A system with hysteresis can be summarised as a system that may be in any number of states, independent of the inputs to the system. To be exact, a system with hysteresis exhibits path-dependence, or "rate-independent memory"^{[citation needed]}. By contrast, consider a deterministic system with no hysteresis and no dynamics. In that case, we can predict the output of the system at some instant in time, given only the input to the system at that instant. If the system has hysteresis, then this is not the case; we can't predict the output without looking at the history of the input. In order to predict the output, we must look at the path that the input followed before it reached its current value. The term deterministic may refer to: the more general notion of determinism from philosophy, see determinism a type of algorithm as discussed in computer science, see deterministic algorithm scientific determinism as used by Karl Popper and Stephen Hawking deterministic system in mathematics deterministic system in philosophy deterministic finite state machine... The Lorenz attractor is an example of a non-linear dynamical system. ...

Many physical systems naturally exhibit hysteresis. A piece of iron that is brought into a magnetic field retains some magnetization, even after the external magnetic field is removed. Once magnetized, the iron will stay magnetized indefinitely. In order to demagnetize the iron, it would be necessary to apply a magnetic field in the opposite direction. This effect is exploited commercially; for example, it provides the element of memory in a hard disk drive. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... General Name, symbol, number iron, Fe, 26 Chemical series transition metals Group, period, block 8, 4, d Appearance lustrous metallic with a grayish tinge Standard atomic weight 55. ... A hard disk drive (HDD), commonly referred to as a hard drive, hard disk or fixed disk drive,[1] is a non-volatile storage device which stores digitally encoded data on rapidly rotating platters with magnetic surfaces. ...

Human-designed systems will sometimes intentionally exhibit hysteresis. For example, consider a thermostat that controls a furnace. 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 we wish to maintain a temperature of 20 degrees, then we might set the thermostat to turn the furnace on when the temperature drops below 18 degrees, and turn it off when the temperature exceeds 22 degrees. This thermostat has hysteresis. Let us say that the temperature is 21 degrees. Given this information, we cannot predict whether the furnace will be on or off; it's not possible to predict the instantaneous output of the thermostat, knowing only its instantaneous input. Bi-metallic thermostat for buildings A thermostat is a device for regulating the temperature of a system so that the systems temperature is maintained near a desired setpoint temperature. ... Look up binary in Wiktionary, the free dictionary. ...

The term derives from an ancient Greek word υστέρησις, meaning "deficiency", or "lagging behind". It was coined by Sir James Alfred Ewing. Beginning of Homers Odyssey The Ancient Greek language is the historical stage of the Greek language[1] as it existed during the Archaic (9th–6th centuries BC) and Classical (5th–4th centuries BC) periods in Ancient Greece. ... Sir James Alfred Ewing (March 27, 1855 - January 7, 1935) was a British physicist and engineer, best known for his work on the magnetic properties of metals and, in particular, for his discovery of, and coinage of the word, hysteresis. ...

Introduction

Hysteresis phenomena occur in magnetic and ferromagnetic materials, as well as in the elastic and electromagnetic behavior of materials, in which a lag occurs between the application and the removal of a force or field and its subsequent effect. Electric hysteresis occurs when applying a varying electric field, and elastic hysteresis occurs in response to a varying force. The term "hysteresis" is sometimes used in other fields, such as economics or biology; where it describes a memory, or lagging effect, in which the order of previous events can influence the order of subsequent events.^{[citation needed]} For other senses of this word, see magnetism (disambiguation). ... Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism. ... In solid mechanics, elasticity is the property of materials which undergo reversible deformations under applied loads. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... For other uses, see Force (disambiguation). ... The magnitude of an electric field surrounding two equally charged (repelling) particles. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... A system with hysteresis can be summarised as a system that may be in any number of states, independent of the inputs to the system. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: βίος, bio, life; and λόγος, logos, speech lit. ...

The word "lag" above should not necessarily be interpreted as a time lag. After all, even relatively simple linear systems such as an electric circuit containing resistors and capacitors exhibit a time lag between the input and the output. For most hysteretic systems, there is a very short time scale when its dynamic behavior and various related time dependences are observed. In magnetism, for example, the dynamic processes occurring on this very short time scale have been referred to as Barkhausen jumps. If observations are carried out over very long periods, creep or slow relaxation typically toward true thermodynamic equilibrium (or other types of equilibria that depend on the nature of the system) can be noticed. When observations are carried out without regard for very swift dynamic phenomena or very slow relaxation phenomena, the system appears to display irreversible behavior whose rate is practically independent of the driving force rate. This rate-independent irreversible behavior is the key feature that distinguishes hysteresis from most other dynamic processes in many systems. Magnetization (J) or flux density (B) curve as a function of magnetic field intesity (H) in ferromagnetic material. ...

If the displacement of a system with hysteresis is plotted on a graph against the applied force, the resulting curve is in the form of a loop. In contrast, the curve for a system without hysteresis is a single, not necessarily straight, line. Although the hysteresis loop depends on the material's physical properties, there is no complete theoretical description that explains the phenomenon. The family of hysteresis loops, from the results of different applied varying voltages or forces, form a closed space in three dimensions, called the hysteroid. International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

Hysteresis was initially seen as problematic, but is now thought to be of great importance in technology. For example, the properties of hysteresis are applied when constructing non-volatile storage for computers; as hysteresis allows most superconductors to operate at the high currents needed to create strong magnetic fields. Hysteresis is also important in living systems. Many critical processes occurring in living (or dying) cells use hysteresis to help stabilize them against the various effects of random chemical fluctuations. Non-volatile storage is a category of computer storage. ...

Some early work on describing hysteresis in mechanical systems was performed by James Clerk Maxwell. Subsequently, hysteresis models have received significant attention in the works of Preisach (Preisach model of hysteresis), Neel and Everett in connection with magnetism and absorption. A simple parametric description of various hysteresis loops may be found here ^[1] (with the model, substitution of rectangle, triangle or trapezoidal pulses instead of the harmonic functions also allows to built piecewise-linear hysteresis loops frequently used in discrete automatics). More formal mathematical theory of systems with hysteresis was developed in 1970s, by a group of Russian mathematicians, which was led by Mark Krasnosel'skii, one of the founders of nonlinear analysis. He suggested an investigation of hysteresis phenomena using the theory of nonlinear operators.^{[citation needed]} James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... Mark Krasnoselskii Mark Alexandrovich Krasnoselskii (Russian: ) (April 27, 1920 – February 13, 1997) was a Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications. ...

Informal definition

The phenomenon of hysteresis can conceptually be explained as follows: a system can be divided into subsystems or domains, much larger than an atomic volume, but still microscopic. Such domains occur in ferroelectric and ferromagnetic systems, since individual dipoles tend to group with each other, forming a small isotropic region. Each of the system's domains can be shown to have a metastable state. The metastable domains can in turn have two or more substates. Such a metastable state fluctuates widely from domain to domain, but the average represents the configuration of lowest energy. The hysteresis is simply the sum of all domains, or the sum of all metastable states. Look up domain in Wiktionary, the free dictionary. ... For other uses, see Atom (disambiguation). ... In physics, the ferroelectric effect is an electrical phenomenon whereby certain ionic crystals may exhibit a spontaneous dipole moment. ... Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism. ... The Earths magnetic field, which is approximately a dipole. ... Isotropy (the opposite of anisotropy) is the property of being independent of direction. ... Metastability is the ability of a non-equilibrium state to persist for a long period of time. ...

Magnetic hysteresis

Hysteresis is well known in ferromagnetic materials. When an external magnetic field is applied to a ferromagnet, the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the alignment will be retained: the material has become magnetized. Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ... For the indie-pop band, see The Magnetic Fields. ... The Earths magnetic field, which is approximately a dipole. ...

A family of B-H loops for grain-oriented electrical steel (B_R denotes remanence and H_C is the coercivity).

The relationship between magnetic field strength (H) and magnetic flux density (B) is not linear in such materials. If the relationship between the two is plotted for increasing levels of field strength, it will follow a curve up to a point where further increases in magnetic field strength will result in no further change in flux density. This condition is called magnetic saturation. Image File history File links Download high resolution version (929x560, 31 KB) Summary A family of B-H loops measured under flux density controlled as sine (with the peak varying from 0. ... Image File history File links Download high resolution version (929x560, 31 KB) Summary A family of B-H loops measured under flux density controlled as sine (with the peak varying from 0. ... Remanence is the magnetization left behind in a medium after an external magnetic field is removed. ... In material science, the Coercivity of a ferromagnetic material is the intensity of the magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has reached saturation. ... In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ... Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ... For magnetic materials, saturation is the state when the material can not absorb a stronger magnetic field, such that an increase of magnetization produces no significant change in magnetic flux density. ...

If the magnetic field is now reduced linearly, the plotted relationship will follow a different curve back towards zero field strength at which point it will be offset from the original curve by an amount called the remanent flux density or remanence. Remanence is the magnetization left behind in a medium after an external magnetic field is removed. ...

If this relationship is plotted for all strengths of applied magnetic field the result is a sort of S- shaped loop. The 'thickness' of the middle bit of the S describes the amount of hysteresis, related to the coercivity of the material. In material science, the Coercivity of a ferromagnetic material is the intensity of the magnetic field required to reduce the magnetization of that material to zero after the magnetization of the sample has reached saturation. ...

Its practical effects might be, for example, to cause a relay to be slow to release due to the remaining magnetic field continuing to attract the armature when the applied electric current to the operating coil is removed. In electrical engineering, an armature is usually the rotating part of an electric motor or dynamo. ...

Hysteresis loop: magnetization (M) as function of magnetic field strength (H)

This curve for a particular material influences the design of a magnetic circuit. Image File history File links Hysteresiscurve. ... Image File history File links Hysteresiscurve. ... Magnetization is a property of some materials (e. ... In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ...

This is also a very important effect in magnetic tape and other magnetic storage media like hard disks. In these materials it would seem obvious to have one polarity represent a bit, say north for 1 and south for 0. However, if you want to change the storage from one to the other, the hysteresis effect requires you to know what was already there, because the needed field will be different in each case. In order to avoid this problem, recording systems first overdrive the entire system into a known state using a process known as bias. Analog magnetic recording also uses this technique. Different materials require different biasing, which is why there is a selector for this on the front of most cassette recorders. Compact audio cassette Magnetic tape is a non-volatile storage medium consisting of a magnetic coating on a thin plastic strip. ... Typical hard drives of the mid-1990s. ... This article is about the unit of information. ... Tape bias is a high-frequency signal (generally from 40 to 150 kHz) added to the audio signal recorded on an analog tape recorder. ... Typical 60-minute Compact Cassette. ...

In order to minimize this effect and the energy losses associated with it, ferromagnetic substances with low coercivity and low hysteresis loss are used, like permalloy. Permalloy is a nickel iron alloy with about 20% iron and 80% nickel content. ...

In many applications small hysteresis loops are driven around points in the B-H plane. Loops near the origin have a higher µ. The smaller loops the more they have a soft magnetic (lengthy) shape. As a special case a damped AC field demagnetized any material. In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. ...

Electrical hysteresis

Electrical hysteresis typically occurs in ferroelectric material, where domains of polarization contribute to the total polarization. Polarization is the electrical dipole moment (either C·m^-2 or C·m). In physics, the ferroelectric effect is an electrical phenomenon whereby certain ionic crystals may exhibit a spontaneous dipole moment. ... In physics, the electric dipole moment is a measure of the polarity of a system of electric charges. ... The coulomb (symbol: C) is the SI unit of electric charge. ... This article is about the unit of length. ... The coulomb (symbol: C) is the SI unit of electric charge. ... This article is about the unit of length. ...

Elastic hysteresis

Elastic hysteresis of an idealized rubber band. The area in the centre of the hysteresis loop is the energy dissipated as heat

Elastic hysteresis is analogous to magnetic hysteresis and was one of the first types of hysteresis to be examined. ^[2][3]

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 on to it it will continue to extend because the force the weights are exerting on the band is increasing. When each weight is taken off, or unloaded, it will get shorter as the force is reduced. As the weights are taken off you will find that each weight that produced a specific length as you loaded the band now produces a slightly longer length as you unload it. This is because the band doesn't obey Hooke's law perfectly. Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

In one sense the rubber band was harder to stretch when it was being loaded then when it was being unloaded. In another sense, as you unload the band the cause (the force of the weights) lags behind the effect (the length) because a smaller value of weight produces the same length. In another sense more energy was required during the loading than the unloading; that energy must have gone somewhere, it was dissipated or "lost" as heat.

Elastic hysteresis is more pronounced when the loading and unloading is done quickly than when it's done slowly. ^[4] 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.

Liquid-solid phase transitions

Hysteresis manifests itself in state transitions when melting temperature and freezing temperature do not agree. For example, agar melts at 85 °C and solidifies from 32 to 40 °C. This is to say that once agar is melted at 85 degrees, it retains a liquid state until cooled to 40 degrees Celsius. Therefore, from the temperatures of 40 to 85 degrees Celsius, agar can be either solid or liquid, depending on which state it was before. The dissociation of a double-stranded DNA molecule is often referred to as melting because it occurs quickly once a certain temperature has been reached. ... This does not adequately cite its references or sources. ... For other uses, see Celsius (disambiguation). ...

Contact angle hysteresis

The contact angle formed between a liquid and solid phase can be measured dynamically. 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. The difference between the advancing and receding contact angles is referred to as the contact angle hysteresis. Image from a video contact angle device. ...

Matric potential hysteresis

The relationship between matric water potential and water content is the basis of the water retention curve. Matric potential measurements (Ψ_m) 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_m) of 5kPa, the volumetric water content (θ) of a fine sandy soil matrix could be anything between 8% to 25% ^[5]. This does not cite any references or sources. ... Soil composition Water content or moisture content is the quantity of water contained in a material, such as soil (called soil moisture), rock, ceramics, or wood on a volumetric or gravimetric basis. ... Water retention curve is the relationship between the volume fraction of water and the water potential of the soil, it is characteristic for different types of soil. ...

Tensiometers 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.^[6] A tensiometer is a device used to determine matric water potential (soil moisture tension) in the vadose zone. ... 2002 is a common year starting on Tuesday of the Gregorian calendar. ... This article or section does not cite its references or sources. ...

Energy

When hysteresis occurs with extensive and intensive variables, the work done on the system is the area under the hysteresis graph. In the physical sciences an intensive property (also called a bulk property) of a system is a physical property of the system that does not depend on the system size or the amount of material in the system. ...

Economics

Some economic systems show signs of hysteresis. For example, export performance is subject to strong hysteresis effects: it may take a big push (ie sizable changes in incentives) to start a country's exports, but once the transition is made, not much may be required to keep them going.

Another example is the notion that inflationary policy leads to a permanently higher 'natural' rate of unemployment (NAIRU), due to the proposition that inflationary expectations are 'sticky' downward because of wage rigidities and imperfections in the labour market. The term NAIRU is an acronym for Non-Accelerating Inflation Rate of Unemployment. ...

Many economists also argue that unemployment itself is subject to hysteresis effects. Unemployment persistence is argued to arise from various factors that include demand deficiency and labour market institutions.

Hysteresis shows in game theory, for example, applied to quality, honesty or corruption. Slightly different initial conditions can lead to opposite results, stable "good" and "bad" equilibria. Game theory is a branch of applied mathematics that is often used in the context of economics. ...

Behavioral economists attempt to measure the utility gain from obtaining an item, and the utility loss from losing the same item. With great regularity, the utility loss is greater than the utility gain, meaning that if a person goes through a complete cycle of gaining and losing, the person may be worse off than if he or she had never received the initial gain.

User interface design

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. This article or section does not cite its references or sources. ...

Electronics

Sharp hysteresis loop of a Schmitt trigger

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. 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. Image File history File links Hysteresis_sharp_curve. ... Image File history File links Hysteresis_sharp_curve. ... In electronics, a Schmitt (or Schmidt) trigger is a comparator circuit that incorporates positive feedback. ... Bi-metallic thermostat for buildings A thermostat is a device for regulating the temperature of a system so that the systems temperature is maintained near a desired setpoint temperature. ...

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 (or digital algorithm) to prevent unwanted rapid switching. This and similar techniques are used to compensate for contact bounce in switches, or noise in an electrical signal. In electronics, a Schmitt (or Schmidt) trigger is a comparator circuit that incorporates positive feedback. ... Electrical switches. ... Electronic noise In any electronic circuit, there exist random variations in current or voltage caused by the random movement of the electrons carrying the current as they are jolted around by thermal energy. ...

A latching relay uses a solenoid to actuate a ratcheting motion that keeps the relay closed even if power to the relay is terminated. Automotive style miniature relay A relay is an electrical switch that opens and closes under the control of another electrical circuit. ...

Cell biology

Cells undergoing cell division exhibit hysteresis in that it takes a higher concentration of cyclins to switch them from G2 phase into mitosis than to stay in mitosis once begun. ^[7] Cell biology (also called cellular biology or formerly cytology, from the Greek kytos, container) is an academic discipline that studies cells. ... This does not adequately cite its references or sources. ... Cyclins are a family of proteins involved in the progression of cells through the cell cycle. ... Mitosis divides genetic information during cell division. ...

Neuroscience

The property by which some neurons do not return to their basal conditions from a stimulated condition immediately after removal of the stimulus is an example of hysteresis.

Respiratory physiology

The 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 ^[8].

Applications

Hysteresis represents states, and the characteristic curve shape is sometimes remiscent of a two-value state, also called a bistable state. The hysteresis curve really contains infinitely many states, but a simple application is to let the threshold regions (usually to the left and to the right) represent respectively the on and off states. In this way, the system can be regarded as bistable. Note that even if no external field is applied, the position of the hysteresis curve might change with time: it is not necessarily stationary; i.e. the system may not stay in the exact same state as it had previously. The system might need new energy transfer to be stationary. Something that is bistable can be resting in two states. ...

The hysteresis effect can be used when connecting complex circuits with the so-called passive matrix addressing. This scheme is praised as a technique that can be used in modern nanoelectronics, electrochrome cells, memory effect, etc. In this scheme, 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. That is, one can address all rows at the same time instead of doing each individually. Passive matrix addressing is an addressing scheme used in earlier LCD displays, and is likely to be used in future LCD displays. ... With batteries, the memory effect, also known as lazy battery effect, is an effect observed in some rechargeable batteries that causes them to hold less charge. ... In telecommunication, the term crosstalk (XT) has the following meanings: 1. ...

In economics, hysteresis is used extensively in the area of Labour 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 (>52 weeks). Hysteresis has been put forward as a possible explanation for the poor unemployment performance of many economies in the 1990s. Labour market reform, and/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.

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. A noise gate is an electronic device or software logic that is used to control the volume of an audio signal. ...

Small vehicle suspensions using rubber (or other elastomers) 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 bikes have frequently made use of elastomer suspension, as did the original Mini car. This does not cite any references or sources. ... The term elastomer is often used interchangeably with the term rubber, and is preferred when referring to vulcanisates. ... A cross country mountain bike race A hardtail mountain bike A mountain bike or mountain bicycle (abbreviated MTB or ATB (All Terrain Bicycle)) is a bicycle designed for mountain biking, either on dirt trails or other unpaved environments. ... For the new MINI, see MINI (BMW). ...

See also

• Remanence
• Hysteresivity
• Path dependence
• Backlash (engineering)
• Mark Krasnosel'skii and Alexei Pokrovskii, Systems with Hysteresis, Springer-Verlag, New York, 1989.
• Isaak D. Mayergoyz, Mathematical Models of Hysteresis and their Applications : Second Edition (Electromagnetism), Academic Press, 2003.
• The Science of Hysteresis (3-volume set), ed. by Isaak D. Mayergoyz, Giorgio Bertotti, Academic , 2005.

Remanence is the magnetization left behind in a medium after an external magnetic field is removed. ... “Hysteresivity” derives from “hysteresis”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state. ... Path-dependence is a phrase used to mean one of two things (Pierson 2004). ... In mechanical engineering, backlash is purposeful clearance between mating components, sometimes described as the amount of lost motion due to clearance or slackness when movement is reversed and contact is re-established. ...

References

1. ^ Analytical model for the approximation of hysteresis loop and its application to the scanning tunneling microscope. Retrieved on 2007-06-05.
2. ^ Augustus E. Love (1927). Treatise on the Mathematical Theory of Elasticity (Dover Books on Physics & Chemistry). New York: Dover Publications. ISBN 0-486-60174-9. 
3. ^ J.A Ewing, Brit. Assoc. Rep., 1889, p. 502
4. ^ B. Hopkinson and G.T. Williams, London, Roy. Soc. Proc. (Ser.A), vol. 87, 1812, p502.
5. ^ Accuracy of capacitance soil moisture .... Retrieved on 2007-06-05.
6. ^ Scanlon, B. R., Andraski, B. J., and Bilskie, J. (2002). "Methods of soil analysis: Physical Methods: Miscellaneous methods for measuring matric or water potential" (PDF). Soil Science Society of America 4: 643–670. ISBN 0-89118-810-X. Retrieved on 2006-05-26. 
7. ^ Joseph R. Pomerening, Eduardo D. Sontag, James E. Ferrell Jr (2003). "Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2". Nature Cell Biology 5: 346-251. 
8. ^ John B. West (2005). Respiratory physiology: the essentials. Hagerstown, MD: Lippincott Williams & Wilkins. ISBN 0-7817-5152-7. 

Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 156th day of the year (157th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 156th day of the year (157th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 146th day of the year (147th in leap years) in the Gregorian calendar. ...

External links

• Overview of contact angle Hysteresis
• Preisach model of hysteresis -- Matlab codes developed by Zs. Szabó and Gy. Kádár
• Hysteresis
• What's hysteresis?
• Dynamical systems with hysteresis (interactive web page)
• Magnetization reversal applet (coherent rotation)
• Elastic hysteresis and rubber bands