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Contents
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* 1Etymology and history
2Types
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* 2.1Rate-dependent
2.2Rate-independent
3In engineering
(BUTTON) Toggle In engineering subsection
* 3.1Control systems
3.2Electronic circuits
3.3User interface design
3.4Aerodynamics
3.5Hydraulics
3.6Backlash
4In mechanics
(BUTTON) Toggle In mechanics subsection
* 4.1Elastic hysteresis
4.2Contact angle hysteresis
4.3Bubble shape hysteresis
4.4Adsorption hysteresis
4.5Matric potential hysteresis
5In materials
(BUTTON) Toggle In materials subsection
* 5.1Magnetic hysteresis
* 5.1.1Physical origin
5.1.2Magnetic hysteresis models
5.1.3Applications
5.2Electrical hysteresis
5.3Liquid-solid-phase transitions
6In biology
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* 6.1Cell biology and genetics
6.2Immunology
6.3Neuroscience
6.4Neuropsychology
6.5Respiratory physiology
6.6Voice and speech physiology
6.7Ecology and epidemiology
7In ocean and climate science
8In economics
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* 8.1Permanently higher unemployment
9Models
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* 9.1List of models
10Energy
11See also
12References
13Further reading
14External links
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Hysteresis
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From Wikipedia, the free encyclopedia
Dependence of the state of a system on its history
Not to be confused with [97]Hysteria.
[98][220px-Ehysteresis.PNG] [99]Electric displacement field D of a
[100]ferroelectric material as the [101]electric field E is first decreased, then
increased. The curves form a hysteresis loop.
Hysteresis is the dependence of the state of a system on its history. For
example, a [102]magnet may have more than one possible [103]magnetic moment in a
given [104]magnetic field, depending on how the field changed in the past. Plots
of a single component of the moment often form a loop or hysteresis curve, where
there are different values of one variable depending on the direction of change
of another variable. This history dependence is the basis of memory in a
[105]hard disk drive and the [106]remanence that retains a record of the
[107]Earth's magnetic field magnitude in the past. Hysteresis occurs in
[108]ferromagnetic and [109]ferroelectric materials, as well as in the
[110]deformation of [111]rubber bands and [112]shape-memory alloys and many other
natural phenomena. In natural systems, it is often associated with
[113]irreversible thermodynamic change such as [114]phase transitions and with
[115]internal friction; and [116]dissipation is a common side effect.
Hysteresis can be found in [117]physics, [118]chemistry, [119]engineering,
[120]biology, and [121]economics. It is incorporated in many artificial systems:
for example, in [122]thermostats and [123]Schmitt triggers, it prevents unwanted
frequent switching.
Hysteresis can be a dynamic [124]lag between an input and an output that
disappears if the input is varied more slowly; this is known as rate-dependent
hysteresis. However, phenomena such as the magnetic hysteresis loops are mainly
rate-independent, which makes a durable memory possible.
Systems with hysteresis are [125]nonlinear, and can be mathematically challenging
to model. Some hysteretic models, such as the [126]Preisach model (originally
applied to ferromagnetism) and the [127]Bouc-Wen model, attempt to capture
general features of hysteresis; and there are also phenomenological models for
particular phenomena such as the [128]Jiles-Atherton model for ferromagnetism.
It is difficult to define hysteresis precisely. [129]Isaak D. Mayergoyz wrote
"...the very meaning of hysteresis varies from one area to another, from paper to
paper and from author to author. As a result, a stringent mathematical definition
of hysteresis is needed in order to avoid confusion and ambiguity"..^[130][1]
Etymology and history[[131]edit]
The term "hysteresis" is derived from [132]huste'rysi*s, an [133]Ancient Greek
word meaning "deficiency" or "lagging behind". It was coined in 1881 by [134]Sir
James Alfred Ewing to describe the behaviour of magnetic materials.^[135][2]
Some early work on describing hysteresis in mechanical systems was performed by
[136]James Clerk Maxwell. Subsequently, hysteretic models have received
significant attention in the works of [137]Ferenc Preisach ([138]Preisach model
of hysteresis), [139]Louis Néel and [140]Douglas Hugh 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
[141]Mark Krasnosel'skii.
Types[[142]edit]
Rate-dependent[[143]edit]
One type of hysteresis is a [144]lag between input and output. An example is a
[145]sinusoidal input X(t) that results in a sinusoidal output Y(t), but with a
phase lag f:
[MATH:
X ( t )
= X 0 sin
⁡ w t
Y ( t ) =
Y 0
sin ⁡ ( w
t - f ) .
{\displaystyle
{\begin{aligned}X(t)&=X_{0}\sin \omega t\\Y(t)&=Y_{0}\sin \left(\omega
t-\varphi \right).\end{aligned}}} :MATH]
{\displaystyle {\begin{aligned}X(t)&=X_{0}\sin \omega t\\Y(t)&=Y_{0}\sin
\left(\omega t-\varphi \right).\end{aligned}}}
Such behavior can occur in linear systems, and a more general form of response is
[MATH: Y ( t ) =
x i
X ( t ) + \int 0
infty F
d ( t
) X (
t - t ) d t ,
{\displaystyle Y(t)=\chi
_{\text{i}}X(t)+\int _{0}^{\infty }\Phi _{\text{d}}(\tau )X(t-\tau
)\,\mathrm {d} \tau ,} :MATH]
{\displaystyle Y(t)=\chi _{\text{i}}X(t)+\int _{0}^{\infty }\Phi
_{\text{d}}(\tau )X(t-\tau )\,\mathrm {d} \tau ,}
where
[MATH: x
i {\displaystyle \chi _{\text{i}}}
:MATH]
{\displaystyle \chi _{\text{i}}} is the instantaneous response and
[MATH: F d (
t ) {\displaystyle \Phi _{d}(\tau )}
:MATH]
{\displaystyle \Phi _{d}(\tau )} is the [146]impulse response to an impulse that
occurred
[MATH: t {\displaystyle \tau }
:MATH]
{\displaystyle \tau } time units in the past. In the [147]frequency domain, input
and output are related by a complex generalized susceptibility that can be
computed from
[MATH: F d {\displaystyle \Phi _{d}}
:MATH]
{\displaystyle \Phi _{d}} ; it is mathematically equivalent to a [148]transfer
function in linear filter theory and analogue signal processing.^[149][3]
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 the input, and
goes to zero as the frequency decreases.^[150][3]
When rate-dependent hysteresis is due to [151]dissipative effects like
[152]friction, it is associated with power loss.^[153][3]
Rate-independent[[154]edit]
Systems with rate-independent hysteresis have a persistent memory of the past
that remains after the transients have died out.^[155][4] The future development
of such a system depends on the history of states visited, but does not fade as
the events recede into the past. If an input variable X(t) cycles from X[0] to
X[1] and back again, the output Y(t) may be Y[0] initially but a different value
Y[2] upon return. The values of Y(t) depend on the path of values that X(t)
passes through but not on the speed at which it traverses the path.^[156][3] Many
authors restrict the term hysteresis to mean only rate-independent
hysteresis.^[157][5] Hysteresis effects can be characterized using the
[158]Preisach model and the generalized [159]Prandtl-Ishlinskii model.^[160][6]
In engineering[[161]edit]
Control systems[[162]edit]
In control systems, hysteresis can be used to filter signals so that the output
reacts less rapidly than it otherwise would by taking recent system history into
account. For example, a [163]thermostat controlling a heater may switch the
heater on when the temperature drops below A, but not turn it off until the
temperature rises above B. (For instance, if one wishes to maintain a temperature
of 20 °C then one might set the thermostat to turn the heater on when the
temperature drops to below 18 °C and off when the temperature exceeds 22 °C).
Similarly, a pressure switch can be designed to exhibit hysteresis, with pressure
set-points substituted for temperature thresholds.
Electronic circuits[[164]edit]
[165][220px-Hysteresis_sharp_curve.svg.png] Sharp hysteresis loop of a
[166]Schmitt trigger
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 [167]contact bounce in switches, or [168]noise in an electrical
signal.
A [169]Schmitt trigger is a simple electronic circuit that exhibits this
property.
A [170]latching relay uses a [171]solenoid to actuate a ratcheting mechanism that
keeps the relay closed even if power to the relay is terminated.
Some positive feedback from the output to one input of a comparator can increase
the natural hysteresis (a function of its gain) it exhibits.
Hysteresis is essential to the workings of some [172]memristors (circuit
components which "remember" changes in the current passing through them by
changing their resistance).^[173][7]
Hysteresis can be used when connecting arrays of elements such as
[174]nanoelectronics, [175]electrochrome cells and [176]memory effect devices
using [177]passive matrix addressing. Shortcuts are made between adjacent
components (see [178]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.
In the field of audio electronics, a [179]noise gate often implements hysteresis
intentionally to prevent the gate from "chattering" when signals close to its
threshold are applied.
User interface design[[180]edit]
A hysteresis is sometimes intentionally added to [181]computer algorithms. The
field of [182]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.
Aerodynamics[[183]edit]
In [184]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 at which the flow on top of the wing reattaches is generally lower than
the angle of attack at which the flow separates during the increase of the angle
of attack.^[185][8]
Hydraulics[[186]edit]
Hysteresis can be observed in the stage-flow relationship of a river during
rapidly changing conditions such as passing of a flood wave. It is most
pronounced in low gradient streams with steep leading edge hydrographs.
[187]https://pubs.usgs.gov/ja/70193968/70193968.pdf
Backlash[[188]edit]
Moving parts within machines, such as the components of a [189]gear train,
normally have a small gap between them, to allow movement and lubrication. As a
consequence of this gap, any reversal in direction of a drive part will not be
passed on immediately to the driven part.^[190][9] This unwanted delay is
normally kept as small as practicable, and is usually called [191]backlash. The
amount of backlash will increase with time as the surfaces of moving parts wear.
In mechanics[[192]edit]
Elastic hysteresis[[193]edit]
[194][220px-Elastic_Hysteresis.svg.png] Elastic hysteresis of an idealized rubber
band. The area in the centre of the hysteresis loop is the energy dissipated due
to internal friction.
In the elastic hysteresis of rubber, the area in the centre of a hysteresis loop
is the energy dissipated due to material [195]internal friction.
Elastic hysteresis was one of the first types of hysteresis to be
examined.^[196][10]^[197][11]
The effect can be demonstrated using a [198]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 stretch and get longer. As more
weights are loaded onto it, the band will continue to stretch because the force
the weights are exerting on the band is increasing. When each weight is taken
off, or unloaded, the band will contract 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 contracts less, resulting in a slightly longer length as it is
unloaded. This is because the band does not obey [199]Hooke's law perfectly. The
hysteresis loop of an idealized rubber band is shown in the figure.
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
effect (the length) lagged behind the cause (the force of the weights) because
the length has not yet reached the value it had for the same weight during the
loading part of the cycle. In terms of energy, more energy was required during
the loading than the unloading, the excess energy being dissipated as thermal
energy.
Elastic hysteresis is more pronounced when the loading and unloading is done
quickly than when it is done slowly.^[200][12] 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.
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 [201]thermally
isolated.
Small vehicle suspensions using [202]rubber (or other [203]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. [204]Mountain bikes have made use of elastomer
suspension, as did the original [205]Mini car.
The primary cause of [206]rolling resistance when a body (such as a ball, tire,
or wheel) rolls on a surface is hysteresis. This is attributed to the
[207]viscoelastic characteristics of the material of the rolling body.
Contact angle hysteresis[[208]edit]
The [209]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 [210]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 [211]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.
Bubble shape hysteresis[[212]edit]
The equilibrium shapes of [213]bubbles expanding and contracting on capillaries
([214]blunt needles) can exhibit hysteresis depending on the relative magnitude
of the [215]maximum capillary pressure to ambient pressure, and the relative
magnitude of the bubble volume at the maximum capillary pressure to the dead
volume in the system.^[216][13] The bubble shape hysteresis is a consequence of
gas [217]compressibility, which causes the bubbles to behave differently across
expansion and contraction. During expansion, bubbles undergo large non
equilibrium jumps in volume, while during contraction the bubbles are more stable
and undergo a relatively smaller jump in volume resulting in an asymmetry across
expansion and contraction. The bubble shape hysteresis is qualitatively similar
to the adsorption hysteresis, and as in the contact angle hysteresis, the
interfacial properties play an important role in bubble shape hysteresis.
The existence of the bubble shape hysteresis has important consequences in
[218]interfacial rheology experiments involving bubbles. As a result of the
hysteresis, not all sizes of the bubbles can be formed on a capillary. Further
the gas compressibility causing the hysteresis leads to unintended complications
in the phase relation between the applied changes in interfacial area to the
expected interfacial stresses. These difficulties can be avoided by designing
experimental systems to avoid the bubble shape hysteresis.^[219][13]^[220][14]
Adsorption hysteresis[[221]edit]
Hysteresis can also occur during physical [222]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 [223]cavitation and pore blocking.
In physical adsorption, hysteresis is evidence of [224]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.^[225][15] 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.^[226][16] 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.^[227][17]
Matric potential hysteresis[[228]edit]
The relationship between matric [229]water potential and [230]water content is
the basis of the [231]water retention curve. [232]Matric potential measurements
(Q[m]) are converted to volumetric water content (th) 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 (Q[m]) of 5 kPa, the volumetric water content (th) of a fine
sandy soil matrix could be anything between 8% and 25%.^[233][18]
[234]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^[235][update], only desorption curves are usually
measured during calibration of [236]soil moisture sensors. Despite the fact that
it can be a source of significant error, the sensor specific effect of hysteresis
is generally ignored.^[237][19]
In materials[[238]edit]
Magnetic hysteresis[[239]edit]
Main article: [240]Magnetic hysteresis
[241][400px-StonerWohlfarthMainLoop.svg.png] [242]Theoretical model of
[243]magnetization m against [244]magnetic field h. 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
h[c] and m[rs] are the [245]coercivity and [246]saturation remanence.
When an external [247]magnetic field is applied to a [248]ferromagnetic material
such as [249]iron, the atomic [250]domains 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 [251]demagnetize it requires heat or a magnetic field in the opposite
direction. This is the effect that provides the element of memory in a [252]hard
disk drive.
The relationship between field strength H and magnetization M is not linear in
such materials. If a magnet is demagnetized (H = M = 0) and the relationship
between H and M is plotted for increasing levels of field strength, M follows the
initial magnetization curve. This curve increases rapidly at first and then
approaches an [253]asymptote called [254]magnetic saturation. If the magnetic
field is now reduced monotonically, M follows a different curve. At zero field
strength, the magnetization is offset from the origin by an amount called the
[255]remanence. If the H-M 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 [256]coercivity of the material.^[257][20]
A closer look at a magnetization curve generally reveals a series of small,
random jumps in magnetization called [258]Barkhausen jumps. This effect is due to
[259]crystallographic defects such as [260]dislocations.^[261][21]
Magnetic hysteresis loops are not exclusive to materials with ferromagnetic
ordering. Other magnetic orderings, such as [262]spin glass ordering, also
exhibit this phenomenon.^[263][22]
Physical origin[[264]edit]
Main article: [265]Ferromagnetism
The phenomenon of hysteresis in [266]ferromagnetic materials is the result of two
effects: rotation of [267]magnetization and changes in size or number of
[268]magnetic domains. In general, the magnetization varies (in direction but not
magnitude) across a magnet, but in sufficiently small magnets, it does not. In
these [269]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, [270]magnetic recording).
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 [271]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).
Magnetic hysteresis models[[272]edit]
The most known empirical models in hysteresis are [273]Preisach and
[274]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. A
more recent model, with a more consistent thermodynamical foundation, is the
vectorial incremental nonconservative consistent hysteresis (VINCH) model of
Lavet et al. (2011)^[275][23]
Applications[[276]edit]
Main article: [277]Magnet § Common uses
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 [278]magnetic
tape, [279]hard disks, and [280]credit cards. In these applications, hard magnets
(high coercivity) like [281]iron are desirable, such that as much energy is
absorbed as possible during the write operation and the resultant magnetized
information is not easily erased.
On the other hand, magnetically soft (low coercivity) iron is used for the cores
in [282]electromagnets. The low coercivity minimizes the energy loss associated
with hysteresis, as the magnetic field periodically reverses in the presence of
an alternating current. The low energy loss during a hysteresis loop is the
reason why soft iron is used for transformer cores and electric motors.
Electrical hysteresis[[283]edit]
Electrical hysteresis typically occurs in [284]ferroelectric material, where
domains of polarization contribute to the total polarization. Polarization is the
[285]electrical dipole moment (either [286]C·[287]m^-2 or [288]C·[289]m). The
mechanism, an organization of the polarization into domains, is similar to that
of magnetic hysteresis.
Liquid-solid-phase transitions[[290]edit]
Hysteresis manifests itself in state transitions when [291]melting temperature
and freezing temperature do not agree. For example, [292]agar melts at 85 °C
(185 °F) and solidifies from 32 to 40 °C (90 to 104 °F). 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.
In biology[[293]edit]
Cell biology and genetics[[294]edit]
Main article: [295]Cell biology
Hysteresis in cell biology often follows [296]bistable systems where the same
input state can lead to two different, stable outputs. Where bistability can lead
to digital, switch-like outputs from the continuous inputs of chemical
concentrations and activities, hysteresis makes these systems more resistant to
noise. These systems are often characterized by higher values of the input
required to switch into a particular state as compared to the input required to
stay in the state, allowing for a transition that is not continuously reversible,
and thus less susceptible to noise.
Cells undergoing [297]cell division exhibit hysteresis in that it takes a higher
concentration of [298]cyclins to switch them from G2 phase into [299]mitosis than
to stay in mitosis once begun.^[300][24] ^[301][25]
Biochemical systems can also show hysteresis-like output when slowly varying
states that are not directly monitored are involved, as in the case of the cell
cycle arrest in yeast exposed to mating pheromone.^[302][26] Here, the duration
of cell cycle arrest depends not only on the final level of input Fus3, but also
on the previously achieved Fus3 levels. This effect is achieved due to the slower
time scales involved in the transcription of intermediate Far1, such that the
total Far1 activity reaches its equilibrium value slowly, and for transient
changes in Fus3 concentration, the response of the system depends on the Far1
concentration achieved with the transient value. Experiments in this type of
hysteresis benefit from the ability to change the concentration of the inputs
with time. The mechanisms are often elucidated by allowing independent control of
the concentration of the key intermediate, for instance, by using an inducible
promoter.
Main article: [303]Chromatin
Darlington in his classic works on [304]genetics^[305][27]^[306][28] discussed
hysteresis of the [307]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 [308]cell nucleus.
Main article: [309]Morphogen
In [310]developmental biology, cell type diversity is regulated by long
range-acting signaling molecules called [311]morphogens that pattern uniform
pools of cells in a concentration- and time-dependent manner. The morphogen
[312]sonic hedgehog (Shh), for example, acts on [313]limb bud and [314]neural
progenitors to induce expression of a set of [315]homeodomain-containing
[316]transcription factors to subdivide these tissues into distinct domains. It
has been shown that these tissues have a 'memory' of previous exposure to
Shh.^[317][29] In neural tissue, this hysteresis is regulated by a homeodomain
(HD) feedback circuit that amplifies Shh signaling.^[318][30] In this circuit,
expression of [319]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.
Immunology[[320]edit]
There is some evidence that [321]T cells exhibit hysteresis in that it takes a
lower signal threshold to [322]activate T cells that have been previously
activated. [323]Ras GTPase activation is required for downstream effector
functions of activated T cells.^[324][31] 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.
Neuroscience[[325]edit]
See also: [326]Refractory period (physiology)
The property by which some [327]neurons do not return to their basal conditions
from a stimulated condition immediately after removal of the stimulus is an
example of hysteresis.
Neuropsychology[[328]edit]
Main articles: [329]Context-dependent memory and [330]State-dependent memory
[331]Neuropsychology, in exploring the [332]neural correlates of consciousness,
interfaces with [333]neuroscience, although the complexity of the [334]central
nervous system is a challenge to its study (that is, its operation resists easy
[335]reduction). [336]Context-dependent memory and [337]state-dependent memory
show hysteretic aspects of [338]neurocognition.
Respiratory physiology[[339]edit]
Lung hysteresis is evident when observing the compliance of a lung on inspiration
versus expiration. The difference in compliance (Dvolume/Dpressure) is due to the
additional energy required to overcome surface tension forces during inspiration
to recruit and inflate additional alveoli.^[340][32]
The [341]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.^[342][33]
Voice and speech physiology[[343]edit]
A hysteresis effect may be observed in voicing onset versus offset.^[344][34] The
threshold value of the subglottal pressure required to start the vocal fold
vibration is lower than the threshold value at which the vibration stops, when
other parameters are kept constant. In utterances of vowel-voiceless
consonant-vowel sequences during speech, the intraoral pressure is lower at the
voice onset of the second vowel compared to the voice offset of the first vowel,
the oral airflow is lower, the transglottal pressure is larger and the glottal
width is smaller.
Ecology and epidemiology[[345]edit]
Hysteresis is a commonly encountered phenomenon in ecology and epidemiology,
where the observed equilibrium of a system can not be predicted solely based on
environmental variables, but also requires knowledge of the system's past
history. Notable examples include the theory of [346]spruce budworm outbreaks and
behavioral-effects on disease transmission.^[347][35]
It is commonly examined in relation to [348]critical transitions between
ecosystem or community types in which dominant competitors or entire landscapes
can change in a largely irreversible fashion.^[349][36]^[350][37]
In ocean and climate science[[351]edit]
Complex [352]ocean and [353]climate models rely on the
principle.^[354][38]^[355][39]
In economics[[356]edit]
Main article: [357]Hysteresis (economics)
Economic systems can exhibit hysteresis. For example, [358]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.
When some negative shock reduces employment in a company or industry, fewer
employed workers then remain. 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
[359]equilibrium wage level, where the supply and demand of workers would match.
This causes hysteresis: the unemployment becomes permanently higher after
negative shocks.^[360][40]^[361][41]
Permanently higher unemployment[[362]edit]
The idea of hysteresis is used extensively in the area of labor economics,
specifically with reference to the [363]unemployment rate.^[364][42] According to
theories based on hysteresis, severe economic downturns (recession) and/or
persistent stagnation (slow demand growth, usually after a recession) cause
unemployed individuals to lose their job skills (commonly developed on the job)
or to find that their skills have become obsolete, or become demotivated,
disillusioned or depressed or lose job-seeking skills. In addition, employers may
use time spent in unemployment as a screening tool, i.e., to weed out less
desired employees in hiring decisions. Then, in times of an economic upturn,
recovery, or "boom", the affected workers will not share in the prosperity,
remaining unemployed for long periods (e.g., over 52 weeks). This makes
unemployment "structural", i.e., extremely difficult to reduce simply by
increasing the aggregate demand for products and labor without causing increased
inflation. That is, it is possible that a [365]ratchet effect in unemployment
rates exists, so a short-term rise in unemployment rates tends to persist. For
example, traditional anti-inflationary policy (the use of recession to fight
inflation) leads to a permanently higher "natural" rate of unemployment (more
scientifically known as the [366]NAIRU). This occurs first because inflationary
expectations are "[367]sticky" downward due to wage and price rigidities (and so
adapt slowly over time rather than being approximately correct as in theories of
[368]rational expectations) and second because labor markets do not clear
instantly in response to unemployment.
The existence of hysteresis has been put forward as a possible explanation for
the persistently high unemployment of many economies in the 1990s. Hysteresis has
been invoked by [369]Olivier Blanchard among others to explain the differences in
long run unemployment rates between Europe and the United States. Labor market
reform (usually meaning institutional change promoting more flexible wages,
firing, and hiring) or strong demand-side economic growth may not therefore
reduce this pool of long-term unemployed. Thus, specific targeted training
programs are presented as a possible policy solution.^[370][40] However, the
hysteresis hypothesis suggests such training programs are aided by persistently
high demand for products (perhaps with [371]incomes policies to avoid increased
inflation), which reduces the transition costs out of unemployment and into paid
employment easier.
Models[[372]edit]
Hysteretic models are [373]mathematical models capable of simulating complex
[374]nonlinear behavior (hysteresis) characterizing [375]mechanical systems and
[376]materials used in different fields of [377]engineering, such as
[378]aerospace, [379]civil, and [380]mechanical engineering. Some examples of
mechanical systems and materials having hysteretic behavior are:
* materials, such as [381]steel, [382]reinforced concrete, [383]wood;
* structural elements, such as steel, reinforced concrete, or wood joints;
* devices, such as seismic isolators^[384][43] and dampers.
Each subject that involves hysteresis has models that are specific to the
subject. In addition, there are hysteretic models that capture general features
of many systems with hysteresis.^[385][44]^[386][45]^[387][46] An example is the
[388]Preisach model of hysteresis, which represents a hysteresis nonlinearity as
a [389]linear superposition of square loops called non-ideal relays.^[390][44]
Many complex models of hysteresis arise from the simple parallel connection, or
superposition, of elementary carriers of hysteresis termed hysterons.
A simple and intuitive parametric description of various hysteresis loops may be
found in the [391]Lapshin model.^[392][45]^[393][46] Along with the smooth loops,
substitution of trapezoidal, triangular or rectangular pulses instead of the
harmonic functions allows piecewise-linear hysteresis loops frequently used in
discrete automatics to be built in the model. There are implementations of the
hysteresis loop model in [394]Mathcad^[395][46] and in [396]R programming
language.^[397][47]
The [398]Bouc-Wen model of hysteresis is often used to describe non-linear
hysteretic systems. It was introduced by Bouc^[399][48]^[400][49] and extended by
Wen,^[401][50] 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
[402]torsional response of hysteretic systems two- and three-dimensional
continua, and [403]soil liquefaction among others. The Bouc-Wen model and its
variants/extensions have been used in applications of [404]structural control, in
particular in the modeling of the behaviour of [405]magnetorheological dampers,
[406]base isolation devices for buildings and other kinds of damping devices; it
has also been used in the modelling and analysis of structures built of
reinforced concrete, steel, masonry and timber.^[[407]citation needed]. The most
important extension of Bouc-Wen Model was carried out by Baber and Noori and
later by Noori and co-workers. That extended model, named, BWBN, can reproduce
the complex shear pinching or slip-lock phenomenon that earlier model could not
reproduce. The BWBN model has been widely used in a wide spectrum of applications
and implementations are available in software such as [408]OpenSees.
Hysteretic models may have a generalized displacement
[MATH: u {\displaystyle u} :MATH]
{\displaystyle u} as input variable and a generalized force
[MATH: f {\displaystyle f} :MATH]
{\displaystyle f} as output variable, or vice versa. In particular, in
rate-independent hysteretic models, the output variable does not depend on the
rate of variation of the input one.^[409][51]^[410][52]
Rate-independent hysteretic models can be classified into four different
categories depending on the type of equation that needs to be solved to compute
the output variable:
* algebraic models
* transcendental models
* differential models
* integral models
List of models[[411]edit]
Some notable hysteretic models are listed below with their associated fields.
* [412]Bean's critical state model (magnetism)
* [413]Bouc-Wen model (structural engineering)
* [414]Ising model (magnetism)
* [415]Jiles-Atherton model (magnetism)
* [416]Novak-Tyson model (cell-cycle control)
* [417]Preisach model (magnetism)
* [418]Stoner-Wohlfarth model (magnetism)
Energy[[419]edit]
When hysteresis occurs with [420]extensive and intensive variables, the work done
on the system is the area under the hysteresis graph.
See also[[421]edit]
* [422]Backlash (engineering)
* [423]Bean's critical state model
* [424]Black box
* [425]Deadband
* [426]Fuzzy control system
* [427]Hysteresivity
* [428]Markov property
* [429]Memristor
* [430]Path dependence
* [431]Path dependence (physics)
* [432]Remanence
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Hysteresis (Tools for Modeling Rate-Dependent Hysteretic Processes and
Ellipses)". R-project. Retrieved June 11, 2020.
48. [696]^ Bouc, R. (1967). "Forced vibration of mechanical systems with
hysteresis". Proceedings of the Fourth Conference on Nonlinear Oscillation.
Prague, Czechoslovakia. p. 315.
49. [697]^ Bouc, R. (1971). "Modèle mathématique d'hystérésis: application aux
systèmes à un degré de liberté". Acustica (in French). 24: 16-25.
50. [698]^ Wen, Y. K. (1976). [699]"Method for random vibration of hysteretic
systems". Journal of Engineering Mechanics. 102 (2): 249-263.
51. [700]^ Dimian, Mihai; Andrei, Petru (4 November 2013). Noise-driven phenomena
in hysteretic systems. Springer. [701]ISBN [702]9781461413745.
52. [703]^ Vaiana, Nicolò; Sessa, Salvatore; Rosati, Luciano (January 2021). "A
generalized class of uniaxial rate-independent models for simulating
asymmetric mechanical hysteresis phenomena". Mechanical Systems and Signal
Processing. 146: 106984. [704]Bibcode:[705]2021MSSP..14606984V.
[706]doi:[707]10.1016/j.ymssp.2020.106984. [708]S2CID [709]224951872.
Further reading[[710]edit]
*
Chikazumi, Soshin (1997). Physics of Ferromagnetism. Clarendon Press.
[711]ISBN [712]978-0-19-851776-4.
Jiles, D. C.; Atherton, D. L. (1986). "Theory of ferromagnetic hysteresis".
[713]Journal of Magnetism and Magnetic Materials. 61 (1-2): 48-60.
[714]Bibcode:[715]1986JMMM...61...48J.
[716]doi:[717]10.1016/0304-8853(86)90066-1.
Krasnosel'skii, Mark; Pokrovskii, Alexei (1989). Systems with Hysteresis. New
York: [718]Springer-Verlag. [719]ISBN [720]978-0-387-15543-2.
Mayergoyz, Isaak D.; Bertotti, Giorgio, eds. (2005). The Science of Hysteresis
(3-volume set). [721]Academic Press. [722]ISBN [723]978-0-12-480874-4.
Mielke, A.; Roubícek, T. (2015). Rate-Independent Systems: Theory and
Application. New York: Springer. [724]ISBN [725]978-1-4939-2705-0.
[726]Truesdell, C.; [727]Noll, Walter (2004). Antman, Stuart (ed.). The
Non-Linear Field Theories of Mechanics (Third ed.). Springer.
[728]ISBN [729]978-3-540-02779-9. Originally published as Volume III/3 of
Handbuch der Physik in 1965.
Visintin, Augusto (1994). Differential Models of Hysteresis. [730]Springer.
[731]ISBN [732]978-3-540-54793-8.
Noori, Hamid R. (2014). Hysteresis Phenomena in Biology. Springer.
[733]ISBN [734]978-3-642-38217-8.
External links[[735]edit]
Look up [736]hysteresis in Wiktionary, the free dictionary.
[737]Elastic hysteresis of household string is examined at Wikiversity
* [738]Overview of contact angle Hysteresis
* [739]Preisach model of hysteresis - Matlab codes developed by Zs. Szabó
* [740]Hysteresis
* [741]What's hysteresis? [742]Archived 2009-09-04 at the [743]Wayback Machine
* [744]Dynamical systems with hysteresis (interactive web page)
* [745]Magnetization reversal app (coherent rotation)^[[746]permanent dead
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100. https://en.wikipedia.org/wiki/Ferroelectricity
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102. https://en.wikipedia.org/wiki/Magnet
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104. https://en.wikipedia.org/wiki/Magnetic_field
105. https://en.wikipedia.org/wiki/Hard_disk_drive
106. https://en.wikipedia.org/wiki/Remanence
107. https://en.wikipedia.org/wiki/Earth%27s_magnetic_field
108. https://en.wikipedia.org/wiki/Ferromagnetic
109. https://en.wikipedia.org/wiki/Ferroelectricity
110. https://en.wikipedia.org/wiki/Deformation_(mechanics)
111. https://en.wikipedia.org/wiki/Rubber_band
112. https://en.wikipedia.org/wiki/Shape-memory_alloy
113. https://en.wikipedia.org/wiki/Irreversible_process
114. https://en.wikipedia.org/wiki/Phase_transitions
115. https://en.wikipedia.org/wiki/Internal_friction
116. https://en.wikipedia.org/wiki/Dissipation
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119. https://en.wikipedia.org/wiki/Engineering
120. https://en.wikipedia.org/wiki/Biology
121. https://en.wikipedia.org/wiki/Economics
122. https://en.wikipedia.org/wiki/Thermostat
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139. https://en.wikipedia.org/wiki/Louis_N%C3%A9el
140. https://en.wikipedia.org/wiki/Douglas_Hugh_Everett
141. https://en.wikipedia.org/wiki/Mark_Krasnosel%27skii
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145. https://en.wikipedia.org/wiki/Sine_wave
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147. https://en.wikipedia.org/wiki/Frequency_domain
148. https://en.wikipedia.org/wiki/Transfer_function
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151. https://en.wikipedia.org/wiki/Dissipative
152. https://en.wikipedia.org/wiki/Friction
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157. https://en.wikipedia.org/wiki/Hysteresis#cite_note-Visintin1994p13-5
158. https://en.wikipedia.org/wiki/Preisach_model
159. https://en.wikipedia.org/w/index.php?title=Prandtl%E2%88%92Ishlinskii_model&action=edit&redlink=1
160. https://en.wikipedia.org/wiki/Hysteresis#cite_note-6
161. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=5
162. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=6
163. https://en.wikipedia.org/wiki/Thermostat
164. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=7
165. https://en.wikipedia.org/wiki/File:Hysteresis_sharp_curve.svg
166. https://en.wikipedia.org/wiki/Schmitt_trigger
167. https://en.wikipedia.org/wiki/Switch#Contact_bounce
168. https://en.wikipedia.org/wiki/Noise_(electronic)
169. https://en.wikipedia.org/wiki/Schmitt_trigger
170. https://en.wikipedia.org/wiki/Relay#Latching_relay
171. https://en.wikipedia.org/wiki/Solenoid
172. https://en.wikipedia.org/wiki/Memristor
173. https://en.wikipedia.org/wiki/Hysteresis#cite_note-7
174. https://en.wikipedia.org/wiki/Nanoelectronic
175. https://en.wikipedia.org/w/index.php?title=Electrochrome_cell&action=edit&redlink=1
176. https://en.wikipedia.org/wiki/Memory_effect
177. https://en.wikipedia.org/wiki/Passive_matrix_addressing
178. https://en.wikipedia.org/wiki/Crosstalk
179. https://en.wikipedia.org/wiki/Noise_gate
180. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=8
181. https://en.wikipedia.org/wiki/Computer_algorithm
182. https://en.wikipedia.org/wiki/User_interface_design
183. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=9
184. https://en.wikipedia.org/wiki/Aerodynamic
185. https://en.wikipedia.org/wiki/Hysteresis#cite_note-8
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197. https://en.wikipedia.org/wiki/Hysteresis#cite_note-Ewing-11
198. https://en.wikipedia.org/wiki/Rubber_band
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201. https://en.wikipedia.org/wiki/Adiabatically
202. https://en.wikipedia.org/wiki/Rubber
203. https://en.wikipedia.org/wiki/Elastomer
204. https://en.wikipedia.org/wiki/Mountain_bike
205. https://en.wikipedia.org/wiki/Mini
206. https://en.wikipedia.org/wiki/Rolling_resistance
207. https://en.wikipedia.org/wiki/Viscoelasticity
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223. https://en.wikipedia.org/wiki/Cavitation
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231. https://en.wikipedia.org/wiki/Water_retention_curve
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243. https://en.wikipedia.org/wiki/Magnetization
244. https://en.wikipedia.org/wiki/Magnetic_field
245. https://en.wikipedia.org/wiki/Coercivity
246. https://en.wikipedia.org/wiki/Remanence#Saturation_remanence
247. https://en.wikipedia.org/wiki/Magnetic_field
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286. https://en.wikipedia.org/wiki/Coulomb
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605. https://en.wikipedia.org/wiki/PMID_(identifier)
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608. https://en.wikipedia.org/wiki/Steven_Strogatz
609. https://en.wikipedia.org/wiki/ISBN_(identifier)
610. https://en.wikipedia.org/wiki/Special:BookSources/0-7382-0453-6
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618. https://doi.org/10.2307%2F3868190
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620. https://doi.org/10.2307%2F3868190
621. https://en.wikipedia.org/wiki/JSTOR_(identifier)
622. https://www.jstor.org/stable/3868190
623. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-38
624. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2791639
625. https://en.wikipedia.org/wiki/Doi_(identifier)
626. https://doi.org/10.1073%2Fpnas.0909146106
627. https://en.wikipedia.org/wiki/ISSN_(identifier)
628. https://www.worldcat.org/issn/0027-8424
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631. https://en.wikipedia.org/wiki/PMID_(identifier)
632. https://pubmed.ncbi.nlm.nih.gov/19897722
633. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-39
634. https://en.wikipedia.org/wiki/Doi_(identifier)
635. https://doi.org/10.1103%2FPhysRevE.101.062145
636. https://en.wikipedia.org/wiki/ISSN_(identifier)
637. https://www.worldcat.org/issn/2470-0045
638. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Ball_40-0
639. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Ball_40-1
640. https://en.wikipedia.org/wiki/Laurence_M._Ball
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642. https://en.wikipedia.org/wiki/Doi_(identifier)
643. https://doi.org/10.3386%2Fw14818
644. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-41
645. https://www.nber.org/chapters/c4245
646. https://en.wikipedia.org/wiki/Doi_(identifier)
647. https://doi.org/10.2307%2F3585159
648. https://en.wikipedia.org/wiki/JSTOR_(identifier)
649. https://www.jstor.org/stable/3585159
650. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Hargreaves-Heap_42-0
651. https://en.wikipedia.org/wiki/JSTOR_(identifier)
652. https://www.jstor.org/stable/2231931
653. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-43
654. https://linkinghub.elsevier.com/retrieve/pii/S0141029617306272
655. https://en.wikipedia.org/wiki/Bibcode_(identifier)
656. https://ui.adsabs.harvard.edu/abs/2017EngSt.140..498V
657. https://en.wikipedia.org/wiki/Doi_(identifier)
658. https://doi.org/10.1016%2Fj.engstruct.2017.02.057
659. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Mayergoyz2003_44-0
660. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Mayergoyz2003_44-1
661. https://en.wikipedia.org/wiki/Isaak_D._Mayergoyz
662. https://en.wikipedia.org/wiki/Academic_Press
663. https://en.wikipedia.org/wiki/ISBN_(identifier)
664. https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-480873-7
665. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Lapshin1995_45-0
666. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Lapshin1995_45-1
667. http://www.lapshin.fast-page.org/publications/R.%20V.%20Lapshin,%20Analytical%20model%20for%20the%20approximation%20of%20hysteresis%20loop%20and%20its%20application%20to%20the%20scanning%20tunneling%20microscope.pdf
668. https://en.wikipedia.org/wiki/ArXiv_(identifier)
669. https://arxiv.org/abs/2006.02784
670. https://en.wikipedia.org/wiki/Bibcode_(identifier)
671. https://ui.adsabs.harvard.edu/abs/1995RScI...66.4718L
672. https://en.wikipedia.org/wiki/Doi_(identifier)
673. https://doi.org/10.1063%2F1.1145314
674. https://en.wikipedia.org/wiki/ISSN_(identifier)
675. https://www.worldcat.org/issn/0034-6748
676. https://en.wikipedia.org/wiki/S2CID_(identifier)
677. https://api.semanticscholar.org/CorpusID:121671951
678. http://www.lapshin.fast-page.org/publications/R.%20V.%20Lapshin,%20Analytical%20model%20for%20the%20approximation%20of%20hysteresis%20loop%20and%20its%20application%20to%20the%20scanning%20tunneling%20microscope.ru.pdf
679. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Lapshin2020_46-0
680. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Lapshin2020_46-1
681. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Lapshin2020_46-2
682. https://en.wikipedia.org/wiki/ArXiv_(identifier)
683. https://arxiv.org/abs/1701.08070
684. https://en.wikipedia.org/wiki/Bibcode_(identifier)
685. https://ui.adsabs.harvard.edu/abs/2020RScI...91f5106L
686. https://en.wikipedia.org/wiki/Doi_(identifier)
687. https://doi.org/10.1063%2F5.0012931
688. https://en.wikipedia.org/wiki/ISSN_(identifier)
689. https://www.worldcat.org/issn/0034-6748
690. https://en.wikipedia.org/wiki/PMID_(identifier)
691. https://pubmed.ncbi.nlm.nih.gov/32611047
692. https://en.wikipedia.org/wiki/S2CID_(identifier)
693. https://api.semanticscholar.org/CorpusID:13489477
694. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-PckgHyst_47-0
695. https://cran.r-project.org/web/packages/hysteresis/index.html
696. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Bouc67_48-0
697. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Bouc71_49-0
698. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-Wen76_50-0
699. http://cedb.asce.org/cgi/WWWdisplay.cgi?6630
700. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-51
701. https://en.wikipedia.org/wiki/ISBN_(identifier)
702. https://en.wikipedia.org/wiki/Special:BookSources/9781461413745
703. https://en.wikipedia.org/wiki/Hysteresis#cite_ref-:1_52-0
704. https://en.wikipedia.org/wiki/Bibcode_(identifier)
705. https://ui.adsabs.harvard.edu/abs/2021MSSP..14606984V
706. https://en.wikipedia.org/wiki/Doi_(identifier)
707. https://doi.org/10.1016%2Fj.ymssp.2020.106984
708. https://en.wikipedia.org/wiki/S2CID_(identifier)
709. https://api.semanticscholar.org/CorpusID:224951872
710. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=41
711. https://en.wikipedia.org/wiki/ISBN_(identifier)
712. https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-851776-4
713. https://en.wikipedia.org/wiki/Journal_of_Magnetism_and_Magnetic_Materials
714. https://en.wikipedia.org/wiki/Bibcode_(identifier)
715. https://ui.adsabs.harvard.edu/abs/1986JMMM...61...48J
716. https://en.wikipedia.org/wiki/Doi_(identifier)
717. https://doi.org/10.1016%2F0304-8853%2886%2990066-1
718. https://en.wikipedia.org/wiki/Springer-Verlag
719. https://en.wikipedia.org/wiki/ISBN_(identifier)
720. https://en.wikipedia.org/wiki/Special:BookSources/978-0-387-15543-2
721. https://en.wikipedia.org/wiki/Academic_Press
722. https://en.wikipedia.org/wiki/ISBN_(identifier)
723. https://en.wikipedia.org/wiki/Special:BookSources/978-0-12-480874-4
724. https://en.wikipedia.org/wiki/ISBN_(identifier)
725. https://en.wikipedia.org/wiki/Special:BookSources/978-1-4939-2705-0
726. https://en.wikipedia.org/wiki/Clifford_Truesdell
727. https://en.wikipedia.org/wiki/Walter_Noll
728. https://en.wikipedia.org/wiki/ISBN_(identifier)
729. https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-02779-9
730. https://en.wikipedia.org/wiki/Springer_Science%2BBusiness_Media
731. https://en.wikipedia.org/wiki/ISBN_(identifier)
732. https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-54793-8
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734. https://en.wikipedia.org/wiki/Special:BookSources/978-3-642-38217-8
735. https://en.wikipedia.org/w/index.php?title=Hysteresis&action=edit§ion=42
736. https://en.wiktionary.org/wiki/hysteresis
737. https://en.wikiversity.org/wiki/Physics_and_Astronomy_Labs/Hooke%27s_law_and_Young%27s_modulus
738. http://www.ramehart.com/contactangle.htm
739. http://sourceforge.net/projects/hysteresis/
740. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/hyst.html
741. http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html
742. https://web.archive.org/web/20090904012600/http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html
743. https://en.wikipedia.org/wiki/Wayback_Machine
744. https://web.archive.org/web/20051102025906/http://euclid.ucc.ie/hysteresis/
745. http://magneticslab.ua.edu/magnetation-reversal.html
746. https://en.wikipedia.org/wiki/Wikipedia:Link_rot
747. https://web.archive.org/web/20080327034229/http://www.madphysics.com/exp/hysteresis_and_rubber_bands.htm
748. https://en.wikipedia.org/wiki/Help:Authority_control
749. https://www.wikidata.org/wiki/Q190837#identifiers
750. https://d-nb.info/gnd/4132813-9
751. http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007535994605171
752. https://id.loc.gov/authorities/sh85063849
753. https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000310307&P_CON_LNG=ENG
754. https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph134814&CON_LNG=ENG
755. https://en.wikipedia.org/w/index.php?title=Hysteresis&oldid=1221810308
756. https://en.wikipedia.org/wiki/Help:Category
757. https://en.wikipedia.org/wiki/Category:Hysteresis
758. https://en.wikipedia.org/wiki/Category:Magnetic_ordering
759. https://en.wikipedia.org/wiki/Category:Materials_science
760. https://en.wikipedia.org/wiki/Category:Nonlinear_systems
761. https://en.wikipedia.org/wiki/Category:Dynamical_systems
762. https://en.wikipedia.org/wiki/Category:CS1_French-language_sources_(fr)
763. https://en.wikipedia.org/wiki/Category:Articles_with_short_description
764. https://en.wikipedia.org/wiki/Category:Short_description_matches_Wikidata
765. https://en.wikipedia.org/wiki/Category:Articles_containing_Ancient_Greek_(to_1453)-language_text
766. https://en.wikipedia.org/wiki/Category:Articles_containing_potentially_dated_statements_from_2002
767. https://en.wikipedia.org/wiki/Category:All_articles_containing_potentially_dated_statements
768. https://en.wikipedia.org/wiki/Category:All_articles_with_unsourced_statements
769. https://en.wikipedia.org/wiki/Category:Articles_with_unsourced_statements_from_September_2011
770. https://en.wikipedia.org/wiki/Category:Webarchive_template_wayback_links
771. https://en.wikipedia.org/wiki/Category:All_articles_with_dead_external_links
772. https://en.wikipedia.org/wiki/Category:Articles_with_dead_external_links_from_January_2018
773. https://en.wikipedia.org/wiki/Category:Articles_with_permanently_dead_external_links
774. https://en.wikipedia.org/wiki/Category:Articles_with_GND_identifiers
775. https://en.wikipedia.org/wiki/Category:Articles_with_J9U_identifiers
776. https://en.wikipedia.org/wiki/Category:Articles_with_LCCN_identifiers
777. https://en.wikipedia.org/wiki/Category:Articles_with_LNB_identifiers
778. https://en.wikipedia.org/wiki/Category:Articles_with_NKC_identifiers
779. https://en.wikipedia.org/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License
780. https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use
781. https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy
782. https://www.wikimediafoundation.org/
783. https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy
784. https://en.wikipedia.org/wiki/Wikipedia:About
785. https://en.wikipedia.org/wiki/Wikipedia:General_disclaimer
786. https://en.wikipedia.org/wiki/Wikipedia:Contact_us
787. https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct
788. https://developer.wikimedia.org/
789. https://stats.wikimedia.org/#/en.wikipedia.org
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791. https://en.m.wikipedia.org/w/index.php?title=Hysteresis&mobileaction=toggle_view_mobile
792. https://wikimediafoundation.org/
793. https://www.mediawiki.org/
Hidden links:
795. https://en.wikipedia.org/wiki/Hysteresis
796. https://en.wikipedia.org/wiki/Hysteresis#Etymology_and_history
797. https://en.wikipedia.org/wiki/Hysteresis#Types
798. https://en.wikipedia.org/wiki/Hysteresis#Rate-dependent
799. https://en.wikipedia.org/wiki/Hysteresis#Rate-independent
800. https://en.wikipedia.org/wiki/Hysteresis#In_engineering
801. https://en.wikipedia.org/wiki/Hysteresis#Control_systems
802. https://en.wikipedia.org/wiki/Hysteresis#Electronic_circuits
803. https://en.wikipedia.org/wiki/Hysteresis#User_interface_design
804. https://en.wikipedia.org/wiki/Hysteresis#Aerodynamics
805. https://en.wikipedia.org/wiki/Hysteresis#Hydraulics
806. https://en.wikipedia.org/wiki/Hysteresis#Backlash
807. https://en.wikipedia.org/wiki/Hysteresis#In_mechanics
808. https://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis
809. https://en.wikipedia.org/wiki/Hysteresis#Contact_angle_hysteresis
810. https://en.wikipedia.org/wiki/Hysteresis#Bubble_shape_hysteresis
811. https://en.wikipedia.org/wiki/Hysteresis#Adsorption_hysteresis
812. https://en.wikipedia.org/wiki/Hysteresis#Matric_potential_hysteresis
813. https://en.wikipedia.org/wiki/Hysteresis#In_materials
814. https://en.wikipedia.org/wiki/Hysteresis#Magnetic_hysteresis
815. https://en.wikipedia.org/wiki/Hysteresis#Physical_origin
816. https://en.wikipedia.org/wiki/Hysteresis#Magnetic_hysteresis_models
817. https://en.wikipedia.org/wiki/Hysteresis#Applications
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822. https://en.wikipedia.org/wiki/Hysteresis#Immunology
823. https://en.wikipedia.org/wiki/Hysteresis#Neuroscience
824. https://en.wikipedia.org/wiki/Hysteresis#Neuropsychology
825. https://en.wikipedia.org/wiki/Hysteresis#Respiratory_physiology
826. https://en.wikipedia.org/wiki/Hysteresis#Voice_and_speech_physiology
827. https://en.wikipedia.org/wiki/Hysteresis#Ecology_and_epidemiology
828. https://en.wikipedia.org/wiki/Hysteresis#In_ocean_and_climate_science
829. https://en.wikipedia.org/wiki/Hysteresis#In_economics
830. https://en.wikipedia.org/wiki/Hysteresis#Permanently_higher_unemployment
831. https://en.wikipedia.org/wiki/Hysteresis#Models
832. https://en.wikipedia.org/wiki/Hysteresis#List_of_models
833. https://en.wikipedia.org/wiki/Hysteresis#Energy
834. https://en.wikipedia.org/wiki/Hysteresis#See_also
835. https://en.wikipedia.org/wiki/Hysteresis#References
836. https://en.wikipedia.org/wiki/Hysteresis#Further_reading
837. https://en.wikipedia.org/wiki/Hysteresis#External_links
838. https://en.wikipedia.org/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License
Usage: http://www.kk-software.de/kklynxview/get/URL
e.g. http://www.kk-software.de/kklynxview/get/http://www.kk-software.de
Errormessages are in German, sorry ;-)