Constructive and Disruptive Effects of Noise in Nonlinear Systems with Hysteresis

The project entitled “Constructive and disruptive effects of noise in nonlinear systems with hysteresis” is aimed at providing a comprehensive analysis for stochastically driven hysteretic systems from various areas of science. While the quasi-static analysis of hysteretic systems has reached some degree of maturity, the stochastic and dynamic analysis is currently under major developments.

This research is supported by Marie Curie International Reintegration Grant no. PIRG-02-GA-2007-224904 within the 7th European Community Framework Programme for period May 1st, 2008 – April 30th, 2012. These Marie Curie Actions are individual grants which are aimed at researchers from the EU and Associated States who have carried out research outside Europe for at least 5 years and who wish to return to Europe. The project is implemented at “Stefan cel Mare” University of Suceava, Romania by Dr. Mihai Dimian, who had performed research in United States of America for more than 5 years at University of Maryland, College Park and Howard University, Washington DC where he held the positions of Distinguished Graduate Research Assistant and Assistant Professor, respectively.

For the first reporting period (01.05.2008-30.04.2010), the three scientific objectives of the project were the development of methods for the stochastic analysis of systems with hysteresis, the characterization of the alternative solutions to the data storage technology, and description of noise effects in photonic devices. In addition, the researcher aimed at establishing a laboratory for research of hysteretic systems at the host institution, as well as developing national and international collaborations in the area of the project.

In 2008, the researcher founded at Stefan cel Mare University of Suceava, the Laboratory for Research of Hysteretic Systems (LRHS) as a component of the Systems and Processes Control Center. The laboratory room has been recently renovated and furnished by the University and has been made available since the first day of my reintegration project. The main IT infrastructure of RHS lab includes 14 computer workstations and 7 portable computers with diverse simulation and data analysis software, while the experimental research infrastructure includes Nanosurf Scanning Tunneling Microscope, Signal and noise generators, Oscilloscopes and spectrum analyzers, Antenna Training and Measurement System, Diode-Pumped Solid-State Laser Kit, and Microwave Technology Training System. Most of the infrastructure has been acquired since the researcher reintegration with the financial support from the Stefan cel Mare University and Romanian Ministry of Education, Research and Innovation.

Regarding the scientific objectives, the researcher has developed in collaboration with Dr. Petru Andrei from Florida State University 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. Various differential, integral, and algebraic models of hysteresis were 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 or derived by the researcher based on the Preisach formalism of hysteresis and the theory of stochastic processes on graphs. 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.

Another important limitation addressed by this project is related to the fact that noise is usually an internal feature of a physical system with limited control from experimental point of view. His experimental approach circumvents this difficulty by using electronic noise generators, 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.

In the area of photonic devices, a special research interest of this project has been devoted to the needs for interconnections between various types of physical systems. Mechanical-electrical optoisolator transducers have been developed by his group using Polaroid optocouplers to convert a rotational and/or a translation movement into electrical signal. By using a Schmitt trigger circuit, the Polaroid optocoupler has been transformed into a mechanical-electrical transducer with hysteresis which has various potential applications in the area of automation, communications and mechatronics. An additional research focus in the area of photonics has been oriented towards spin crossover (SCO) phenomena that occur in some transition metal complexes. Atom-phonon coupling model has been used to explain, in a relatively simple manner, the thermodynamic behavior of SCO materials upon application of thermal noise or light.

An intensive activity has been done during the first two years of the project in order to develop national and international research collaborations for the newly founded laboratory and to integrate the project research in international research networks. At the international level, the researcher had close and productive research collaborations with the groups led by Prof. dr. Petru Andrei from Florida State University (U.S.A.), Prof. dr. Jorge Linares from University of Versailles St. Quentin (France), and  Prof. dr. Lieven de Stryker from KaHo University, Gent (Belgium), respectively. At the national level, collaborations have been established with the groups led by Prof.dr. Alexandru Stancu from “Al.I.Cuza” University, Iasi, and Prof.dr. Horia Gavrila from Politehnica University, Bucharest.

For the second reporting period (May 1st, 2010 – April 30th, 2012), the three scientific objectives of the project were the identification of noise benefits in hysteretic systems, the description of noise influence on the behavior of shape-memory alloys, and the description of the role of noise in the neuron activity. In addition, the researcher aimed at stimulating student interest in the research activities related to the project topics and at forming human resources capable to develop research projects in this area at the European standards. A special objective in the last part of the project was to attract complementary resources for funding the project research directions after the termination of this grant.

While it is mostly experienced as a disruptive effect, noise can also play a constructive role in hysteretic systems, activating a resonance response. Recent studies on nonlinear systems proved that such phenomena are quite common and their applications range from signal processing to climate models. This phenomenon is generally known as coherence resonance, when is solely induced by noise, and stochastic resonance, when an external oscillatory signal is present. However, most of these systems can be theoretically framed into two-state models or simple variants thereof. Dr. Dimian has developed in collaboration with Dr. Petru Andrei from Florida State University a general framework for the analysis of noise induced phenomena in hysteretic systems with complex metastable state configuration driven by arbitrary colored noise. It was proved that various complex hysteretic systems can exhibit such noise induced resonance of the system response. The quantities used in our study to characterize this behavior are signal amplification and signal-to-noise ratio, which displays a maximum at the resonant noise strength. The resulting statistical technique that includes various algebraic, differential, and integral models of hysteresis as well as arbitrary colored noise have been implemented in freely available academic software. This general framework has also been used to study noise influence on neuronal models. Exceeding this proposal objective, the researcher has also started an interesting work on modeling neuron stimulations by using rapidly changing magnetic field.

Various hysteretic models have been used for modeling and simulating the behavior of shape memory alloy with a special emphasize on designing phase shifter for smart antenna. Several type of phase shifter have been considered and used to design efficient linear and circular phased antenna arrays. Based on the collaboration with Dr. Dimian on this topic, one of our PhD students had successfully defended his thesis by designing, building, and testing phased antenna arrays. Actually, Dr. Dimian has played an important role in stimulating many of our students to do research. He was especially attentive to the undergraduate and graduate students who joined his research group making them capable of producing publishable research results as well as developing research projects in this area at the European standards. Three of them have successfully defended their doctoral theses and seven have received their master degree. Most of group members have obtained various scholarships to performed research in prestigious universities from Belgium, France, Italy and Germany. His work with the students has also tried to meet the student interests and abilities leading to a variety of topics from the proposal area and even beyond, such as radio-frequency identification systems, smart lighting systems or cyber-infrastructures development.

A special effort has been devoted to attract funding for the continuation of project research directions after the termination of this grant. Dr. Dimian has been very successful in this endeavor being awarded one of the very few national grants for a Young Research Team in value of 547000 lei (approximately 125000 euro) with the project “Analysis of noise and fluctuations induced phenomena in spintronic and semiconductor devices.”

In conclusion, the activities have been performed according to the proposed plan and the project objectives have been fully achieved. The scientific results had been disseminated in seventeen peer-reviewed publications, one book and in twenty three presentations at international conferences, as well as through the project website http://www.eed.usv.ro/condishyst . Other manuscripts featuring results obtained in this project are currently in preparation, including a second book. For his research activity, Dr. Dimian has received a prestigious award in the competition “Romanian Researcher of the Year” organized by “Dinu Patriciu” Foundation.   Based on his outstanding results Dr. Mihai Dimian has been appointed full professor with tenure at “Stefan cel Mare” University of Suceava by the Romanian Minister of Education, Youth and Sports, being one of the youngest full professors in Romania. His recognition as one of the national leaders in engineering research is also proven by his selection as a member of the Engineering Commission of the National Research Council. By taken also into account that Dr. Dimian has been elected and appointed on May 1st, 2012, as Vice-Rector for Scientific Activities of “Stefan cel Mare” University of Suceava, it can be concluded that he has fully and successfully reintegrated in the European Union due to this Marie Curie grant. 

• Prof. Dr. Isaak Mayergoyz, University of Maryland, College Park, USA
• Prof. Dr. Alexandru Stancu, “Al. I. Cuza” University, Iasi, Romania
• Prof. Dr. Stefan Muller, Director, Max Planck Institut, Germany
• Prof. Dr. Giorgio Bertotti, Vice-President IEN Galileo Ferraris, Italy
• Assoc. Prof. Dr. Hamid Kachkachi, University of Versailles – St. Quentin, France
• Prof. Dr. Romel Gomez, University of Maryland, College Park, USA
• Assoc. Prof. Dr. Claudio Serpico, “Frederico II” University, Naples, Italy
• Assoc. Prof. Dr. John Anderson, Howard University, Washington DC, USA
• Assist. Prof. Dr. Petru Andrei, Florida State University, Tallahassee, USA