======================================================================
= Hysteresis =
======================================================================
Introduction
======================================================================
Hysteresis is the dependence of the state of a system on its history.
For example, a magnet may have more than one possible magnetic moment
in a given 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 hard disk drive and the
remanence that retains a record of the Earth's magnetic field
magnitude in the past. Hysteresis occurs in ferromagnetic and
ferroelectric materials, as well as in the deformation of rubber bands
and shape-memory alloys and many other natural phenomena. In natural
systems it is often associated with irreversible thermodynamic change
such as phase transitions and with internal friction; and dissipation
is a common side effect.
Hysteresis can be found in physics, chemistry, engineering, biology,
and economics. It is incorporated in many artificial systems: for
example, in thermostats and Schmitt triggers, it prevents unwanted
frequent switching.
Hysteresis can be a dynamic 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 nonlinear, and can be mathematically
challenging to model. Some models such as the Preisach model
(originally applied to ferromagnetism) and the Bouc-Wen model attempt
to capture general features of hysteresis; and there are also
phenomenological models for particular phenomena such as the
Jiles-Atherton model for ferromagnetism. See also Hysteretic model.
Etymology and history
======================================================================
The term "hysteresis" is derived from , an Ancient Greek word meaning
"deficiency" or "lagging behind". It was coined around 1890 by Sir
James Alfred Ewing to describe the behaviour of magnetic materials.
Some early work on describing hysteresis in mechanical systems was
performed by James Clerk Maxwell. Subsequently, hysteretic models have
received significant attention in the works of Ferenc Preisach
(Preisach model of hysteresis), Louis Néel and 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 Mark Krasnosel'skii.
Rate-dependent
================
One type of hysteresis is a lag between input and output. An example
is a sinusoidal input that results in a sinusoidal output , but with
a phase lag :
: \begin{align}
X(t) &= X_0 \sin \omega t \\ Y(t) &= Y_0 \sin\left(\omega
t-\varphi\right).
\end{align}
Such behavior can occur in linear systems, and a more general form of
response is
: Y(t) = \chi_\text{i} X(t) + \int_0^{\infty} \Phi_\text{d} (\tau)
X(t-\tau) \, \mathrm{d}\tau,
where \chi_\text{i} is the instantaneous response and \Phi_d(\tau) is
the impulse response to an impulse that occurred \tau time units in
the past. In the frequency domain, input and output are related by a
complex 'generalized susceptibility' that can be computed from \Phi_d;
it is mathematically equivalent to a transfer function in linear
filter theory and analogue signal processing.
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.
When rate-dependent hysteresis is due to dissipative effects like
friction, it is associated with power loss.
Rate-independent
==================
Systems with 'rate-independent hysteresis' have a 'persistent' memory
of the past that remains after the transients have died out. 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 cycles from to and back again, the output may be
initially but a different value upon return. The values of depend
on the path of values that passes through but not on the speed at
which it traverses the path. Many authors restrict the term hysteresis
to mean only rate-independent hysteresis. Hysteresis effects can be
characterized using the Preisach model and the generalized
Prandtl�Ishlinskii model.
Control systems
=================
In control systems, hysteresis can be used to filter signals so that
the output reacts less rapidly than it otherwise would, by taking
recent history into account. For example, a 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
=====================
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 contact bounce in
switches, or noise in an electrical signal.
A Schmitt trigger is a simple electronic circuit that exhibits this
property.
A latching relay uses a solenoid to actuate a ratcheting mechanism
that keeps the relay closed even if power to the relay is terminated.
Hysteresis is essential to the workings of some memristors (circuit
components which "remember" changes in the current passing through
them by changing their resistance).
Hysteresis can be used when connecting arrays of elements such as
nanoelectronics, electrochrome cells and memory effect devices using
passive matrix addressing. Shortcuts are made between adjacent
components (see crosstalk) and the hysteresis helps to keep the
components in a particular state while the other components change
states. Thus, all rows can be addressed at the same time instead of
individually.
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.
User interface design
=======================
A hysteresis is sometimes intentionally added to computer algorithms.
The field of user interface design has borrowed the term hysteresis to
refer to times when the state of the user interface intentionally lags
behind the apparent user input. For example, a menu that was drawn in
response to a mouse-over event may remain on-screen for a brief moment
after the mouse has moved out of the trigger region and the menu
region. This allows the user to move the mouse directly to an item on
the menu, even if part of that direct mouse path is outside of both
the trigger region and the menu region. For instance, right-clicking
on the desktop in most Windows interfaces will create a menu that
exhibits this behavior.
Aerodynamics
==============
In aerodynamics, hysteresis can be observed when decreasing the angle
of attack of a wing after stall, regarding the lift and drag
coefficients. The angle of attack 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.
Elastic hysteresis
====================
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 internal
friction.
Elastic hysteresis was one of the first types of hysteresis to be
examined.
The effect can be demonstrated using a rubber band with weights
attached to it. If the top of a rubber band is hung on a hook and
small weights are attached to the bottom of the band one at a time, it
will get longer. As more weights are 'loaded' onto it, the band will
continue to extend because the force the weights are exerting on the
band is increasing. When each weight is taken off, or 'unloaded', the
band will get shorter as the force is reduced. As the weights are
taken off, each weight that produced a specific length as it was
loaded onto the band now produces a slightly longer length as it is
unloaded. This is because the band does not obey Hooke's law
perfectly. The hysteresis loop of an idealized rubber band is shown in
the figure.
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. 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 adiabatically isolated.
Small vehicle suspensions using rubber (or other elastomers) can
achieve the dual function of springing and damping because rubber,
unlike metal springs, has pronounced hysteresis and does not return
all the absorbed compression energy on the rebound. Mountain bikes
have made use of elastomer suspension, as did the original Mini car.
The primary cause of rolling resistance when a body (such as a ball,
tire, or wheel) rolls on a surface is hysteresis. This is attributed
to the viscoelastic characteristics of the material of the rolling
body.
Contact angle hysteresis
==========================
The contact angle formed between a liquid and solid phase will exhibit
a range of contact angles that are possible. There are two common
methods for measuring this range of contact angles. The first method
is referred to as the tilting base method. Once a drop is dispensed on
the surface with the surface level, the surface is then tilted from 0°
to 90°. As the drop is tilted, the downhill side will be in a state of
imminent wetting while the uphill side will be in a state of imminent
dewetting. As the tilt increases the downhill contact angle will
increase and represents the advancing contact angle while the uphill
side will decrease; this is the receding contact angle. The values for
these angles just prior to the drop releasing will typically represent
the advancing and receding contact angles. The difference between
these two angles is the contact angle hysteresis.
The second method is often referred to as the add/remove volume
method. When the maximum liquid volume is removed from the drop
without the interfacial area decreasing the receding contact angle is
thus measured. When volume is added to the maximum before the
interfacial area increases, this is the advancing contact angle. As
with the tilt method, the difference between the advancing and
receding contact angles is the contact angle hysteresis. Most
researchers prefer the tilt method; the add/remove method requires
that a tip or needle stay embedded in the drop which can affect the
accuracy of the values, especially the receding contact angle.
Bubble shape hysteresis
=========================
The equilibrium shapes of bubbles expanding and contracting on
capillaries (blunt needles) can exhibit hysteresis depending on the
relative magnitude of the 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. The
bubble shape hysteresis is a consequence of gas 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 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.
Adsorption hysteresis
=======================
Hysteresis can also occur during physical adsorption processes. In
this type of hysteresis, the quantity adsorbed is different when gas
is being added than it is when being removed. The specific causes of
adsorption hysteresis are still an active area of research, but it is
linked to differences in the nucleation and evaporation mechanisms
inside mesopores. These mechanisms are further complicated by effects
such as cavitation and pore blocking.
In physical adsorption, hysteresis is evidence of mesoporosity-indeed,
the definition of mesopores (2-50 nm) is associated with the
appearance (50 nm) and disappearance (2 nm) of mesoporosity in
nitrogen adsorption isotherms as a function of Kelvin radius. 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. 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.
Matric potential hysteresis
=============================
The relationship between matric water potential and water content is
the basis of the water retention curve. Matric potential measurements
(Ψm) 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
(Ψm) of , the volumetric water content (θ) of a fine sandy soil matrix
could be anything between 8% to 25%.
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. , only desorption curves are
usually measured during calibration of soil moisture sensors. Despite
the fact that it can be a source of significant error, the sensor
specific effect of hysteresis is generally ignored.
Magnetic hysteresis
=====================
When an external magnetic field is applied to a ferromagnetic material
such as iron, the atomic 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 demagnetize it requires heat or a
magnetic field in the opposite direction. This is the effect that
provides the element of memory in a hard disk drive.
The relationship between field strength and magnetization is not
linear in such materials. If a magnet is demagnetized () and the
relationship between and is plotted for increasing levels of field
strength, follows the 'initial magnetization curve'. This curve
increases rapidly at first and then approaches an asymptote called
magnetic saturation. If the magnetic field is now reduced
monotonically, follows a different curve. At zero field strength,
the magnetization is offset from the origin by an amount called the
remanence. If the relationship is plotted for all strengths of
applied magnetic field the result is a hysteresis loop called the
'main loop'. The width of the middle section is twice the coercivity
of the material.
A closer look at a magnetization curve generally reveals a series of
small, random jumps in magnetization called Barkhausen jumps. This
effect is due to crystallographic defects such as dislocations.
Magnetic hysteresis loops are not exclusive to materials with
ferromagnetic ordering. Other magnetic orderings, such as spin glass
ordering, also exhibit this phenomenon.
Physical origin
=================
The phenomenon of hysteresis in ferromagnetic materials is the result
of two effects: rotation of magnetization and changes in size or
number of 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 single-domain magnets, the
magnetization responds to a magnetic field by rotating. Single-domain
magnets are used wherever a strong, stable magnetization is needed
(for example, magnetic recording).
Larger magnets are divided into regions called 'domains'. Across each
domain, the magnetization does not vary; but between domains are
relatively thin 'domain walls' in which the direction of magnetization
rotates from the direction of one domain to another. If the magnetic
field changes, the walls move, changing the relative sizes of the
domains. Because the domains are not magnetized in the same direction,
the magnetic moment per unit volume is smaller than it would be in a
single-domain magnet; but domain walls involve rotation of only a
small part of the magnetization, so it is much easier to change the
magnetic moment. The magnetization can also change by addition or
subtraction of domains (called 'nucleation' and 'denucleation').
Magnetic hysteresis models
============================
The most known empirical models in hysteresis are Preisach and
Jiles-Atherton models. These models allow an accurate modeling of the
hysteresis loop and are widely used in the industry. However, these
models lose the connection with thermodynamics and the energy
consistency is not ensured. A more recent model, with a more
consistent thermodynamical foundation, is the vectorial incremental
nonconservative consistent hysteresis (VINCH) model of Lavet et al.
(2011)
Applications
==============
There are a great variety of applications of the hysteresis in
ferromagnets. Many of these make use of their ability to retain a
memory, for example magnetic tape, hard disks, and credit cards. In
these applications, 'hard' magnets (high coercivity) like iron are
desirable so the memory is not easily erased.
Magnetically 'soft' (low coercivity) iron is used for the cores in
electromagnets. The low coercivity reduces that energy loss associated
with hysteresis. The low energy loss during a hysteresis loop is also
the reason why soft iron is used for transformer cores and electric
motors.
Electrical hysteresis
=======================
Electrical hysteresis typically occurs in ferroelectric material,
where domains of polarization contribute to the total polarization.
Polarization is the electrical dipole moment (either C·m�2 or C·m).
The mechanism, an organization of the polarization into domains, is
similar to that of magnetic hysteresis.
Liquid�solid-phase transitions
================================
Hysteresis manifests itself in state transitions when melting
temperature and freezing temperature do not agree. For example, agar
melts at 85 °C and solidifies from 32 to 40 °C. This is to say that
once agar is melted at 85 °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.
Cell biology and genetics
===========================
Hysteresis in cell biology often follows 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 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.
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.
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.
Darlington in his classic works on genetics discussed hysteresis of
the chromosomes, by which he meant "failure of the external form of
the chromosomes to respond immediately to the internal stresses due to
changes in their molecular spiral", as they lie in a somewhat rigid
medium in the limited space of the cell nucleus.
In developmental biology, cell type diversity is regulated by long
range-acting signaling molecules called morphogens that pattern
uniform pools of cells in a concentration- and time-dependent manner.
The morphogen sonic hedgehog (Shh), for example, acts on limb bud and
neural progenitors to induce expression of a set of
homeodomain-containing transcription factors to subdivide these
tissues into distinct domains. It has been shown that these tissues
have a 'memory' of previous exposure to Shh.
In neural tissue, this hysteresis is regulated by a homeodomain (HD)
feedback circuit that amplifies Shh signaling. In this circuit,
expression of Gli transcription factors, the executors of the Shh
pathway, is suppressed. Glis are processed to repressor forms (GliR)
in the absence of Shh, but in the presence of Shh, a proportion of
Glis are maintained as full-length proteins allowed to translocate to
the nucleus, where they act as activators (GliA) of transcription. By
reducing Gli expression then, the HD transcription factors reduce the
total amount of Gli (GliT), so a higher proportion of GliT can be
stabilized as GliA for the same concentration of Shh.
Immunology
============
There is some evidence that T cells exhibit hysteresis in that it
takes a lower signal threshold to activate T cells that have been
previously activated. Ras activation is required for downstream
effector functions of activated T cells. 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
==============
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
========================
Lung hysteresis is evident when observing the compliance of a lung on
inspiration versus expiration. The difference in compliance
(�volume/�pressure) is due to the additional energy required to
overcome surface tension forces during inspiration to recruit and
inflate additional alveoli.
The transpulmonary pressure vs Volume curve of inhalation is different
from the Pressure vs Volume curve of exhalation, the difference being
described as hysteresis. Lung volume at any given pressure during
inhalation is less than the lung volume at any given pressure during
exhalation.
Voice and speech physiology
=============================
A hysteresis effect may be observed in voicing onset versus offset.
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
==========================
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 spruce budworm outbreaks and behavioral-effects on disease
transmission.
In economics
======================================================================
Economic systems can exhibit hysteresis. For example, export
performance is subject to strong hysteresis effects: because of the
fixed transportation costs it may take a big push to start a country's
exports, but once the transition is made, not much may be required to
keep them going.
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 equilibrium wage level, where
the supply and demand of workers would match. This causes hysteresis:
the unemployment becomes permanently higher after negative shocks.
Permanently higher unemployment
=================================
The idea of hysteresis is used extensively in the area of labor
economics, specifically with reference to the unemployment rate.
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 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 NAIRU). This occurs
first because inflationary expectations are "sticky" downward due to
wage and price rigidities (and so adapt slowly over time rather than
being approximately correct as in theories of 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 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.
However, the hysteresis hypothesis suggests such training programs are
aided by persistently high demand for products (perhaps with incomes
policies to avoid increased inflation), which reduces the transition
costs out of unemployment and into paid employment easier.
Game theory
=============
Hysteresis occurs in applications of game theory to economics, in
models with product quality, agent honesty or corruption of various
institutions. Slightly different initial conditions can lead to
opposite outcomes and resulting stable good and bad equilibria.
Models of hysteresis
======================
Each subject that involves hysteresis has models that are specific to
the subject. In addition, there are models that capture general
features of many systems with hysteresis. An example is the Preisach
model of hysteresis, which represents a hysteresis nonlinearity as a
linear superposition of square loops called non-ideal relays. 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 Lapshin model. Along with the classical
loop, substitution of trapezoidal or triangle pulses instead of the
harmonic functions allows piecewise-linear hysteresis loops frequently
used in discrete automatics to be built in the model. There is an
implementation of the hysteresis model in R programming language
(package Hysteresis).
The Bouc-Wen model of hysteresis is often used to describe non-linear
hysteretic systems. It was introduced by Bouc and extended by Wen, 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 torsional response of
hysteretic systems two- and three-dimensional continua, and soil
liquefaction among others. The Bouc-Wen model and its
variants/extensions have been used in applications of structural
control, in particular in the modeling of the behaviour of
magnetorheological dampers, 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.. 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. BWBN model has been widely used in a wide spectrum of
applications and have been incorporated in several software codes such
as OpenSees.
Energy
========
When hysteresis occurs with extensive and intensive variables, the
work done on the system is the area under the hysteresis graph.
See also
======================================================================
*Backlash (engineering)
*Bean's critical state model
*Black box
*Deadband
*Fuzzy control system
*Hysteresivity
*Markov property
*Path dependence
*Path dependence (physics)
*Remanence
Further reading
======================================================================
*
*
*
*
*
* Originally published as Volume III/3 of 'Handbuch der Physik' in
1965.
*
*
External links
======================================================================
* [
http://www.ramehart.com/contactangle.htm Overview of contact angle
Hysteresis]
* [
http://sourceforge.net/projects/hysteresis/ Preisach model of
hysteresis - Matlab codes developed by Zs. Szabó]
* [
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/hyst.html
Hysteresis]
*
[
http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html
What's hysteresis?]
*
[
https://web.archive.org/web/20051102025906/http://euclid.ucc.ie/hysteresis/
Dynamical systems with hysteresis] (interactive web page)
* [
http://magneticslab.ua.edu/magnetation-reversal.html Magnetization
reversal app (coherent rotation)]
*
[
https://web.archive.org/web/20080327034229/http://www.madphysics.com/exp/hyster
esis_and_rubber_bands.htm
Elastic hysteresis and rubber bands]
License
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Original Article:
http://en.wikipedia.org/wiki/Hysteresis
