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". By contrast, consider a deterministic system with no hysteresis and no dynamics. Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position 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.

Many physical systems naturally exhibit hysteresis. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. A piece of iron that is brought into a magnetic field retains some magnetization, even after the external magnetic field is removed. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 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 hard disk drive ( HDD) commonly referred to as a hard drive, hard disk, or fixed disk drive, is a Non-volatile storage device

Human-designed systems will sometimes intentionally exhibit hysteresis. For example, consider a thermostat that controls a furnace. A thermostat is a device for regulating the Temperature of a System so that the system's temperature is maintained near a desired setpoint 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.

The term derives from an ancient Greek word υστέρησις, meaning "deficiency", or "lagging behind". The Ancient Greek language is the historical stage in the development of the Hellenic language family spanning the Archaic (c It was coined by Sir James Alfred Ewing. Sir James Alfred Ewing KCB ( 27 March 1855 - 7 January 1935) was a Scottish Physicist and Engineer, best known

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. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it A material is said to be elastic if it deforms under stress (e Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, a force is whatever can cause an object with Mass to Accelerate. In Physics, a field is a Physical quantity associated to each point of Spacetime. Electric hysteresis occurs when applying a varying electric field, and elastic hysteresis occurs in response to a varying force. 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 (that can 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 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. Economics is the social science that studies the production distribution, and consumption of goods and services. Foundations of modern biology There are five unifying principles

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. The Barkhausen effect is a name given to the noise in the magnetic output of a Ferromagnet when the magnetizing force applied to it is changed 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.

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. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical

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. Non-volatile memory, nonvolatile memory, NVM or non-volatile storage, is Computer memory that can retain the stored information 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.

Some early work on describing hysteresis in mechanical systems was performed by James Clerk Maxwell. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. 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. The Preisach model of hysteresis generalizes Hysteresis loops as the parallel connection of independent relay hysterons 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. Mark Alexandrovich Krasnosel'skii (Марк Александрович Красносельский ( April 27, 1920 &ndash February 13 1997 He suggested an investigation of hysteresis phenomena using the theory of nonlinear operators.

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. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny Such domains occur in ferroelectric and ferromagnetic systems, since individual dipoles tend to group with each other, forming a small isotropic region. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a Isotropy is uniformity in all directions Precise definitions depend on the subject area Each of the system's domains can be shown to have a metastable state. Metastability is a general scientific concept which describes states of delicate equilibrium 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.

Magnetic hysteresis

Hysteresis is well known in ferromagnetic materials. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it When an external magnetic field is applied to a ferromagnet, the atomic dipoles align themselves with the external field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a Even when the external field is removed, part of the alignment will be retained: the material has become magnetized.

A family of B-H loops for grain-oriented electrical steel (B_R denotes remanence and H_C is the coercivity). Remanence is the magnetization left behind in a medium after an external Magnetic field is removed In Materials science, the coercivity, also called the coercive field, of a ferromagnetic material is the intensity of the applied Magnetic

The relationship between magnetic field strength (H) and magnetic flux density (B) is not linear in such materials. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges 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. Seen in some Magnetic materials saturation is the state reached when an increase in applied external Magnetizing field H cannot increase the

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 Materials science, the coercivity, also called the coercive field, of a ferromagnetic material is the intensity of the applied Magnetic

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 one of the two principal electrical components of an Electromechanical machine--a motor or generator

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

This curve for a particular material influences the design of a magnetic circuit. Magnetization is defined as the quantity of Magnetic moment per unit volume In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

This is also a very important effect in magnetic tape and other magnetic storage media like hard disks. Magnetic tape is a medium for Magnetic recording generally consisting of a thin magnetizable coating on a long and narrow strip of Plastic. A hard disk drive ( HDD) commonly referred to as a hard drive, hard disk, or fixed disk drive, is a Non-volatile storage device In these materials it would seem obvious to have one polarity represent a bit, say north for 1 and south for 0. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 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. Tape bias is the term for two phenomena DC bias and AC bias, that improve the fidelity of analogue Magnetic tape sound recordings DC bias is the addition 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. The Compact Cassette, often referred to as audio cassette, cassette tape, cassette, or simply tape, is a Magnetic tape sound

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 the term for a Nickel Iron magnetic Alloy. Generically it refers to an 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. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. The smaller loops the more they have a soft magnetic (lengthy) shape. As a special case, a damped AC field demagnetizes any material.

Electrical hysteresis

Electrical hysteresis typically occurs in ferroelectric material, where domains of polarization contribute to the total polarization. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent Polarization is the electrical dipole moment (either C·m^-2 or C·m). In Physics, the electric dipole moment (or electric dipole for short is a measure of the polarity of a system of Electric charges. The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

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. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the

In one sense the rubber band was harder to stretch when it was being loaded than 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. Agar or agar agar is a Gelatinous substance derived from Seaweed. The Celsius Temperature scale was previously known as the centigrade scale. 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.

Contact angle hysteresis

The contact angle formed between a liquid and solid phase can be measured dynamically. The contact angle is the Angle at which a Liquid / Vapor interface meets the solid surface When the maximum liquid volume is removed from the drop without the interfacial area decreasing the receding contact angle is thus measured. The contact angle is the Angle at which a Liquid / Vapor interface meets the solid surface The contact angle is the Angle at which a Liquid / Vapor interface meets the solid surface When volume is added to the maximum before the interfacial area increases, this is the advancing contact angle. The contact angle is the Angle at which a Liquid / Vapor interface meets the solid surface The difference between the advancing and receding contact angles is referred to as the contact angle hysteresis.

Matric potential hysteresis

The relationship between matric water potential and water content is the basis of the water retention curve. Water potential is the Potential energy of Water relative to pure water (e Water content or moisture content is the quantity of Water contained in a material such as Soil (called soil moisture) rock, Water retention curve is the relationship between the Water content, θ and the soil water potential ψ 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].

Tensiometers are directly influenced by this type of hysteresis. A tensiometer is a device used to determine matric water potential \Psi_m ( Soil moisture tension in the Vadose zone. 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. See also 2002 (disambiguation Year 2002 ( MMII) was a Common year starting on Tuesday of the Gregorian calendar. Water content or moisture content is the quantity of Water contained in a material such as Soil (called soil moisture) rock, Despite the fact that it can be a source of significant error, the sensor specific effect of hysteresis is generally ignored. ^[6]

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) is a Physical property of a system that does not depend on the

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.

Hysteresis is a hypothesized property of unemployment rates: that there is a ratcheting effect, so a short-term rise in unemployment rates tends to persist. An 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 N on- A ccelerating '''I'''nflation R ate of '''U'''nemployment.

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. Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, Slightly different initial conditions can lead to opposite results, stable "good" and "bad" equilibria.

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. User interface design or user interface engineering is the design of Computers Appliances machines mobile communication devices, Software 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.

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. In Electronics, a Schmitt trigger is a Comparator circuit that incorporates positive Feedback. 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. A thermostat is a device for regulating the Temperature of a System so that the system's temperature is maintained near a desired setpoint 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.

A Schmitt trigger is a simple electronic circuit that also exhibits this property. In Electronics, a Schmitt trigger is a Comparator circuit that incorporates positive Feedback. 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. A switch is a mechanical device used to connect and disconnect an electric Circuit at will Electronic noise is an unwanted signal characteristic of all electronic circuits.

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

Hysterisis is essential to the workings of the memristor, a circuit component which "remembers" changes in the current passing through it by changing its resistance. Memristors /memˈrɪstɚ/ ("memory resistors" are a class of passive two-terminal Circuit elements that maintain a functional relationship between ^[7]

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. See also List of basic cell biology topics. Cell biology (also called cellular biology or formerly cytology, from the Cell division is a process by which a cell, called the parent cell divides into two or more cells called daughter cells. Cyclins are a family of Proteins involved in the progression of cells through the Cell cycle. Mitosis is the process in which a Eukaryotic cell separates the Chromosomes in its Cell nucleus, into two identical sets in two daughter nuclei ^[8]

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 ^[9].

Applications

Hysteresis represents states, and the characteristic curve shape is sometimes remiscent of a two-value state, also called a bistable state. Something that is bistable can be resting in two states In physics for an ensemble of particles the bistability comes from the fact that its free energy 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.

The hysteresis effect can be used when connecting complex circuits with the so-called passive matrix addressing. Passive matrix addressing is an addressing scheme used in earlier LCD displays and may be used in future LCD displays This scheme is praised as a technique that can be used in modern nanoelectronics, electrochrome cells, memory effect, etc. Memory effect, also known as lazy battery effect or battery memory, is an effect observed in nickel cadmium Rechargeable batteries that causes them to 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. In Electronics, the term crosstalk ( XT) refers to any phenomenon by which a signal transmitted on one circuit or channel of a Transmission system That is, one can address all rows at the same time instead of doing each individually.

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 or 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. An elastomer is a Polymer with the property of Elasticity. The term which is derived from elastic polymer, is often used interchangeably with the term Mountain bikes have frequently made use of elastomer suspension, as did the original Mini car. A mountain bike or mountain bicycle (abbreviated MTB or ATB (all terrain bicycle is a Bicycle designed for off-road cycling including The Mini is a small car that was produced by the British Motor Corporation (BMC and its successors from 1959 until 2000

See also

• Remanence
• Hysteresivity
• Path dependence
• Backlash (engineering)
• Metastability

References

1. ^ Analytical model for the approximation of hysteresis loop and its application to the scanning tunneling microscope. Remanence is the magnetization left behind in a medium after an external Magnetic field is removed Hysteresivity derives from “ Hysteresis ” meaning “lag” Path-dependence explains how the set of decisions one faces for any given circumstance is limited by the decisions one has made in the past even though past circumstances may no longer In Mechanical engineering, backlash, sometimes called lash or play, is clearance between mating components sometimes described as the amount of lost Metastability is a general scientific concept which describes states of delicate equilibrium Retrieved on 2007-06-05. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 70 - Titus and his Roman Legions breach the middle wall of Jerusalem in the Siege of Jerusalem
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. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 70 - Titus and his Roman Legions breach the middle wall of Jerusalem in the Siege of Jerusalem
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.  
7. ^ EETimes April 30, 2008
8. ^ 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. doi:10.1038/ncb954. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
9. ^ John B. West (2005). Respiratory physiology: the essentials. Hagerstown, MD: Lippincott Williams & Wilkins. ISBN 0-7817-5152-7.  

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

Further reading

• 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.