CONSTRUCTIVE AND
DISRUPTIVE EFFECTS OF NOISE IN NONLINEAR SYSTEMS WITH
HYSTERESIS
INTRODUCTION
The
systematic study of nonlinear systems with hysteresis has started in the
last quarter of the twentieth century and it led to the appearance of the
first monograph on this theme in 1983 [1]. Since then, the interest in the
identification, analysis and applications of hysteresis phenomena in
diverse physical and social systems has been continuously growing [2-6] and
it has extended far beyond the classical areas of magnetism and plasticity.
For example, optical hysteresis [5], superconducting hysteresis [6] and
economic hysteresis [7] became well-established scientific domains, and
many pioneering studies appeared in other areas, such as ecology, biology,
psychology, computer science, and wireless communications. A general
overview of the state of the art in the area of hysteretic systems has been
recently presented in the three-volume handbook Science of Hysteresis,
edited by Mayergoyz and Bertotti [8].
Relation
between noise and hysteresis has a long and sinuous history, from the
Barkhausen work in the beginning of the last century to the current
challenges in magnetic recording due to the superparamagnetic effect. While
there are extensive studies dealing with various manifestations of noise in
hysteretic phenomena, a systematic analysis of hysteretic materials and
devices driven by noisy input has been rather limited. An important reason for this situation is
related to the lack of general analytical tools for addressing complex
non-Markovian processes found at the output of hysteretic systems. As
opposed to memoryless linear and nonlinear systems, analyzing non-Markovian
processes involves ad hoc techniques that are rarely suitable for studying
another class of stochastic processes with memory. Our analytical approach
to the analysis of noise passage through hysteretic systems is suitable for
any Preisach systems by decomposing the general stochastic characteristics
of the output into a superposition of characteristics for binary
non-Markovian processes which can be embedded into multidimensional
Markovian processes defined on graphs [9-11]. Another important limitation
in this area of research is related to the fact that noise is usually an
internal feature of a physical system with limited control from
experimental point of view. Our experimental approach circumvents this
difficulty by using electronic noise generators Hameg 8131-2, which provide
a wide selection for noise characteristics, and a set of parallel-connected
Schmidt triggers, which play the role of hysteretic rectangular loop
operators [11]. In addition, we developed a general numerical approach to
complex hysteretic systems with stochastic inputs, which leads to a unitary
framework for the analysis of various stochastic aspects of hysteresis,
including thermal relaxation, data collapse, field cooling/zero field
cooling, and noise passage [12]. Various differential, integral, and
algebraic models of hysteresis are considered while the input processes are
generated from arbitrary given spectra. The resulting statistical
technique, based on Monte-Carlo simulations, has been successfully tested
against several analytical results available in the literature and has been
implemented in the new version of HysterSoft by Dr. Petru Andrei [13]. The
developed method is suitable for the analysis of a wide range of noise
induced phenomena in nonlinear systems with hysteresis from various areas
of science and engineering, as well as for the design and control of diverse
magnetic, micro-electromechanical, electronics and photonic devices with
hysteresis. A special attention of
this work has been devoted to noise influence on current magnetic recording
techniques, as well as on several unconventional alternatives, such as spin
polarized current assisted recording, precessional switching, toggle
switching where temperature-dependent operating regions were obtained.
[1] M. A. Krasnoselskii and A.
Pokrovskii, Systems with Hysteresis,
Nauka, 1983 (English, 1989)
[2] I. D. Mayergoyz, Mathematical Models of Hysteresis,
Springer (1991)
[3] A. Visintin, Differential Models of Hysteresis,
Springer (1994)
[4] M. Brokate and J. Sprekels, Hysteresis
and Phase Transitions, Springer (1996)
[5] N. N. Rosanov, Spatial
Hysteresis and Optical Patterns, Springer (2002)
[6] I. D. Mayergoyz, Mathematical
Models of Hysteresis and their Applications, Elsevier, (2003)
[7] J. B. Davids (ed), The
Handbook of Economics Methodology, Edward Elgor (1998)
[8] I. D. Mayergoyz and G. Bertotti
(eds.), Science of Hysteresis,
Academic Press (2006)
[9] M. Dimian and I. Mayergoyz, Phys. Rev. E 70, 046124 (2004)
[10] M. Dimian, NANO 3 (5), 391–397 (2008)
[11] M. Dimian, E. Coca, and V. Popa, J. App. Phys. 105 (7), 07D515,
(2009)
[12] M. Dimian, A. Gîndulescu,
and P. Andrei, IEEE Trans. Magn.
46 (2), 266-269 (2010)
[13] HysterSoft ver. User Guide
v. 1.8. Available: http://www.eng.fsu.edu/ms/HysterSoft
