Phase-field systems as mathematical models to forecast the evolution of processes involving phase transitions have drawn considerable interest in recent years. However, while being capable of capturing many of the experimentally observed phenomena, they are only of restricted value in modeling hysteresis effects occurring during phase transition processes under cyclic loads. To overcome this shortcoming, a new approach to phase-field models, based on the mathematical theory of hysteresis operators, has recently been proposed by P. Krej and J. Sprekels in a series of papers.

Ph: (312) 996-9611 FAX:  312-413-0447
Email: scetin@uic.edu  
http://www.me.uic.edu/faculty/cetinkunt.html
http://www.uic.edu/orgs/mrc

Ultra Precision Motion Control and Physical Challanges

In order to meet the needs of smaller and smaller devices, i.e hand-held devices, machines and processes need to be developed which can manipulate smaller objects at ever increasing accuracy.   Ultra-precision positioning devices are the foundation of machines that can operate at sub-micron accuracy or even sub-nanometeric accuracy.

The development of machines which have nano-metric accuracy requires close consideration in two areas:  1. mechanical design including material and environmental control considerations,  2. control system design that will have the capability to measure and react at nano-metric resolution.

Low cost availability of PC based open architecture controllers allows us to develop ultra-precision motion control systems using mostly off-the-shelf components at a very reasonable cost.  The control algorithms can be quickly implemented using high level languages (such as C++) and can be highly detailed and be implemented in real-time.

In nanometric accuracy macroscopic machines, the biggest challange is how to deal with mechanical imprecisions due to hysterisis, friction, backlash, compliance, and environmental condition changes.  We will address the current challenges and results of our recent research effort in ultra-precision motion control and its applications in ultra-precision machine tools.

Tel: (312) 413-7951
 Fax: (312) 413-0447
E-mail: troyston@uic.edu
Lab website: acoustics.me.uic.edu

Rate-independent dielectric hysteresis in three piezoceramic (PZT) electromechanical transducers is investigated experimentally and theoretically. These include a monolithic PZT wafer, a 1-3 piezocomposite and an active fiber composite (AFC). The applicability of three different types of hysteresis models to piezoceramic transducers is investigated. Models considered include the classical Preisach model, the Maxwell resistive capacitor model and the Jiles-Atherton model. Equivalence of the three models for certain conditions is demonstrated.

Due to their tribological characteristics, chemical inertness and temperture stability PTFE compounds are used for rotary shaft seals in automotives.
In order to prepare a numerical simulation of the sealing system thermomechanical experiments were carried out to study the temperature dependant hysteresis effects of this material. It was observed that the hysteresis effects were not only caused by the plastic and viscoelastic deformations, but also by the so called Plastic Memory Effect (PME).
The PME is of special interest, because it is possible to increase the inelastic deformation of a mechanically strained specimen through a temperature treatment to higher values. These additional inelastic deformation can be recovered through another temperature treatment in the unstrained state.
The experimental investigations on this special kind of hysteresis were performed on tensile test pieces (90% PTFE, 5% short cylindrical glass fibers, 5% MoS2) using an electromechanical test machine in combination with a temperature chamber.
The results show that:

? it is impossible to implement the PME without a temperature treatment
? the total strain and the activation temperature have a strong influence on this effect
? it is possible to implement and activate the PME several times on the same test piece.

With these results and other experiments like relaxation tests, we have the physical background necessary to formulate a material law to describe the thermomechanical behaviour of PTFE and its compounds.
 

Tel:  ++39 (011) 3919-724
Fax:  ++39 (011) 3919-782
         ++39 (011) 6507611
E-mail: bertotti@omega.ien.it
             bertotti@ien.it
Homepage: http://www.ien.it/~bertotti/

An overview is given of the present understanding of hysteresis phenomena in magnetism, and of some unresolved issues under current debate. In particular, emphasis will be given to the following aspects.

(i) The emergence of rate-independent hysteresis from micromagnetics. This is basically a zero-temperature approach, where hysteresis reflects the multi-valley structure of the system free energy. In particular, the case of domain wall motion in random potentials can be theoretically investigated in considerable detail.

(ii) The connection between hysteresis and magnetic viscosity when thermal fluctuations become important. Hysteretic systems relax starting from far-from-equilibrium, history-dependent states. Consequently, magnetic viscosity itself must be described by history-dependent laws. Simple universal laws ( e.g., log-type relaxation ) hold only under very special conditions.

(iii) The role of dynamic effects when the magnetization frequency becomes substantial. In particular, it is important to understand the conditions under which magnetization dynamics (e.g., domain-wall motion coupled to Maxwell equations ) can be summarized by phenomenological, rate-dependent hysteresis models.

E-mail : sethna@lassp.cornell.edu
Phone:  (607) 255-5132

Web: http://www.lassp.cornell.edu/sethna/sethna.html

In recent years, crackling noise has been promoted into a proper field of science. From early work in the dynamics of charge-density waves, through the study of earthquakes, avalanches and self-organized criticality, and now Barkhausen noise in magnets, there is growing recognition that certain types of noisy systems are comprehensible. All these systems crackle: the noise consists of discrete pulses spanning a broad range of sizes and durations. Simple behavior spanning decades in length and time scales is precisely where our scientific theories become useful: the behavior cannot depend upon either microscopic details of individual domains or macroscopic features of sample shape.

What quantitative predictions should our theories be able to make? It is traditional to focus on critical exponents: power laws giving the distribution of event sizes or durations. However, just as in theories of hydrodynamics or elasticity, these theories should give quantitative, universal predictions about everything occuring on long length and time scales. I argue here that these critical exponents are not the sharpest test of these theories, and that there is a wealth of quantitative, universal predictions from the theoretical models that are embodied in scaling functions. Examples will include the scaling form of the avalanche size distribution, and average avalanche shapes for a given size or time.

Shape Memory Materials (SMM) are widely used in various engineering fields for several applications including actuators, composites, servomechanisms among the others. A further application field is offered by the exploitation of the pseudoelastic effect (hysteresis without residual displacements at unloading) for the reduction of the vibrations. To this end, various SMM elements are arranged to give rise to a device that produces the desired behavior. In other cases the vibration reduction devices may be obtained from the combination of SMM and non-SMM elements, likely elastoplastic, to increase the amount of energy dissipation. While all models for SMM refer to the behavior of the material alone, in this work the attention is focused on the device-level and a suitable framework is proposed to deal with the above mentioned applications. The proposed model for SMM is based on the rate-independent hysteresis algorithm formulated by Ivshin and Pence. Proper modifications aimed to the modeling of the vibration devices are introduced. The model belongs to the class of Duhem hysteresis models in the sense of Visintin and it is embedded in a thermomechanical framework that enables to quantitatively describe the SMM response under arbitrary loading paths including internal subloops and the dependence of the hysteresis loop shape on the temperature. The analysis of the dynamic stationary response of the device under harmonic forcing excitation is presented through excitation frequency-response amplitude curves.

We discuss Barkhausen noise in magnetic systems in terms of avalanches near a disorder induced critical point, using the hysteretic zero-temperature random-field Ising model and recent variants. As the disorder is decreased, one finds a transition from smooth hysteresis loops to loops with a sharp jump in magnetization (corresponding to an infinite avalanche). In a large region near the transition point the model exhibits power law distributions of noise (avalanches), universal behavior and a diverging length scale. Universal properties of this critical point are reported that were obtained using renormalization group methods and numerical simulations. Connections to other experimental systems such as athermal martensitic phase transitions (with and without "bursts") and the effect of finite field sweep rate are also discussed.

Hysteresis nonlinearities are typically non-differentiable in any reasonable sense and have intricate spaces of internal states. These peculiarities cause serious troubles when applying standard approaches to analysis
of hysteretic systems.
I will discuss the role of some new topological methods in analysis of oscillations, bifurcations, chaotic-type behaviour etc in systems with hysteresis. A special attention will be paid to systems with Preisach-Giltay nonlinearity and its multi-dimensional analogues suggested by
I. Mayergoyz and G. Friedman.

Luc Dupre
St. Pietersnieuwstraat 41
Department of Electrical Power Engineering
Ghent University
B-9000 Ghent
Belgium

E-mail: luc.dupre@rug.ac.be
Tel. + 32 / 9 264 34 24
Fax. + 32 / 9 264 35 82

Dynamic hysteresis model  with  f^1/(1+s)  excess loss dependency

Luc Dupre, Roger Van Keer, Jan Melkebeek

A general approach to the calculation of iron losses in soft magnetic laminated materials is based on the separation of losses into three components:  the hysteresis losses P_h, the classical losses P_c and the excess losses P_e.  According to the statistical loss theory [1], the magnetisation process  can be described in terms of n simultaneously active magnetic objects.  For several alloys, n is proportional to the excess field H_ex=P_e/(4fB) corresponding to excess losses per cycle P_e/f  being proportional  to f^0.5.  The scalar Preisach model, see e.g. [2] is one of the most accurate methods of describing the hysteresis effects that are encountered in magnetic materials.  In the dynamic Preisach model of [3], the switching rate of each dipole is proportional to the difference between the magnetic field and the switching fields  a or b, e.g. df/dt=k_d(H-a), which result in P_e/f  being proportional  to f^0.5 ( f being the magnetisation of the dipole). 

In [1], it is also shown that for other alloys, like 50-50 NiFe and GO SiFe, cut transversally to rolling direction,   P_e/f is less than proportional to f^0.5, or, equivalently, n varies faster than linear with the excess field H_ex . 

In this paper, it is shown that a generalised rate-dependent  Preisach model for which the switching  of the dipole is given by  df/dt=k_d(H-a)^s (when Ha) and df/dt=k_d(H-b)^s  (when H<b), results in P_e/f  being proportional to f^1/(s+1), introducing an extra material parameter s.

[1] G. Bertotti, IEEE Trans.Magn.,  24, pp.621-630, 1988.
[2] I. D. Mayergoyz, Mathematical models of Hysteresis, New York, Springer-Verlag, 1991.
[3] G. Bertotti, IEEE Trans.Magn.,  28, pp.2599-2601, 1992.

E-mail:  vdomni1@uic.edu 

E-mail:  ygogotsi@uic.edu

Phone: 312-413-9621
Fax: 312-413-0447
E-mail: orlovsk@uic.edu

Phone +39-0461-881635 (office), +39-0461-881625 (secretary)
Fax +39-0461-881624 
Email: Visintin@science.unitn.it

Electromagnetic processes in ferromagnetic metals can be described by coupling the Maxwell equations with the Ohm law, and neglecting displacement currents. In Gauss units, this yields

here represents a prescribed applied electromotive force. A further constitutive law must represent the vs. dependence, and account for hysteresis: formally,

being a hysteresis operator. For a one-dimensional system, may represent either the Preisach model, or one of it generalizations. This problem is mathematically well-behaved, cf. [5]. A vector extension of the Preisach model was proposed by Damlamian and Visintin [1], and independently by Mayergoyz and Friedman [2,3], see also [4]. The corresponding system (1), (2), coupled with appropriate initial and boundary condition, can be approximated by a time-discretization scheme of implicit type. One can prove that the solution of the latter converges to a solution of the exact problem as the time step vanishes.

Phone: 301-405-6843
Fax: 301-314-9920
E-mail: krishna@isr.umd.edu

Magnetostrictive materials such as Terfenol-D, an alloy of Terbium, Iron and Dysprosium, are prototypical examples of materials that can be controlled by the application of electromagnetic fields. In realizations as rods and thin films, these are of interest as actuators for diverse applications. Models of such materials as systems of interacting spins, coupled to elastodynamics, are being investigated actively. In this talk, we discuss ways to gain insight into this rich class of (many-body) problems, from the viewpoint of modeling and control of hysteresis. We discuss the geometric structures that arise in descriptions of such models (Landau-Lifshitz equations and other related equations). We also report on some computational experience (joint work with Xiabo Tan and John Baras) based on such models, and some experimental results with available actuators using such materials. We also discuss some recent work (joint with Ram Venkataraman) on low dimensional models of hysteresis in such actuators.

ECE Department University of Maryland
College Park, Maryland  20742

Phone: 301-405-3657
E-mail: isaak@Glue.umd.edu

The talk will review some previous work on stochastic problem in hysteresis. A special emphasis will be made on stochastic definitions of hysteresis models as well as on models of thermal relaxations in hysteretic systems and their technological relevance and importance. Some new results related to the application of stochastic procecesses on graphs to the analysis of noise in hysteretic systems will be also presented. Finally, the recovery of some fundamental hysteretic properties (such as coercivity, for instance) from intrinsically noisy measurements will be discussed.

tel.: (+49)-30-20372 448
fax: (+49)-30-204 4975
E-mail: krejci@wias-berlin.de

Safety in structural design depends on finding the minimum loadings that can be responsible for failure under service conditions. One failure mode of this type is incremental collapse---a progressive unbounded distortion of elastic-plastic structures under repeated loadings. This behavior can be characterized by hysteresis: below a critical load level hysteresis fades and the structures 'shake down' to asymptotic elastic response; above the critical load hysteresis persists, and the structures ultimately fail under cyclic loadings due to an incremental loss of rigidity. Extensive measurements have shown that the shakedown limit os structural lattices is completely analogous to the fatigue limit of materials. In both situations the demarcation between stabilizing and destructive hysteresis is equivalent to a dynamic phase transition.

Phone:  (919) 515-7552
Fax: (919) 515-1636
E-mail: rsmith@eos.ncsu.edu

This talk will focus on the mathematical modeling of hysteresis and constitutive nonlinearities inherent to piezoceramic, electrostrictive and magnetostrictive materials at moderate to high drive levels. The hysteretic and nonlinear behavior of these materials can be attributed to their underlying domain structure and this common ferroic framework is utilized to construct unified constitutive models for the materials. These models are constructed in two steps. In the first, Boltzmann principles are used to quantify the anhysteretic behavior which would result in the absence of inclusions in the material. In the second step, energy relations are employed to quantify the irreversible and reversible motion of domains walls about pinning sites in the material. The resulting models are formulated as ODE having five parameters. The relationship of the model parameters to physical attributes of the materials is discussed and algorithms for determining estimates of the parameters using measured values of the coercive field, differential susceptibility and saturation properties of the materials are detailed. The accuracy of the models and their capability for predicting measured polarization and magnetization values at various drive levels are illustrated through comparison with experimental data from PZT, PMN and Terfenol-D compounds. Finally, the ODE model formulation is amenable to inversion which facilitates the construction of an inverse compensator for linear control design.

Phone: 530-752-4711
E-mail: pazmandi@cascade.atomki.hu

We study the hysteretic and relaxational behaviour of long and short ranged magnetic models with uniaxial anisotropy. First, we concentrate on the case of infinite-range interaction, the Sherrington - Kirkpatrick model. We establish that, in contrast to the Random Field Ising system, the model exhibits Self Organized Criticality (SOC) everywhere on the hysteresis loop. Then we study the relaxation of the model and find that, in accordance with the presence of SOC, the magnetization relaxes as a power law at long times. The exponent of the decay depends on the temperature, but is independent of the magnetic field. For short range models we study the Edwards - Anderson model, and establish that the density of states for the lowest lying excitations is finite. This result favors the replica based picture of spin glasses, and is at odds with the droplet model. Finally, we analyze the dynamics of moving domain walls. We expand the ABBM model to include non - elastic processes, such as the tearing of the wall at strong pins, leaving behind small domains of opposite polarization. These "viscous" processes turn the depinning transition first order in some parameter ranges. From a methodological vantage point our work establishes that performing hysteretic cycles with decreasing amplitudes ("degaussing") is a particularly effective way to identify the lowest energy states of a wide range of models. We found more than one order of magnitude enhancements in speed over the accepted standard, the Simulated Annealing approach.

In this talk we will discuss some theory and applications of hysteretic systems with stochastic inputs. During the past ten years we have employed this formalism to model aftereffect phenomena in magnetic and superconductive hysteretic systems. The accuracy of the model has been verified by both experiment and simulation . It turns out that the mathematical formalism employed in this research can also be applied to some interesting problems in detection theory. Once we review our earlier work, we will focus on some recent work in which rectangular hysteresis operators are employed in binary detectors. Such detectors are proposed as suboptimal solutions for bit rate transparent midspan repeaters in an all optical networks. It is shown that key computations for the bit error rate are reduced to the well known "exit problem" of stochastic differential equation theory. This formalism is employed to derive closed form expressions in the transform domain for the probability density function of the detector output in the presence of additive white Gaussian noise. Applying inverse transformations, these expressions can be utilized to determine various performance measures of binary detectors with hysteresis.

Phone: (312) 413-7951
E-mail: htbanks@unity.ncsu.edu

We discuss our recent efforts in modeling,computation and experimental validation for extension and shear in filled viscoelastic rubbers. Theoretical results for models including nonlinear internal dynamics are given and shown to be useful in development of computational methods for both simulation and inverse problem applications. We also discuss the relationship of our results to similar formulations for nonlinear polarization laws (e.g.,nonlinear generalizations of the Debye, Lorentz and other laws ) in electromagnetic interrogation problems for dielectric materials.

[2] Olga Perkovic et al., Phys. Rev. Lett. 75, 4528 (1995)

E-mail: serpico@unina.it

The magnetization dynamics described by Landau-Lifshitz equation is considered. This equation has been used in most studies of the dynamics of ferromagnetic materials especially for the description of ferromagnetic resonance and magnetization switching in thin films and small particles. In this paper, Landau-Lifshitz equation is employed to describe the time evolution of magnetization in a uniformly magnetized spheroidal particle with uniaxial anisotropy subjected to time-harmonic applied magnetic fields. The qualitative dynamics of magnetization is strongly affected by the polarization of the applied field. In the case of circularly polarized applied magnetic fields, the problem can be reduced to the study of an autonomous dynamical system on the sphere. As a result of this reduction, only periodic and quasiperiodic regimes may occur. In the general case of elliptically polarized fields, along with periodic and quasiperiodic modes, the dynamical system may exhibit chaotic dynamics.
The presence of multiple asymptotic regimes in the Landau-Lifshitz dynamics may lead to the emergence of multistability. A typical example of this behaviour is the foldover effect occuring in the ferromagnetic resonance condition.
A very interesting limiting case of this dynamical system is the zero-frequency limit which leads to the classical Stoner-Wohlfart model. In this sense, Landau-Lifshitz for uniformly magnetized spheroidal particles can be considered as the dynamical generalization of Stoner-Wohlfart model. The connection with Stoner-Wohlfart theory and its implications on the dynamical behaviour of the system are discussed in the paper.

Gary Friedman
University of Illinois at Chicago             
Department of Electrical Engineering   
851 South Morgan
Mail Code 154
Chicago, Illinois 60607

Phone: 312-996-0827
Fax: 312-413-0024
E-mail: garyf@uic.edu

Approximation of Hysteresis Transducers with the Wipe-Out Memory

Wipe-out (also called return point memory) has been observed in magnetic materials, in superconductors, in ferroelectric materials, in shape memory alloys and many other hysteretic systems. The question arises: How can hysteresis non-linearities that exhibit wipe-out memory be represented in general. If this is not possible, can such non-linearities be at least approximated in some way? Preisach model and some of its variations do describe some hysteresis non-linearities with wipe-out memory because they are based on simple hysteresis operators - bistable relays - each of which has wipe-out memory. In this work it will be shown that, when a hysteresis non-linearity is a smooth mapping between history of the input and the output, it can be approximated with an arbitrary accuracy using a series expansion. Each term in this series expansion can be viewed as a hysteresis operator based on products of bistable relays. The first term of this series will, in fact, be the Preisach mod! el. The second term will be based on products of two bistable relays, the third term will be based on products of three bistable relays and so on. The problem of parameter identification for an expansion of a hysteresis non-linearity with wipe-out memory will be addressed.