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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 |