demonstrated that when the linear part of the absorptive anisotropy is close to zero [127], the laser is bistable and switches stochastically between two polarisations [128]. The analysis of large fluctuations of polarizations in this system [84] reveals what authors have called a stochastic inversion symmetry (see Fig. 10), which is analogous to the time-reversal symmetry observed for the model (17) and shown in Fig. 7. 

Results demonstrate that when agitators are switched the slope of the pathline becomes discontinuous. We will see later in this chapter how this mechanism may produce an essentially stochastic response in the Lagrangian sense. Aref termed this chaotic advection, which he suggested to be a new intermediate regime between turbulent and laminar advection. The chaos has a kinematic origin, it is temporal—that is, along trajectories associated with the motion of individual fluid particles. Chaos is used in the sense of sensitivity of the motion to the initial position of the particle, and exponential divergence of adjacent trajectories. 

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. 

As another example of hybrid simulation touched upon above, Haseltine and Rawlings (2002) treated fast reactions either deterministically or with Langevin equations and slow reactions as stochastic events. Vasudeva and Bhalla (2004) presented an adaptive, hybrid, deterministic-stochastic simulation scheme of fixed time step. This scheme automatically switches reactions from one type to the other based on population size and magnitude of transition probability. 

Two prototype reaction examples (reversible first-order and irreversible second-order kinetics) were discussed to address issues of rounding when switching from deterministic variables to stochastic (i.e., conversion of real numbers to integers), as well as the thresholds of population sizes and transition probabilities to control accuracy in the first two moments of the population (mean and variance). Other more complex examples were also mentioned. The... 

In this section we analyze experimental data and make comparisons with theory. Data were obtained for 100 CdSe-ZnS nanocrystals at room temperature.1 We first performed data analysis (similar to standard approach) based on the distribution of on and off times and found that a+= 0.735 0.167 and v = 0.770 0.106,2 for the total duration time T = T = 3600 s (bin size 10 ms, threshold was taken as 0.16 max I(t) for each trajectory). Within error of measurement, a+ a k 0.75. The value of a 0.75 implies that the simple diffusion model with a = 0.5 is not valid in this case. An important issue is whether the exponents vary from one NC to another. In Fig. 13 (top) we show the distribution of a obtained from data analysis of power spectra. The power spectmm method [26] yields a single exponent apSd for each stochastic trajectory (which is in our case a+ a apSd). Figure 13 illustrates that the spread of a in the interval 0 < a < 1 is not large. Numerical simulation of 100 trajectories switching between 1 and 0, with /+ (x) = / (x) and a = 0.8, and with the same number of bins as the experimental trajectories, was performed and the... 

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