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| [[File:Ehysteresis.PNG|thumb|right|[[Electric displacement field]] {{math|<var>D</var>}} of a [[ferroelectricity|ferroelectric]] material as the [[electric field]] {{math|<var>E</var>}} is first decreased, then increased. The curves form a ''hysteresis loop''.]]
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| '''Hysteresis''' is the dependence of a system not only on its current environment but also on its past environment. This dependence arises because the system can be in more than one internal state. To predict its future development, either its internal state or its history must be known.<ref>{{Cite journal |last1=Mielke |first1=A. |first2=T. |last2=Roubícek |year=2003 |title=A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys |journal=Multiscale Model. Simul. |volume=1 |issue=4 |pages=571–597 |doi=10.1137/S1540345903422860}}</ref> If a given input alternately increases and decreases, the output tends to form a [[loop (topology)|loop]] as in the figure. However, loops may also occur because of a dynamic [[lag]] between input and output. Often, this effect is also referred to as hysteresis, or ''rate-dependent hysteresis''. However, this effect disappears as the input changes more slowly.
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| Hysteresis occurs in [[ferromagnetic]] materials and [[ferroelectricity|ferroelectric]] materials, as well as in the [[deformation (mechanics)|deformation]] of some materials (such as [[rubber band]]s and [[shape-memory alloy]]s) in response to a varying force. In natural systems hysteresis is often associated with [[irreversible process|irreversible thermodynamic change]]. Many artificial systems are designed to have hysteresis: for example, in [[thermostat]]s and [[Schmitt trigger]]s, hysteresis is used to avoid unwanted rapid switching. Hysteresis has been identified in many other fields, including [[economics]] and [[biology]].
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| {{TOC limit|depth=2}}
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| ==Etymology and history==
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| The term "hysteresis" is derived from {{lang|grc|ὑστέρησις}}, an [[ancient Greek]] word meaning "deficiency" or "lagging behind". It was coined around 1890 by [[James Alfred Ewing|Sir James Alfred Ewing]] to describe the behaviour of magnetic materials.
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| Some early work on describing hysteresis in mechanical systems was performed by [[James Clerk Maxwell]]. Subsequently, hysteretic models have received significant attention in the works of [[Ferenc Preisach]] ([[Preisach model of hysteresis]]), [[Louis Néel]] and D. H. Everett in connection with magnetism and absorption. A more formal mathematical theory of systems with hysteresis was developed in the 1970s by a group of Russian mathematicians led by [[Mark Krasnosel'skii]], one of the founders{{citation needed|date=November 2011}} of nonlinear analysis. He suggested an investigation of hysteresis phenomena using the theory of nonlinear operators.<ref name="Mayergoyz2003">{{cite book|first=Isaak D.|last= Mayergoyz|title= Mathematical Models of Hysteresis and their Applications: Second Edition (Electromagnetism)|publisher= [[Academic Press]]|year= 2003 |isbn=978-0-12-480873-7}}</ref>
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| ==Types of hysteresis==
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| ===Rate-dependent===
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| One type of hysteresis is a simple [[lag]] between input and output. A simple example would be a sinusoidal input {{math|<var>X(t)</var>}} and output {{math|<var>Y(t)</var>}} that are separated by a phase lag {{math|<var>φ</var>}}:
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| :<math> \begin{align} | |
| X(t) &= X_0 \sin \omega t \\ Y(t) &= Y_0 \sin\left(\omega t-\phi\right).
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| \end{align}</math>
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| Such behavior can occur in linear systems, and a more general form of response is
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| :<math> Y(t) = \chi_\text{i} X(t) + \int_{-\infty}^t \Phi_\text{d} (t-\tau) H(\tau) \, d\tau, </math>
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| where {{math|<var>χ</var><sub>i</sub>}} is the instantaneous response and {{math|<var>Φ</var><sub>d</sub><var>(t-τ)</var>}} is the [[Impulse response|response]] at time {{math|<var>t</var>}} to an impulse at time {{math|<var>τ</var>}}. In the [[frequency domain]], input and output are related by a complex ''generalized susceptibility''.<ref name=Bertotti1998ch2>{{cite book |last1=Bertotti |first1=Giorgio |title=Hysteresis in magnetism: For physicists, materials scientists, and engineers |publisher=[[Academic Press]] |year=1998 |isbn=978-0-12-093270-2 |chapter=Ch. 2}}</ref>
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| This kind of hysteresis is often referred to as ''rate-dependent hysteresis''. If the input is reduced to zero, the output continues to respond for a finite time. This constitutes a memory of the past, but a limited one because it disappears as the output decays to zero. The phase lag depends on the frequency of change of the input, and goes to zero as the frequency decreases.<ref name="Bertotti1998ch2" />
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| Where rate-dependent hysteresis is due to [[dissipative]] effects like [[friction]], it is associated with [[power loss]].<ref name="Bertotti1998ch2" />
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| ===Rate-independent===
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| Systems with ''rate-independent hysteresis'' have a ''persistent'' memory of the past that remains after the transients have died out.<ref name=rate>The term is attributed to {{harvnb|Truesdell|Noll|1965}} by {{harvnb|Visintin|1994|loc=page 13}}.</ref> The future development of such a system depends on the past. If an input variable {{math|<var>X</var>}} cycles from {{math|<var>X</var><sub>0</sub>}} to {{math|<var>X</var><sub>1</sub>}} and back, the output {{math|<var>Y(X)</var>}} may be {{math|<var>Y</var><sub>0</sub>}} initially and a different value {{math|<var>Y</var><sub>2</sub>}} on the return. The values of {{math|<var>Y(X)</var>}} depend on the values that {{math|<var>X</var>}} passes through, but not on the rate of change of {{math|<var>X</var>}}.<ref name="Bertotti1998ch2"/> Many authors define hysteresis as rate-independent hysteresis.<ref name=Visintin1994p13>{{harvnb|Visintin|1994|loc=page 13}}</ref>
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| ==Hysteresis in engineering==
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| ===Control systems===
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| Hysteresis can be used to filter signals so that the output reacts slowly by taking recent history into account. For example, a [[thermostat]] controlling a heater may turn the heater on when the temperature drops below A degrees, but not turn it off until the temperature rises above B degrees (e.g., if one wishes to maintain a temperature of 20 °C, then one might set the thermostat to turn the furnace on when the temperature drops below 18 °C, and turn it off when the temperature exceeds 22 °C). This thermostat has hysteresis. Thus the on/off output of the thermostat to the heater when the temperature is between A and B depends on the history of the temperature. This prevents rapid switching on and off as the temperature drifts around the set point. The furnace is either off or on, with nothing in between. The thermostat is a system; the input is the temperature, and the output is the furnace state. If the temperature is 21 °C, then it is not possible to predict whether the furnace is on or off without knowing the history of the temperature.
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| Similarly a pressure switch also exhibits hysteresis. Its pressure setpoints are substituted for those of temperature corresponding to a thermostat.
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| ===Electronic circuits===
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| [[Image:Hysteresis sharp curve.svg|thumb|Sharp hysteresis loop of a [[Schmitt trigger]]]]
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| A [[Schmitt trigger]] is a simple electronic circuit that also exhibits this property. Often, some amount of hysteresis is intentionally added to an electronic circuit to prevent unwanted rapid switching. This and similar techniques are used to compensate for [[Switch#Contact bounce|contact bounce]] in switches, or [[Noise (electronic)|noise]] in an electrical signal.
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| A [[Relay#Latching relay|latching relay]] uses a solenoid to actuate a ratcheting mechanism that keeps the relay closed even if power to the relay is terminated.
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| Hysteresis is essential to the workings of some [[memristor]]s (circuit components which "remember" changes in the current passing through them by changing their resistance).<ref>{{cite news |url=http://www.eetimes.com/news/latest/showArticle.jhtml?articleID=207403521&pgno=1 |title='Missing link' memristor created: Rewrite the textbooks? |last1=Johnson |first1=R. Colin |newspaper=EE Times April 30, 2008 |accessdate=September 2011}}</ref>
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| Hysteresis can be used when connecting arrays of elements such as [[nanoelectronic]]s, [[electrochrome cells]] and [[memory effect]] devices using [[passive matrix addressing]]. Shortcuts are made between adjacent components (see [[crosstalk]]) and the hysteresis helps to keep the components in a particular state while the other components change states. Thus, all rows can be addressed at the same time instead of individually.
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| In the field of audio electronics, a [[noise gate]] often implements hysteresis intentionally to prevent the gate from "chattering" when signals close to its threshold are applied.
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| ===User interface design===
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| A hysteresis is sometimes intentionally added to computer algorithms. The field of [[user interface design]] has borrowed the term hysteresis to refer to times when the state of the user interface intentionally lags behind the apparent user input. For example, a menu that was drawn in response to a mouse-over event may remain on-screen for a brief moment after the mouse has moved out of the trigger region and the menu region. This allows the user to move the mouse directly to an item on the menu, even if part of that direct mouse path is outside of both the trigger region and the menu region. For instance, right-clicking on the desktop in most Windows interfaces will create a menu that exhibits this behavior.
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| ===Aerodynamics===
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| In aerodynamics, hysteresis can be observed when decreasing the angle of attack of a wing after stall, regarding the lift and drag coefficients. The angle of attack where the flow on top of the wing reattaches is generally lower than the angle of attack where the flow separates during the increase of the angle of attack.<ref>{{cite conference |url=http://www.public.iastate.edu/~huhui/paper/2008/AIAA-2008-0315.pdf |format=pdf |title=An Experimental Investigation on Aerodynamic Hysteresis of a Low-Reynolds Number Airfoil |author=Zifeng Yang |authorlink= |coauthors=Hirofumi Igarashi, Mathew Martin and Hui Hu |date=Jan 7 – 10, 2008 |publisher=American Institute of Aeronautics and Astronautics |conference=46th AIAA Aerospace Sciences Meeting and Exhibit |pages= |location=Reno, Nevada |id=AIAA-2008-0315 }}</ref>
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| ==Hysteresis in mechanics==
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| ===Elastic hysteresis===
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| [[Image:Elastic Hysteresis.svg|thumb|right|Elastic hysteresis of an idealized rubber band. The area in the centre of the hysteresis loop is the energy dissipated due to internal friction.]]
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| In the elastic hysteresis of rubber, the area in the centre of a hysteresis loop is the energy dissipated due to material [[internal friction]].
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| Elastic hysteresis was one of the first types of hysteresis to be examined.<ref name="LoveTreatise">{{cite book |author=Love, Augustus E. |title=Treatise on the Mathematical Theory of Elasticity (Dover Books on Physics & Chemistry) |publisher=Dover Publications |location=New York |year=1927 |isbn=0-486-60174-9}}</ref><ref name="Ewing">{{cite journal |first1=J. A. |last1= Ewing |authorlink1=James Alfred Ewing |title=On hysteresis in the relation of strain to stress |journal=British Association Reports |year=1889 |pages=502|url=https://archive.org/details/reportofbritisha90brit}}</ref>
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| A simple way to understand it is in terms of a rubber band with weights attached to it. If the top of a rubber band is hung on a hook and small weights are attached to the bottom of the band one at a time, it will get longer. As more weights are ''loaded'' onto it, the band will continue to extend because the force the weights are exerting on the band is increasing. When each weight is taken off, or ''unloaded'', the band will get shorter as the force is reduced. As the weights are taken off, each weight that produced a specific length as it was loaded onto the band now produces a slightly longer length as it is unloaded. This is because the band does not obey [[Hooke's law]] perfectly. The hysteresis loop of an idealized rubber band is shown in the figure.
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| In terms of force, the rubber band was harder to stretch when it was being loaded than when it was being unloaded. In terms of time, when the band is unloaded, the cause (the force of the weights) lagged behind the effect (the length) because a smaller value of weight produced the same length. In terms of energy, more was required during the loading than the unloading, the excess energy being dissipated as heat.
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| Elastic hysteresis is more pronounced when the loading and unloading is done quickly than when it is done slowly.<ref>{{cite journal|first1=B. |last1=Hopkinson |first2=G. T. |last2=Williams |journal=[[Proceedings of the Royal Society]] |volume= 87 |year=1912 |pages=502 |doi=10.1098/rspa.1912.0104|title=The Elastic Hysteresis of Steel |bibcode = 1912RSPSA..87..502H|issue=598 }}</ref> Some materials such as hard metals don't show elastic hysteresis under a moderate load, whereas other hard materials like granite and marble do. Materials such as rubber exhibit a high degree of elastic hysteresis.
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| When the intrinsic hysteresis of rubber is being measured, the material can be considered to behave like a gas. When a rubber band is stretched it heats up, and if it is suddenly released, it cools down perceptibly. These effects correspond to a large hysteresis from the thermal exchange with the environment and a smaller hysteresis due to internal friction within the rubber. This proper, intrinsic hysteresis can be measured only if the rubber band is adiabatically isolated.
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| Small vehicle suspensions using [[rubber]] (or other [[elastomer]]s) can achieve the dual function of springing and damping because rubber, unlike metal springs, has pronounced hysteresis and does not return all the absorbed compression energy on the rebound. [[Mountain bike]]s have made use of elastomer suspension, as did the original [[Mini]] car.
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| ===Contact angle hysteresis===
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| The [[contact angle]] formed between a liquid and solid phase will exhibit a range of contact angles that are possible. There are two common methods for measuring this range of contact angles. The first method is referred to as the tilting base method. Once a drop is dispensed on the surface with the surface level, the surface is then tilted from 0° to 90°. As the drop is tilted, the downhill side will be in a state of imminent wetting while the uphill side will be in a state of imminent dewetting. As the tilt increases the downhill contact angle will increase and represents the advancing contact angle while the uphill side will decrease; this is the receding contact angle. The values for these angles just prior to the drop releasing will typically represent the advancing and receding contact angles. The difference between these two angles is the contact angle hysteresis. The second method is often referred to as the add/remove volume method. When the maximum liquid volume is removed from the drop without the [[interfacial area]] decreasing the receding contact angle is thus measured. When volume is added to the maximum before the [[interfacial area]] increases, this is the [[advancing contact angle]]. As with the tilt method, the difference between the advancing and receding contact angles is the contact angle hysteresis. Most researchers prefer the tilt method; the add/remove method requires that a tip or needle stay embedded in the drop which can affect the accuracy of the values, especially the receding contact angle.
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| ===Adsorption hysteresis===
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| Hysteresis can also occur during physical [[adsorption]] processes. In this type of hysteresis, the quantity adsorbed is different when gas is being added than it is when being removed. The specific causes of adsorption hysteresis are still an active area of research, but it is linked to differences in the nucleation and evaporation mechanisms inside mesopores. These mechanisms are further complicated by effects such as [[cavitation]] and pore blocking.
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| In physical adsorption, hysteresis is evidence of [[mesoporosity]]-indeed, the definition of mesopores (2–50 nm) is associated with the appearance (50 nm) and disappearance (2 nm) of mesoporosity in nitrogen adsorption isotherms as a function of Kelvin radius.<ref>{{cite book|last1=Gregg |first1=S. J. |last2=Sing |first2=Kenneth S. W. |title=Adsorption, Surface Area, and Porosity|edition=Second|location=London|publisher=[[Academic Press]]|year=1982 |isbn=978-0-12-300956-2}}</ref> An adsorption isotherm showing hysteresis is said to be of Type IV (for a wetting adsorbate) or Type V (for a non-wetting adsorbate), and hysteresis loops themselves are classified according to how symmetric the loop is.<ref>{{cite journal|first1=K. S. W. |last1=Sing |first2=D. H. |last2=Everett |first3=R. A. W. |last3=Haul |first4=L. |last4=Moscou |first5=R. A. |last5=Pierotti |first6=J. |last6=J. Roquérol |first7=T. |last7=Siemieniewska |journal=[[Pure and Applied Chemistry]] |volume=57|issue=4 |pages=603–619|year=1985|doi=10.1351/pac198557040603|title=Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (Recommendations 1984)}}</ref> Adsorption hysteresis loops also have the unusual property that it is possible to scan within a hysteresis loop by reversing the direction of adsorption while on a point on the loop. The resulting scans are called "crossing," "converging," or "returning," depending on the shape of the isotherm at this point.<ref>{{cite journal|first1=G. A. |last1=Tompsett |first2=L. |last2=Krogh |first3=D. W. |last3=Griffin |first4=W. C. |last4=Conner |journal=[[Langmuir (journal)|Langmuir]] |volume=21|issue=8|pages=8214–8225|year=2005|pmid=16114924|doi=10.1021/la050068y|title=Hysteresis and Scanning Behavior of Mesoporous Molecular Sieves}}</ref>
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| ===Matric potential hysteresis===
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| The relationship between matric [[water potential]] and [[water content]] is the basis of the [[water retention curve]]. [[Matric potential]] measurements (Ψ<sub>m</sub>) are converted to volumetric water content (θ) measurements based on a site or soil specific calibration curve. Hysteresis is a source of water content measurement error. Matric potential hysteresis arises from differences in wetting behaviour causing dry medium to re-wet; that is, it depends on the saturation history of the porous medium. Hysteretic behaviour means that, for example, at a matric potential (Ψ<sub>m</sub>) of {{nowrap|5 kPa}}, the volumetric water content (θ) of a fine sandy soil matrix could be anything between 8% to 25%.<ref>{{cite mailing list |url=http://www.sowacs.com/archives/99-04/msg00000.html |title=Subject: Accuracy of capacitance soil moisture ... |date=8 April 1999 |accessdate=28 September 2011 |mailinglist=SOWACS |last1=Parkes |first1=Martin}}</ref>
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| [[Tensiometer (soil science)|Tensiometer]]s are directly influenced by this type of hysteresis. Two other types of sensors used to measure soil water matric potential are also influenced by hysteresis effects within the sensor itself. Resistance blocks, both nylon and gypsum based, measure matric potential as a function of electrical resistance. The relation between the sensor’s electrical resistance and sensor matric potential is hysteretic. Thermocouples measure matric potential as a function of heat dissipation. Hysteresis occurs because measured heat dissipation depends on sensor water content, and the sensor water content–matric potential relationship is hysteretic. {{As of|2002}}, only desorption curves are usually measured during calibration of [[soil moisture sensors]]. Despite the fact that it can be a source of significant error, the sensor specific effect of hysteresis is generally ignored.<ref>{{cite journal
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| |last1 = Scanlon
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| |first1= B. R.
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| |last2= Andraski
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| |first2= B. J.
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| |last3=Bilskie
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| |first3= J.
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| |year = 2002
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| |title = Methods of soil analysis: Physical Methods: Miscellaneous methods for measuring matric or water potential
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| |journal = Soil Science Society of America
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| |volume = 4
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| |pages = 643–670
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| |isbn = 0-89118-810-X
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| |url = http://www.beg.utexas.edu/environqlty/vadose/pdfs/webbio_pdfs/Chapt3-2-4.pdf
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| |format =PDF
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| |accessdate = 2006-05-26
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| }}</ref>
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| ==Hysteresis in materials==
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| ===Magnetic hysteresis===
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| {{main|Magnetic hysteresis}}
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| <!--NOTE TO EDITORS: This section is linked to from [[Kilogram]] and [[Magnetic field]]. Please do not rename without changing the referring link.-->
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| [[Image:StonerWohlfarthMainLoop.svg|thumb|right|400px|[[Stoner–Wohlfarth model|Theoretical model]] of [[magnetization]] {{math|<var>m</var>}} against [[magnetic field]] {{math|<var>h</var>}}. Starting at the origin, the upward curve is the ''initial magnetization curve''. The downward curve after saturation, along with the lower return curve, form the ''main loop''. The intercepts {{math|<var>h</var><sub>c</sub>}} and {{math|<var>m</var><sub>rs</sub>}} are the ''[[coercivity]]'' and ''[[remanence#Saturation remanence|saturation remanence]]''. ]]
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| When an external [[magnetic field]] is applied to a [[ferromagnetism|ferromagnet]] such as [[iron]], the atomic [[dipole]]s align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become ''magnetized''. Once magnetized, the magnet will stay magnetized indefinitely. To [[Magnet#Demagnetizing ferromagnets|demagnetize]] it requires heat or a magnetic field in the opposite direction. This is the effect that provides the element of memory in a [[hard disk drive]].
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| The relationship between field strength {{math|<var>H</var>}} and magnetization {{math|<var>M</var>}} is not linear in such materials. If a magnet is demagnetized ({{math|<var>H{{=}}M{{=}}0</var>}}) and the relationship between {{math|<var>H</var>}} and {{math|<var>M</var>}} is plotted for increasing levels of field strength, {{math|<var>M</var>}} follows the ''initial magnetization curve''. This curve increases rapidly at first and then approaches an [[asymptote]] called [[Saturation (magnetic)|magnetic saturation]]. If the magnetic field is now reduced monotonically, {{math|<var>M</var>}} follows a different curve. At zero field strength, the magnetization is offset from the origin by an amount called the [[remanence]]. If the {{math|<var>H-M</var>}} relationship is plotted for all strengths of applied magnetic field the result is a hysteresis loop called the ''main loop''. The width of the middle section is twice the [[coercivity]] of the material.<ref name=Chikazumi1997ch1>{{harvnb|Chikazumi|1997|loc=Chapter 1}}</ref>
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| A closer look at a magnetization curve generally reveals a series of small, random jumps in magnetization called [[Barkhausen effect|Barkhausen jumps]]. This effect is due to [[crystallographic defect]]s such as [[dislocation]]s.<ref name=Chikazumi1997ch15>{{harvnb|Chikazumi|1997|loc=Chapter 15}}</ref>
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| Magnetic hysteresis loops are not exclusive to materials with ferromagnetic ordering. Other magnetic orderings, such as [[spin glass]] ordering, also exhibit this phenomena.<ref>{{cite journal |last1=Monod |first1=P. |last2=PréJean |first2=J. J. |last3=Tissier |first3=B. |year=1979 |title=Magnetic hysteresis of CuMn in the spin glass state |journal=J. Appl. Phys. |volume=50 |issue=B11|pages=7324 |publisher=American Institute of Physics |doi=10.1063/1.326943 |url=http://dx.doi.org/10.1063/1.326943 |accessdate=9 March 2013|bibcode = 1979JAP....50.7324M }}</ref>
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| ====Physical origin====
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| {{Main|Ferromagnetism}}
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| The phenomenon of hysteresis in [[ferromagnetism|ferromagnetic]] materials is the result of two effects: rotation of [[magnetization]] and changes in size or number of [[magnetic domain]]s. In general, the magnetization varies (in direction but not magnitude) across a magnet, but in sufficiently small magnets, it does not. In these [[Single domain (magnetic)|single-domain]] magnets, the magnetization responds to a magnetic field by rotating. Single-domain magnets are used wherever a strong, stable magnetization is needed (for example, [[magnetic recording]]).
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| Larger magnets are divided into regions called ''domains''. Across each domain, the magnetization does not vary; but between domains are relatively thin ''domain walls'' in which the direction of magnetization rotates from the direction of one domain to another. If the magnetic field changes, the walls move, changing the relative sizes of the domains. Because the domains are not magnetized in the same direction, the [[magnetic moment]] per unit volume is smaller than it would be in a single-domain magnet; but domain walls involve rotation of only a small part of the magnetization, so it is much easier to change the magnetic moment. The magnetization can also change by addition or subtraction of domains (called ''nucleation'' and ''denucleation'').
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| ====Magnetic hysteresis models====
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| The most known empirical models in hysteresis are [[Preisach model of hysteresis|Preisach]] and Jiles-Atherton models. These models allow an accurate modeling of the hysteresis loop and are widely used in the industry. However, these models lose the connection with thermodynamics and the energy consistency is not ensured. Last models rely on a consistent thermodynamic formulation. VINCH model<ref>Vincent Francois-Lavet et al (2011-11-14). [http://vincent.francois-l.be/VINCH_model.pdf Vectorial Incremental Nonconservative Consistent Hysteresis model].</ref> is inspired by the [[Work hardening|kinematic hardening]] laws and by the [[thermodynamics]] of [[irreversible process]]es. In particular, in addition to provide an accurate modeling, the stored magnetic energy and the dissipated energy are known at all times. The obtained incremental formulation is variationally consistent, i.e., all internal variables follow from the minimization of a thermodynamic potential. That allows to obtain easily a vectorial model while Preisach and Jiles-Atherton are fundamentally scalar models.
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| ====Applications====
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| {{Main|Magnet#Common uses of magnets}}
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| There are a great variety of applications of the hysteresis in ferromagnets. Many of these make use of their ability to retain a memory, for example [[magnetic tape]], [[hard disks]], and [[credit card]]s. In these applications, ''hard'' magnets (high coercivity) like [[iron]] are desirable so the memory is not easily erased.
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| ''Soft'' magnets (low coercivity) are used as cores in [[electromagnet]]s. The nonlinear response of the magnetic moment to a magnetic field boosts the response of the coil wrapped around it. The low coercivity reduces that energy loss associated with hysteresis.
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| ===Electrical hysteresis===
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| Electrical hysteresis typically occurs in [[ferroelectric]] material, where domains of polarization contribute to the total polarization. Polarization is the [[electrical dipole moment]] (either [[coulomb|C]]·[[metre|m]]<SUP>−2</SUP> or [[coulomb|C]]·[[metre|m]]). The mechanism, an organization of the polarization into domains, is similar to that of magnetic hysteresis.
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| ===Liquid–solid-phase transitions===
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| Hysteresis manifests itself in state transitions when [[melting point|melting temperature]] and freezing temperature do not agree. For example, [[agar]] melts at 85 [[Celsius|°C]] and solidifies from 32 to 40 °C. This is to say that once agar is melted at 85 °C, it retains a liquid state until cooled to 40 °C. Therefore, from the temperatures of 40 to 85 °C, agar can be either solid or liquid, depending on which state it was before.
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| ==Hysteresis in biology==
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| ===Cell biology and genetics===
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| {{Main|Cell biology}}
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| Cells undergoing [[cell division]] exhibit hysteresis in that it takes a higher concentration of [[cyclin]]s to switch them from G2 phase into [[mitosis]] than to stay in mitosis once begun.<ref>{{cite journal
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| |first1 = Joseph R.
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| |last1=Pomerening
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| |first2= Eduardo D.
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| |last2=Sontag
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| |first3= James E.
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| |last3=Ferrell
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| |year = 2003
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| |title = Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2
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| |journal = Nature Cell Biology
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| |pmid = 12629549
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| |volume = 5
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| |issue = 4
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| |pages = 346–251
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| |doi = 10.1038/ncb954}}</ref>
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| {{Main|Chromatin}}
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| Darlington in his classic works on [[genetics]]<ref>{{cite book |last1=Darlington |first1=C. D. |title=Recent Advances in Cytology (Genes, Cells, & Organisms) |edition=Second |publisher=P. Blakiston's Son & Co. | year=1937 |url=http://www.biodiversitylibrary.org/ia/recentadvancesin00darl |isbn=978-0-8240-1376-9 }}</ref><ref>{{cite book |last1=Rieger |first1=R. |last2=Michaelis |first2=A. |last3=M. M. |year=1968 |title=A Glossary of Genetics and Cytogenetics : Classical and Molecular |publisher= [[Springer Science+Business Media|Springer]] |edition=Third |isbn=978-3-540-04316-4}}</ref> discussed hysteresis of the [[chromosomes]], by which he meant "failure of the external form of the chromosomes to respond immediately to the internal stresses due to changes in their molecular spiral", as they lie in a somewhat rigid medium in the limited space of the [[cell nucleus]].
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| {{Main|Morphogen}}
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| In [[developmental biology]], cell type diversity is regulated by long range-acting signaling molecules called [[morphogens]] that pattern uniform pools of cells in a concentration- and time-dependent manner. The morphogen [[Sonic Hedgehog]] (Shh), for example, acts on [[limb bud]] and [[neural progenitors]] to induce expression of a set of [[homeodomain]]-containing [[transcription factors]] to subdivide these tissues into distinct domains. It has been shown that these tissues have a 'memory' of previous exposure to Shh.<ref>{{cite journal
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| |last1 = Harfe
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| |first1=B. D.
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| |last2= Scherz
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| |first2=P. J.
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| |last3= Nissim
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| |first3=S.
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| |last4= Tian
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| |first4=H.
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| |last5= McMahon
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| |first5=A. P.
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| |last6= Tabin
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| |first6=C. J.
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| |year = 2004
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| |title = Evidence for an expansion-based temporal Shh gradient in specifying vertebrate digit identities
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| |journal = Cell
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| |pmid = 15315763
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| |volume = 118
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| |issue = 4
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| |pages = 517–28
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| |doi =10.1016/j.cell.2004.07.024 }}</ref>
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| In neural tissue, this hysteresis is regulated by a homeodomain (HD) feedback circuit that amplifies Shh signaling.<ref>{{cite pmid |21062862}}</ref> In this circuit, expression of [[Gli]] transcription factors, the executors of the Shh pathway, is suppressed. Glis are processed to repressor forms (GliR) in the absence of Shh, but in the presence of Shh, a proportion of Glis are maintained as full-length proteins allowed to translocate to the nucleus, where they act as activators (GliA) of transcription. By reducing Gli expression then, the HD transcription factors reduce the total amount of Gli (GliT), so a higher proportion of GliT can be stabilized as GliA for the same concentration of Shh.
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| ===Immunology===
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| There is some evidence that T cells exhibit hysteresis in that it takes a lower signal threshold to activate T cells that have been previously activated. Ras activation is required for downstream effector functions of activated T cells.<ref>{{cite pmid|19167334 }}</ref> Triggering of the T cell receptor induces high levels of Ras activation, which results in higher levels of GTP-bound (active) Ras at the cell surface. Since higher levels of active Ras have accumulated at the cell surface in T cells that have been previously stimulated by strong engagement of the T cell receptor, weaker subsequent T cell receptor signals received shortly afterwards will deliver the same level of activation due to the presence of higher levels of already activated Ras as compared to a naïve cell.
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| ===Neuroscience===
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| {{See also|Refractory period}}
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| The property by which some [[neuron]]s do not return to their basal conditions from a stimulated condition immediately after removal of the stimulus is an example of hysteresis.
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| ===Respiratory physiology===
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| Lung hysteresis is evident when observing the compliance of a lung on inspiration versus expiration. The difference in compliance (volume/pressure) is due to the additional energy required during inspiration to recruit and inflate additional alveoli.<ref>{{cite journal|last1=Escolar|first1=J. D.|first2=A. |last2=Escolar|title=Lung histeresis: a morphological view|journal=Histology and Histopathology Cellular and Molecular Biology|year=2004|volume=19|issue=1|pages=159–166|pmid=14702184|url=http://www.hh.um.es/pdf/Vol_19/19_1/Escolar-19-159-166-2004.pdf|accessdate=1 March 2011}}</ref>
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| The [[transpulmonary pressure]] vs Volume curve of inhalation is different from the Pressure vs Volume curve of exhalation, the difference being described as hysteresis. Lung volume at any given pressure during inhalation is less than the lung volume at any given pressure during exhalation.<ref name="isbn0-7817-5152-7">{{cite book |first1=John B. |last1=West |title=Respiratory physiology: the essentials |publisher=[[Lippincott Williams & Wilkins]] |location=Hagerstown, MD |year=2005 |isbn=0-7817-5152-7}}</ref>
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| ==Hysteresis in economics==
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| {{main|Hysteresis (economics)}}
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| Economic systems can exhibit hysteresis. For example, [[export]] performance is subject to strong hysteresis effects: because of the fixed transportation costs it may take a big push to start a country's exports, but once the transition is made, not much may be required to keep them going.
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| Hysteresis is used extensively in the area of labor markets. According to theories based on hysteresis, economic downturns (recession) result in an individual becoming unemployed, losing his/her skills (commonly developed 'on the job'), demotivated/disillusioned, and employers may use time spent in unemployment as a screen. In times of an economic upturn or 'boom', the workers affected will not share in the prosperity, remaining long-term unemployed (over 52 weeks). Hysteresis has been put forward as a possible explanation for the poor unemployment performance of many economies in the 1990s. Labor market reform, or strong economic growth, may not therefore aid this pool of long-term unemployed, and thus specific targeted training programs are presented as a possible policy solution.<ref name=Ball>Ball, Laurence M. (2009) [http://www.econ2.jhu.edu/people/ball/w14818.pdf "Hysteresis in Unemployment: Old and New Evidence"], US National Bureau of Economic Research (NBER) Working Paper No. 14818</ref>
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| ===Permanently higher unemployment===
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| Hysteresis is a hypothesized property of [[unemployment rate]]s. It is possible that there is a [[ratchet effect]], so a short-term rise in unemployment rates tends to persist.
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| An example is the notion that inflationary policy leads to a permanently higher 'natural' rate of unemployment ([[NAIRU]]), because inflationary expectations are '[[sticky (economics)|sticky]]' downward due to wage rigidities and imperfections in the labour market.
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| When some negative shock reduces employment in a company or industry, there are fewer employed workers left. As usually the employed workers have the power to set wages, their reduced number incentivizes them to bargain for even higher wages when the economy again gets better instead of letting the wage be at the [[equilibrium wage]] level, where the supply and demand of workers would match. This causes hysteresis: the unemployment becomes permanently higher after negative shocks.<ref>{{cite journal |url=http://www.nber.org/papers/w1950 |title=Hysteresis and the European Unemployment Problem |first1=Olivier J. |last1=Blanchard |first2=Lawrence H. |last2=Summers |journal=NBER Macroeconomics Annual |volume=1 |year= 1986 |pages=15–78 |doi=10.2307/3585159}}</ref><ref name=Ball/>
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| Another channel through which hysteresis can occur is through [[learning by doing]]. Workers who lose their jobs due to a temporary shock may become permanently unemployed because they miss out on the job training and skill acquisition that normally takes place.
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| Hysteresis has been invoked by [[Olivier Blanchard]] among others to explain the differences in long run unemployment rates between Europe and the United States.
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| ===Game theory and capital controls===
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| Hysteresis occurs in applications of [[game theory]] to economics, in models with product quality, agent honesty or corruption of various institutions. Slightly different initial conditions can lead to opposite outcomes and resulting stable "good" and "bad" [[Correlated equilibrium|equilibria]].
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| Another area where hysteresis phenomena are found is capital controls. A developing country can ban a certain kind of capital flow (e.g. engagement with international private equity funds), but when the ban is removed, the system takes a long time to return to the pre-ban state.
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| ==Additional considerations==
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| ===Models of hysteresis===
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| Each subject that involves hysteresis has models that are specific to the subject. In addition, there are models that capture general features of many systems with hysteresis.<ref name="Mayergoyz2003"/> An example is the [[Preisach model of hysteresis]], which represents a hysteresis nonlinearity as a [[linear superposition]] of square loops called non-ideal relays.<ref name="Mayergoyz2003"/> Many complex models of hysteresis arise from the simple parallel connection, or superposition, of elementary carriers of hysteresis termed hysterons.
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| A simple parametric description of various hysteretic loops may be found in the Lapshin model of hysteresis. Along with the classical loop (see figure at the top of the page), substitution of rectangle, triangle or trapezoidal pulses instead of the harmonic functions also allows piecewise-linear hysteresis loops frequently used in discrete automatics to be built in the model (see [[Hysteresis#Electronic circuits|Electronic circuit example]]).<ref name="model1995">{{cite journal|author=Lapshin, R. V. |year=1995|title=Analytical model for the approximation of hysteresis loop and its application to the scanning tunneling microscope|journal=Review of Scientific Instruments|volume=66|issue=9|pages=4718–4730|publisher=AIP|location=USA|issn=0034-6748|doi=10.1063/1.1145314|url=http://www.lapshin.fast-page.org/publications.htm#analytical1995|format=PDF|bibcode=1995RScI...66.4718L}} ([http://www.lapshin.fast-page.org/publications.htm#analytical1995 Russian translation] is available).</ref>{{Primary source-inline|reason=editor is promoting own work. A secondary source is needed.|date=November 2011}}
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| The [[Bouc–Wen model of hysteresis]] is often used to describe non-linear hysteretic systems. It was introduced by Bouc<ref name="Bouc67">{{cite conference |first1=R. |last1=Bouc |year=1967 |title=Forced vibration of mechanical systems with hysteresis |booktitle=Proceedings of the Fourth Conference on Nonlinear Oscillation |location=Prague, Czechoslovakia |pages=315}}</ref><ref name="Bouc71">{{cite journal |first1=R. |last1=Bouc |year=1971 |title=Modèle mathématique d'hystérésis: application aux systèmes à un degré de liberté |journal=Acustica |volume=24 |pages=16–25 |language=French}}</ref> and extended by Wen,<ref name="Wen76">{{cite journal |first1=Y. K. |last1=Wen |year=1976 |title=Method for random vibration of hysteretic systems |journal=Journal of Engineering Mechanics|url=http://cedb.asce.org/cgi/WWWdisplay.cgi?6630|volume=102 |pages=249–263 |issue=2}}</ref> who demonstrated its versatility by producing a variety of hysteretic patterns. This model is able to capture in analytical form, a range of shapes of hysteretic cycles which match the behaviour of a wide class of hysteretical systems; therefore, given its versability and mathematical tractability, the Bouc–Wen model has quickly gained popularity and has been extended and applied to a wide variety of engineering problems, including multi-degree-of-freedom (MDOF) systems, buildings, frames, bidirectional and [[Torsion (mechanics)|torsional]] response of hysteretic systems two- and three-dimensional continua, and [[soil liquefaction]] among others. The Bouc–Wen model and its variants/extensions have been used in applications of [[Structural engineering|structural control]], in particular in the modeling of the behaviour of [[magnetorheological damper]]s, [[base isolation]] devices for buildings and other kinds of damping devices; it has also been in the modelling and analysis of structures built of reinforced concrete, steel, masonry and timber.{{citation needed|date=September 2011}}
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| ===Energy===
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| When hysteresis occurs with [[Intensive and extensive properties|extensive and intensive variable]]s, the work done on the system is the area under the hysteresis graph.
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| ==See also==
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| {{Div col}}
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| *[[Backlash (engineering)]]
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| *[[Bean's critical state model]]
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| *[[Hysteresivity]]
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| *[[Path dependence]]
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| *[[Path dependence (physics)]]
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| {{Div col end}}
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| ==References==
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| {{Reflist|35em}}
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| ==Further reading==
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| {{Refbegin}}
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| *{{cite book
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| |last = Chikazumi
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| |first = Sōshin
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| |title = Physics of Ferromagnetism
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| |publisher = [[Clarendon Press]]
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| |year = 1997
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| |isbn = 0-19-851776-9
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| |ref = harv
| |
| }}
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| *{{cite journal |last1=Jiles |first1=D. C. |last2=Atherton |first2=D. L. |title=Theory of ferromagnetic hysteresis |journal=[[Journal of Magnetism and Magnetic Materials]] |volume=61 |year=1986 |pages=48–60 |doi=10.1016/0304-8853(86)90066-1 |ref=harv|bibcode = 1986JMMM...61...48J }}
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| *{{cite book| first1=Mark |last1=Krasnosel'skii |first2=Alexei |last2=Pokrovskii |title=Systems with Hysteresis |publisher=[[Springer-Verlag]] |location=New York |year=1989 |isbn=978-0-387-15543-2}}
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| *{{cite book|title=The Science of Hysteresis (3-volume set) |editor1-first= Isaak D. |editor1-last=Mayergoyz |editor2-first=Giorgio |editor2-last=Bertotti |publisher=[[Academic Press]] |year=2005 |isbn=978-0-12-480874-4}}
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| *{{cite book |last1=Truesdell |first1=C. |author1-link=Clifford Truesdell |last2=Noll |first2=Walter |author2-link=Walter Noll |editor1-last=Antman |editor1-first=Stuart
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| |title=The Non-Linear Field Theories of Mechanics |edition=Third |year=2004 |isbn= 978-3-540-02779-9 |ref={{harvid|Truesdell|Noll|1965}} }} Originally published as Volume III/3 of Handbuch der Physik in 1965.
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| *{{cite book |last1=Visintin |first1=Augusto |title=Differential models of hysteresis |publisher=[[Springer Science+Business Media|Springer]] |year=1994 |isbn=978-3-540-54793-8 |ref=harv}}
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| {{Refend}}
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| ==External links==
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| {{Wiktionary|hysteresis}}
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| *[http://www.ramehart.com/contactangle.htm Overview of contact angle Hysteresis]
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| *[http://www.evtsz.bme.hu/web/staff/szabo/web_Preisach/preisach_code.html Preisach model of hysteresis – Matlab codes developed by Zs. Szabó and Gy. Kádár]
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| *[http://hyperphysics.phy-astr.gsu.edu/hbase/solids/hyst.html Hysteresis]
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| *[http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html What's hysteresis?]
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| *[http://euclid.ucc.ie/hysteresis/ Dynamical systems with hysteresis '''(interactive web page)''']
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| *[http://www.bama.ua.edu/~tmewes/Java/Reversal/reversal.shtml Magnetization reversal applet (coherent rotation)]
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| *[http://www.madphysics.com/exp/hysteresis_and_rubber_bands.htm Elastic hysteresis and rubber bands]
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| [[Category:Systems theory]]
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| [[Category:Concepts in physics]]
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| [[Category:Magnetic ordering]]
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| [[Category:Materials science]]
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