Complex Hysteresis Research Articles

Optimal compression of generalized Prandtl–Ishlinskii hysteresis models

Prandtl–Ishlinskii (PI) hysteresis models have been used widely in magnetic and smart material-based systems. A generalized PI model, consisting of a weighted superposition of generalized play operators, is capable of characterizing saturated and asymmetric hysteresis. The fidelity of the model hinges on accurate representation of the envelope functions, play operator radii, and corresponding weights. Existing work has typically adopted some predefined play radii, the performance of which could be far from optimal. In this paper, novel schemes are proposed for optimally compressing generalized PI models, subject to a complexity constraint characterized by the number of play operators. An information-theoretic tool, entropy, is adopted to capture the information loss in replacing a group of weighted play operators with a single play operator. The optimal compression algorithm is reformulated as an optimal control problem and solved with dynamic programming, the computational complexity of which is shown to be much lower than that of exhaustive search. Simulation results are first presented to examine the performance of the proposed approach in approximating a PI model consisting of a large number of play operators, where cases with different types of weight distributions are explored. The approach is further applied to compress an experimentally identified generalized PI model for the complex hysteresis behavior between the resistance and temperature of vanadium dioxide, a promising multifunctional material. Both simulation and experimental results demonstrate that the proposed algorithms in general yield far more superior performance than a typically adopted scheme where the play radii are assigned uniformly.

Facile synthesis and characterization of Mn3O4 nanoparticles by auto-combustion method

Mn3O4 nanoparticles of different sizes were synthesized at low-temperature by a facile and simple auto-combustion method. Homogeneous potato-shaped grains with an average diameter of about 30, 60 and 90nm were obtained. The ignition temperature has a significant influence on the particle size of the product. Magnetization of the Mn3O4 nanoparticles shows a ferrimagnetic behavior at low temperature. The coercivity is approximately four times larger than that of bulk Mn3O4 due likely to the particle size effect, which may also be responsible for the observed complex hysteresis that exhibits at least two different magnetic behaviors. This work offers an environmental friendly and industrially robust route towards tailored, uniform and high-quality Mn3O4 nanoparticles.

Theoretical model for fluid-solid coupling in porous materials.

This paper introduces a unifying theory for describing complex behavior for porous materials. The key ingredients are the stored energy in solid-fluid interaction as well as the solid-solid and fluid-fluid interactions. A finite element formulation is employed which naturally accounts for the pore-pore network effects and is easily applicable to most pore geometries such as cellular solids and foams. The interactions, built in at the finite element level, give rise to the mechanical response of the macroscopic material unit. Through numerical studies, we show that there is strong coupling between fluid and solid that induces complex mechanical response, i.e., hysteresis and anisotropy. It is demonstrated that hysteresis arises directly from the fluid-solid coupling. We term this type of hysteresis emergent hysteresis.

A spatial, social and environmental study of tuberculosis in China using statistical and GIS technology.

Tuberculosis (TB) remains a major public health problem in China, and its incidence shows certain regional disparities. Systematic investigations of the social and environmental factors influencing TB are necessary for the prevention and control of the disease. Data on cases were obtained from the Chinese Center for Disease and Prevention. Social and environmental variables were tabulated to investigate the latent factor structure of the data using exploratory factor analysis (EFA). Partial least square path modeling (PLS-PM) was used to analyze the complex causal relationship and hysteresis effects between the factors and TB prevalence. A geographically weighted regression (GWR) model was used to explore the local association between factors and TB prevalence. EFA and PLS-PM indicated significant associations between TB prevalence and its latent factors. Altitude, longitude, climate, and education burden played an important role; primary industry employment, population density, air quality, and economic level had hysteresis with different lag time; health service and unemployment played a limited role but had limited hysteresis. Additionally, the GWR model showed that each latent factor had different effects on TB prevalence in different areas. It is necessary to formulate regional measures and strategies for TB control and prevention in China according to the local regional effects of specific factors.

THE NEXT-GENERATION CONSTITUTIVE CORRELATIONS FOR SIMULATION OF CYCLIC STRESS-STRAIN BEHAVIOUR OF SAND

This paper presents an innovate approach to simulate the stress-strain behaviour of sands subjected to large amplitude regular cyclic loading. New prediction correlations were derived for damping ratio (D) and shear modulus (G) of sand utilizing linear genetic programming (LGP) methodology. The correlations were developed using several cyclic torsional simple shear test results. In order to formulate D and G, new equations were developed to simulate hysteresis strain–stress curves and maximum shear stress (τmax) at different loading cycles. A genetic algorithm analysis was per­formed to optimize the parameters of the proposed formulation for stress-strain relationship. A total of 746 records were extracted from the simple shear test results to develop the τmax predictive model. Sensitivity and parametric analyses were conducted to verify the results. To investigate the applicability of the models, they were employed to simulate the stress-strain curves of portions of test results that were not included in the analysis. The LGP method precisely charac­terizes the complex hysteresis behaviour of sandy soils resulting in a very good prediction performance. The proposed design equations may be used by designers as efficient tools to determine D and G, specifically when laboratory testing is not possible.

Modeling and inverse compensation of hysteresis in vanadium dioxide using an extended generalized Prandtl–Ishlinskii model

Vanadium dioxide , a promising multifunctional smart material, has shown strong promise in microactuation, memory, and optical applications. During thermally induced insulator-to-metal phase transition of , the changes of its electrical, mechanical, and optical properties demonstrate pronounced, complex hysteresis with respect to the temperature, which presents a challenge in the utilization of this material. In this paper, an extended generalized Prandtl–Ishlinskii model is proposed to model the hysteresis in , where a nonlinear memoryless function is introduced to improve its modeling capability. A novel inverse compensation algorithm for this hysteresis model is developed based on fixed-point iteration with which the convergence conditions of the algorithm are derived. The proposed approach is shown to be effective for modeling and compensating the asymmetric and non-monotonic hysteresis with saturation between the curvature output and the temperature input of a -coated microactuator, as well as the asymmetric hysteresis with partial saturation between the resistance output and the temperature input of a film.

Turbidity-based sediment monitoring in northern Thailand: Hysteresis, variability, and uncertainty

Annual total suspended solid (TSS) loads in the Mae Sa Catchment in northern Thailand, determined with an automated, turbidity-based monitoring approach, were approximately 62,000, 33,000, and 14,000 Mg during the three years of observation. These loads were equivalent to basin yields of 839 (603–1170), 445 (217–462), and 192 (108–222) Mg km−2 for the 74.16-km2 catchment during 2006, 2007, and 2008, respectively. The yearly uncertainty ranges indicate our loads may be underestimated by 38–43% or overestimated by 28–33%. In determining the annual loads, discharge (Q) and turbidity (T) values were compared against 333 hand-sampled total suspended solid concentrations (TSS) measured during 18 runoff events and other flow conditions across the three-year period. Annual rainfall varied from 1632 to 1934 mm; and catchment runoff coefficients (annual runoff/annual rainfall) ranged from 0.25 to 0.41. Measured TSS ranged from 8 to 15,900 mg l−1; the low value was associated with dry-season base flow; the latter, a wet-season storm. Storm size and location played an important role in producing clockwise, anticlockwise, and complex hysteresis in the Q-TSS relationship. Turbidity alone was a good estimator for turbidity ranges of roughly 10–2800 NTU (or concentrations approximately 25–4000 mg l−1). However, owing to hysteresis and high sediment concentrations that surpass the detection limits of the turbidity sensor during many annual storms, TSS was estimated best using a complex multiple regression equation based on high/low ranges of turbidity and Q as independent variables. Turbidity was not a good predictor of TSS fractions >2000 μm. Hysteresis in the monthly Q-TSS relationship was generally clockwise over the course of the monsoon season, but infrequent large dry-season storms disrupted the pattern in some years. The large decrease in annual loads during the study was believed to be related to depletion of fine sediment delivered to the stream by several landslides occurring the year prior to the study. The study indicated the importance of monitoring Q and turbidity at fine resolutions (e.g., sub-hourly) to capture the TSS dynamics and to make accurate load estimations in this flashy headwater stream where hysteresis in the Q-TSS signature varied at several time scales.

LNG 저장탱크의 면진시스템 적용을 위한 내진설계

The demand of natural gas is gradually increasing as a clean fuel in the world. Therefore, LNG storage tanks and related facilities of the importance of leading a community-based facility have emerged. The seismic design of LNG storage tank including seismic analysis have been developed steadily. But, the seismic analysis and design techniques for LNG storage tanks are lacking, in Korea. Consequently, it is necessary to develop an analysis model that LNG storage tanks in isolation system can describe the behavior. Further, LNG storage tank capable of ensuring safety and economy, it is necessary to develop design techniques. The studies have suggested seismic design procedures of LNG storage tanks with isolation system including triple-FPB and idealized complex hysteresis model of triple-FPB.

Geometry Rule of Combustor–Inlet Interaction in Ramjet Engines

Combustor–inlet interactions in ramjet engines are associated with such critical operation processes as combustion mode (ramjet mode/scramjet mode) transition and the onset of inlet unstart. Previous studies showed these critical operational processes were characterized by a nonlinear hysteresis property that originated from flow instabilities. This paper describes in detail, discusses, and comes to the conclusion that the complex hysteresis phenomena that are exhibited during the combustor–inlet interaction in a ramjet engine are governed by a certain mathematical rule: the butterfly geometry in Thom’s classification theorem. This conclusion is proved analytically under the assumption of inviscid flow. It shows the bifurcation set of a ramjet engine is a butterfly-shaped geometry. The butterfly geometry is higher in dimension than the formerly found cusp geometry, and it rules the hysteresis behaviors that are exhibited during combustion mode transition and inlet start/unstart, respectively. The formerly found cusp geometry is a local geometry of butterfly geometry. This invariance geometry rule offers not only an explanation of the known hysteresis behaviors but also a way of predicting the unknown hysteresis behaviors that are exhibited during combustor–inlet interaction in a ramjet engine. The hysteresis property introduces complex route-dependent behaviors to ramjet engines, and it is therefore necessary to have a global picture of various hysteresis phenomena for further understanding of the control problems of ramjet engines.

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.

Nonlinear dynamic model with multi-fields coupling effects for giant magnetostrictive actuators

This paper addresses the modeling of complex hysteresis behavior for giant magnetostrictive actuator system under magnetically unbiased conditions. The hysteresis behavior is modeled by establishing a novel nonlinear dynamic model with multi-fields coupling effects, in which both the eddy current effects and the change of stress are considered. The former is included in the nonlinear transient constitutive model with magnetic-elastic-thermal coupling effect, which is employed as the basic constitutive equations of Terfenol-D. The latter is characterized through the structural dynamic behavior of actuator system itself, which is modeled by theorem of momentum. The quantitative agreements between numerical simulation results and existing experimental data indicate that nonlinear dynamic model can accurately describe the complex hysteresis behavior of the giant magnetostrictive actuator system not only under quasi-static operating conditions but also under dynamic operating conditions. The numerical simulation results also indicate that both the eddy current effects and structural dynamic behavior are the origin of frequency-dependent hysteresis behavior for giant magnetostrictive actuator system, and demonstrate the significance and necessity of simultaneously considering the eddy current effects and the change of stress in the system-level. Thus, the nonlinear dynamic model established in this paper is a system-lever coupled theoretical model, which can be directly used in the active vibration control and any other engineering application of the giant magnetostrictive actuators.

Stress-induced magnetic hysteresis in amorphous microwires probed by microwave giant magnetoimpedance measurements

We report the results of a detailed study of the effects of tensile and torsional stresses on the giant magnetoimpedance (GMI) characteristics of vanishing-magnetostrictive Co-rich microwires at microwave frequency. A complex stress-induced hysteresis behaviour is identified in the GMI response in the presence of tensile and torsional stresses. It is also revealed that there exists a competition between these two kinds of stresses on the critical field via the interactions with the intrinsic anisotropy. An “enhanced core-shell” model is proposed here to resolve the physical origin of the low-field hysteresis and the dependence of induced anisotropy field on the applied tensile and/or torsional stress. Our results are of both technical importance to the design of non-contact stress sensors exploiting the GMI of microwires and fundamental significance to the understanding of the microwave GMI characteristics of soft magnetic microwires in the presence of external stresses.

Calculation of Equivalent Damping Ratio to Concrete-Filled Steel Tubular Arch Bridge

Based on the relationship between complex frequency and hysteresis damping coefficient, the formula of equivalent damping ratio of concrete-filled steel tubular arch bridge is deduced. Compared the calculated equivalent damping ratio by finite element model with the measured result, it is shown that the formula deduced in this paper is simple and practical, and can satisfy the engineering demand. At last, the formula given in this paper is closely related to hysteresis damping coefficient of material, with different hysteresis damping coefficient, the equivalent damping ratio will differ a lot.

Frequency and Amplitude Dependent Dynamic Model of Rotor Elastomeric Damper with Refined Nonlinear Stiffness

Elastomeric damper is a very important component for helicopter rotor system; its dynamic property has strong nonlinear behavior characterized by complex hysteresis loops, and dependence on excitation frequency, amplitude and temperature. Based on internal variables theory, combined with the nonlinear spring model, a time domain nonlinear dynamic model of elastomeric damper used for helicopter rotor load prediction is presented. The model was characterized by using the genetic algorithm, the hysteresis loop of elastomeric dampers made of different elastomeric materials under several excitation frequencies and strain amplitudes was calculated with this model and compared with experimental data. It is shown that the presented model can predict the hysteresis loop of the elastomeric dampers with little relative errors, and the model is able to catch the variation of dynamic stiffness. Therefore, the presented method can be used for helicopter rotor load prediction and aeroelastic analysis.

Multiple Coexisting Attractors and Hysteresis in the Generalized Ueda Oscillator

A periodically forced nonlinear oscillator called the generalized Ueda oscillator is proposed. The restoring force term of this equation consists of a nonlinear functionsgn(x)and an absolute function with a variant power. Dynamics is investigated by detailed numerical analysis as well as dynamic simulation, including the largest Lyapunov exponent, phase diagrams, and bifurcation diagrams. Multiple coexisting attractors and complex hysteresis phenomenon are observed. The results show that this system has rich dynamical behaviors, and it has a promising application in the fields of science and engineering.

Feature evaluation of complex hysteresis smoothing and its practical applications to noisy SEM images

Quality of a scanning electron microscopy (SEM) image is strongly influenced by noise. This is a fundamental drawback of the SEM instrument. Complex hysteresis smoothing (CHS) has been previously developed for noise removal of SEM images. This noise removal is performed by monitoring and processing properly the amplitude of the SEM signal. As it stands now, CHS may not be so utilized, though it has several advantages for SEM. For example, the resolution of image processed by CHS is basically equal to that of the original image. In order to find wide application of the CHS method in microscopy, the feature of CHS, which has not been so clarified until now is evaluated correctly. As the application of the result obtained by the feature evaluation, cursor width (CW), which is the sole processing parameter of CHS, is determined more properly using standard deviation of noise Nσ. In addition, disadvantage that CHS cannot remove the noise with excessively large amplitude is improved by a certain postprocessing. CHS is successfully applicable to SEM images with various noise amplitudes.

Modeling and Compensation for Hysteresis Nonlinearity of a Piezoelectrically Actuated Fast Tool Servo Based on a Novel Linear Model

In order to describe and compensate for complex hysteresis nonlinearities of piezoelectrically actuated fast tool servo (FTS), a novel Linear Fractional order Differentiation Hysteresis (LFDH) model is proposed in this paper. By means of the proposed LFDH model which is established on the fractional calculus theory, an analytical description of hysteresis behaviors of the FTS is derived. Furthermore, the LFDH model-based inverse compensation strategy is proposed to suppress the hysteresis effects of the FTS. Finally, a series of experiments are conducted to verify the effectiveness of the LFDH model and the corresponding compensation approach. The results demonstrate that the proposed LFDH model is efficient for describing hysteresis behaviors and the inverse compensation strategy can significantly suppress the inherent hysteresis of the FTS in open-loop operations.

A Luminescent and Sublimable DyIII‐Based Single‐Molecule Magnet

The reaction of [Ln(hfac)(3)]·2H(2)O and pyridine-N-oxide (PyNO) leads to isostructural dimers of the formula [Ln(hfac)(3)(PyNO)](2) (Ln=Eu, Gd, Tb, Dy). The Dy derivative shows a remarkable single-molecule magnet behavior with complex hysteresis at 1.4 K. The dynamics of the magnetization features are two relaxation regimes: a thermally activated one at high temperature (τ(0)=(5.62±0.4)×10(-11) s and Δ=(167±1) K) and a quantum tunneling regime at low temperature with a tunneling frequency of 0.42 Hz. The analysis of the Gd derivative evidences intradimer antiferromagnetic interactions (J=(-0.034±0.001) cm(-1)). Moreover, the Eu, Tb, and Dy derivatives are luminescent with quantum yield of 51, 53, and 0.1%, respectively. The thermal investigation of [Dy(hfac)(3)(PyNO)](2) shows that the dimers can be sublimated intact, suggesting their possible exploit as active materials for surface-confined nanostructures to be investigated by fluorimetry methods.

CARBON BLACK FOR RACING AND MOTORCYCLE TIRE TREADS. PERFORMANCE MODEL DEVELOPMENT

Abstract Racing tires and motorcycle tires present individual segments of the tire market. For instance, while the average life of car and truck tires is 50 000 miles, the average life of race tires is 100 miles. Because tires play a critical role in a race, technical demands to assure safety and performance are growing. Similarly, tires have a large influence on safety, handling/grip, and performance of the rapidly growing world fleet of motorcycles, due to the fact of only two wheels being in contact with the ground. Thus, the common feature of both market segments is that the typical tire compromise of wear, rolling resistance, and traction is strongly weighted toward traction. Most of the recent efforts of rubber scientists have been directed toward lowering rolling resistance of the tread compounds, which left a certain void in the science of compounding for racing and motorcycle treads. Particularly, the industrial assortment of polymers and fillers used for motorcycle treads is commonly different from that used for car or truck treads, but it is not known how the filler properties affect the hysteresis–stiffness compromise. The objective of this study is to evaluate the effects of the carbon black characteristics on the important properties of a typical racing and motorcycle tire tread compound. More than 50 individual carbon blacks were mixed in a SBR formulation. The acquired data were statistically analyzed, and a linear multiple regression model was developed to relate rubber properties (responses), such as static modulus, complex dynamic modulus, hysteresis, and viscosity to the key carbon black characteristics (variables) of surface area, structure, aggregate size distribution, and surface activity. Prediction profiles created from the model demonstrate rubber performance limits for the range of carbon blacks tested, and indicate the niches to provide required combinations of the rubber properties.

Deterministic and non-deterministic switching in chains of magnetic hysterons

This paper presents a fundamental analysis of a single-domain ferromagnetic particles chain hysteresis in perpendicular geometry as a prototype for ultra-high density memories. Due to magnetostatic long range interactions the system has a complex hysteresis but stable features can be found. The loop has a number of deterministic Barkhausen jumps and consequently a number of stable plateaus that could be used in multistate memories. The fundamental elements that sustain this behavior are shown and discussed.