On the Rayleigh law of magnetization: A new mathematical model of hysteresis loops

Due to the existence of multicoupled nonlinear factors in the giant magnetostrictive actuator (GMA), building precise mathematical model is highly important to study GMA’s characteristics and control strategies. Minor hysteresis loops near the bias magnetic field would be often applied because of its relatively good linearity. Load, friction, and disc spring stiffness seriously affect the output characteristics of the GMA in high frequency. Therefore, the current-displacement dynamic minor loops mathematical model coupling of electric-magnetic-machine is established according to Jiles-Atherton (J-A) dynamic model of hysteresis material, GMA structural dynamic equation, Ampere loop circuit law, and nonlinear piezomagnetic equation and demonstrates its correctness and effectiveness in the experiments. Finally, some laws are achieved between key structural parameters and output characteristics of GMA, which provides important theoretical foundation for structural design.

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A Multistable Generalized Meminductor with Coexisting Stable Pinched Hysteresis Loops

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500236 ◽

2020 ◽

Vol 30 (02) ◽

pp. 2050023

Author(s):

Fang Yuan ◽

Yue Deng ◽

Yuxia Li

Keyword(s):

Mathematical Model ◽

Theoretical Analysis ◽

Hysteresis Loops ◽

The Mathematical Model ◽

Pinched Hysteresis

A multistable local active meminductor emulator is proposed in this paper. The mathematical model of the emulator circuits is established. Different periodic stimuli are applied to the presented emulators and coexisting stable pinched hysteresis loops are obtained. The results obtained by experimental equips are consistent with the theoretical analysis, which indicates that the proposed emulators can work as a meminductor.

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A mathematical model for generating microplastic hysteresis loops

Journal of Strain Analysis ◽

10.1243/03093247v031050 ◽

1968 ◽

Vol 3 (1) ◽

pp. 50-56 ◽

Cited By ~ 4

Author(s):

A Esin ◽

W J D Jones

Keyword(s):

Mathematical Model ◽

Cyclic Loading ◽

Total Energy ◽

Yield Point ◽

Plastic Flow ◽

Elastic Limit ◽

Hysteresis Loops ◽

Elastic Region ◽

Proportional Limit ◽

Cycles To Failure

A method is suggested for defining the extent of the microplasticity which can exist in a material at stresses between the ‘true elastic limit’ and the nominal yield point or proportional limit. The suggested mathematical model makes it possible to extrapolate the macroscopic plastic equation into the elastic region in order to take account of the localized nature of the plastic flow. This analysis can be used to calculate the microplastic hysteresis energy absorbed per cycle by a material under cyclic loading and with a knowledge of the total energy to fracture can be used to predict the number of fatigue cycles to failure; an example is given.

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A Novel Floating Memristor Emulator with Minimal Components

Active and Passive Electronic Components ◽

10.1155/2017/1609787 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 2

Author(s):

Zhijun Li ◽

Yicheng Zeng ◽

Minglin Ma

Keyword(s):

Mathematical Model ◽

Hysteresis Loops ◽

Experimental Tests ◽

Operational Amplifiers ◽

Current Feedback ◽

Analog Multipliers ◽

Current Feedback Operational Amplifiers ◽

Memristor Emulator ◽

The Mathematical Model ◽

Pinched Hysteresis

A new floating emulator for the flux-controlled memristor is introduced in this paper. The proposed emulator circuit is very simple and consists of only two current feedback operational amplifiers (CFOAs), two analog multipliers, three resistors, and two capacitors. The emulator can be configured as an incremental or decremental type memristor by using an additional switch. The mathematical model of the emulator is derived to characterize its behavior. The hysteresis behavior of the emulator is discussed in detail, showing that the pinched hysteresis loops in v-i plane depend not only on the amplitude-to-frequency ratio of the exciting signal but also on the time constant of the emulator circuit itself. Experimental tests are provided to validate the emulator’s workability.

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Generalized Memristor Consisting of Diode Bridge with First Order Parallel RC Filter

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501430 ◽

2014 ◽

Vol 24 (11) ◽

pp. 1450143 ◽

Cited By ~ 61

Author(s):

Bocheng Bao ◽

Jingjing Yu ◽

Fengwei Hu ◽

Zhong Liu

Keyword(s):

Mathematical Model ◽

Hysteresis Loops ◽

Experimental Measurements ◽

First Order ◽

The Mathematical Model ◽

Pinched Hysteresis ◽

Order Parallel

A generalized memristor consisting of a memristive diode bridge with a first order parallel RC filter is proposed in this letter. The mathematical model of the circuit is established and its fingerprints are analyzed by the pinched hysteresis loops with different periodic stimuli. The results verified by experimental measurements indicate that the proposed circuit is a simple voltage-controlled generalized memristor.

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Kinetics of CO2 excretion and intravascular pH disequilibria during carbonic anhydrase inhibition

Journal of Applied Physiology ◽

10.1152/jappl.1998.84.2.683 ◽

1998 ◽

Vol 84 (2) ◽

pp. 683-694 ◽

Cited By ~ 15

Author(s):

Victor Cardenas ◽

Thomas A. Heming ◽

Akhil Bidani

Keyword(s):

Mathematical Model ◽

Gas Exchange ◽

Carbonic Anhydrase ◽

Blood Cells ◽

Venous Blood ◽

Hysteresis Loops ◽

Mixed Venous Blood ◽

Carbonic Anhydrase Inhibition ◽

Kinetics Of ◽

Mixed Venous

Cardenas, Victor, Jr., Thomas A. Heming, and Akhil Bidani.Kinetics of CO2 excretion and intravascular pH disequilibria during carbonic anhydrase inhibition. J. Appl. Physiol. 84(2): 683–694, 1998.—Inhibition of carbonic anhydrase (CA) activity (activity in red blood cells and activity available on capillary endothelium) results in decrements in CO2 excretion (V˙co 2) and plasma-erythrocyte CO2-[Formula: see text]-H+disequilibrium as blood travels around the circulation. To investigate the kinetics of changes in blood [Formula: see text]and pH during progressive CA inhibition, we used our previously detailed mathematical model of capillary gas exchange to analyze experimental data of V˙co 2and blood-gas/pH parameters obtained from anesthetized, paralyzed, and mechanically ventilated dogs after treatment with acetazolamide (Actz, 0–100 mg/kg iv). Arterial and mixed venous blood samples were collected via indwelling femoral and pulmonary arterial catheters, respectively. Cardiac output was measured by thermodilution. End-tidal[Formula: see text], as a measure of alveolar[Formula: see text], was obtained from continuous records of airway [Formula: see text] above the carina. Experimental results were analyzed with the aid of a mathematical model of lung and tissue-gas exchange. Progressive CA inhibition was associated with stepwise increments in the equilibrated mixed venous-alveolar [Formula: see text] gradient (9, 19, and 26 Torr at 5, 20, and 100 mg/kg Actz, respectively). The maximum decrements in V˙co 2were 10, 24, and 26% with 5, 20, and 100 mg/kg Actz, respectively, without full recovery ofV˙co 2 at 1 h postinfusion. Equilibrated arterial [Formula: see text]overestimated alveolar [Formula: see text], and tissue [Formula: see text] was underestimated by the measured equilibrated mixed venous blood[Formula: see text]. Mathematical model computations predicted hysteresis loops of the instantaneous CO2-[Formula: see text]-H+relationship and in vivo blood[Formula: see text]-pH relationship due to the finite reaction times for CO2-[Formula: see text]-H+reactions. The shape of the hysteresis loops was affected by the extent of Actz inhibition of CA in red blood cells and plasma.

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