The design of analogue electronic experiments to investigate phenomena in nonlinear dynamics, especially stochastic phenomena, is described in practical terms. The advantages and disadvantages of this approach, in comparison to more conventional digital methods, are discussed. It is pointed out that analogue simulation provides a simple, inexpensive, technique that is easily applied in any laboratory to facilitate the design and implementation of complicated and expensive experimental projects; and that there are some important problems for which analogue methods have so far provided the only experimental approach. Applications to several topical problems are reviewed. Large rare fluctuations are studied through measurements of the prehistory probability distribution, thereby testing for the first time some fundamental tenets of fluctuation theory. It has thus been shown for example that, whereas the fluctuations of equilibrium systems obey time-reversal symmetry, those under non-equilibrium conditions are temporally asymmetric. Stochastic resonance, in which the signal-to-noise ratio for a weak periodic signal in a nonlinear system can be enhanced by added noise, has been widely studied by analogue methods, and the main results are reviewed; the closely related phenomena of noise-enhanced heterodyning and noise-induced linearization are also described. Selected examples of the use of analogue methods for the study of transient phenomena in time-evolving systems are reviewed. Analogue experiments with quasimonochromatic noise, whose power spectral density is peaked at some characteristic frequency, have led to the discovery of a range of interesting and often counter-intuitive effects. These are reviewed and related to large fluctuation phenomena. Analogue studies of two examples of deterministic nonlinear effects, modulation-induced negative differential resistance (MINDR) and zero-dispersion nonlinear resonance (ZDNR) are described. Finally, some speculative remarks about possible future directions and applications of analogue experiments are discussed.

/pdf/analogue-studies-of-nonlinear-systems-1kyvrluro5.pdf

Analogue studies of nonlinear systems

For pt.I see ibid., vol.46, no.9, pp.1205-14 (1999). Stochastic resonance (SR), in which a periodic signal in a nonlinear system can be amplified by added noise, is discussed. The application of circuit modeling techniques to the conventional form of SR, which occurs in static bistable potentials, was considered in a companion paper. Here, the investigation of nonconventional forms of SR in part using similar electronic techniques is described. In the small-signal limit, the results are well described in terms of linear response theory. Some other phenomena of topical interest, closely related to SR, are also treated.

/pdf/stochastic-resonance-in-electrical-circuits-ii-1efpgfl3if.pdf

Stochastic resonance in electrical circuits. II. Nonconventional stochastic resonance

A data acquisition system designed for magnetic resonance instrumentation is presented. Its performance may be suitable for a broad set of applications where repetitive and noisy signals must be time‐averaged in order to increase the signal‐to‐noise ratio. The system is built from easily available, low cost parts on a standard board for the PC‐AT (16‐bit) bus. 12‐bit data acquisition and 32‐bit time averaging take place in the memory of the PC under control of its CPU. The sustained data rate, including on‐line signal averaging, can be as high as 250 kHz (500 kHz with interlaced data acquisitions). Timing is accomplished by on‐board software programmable hardware timers. The CPU is then free for other tasks during the time, if any, between acquisition scans. Thus on‐line display of the time‐averaged data and their FT spectrum may be performed without impairing the timing accuracy, which is limited by the 10‐MHz board clock to 100 ns. All functions of the interface are controlled by machine‐language routines, callable from within quickbasic programs.

A fast, time averaging data acquisition system for the PC‐AT bus

Scanning Electron Acoustic Microscopy(SEAM) with the piezoelectric ceramic sensor is a novel instrument in materials analysis. Normally the signal detected by the sensor is very weak. Signal to noise ratio should be enhanced in order to observe electron acoustic image with good quality. In this paper, the time averaging data acquisition system with computer was described and the data transferred into imaging were processed with a computer. Electron acoustic pictures on PZT-type materials were shown in real time and refined and memorized in computer. Results can also be recalled on the screen at any time.

Computer-controlled image acquisition and processed system for scanning electron -acoustic microscopy

Personal computers are now becoming commonplace and given additional hardware and software, can easily be turned into sophisticated data acquisition systems with data processing and plotting capabilities (figure 1). The drudgery and mistakes of manual reading of instruments, hand calculation of results and final presentation in graphical form can be avoided with an increasing range of data acquisition, manipulation, display and graphing software, clearing the way for time to be concentrated on analysis of the results (figure 2). In reviewing the essential components of PC-based systems and current availabilities and performance, I shall concentrate mainly on hardware and software available in Western Europe – most of it, as it happens, originating in the USA.

A PC user's guide to data acquisition

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A PC user's guide to data acquisition