Nonlinear systems with fast and slow motions. Changes in the probability distribution for fast motions under the influence of slower ones

The influence of slow processes on the probability distribution of fast random processes is investigated. By reviewing four examples we show that such influence is apparently of a universal character and that, in some cases, this universality is of multifractal form. As our examples we consider theoretically stochastic resonance, turbulent jets with acoustic forcing, and two problems studied experimentally by Shnoll on the influence of the Earth’s slow rotation on the probability distribution for the velocities of model Brownian particles and on alpha decay. In the case of stochastic resonance, the slow process is a low frequency, harmonic, external force. In the case of turbulent jets, the slow process is acoustic forcing. In the models based on Shnoll’s experiments, the slow processes are inertial forces arising from the rotation of the Earth, both about its own axis and about the Sun. It is shown that all of these slow processes cause changes in the probability distributions for the velocities of fast processes interacting with them, and that these changes are similar in form.     

Dynamic proton-induced emission switching in donor-functionalized dehydrobenzopyrid[15]annulenes

An isomeric pair of 15-membered dehydrobenzopyridannulenes functionalized with -NBu(2) groups as pi-electron donors was prepared and their steady-state spectroscopic parameters investigated. The property differences arising from placement of the pyridine nitrogen relative to the macrocycle, as well as the differential effects of stepwise protonation of the acceptor and donor nitrogens, were examined. The macrocycles exhibited dynamic shifting in the emission spectra, which is believed to correlate to induced changes in the frontier molecular orbitals of the molecules.     

Decay of quantized vorticity in superfluid He at mK temperatures

An experimental investigation of the free decay of quantized turbulence in isotopically pure superfluid ⁴He at mK temperatures is discussed. Vortices are created by a vibrating grid, and detected by their trapping of negative ions. Preliminary results suggest the existence of a temperature-independent vortex decay mechanism below T70 mK.     

Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

We discuss how the effective parameters characterising averaged motion in nonlinear systems are affected by noise (random fluctuations). In this approach to stochastic dynamics, the stochastic system is replaced by its deterministic equivalent but with noise-dependent parameters. We show that it can help to resolve certain paradoxes and that it has a utility extending far beyond its usual application in passing from the microscopic equations of motion to the macroscopic ones. As illustrative examples, we consider the diode-capacitor circuit, a Brownian ratchet, and a generic stochastic resonance system. In the latter two cases we calculate for the first time their effective parameters of averaged motion as functions of noise intensity. We speculate that many other stochastic problems can be treated in a similar way. PACS: 05.10.Gg, 05.40.-a, 05.40.Jc     

Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.