formulasearchengine - User contributions [en]

Chemical transport reaction

2014-12-29T17:12:43Z

86.173.182.223: /* Halogen lamp */

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Uranyl

2014-12-24T15:44:05Z

86.173.48.191: Corrected false absolute statement.

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History of electromagnetic theory

2014-02-23T10:21:29Z

86.173.146.3: /* See also */ + Biot-Savart law

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Savart

2014-02-23T09:51:08Z

86.173.146.3: ce/tweak dab header

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Contributions of Leonhard Euler to mathematics

2014-02-19T16:21:06Z

86.173.146.3: /* Applied mathematics */ + useful redirect-style link

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Talk:Euler's identity

2014-02-19T15:57:17Z

86.173.146.3: /* "Attribution" vs. "History" */ new section

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Cost of capital

2013-11-27T19:34:59Z

86.173.188.179: /* Weighted average cost of capital */

{{Refimprove|date=January 2007}}
{{Star formation}}
The '''Kelvin–Helmholtz mechanism''' is an [[astronomy|astronomical]] process that occurs when the surface of a [[star]] or a [[planet]] cools. The cooling causes the pressure to drop and the star or planet shrinks as a result. This compression, in turn, heats up the core of the star/planet. This mechanism is evident on [[Jupiter]] and [[Saturn]] and on [[brown dwarf]]s whose central temperatures are not high enough to undergo [[nuclear fusion]]. It is estimated that Jupiter radiates more energy through this mechanism than it receives from the Sun, but Saturn might not.<ref>{{cite book | title = Giant Planets of Our Solar System: Atmospheres, Composition, and Structure | author = Patrick G. J. Irwin | publisher = Springer | year = 2003 | isbn = 3-540-00681-8 | url = http://books.google.com/books?id=p8wCsJweUb0C&pg=PA63&dq=%22kelvin+helmholtz+mechanism%22}}</ref>

The mechanism was originally proposed by [[William Thomson, 1st Baron Kelvin|Kelvin]] and [[Hermann von Helmholtz|Helmholtz]] in the late 19th century to explain the source of energy of the [[Sun]]. By the mid-19th century, [[conservation of energy]] had been accepted, and one consequence of this law of physics is that the Sun must have some energy source to continue to shine. Because nuclear reactions were unknown, the main candidate for the source of solar energy was gravitational contraction.

However, it soon was recognized by Sir [[Arthur Eddington]] and others that the total amount of energy available via this mechanism only allowed for the Sun to shine for millions of years rather than the billions of years that the geological and biological evidence suggested for the age of the Earth. (Kelvin himself had argued that the earth was millions, not billions, of years old.) The true source of the Sun's energy remained uncertain until the 1930s in which it was shown by [[Hans Bethe]] to be [[nuclear fusion]].

== Power generated by a Kelvin–Helmholtz contraction ==

It was theorised that the [[potential energy|gravitational potential energy]] from the contraction of the Sun could be its source of power. To calculate the total amount of energy that would be released by the Sun in such a mechanism (assuming uniform [[density]]), it was approximated to a perfect sphere made up of [[concentric]] shells. The gravitational potential energy could then be found as the integral over all the shells from the centre to its outer radius.

Gravitational potential energy from [[Newtonian mechanics]] is defined as:

:<math>U = -\frac{Gm_1m_2}{r}</math>

Where G is the [[gravitational constant]], and the two masses in this case are that of the thin shells of width dr, and the contained mass within radius r as one integrates between zero and the radius of the total sphere. This gives:

:<math>U = -G\int_0^R \frac{m(r) 4 \pi r^2 \rho}{r}\, dr</math>

Where R is the outer radius of the sphere, and m(r) is the mass contained within the radius r. Changing m(r) into a product of volume and density to satisfy the integral:

:<math>U = -G\int_0^R \frac{4 \pi r^3 \rho 4 \pi r^2 \rho}{3r}\, dr = -\frac{16}{15}G \pi^2 \rho^2 R^5</math>

Recasting in terms of the mass of the sphere gives the final answer:

:<math>U = -\frac{3M^2G}{5R}</math>

While uniform density is not correct, one can get a rough order of magnitude estimate of the expected age of our star by inserting known values for the mass and radius of the Sun, and then dividing by the known [[luminosity]] of the Sun. Note this will involve another approximation, as the power output of the Sun has not always been constant.

:<math>\frac{U}{L_\bigodot} \approx \frac{2.3 \times 10^{41}\ \mathrm{J}}{4 \times 10^{26}\ \mathrm{W}} \approx 18,000,000\ \mathrm{years}</math>

Where L is the luminosity of the Sun. While giving enough power for considerably longer than many other physical methods, such as [[electrochemical potential|electrochemical energy]], this value was clearly still not long enough due to geological and biological evidence that the Earth was billions of years old. It was eventually discovered that [[nuclear fusion|thermonuclear]] energy was responsible for the power output and long lifetimes of stars.

<ref>
{{Cite web
| author = R. Pogge
| title = The Kelvin-Helmholtz Mechanism
| work = Lecture 12: As Long as the Sun Shines
| publisher = Ohio State University
| date = 2006-01-15
| url = http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit2/sunshine.html
| accessdate = 2009-11-05
}}</ref>

==References==
{{reflist}}

{{DEFAULTSORT:Kelvin-Helmholtz Mechanism}}
[[Category:Astrophysics]]
[[Category:Stellar evolution]]
[[Category:Effects of gravitation]]

Clock hypothesis

2012-12-22T15:34:32Z

86.173.44.237: Clarified inclusion of clock hypothesis: any number of null hypotheses were not *explicitly* included

{{about|statistics|mathematical and computer representation of objects|Solid modeling}}

In [[statistics]], a '''parametric model''' or '''parametric family''' or '''finite-dimensional model''' is a family of [[probability distribution|distribution]]s that can be described using a finite number of [[parameter]]s. These parameters are usually collected together to form a single ''k''-dimensional ''parameter vector'' ''θ'' = (''θ''1, ''θ''2, …, ''θ''''k'').

Parametric models are contrasted with the [[semiparametric model|semi-parametric]], [[semi-nonparametric model|semi-nonparametric]], and [[non-parametric model]]s, all of which consist of an infinite set of “parameters” for description. The distinction between these four classes is as follows:{{Citation needed|date=October 2010}}
* in a “''parametric''” model all the parameters are in finite-dimensional parameter spaces;
* a model is “''non-parametric''” if all the parameters are in infinite-dimensional parameter spaces;
* a “''semi-parametric''” model contains finite-dimensional parameters of interest and infinite-dimensional [[nuisance parameter]]s;
* a “''semi-nonparametric''” model has both finite-dimensional and infinite-dimensional unknown parameters of interest.

Some statisticians believe that the concepts “parametric”, “non-parametric”, and “semi-parametric” are ambiguous.<ref>{{harvnb|LeCam|2000}}, ch.7.4</ref> It can also be noted that the set of all probability measures has [[cardinality]] of [[Continuum (set theory)|continuum]], and therefore it is possible to parametrize any model at all by a single number in (0,1) interval.<ref>{{harvnb|Bickel|1998|page=2}}</ref> This difficulty can be avoided by considering only “smooth” parametric models.

==Definition==
{{inline|section|date=May 2012}}
A '''parametric model''' is a collection of [[probability distribution]]s such that each member of this collection, ''Pθ'', is described by a finite-dimensional parameter ''θ''. The set of all allowable values for the parameter is denoted Θ ⊆ '''R'''''k'', and the model itself is written as
: <math>
\mathcal{P} = \big\{ P_\theta\ \big|\ \theta\in\Theta \big\}.
</math>
When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding [[probability density function]]s:
: <math>
\mathcal{P} = \big\{ f_\theta\ \big|\ \theta\in\Theta \big\}.
</math>
The parametric model is called [[identifiable]] if the mapping ''θ'' ↦ ''Pθ'' is invertible, that is there are no two different parameter values ''θ''1 and ''θ''2 such that ''P''''θ''1 = ''P''''θ''2.

===Examples===
<ul>
<li> The [[Poisson distribution|Poisson family]] of distributions is parametrized by a single number ''λ'' > 0:
: <math>
\mathcal{P} = \Big\{\ p_\lambda(j) = \tfrac{\lambda^j}{j!}e^{-\lambda},\ j=0,1,2,3,\dots \ \Big|\ \lambda>0 \ \Big\},
</math>
where ''pλ'' is the [[probability mass function]]. This family is an [[exponential family]].

<li> The [[Normal distribution|normal family]] is parametrized by ''θ'' = (''μ'',''σ''), where ''μ'' ∈ '''R''' is a location parameter, and ''σ'' > 0 is a scale parameter. This parametrized family is both an [[exponential family]] and a [[location-scale family]]:
: <math>
\mathcal{P} = \Big\{\ f_\theta(x) = \tfrac{1}{\sqrt{2\pi}\sigma} e^{ -\frac{1}{2\sigma^2}(x-\mu)^2 }\ \Big|\ \mu\in\mathbb{R}, \sigma>0 \ \Big\}.
</math>

<li> The [[Weibull distribution|Weibull translation model]] has three parameters ''θ'' = (''λ'', ''β'', ''μ''):
: <math>
\mathcal{P} = \Big\{\
f_\theta(x) = \tfrac{\beta}{\lambda}
\left(\tfrac{x-\mu}{\lambda}\right)^{\beta-1}\!
\exp\!\big(\!-\!\big(\tfrac{x-\mu}{\lambda}\big)^\beta \big)\,
\mathbf{1}_{\{x>\mu\}}
\ \Big|\
\lambda>0,\, \beta>0,\, \mu\in\mathbb{R}
\ \Big\}.
</math>
This model is '''not''' regular (see definition below) unless we restrict ''β'' to lie in the interval (2, +∞).
</ul>

==Regular parametric model==

Let ''μ'' be a fixed [[σ-finite measure]] on a [[probability space]] (Ω, ℱ), and <math>\scriptstyle \mathcal{M}_\mu</math> the collection of all probability measures [[measure domination|dominated]] by ''μ''. Then we will call <math style="position:relative;top:-.2em">\mathcal{P}\!=\!\{ P_\theta|\, \theta\in\Theta \} \subseteq \mathcal{M}_\mu</math> a '''regular parametric model''' if the following requirements are met:<ref>{{harvnb|Bickel|1998|page=12}}</ref>
<ol>
<li> Θ is an [[open set|open subset]] of '''R'''''k''.
<li> The map
: <math>\theta\mapsto s(\theta)=\sqrt{dP_\theta/d\mu}</math>
from Θ to [[L2_space#lp_spaces|''L''2(''μ'')]] is [[Fréchet derivative|Fréchet differentiable]]: there exists a vector <math style="position:relative;top:-.3em">\dot{s}(\theta) = (\dot{s}_1(\theta),\,\ldots,\,\dot{s}_k(\theta))</math> such that
: <math>
\lVert s(\theta+h) - s(\theta) - \dot{s}(\theta)'h \rVert = o(|h|)\ \ \text{as }h \to 0,
</math>
where ′ denotes matrix [[transpose]].
<li> The map <math style="position:relative;top:-.2em">\theta\mapsto\dot{s}(\theta)</math> (defined above) is [[continuous function|continuous]] on Θ.
<li> The ''k×k'' [[Fisher information matrix]]
: <math>I(\theta) = 4\int \dot{s}(\theta)\dot{s}(\theta)'d\mu</math>
is [[invertible matrix|non-singular]].
</ol>

===Properties===
<ul>
<li> Sufficient conditions for regularity of a parametric model in terms of ordinary differentiability of the density function ƒ''θ'' are following:<ref>{{harvnb|Bickel|1998}}, p.13, prop.2.1.1</ref>
<ol type="i">
<li>The density function ƒ''θ''(''x'') is continuously differentiable in ''θ'' for ''μ''-almost all ''x'', with gradient ∇ƒ''θ''.
<li> The score function
: <math>
z_\theta = \frac{\nabla f_\theta}{f_\theta} \cdot \mathbf{1}_{\{f_\theta>0\}}
</math>
belongs to the space [[L2_space#lp_spaces|''L''²(''Pθ'')]] of square-integrable functions with respect to the measure ''Pθ''.
<li> The Fisher information matrix ''I''(''θ''), defined as
: <math>
I_\theta = \int \!z_\theta z_\theta' \,dP_\theta
</math>
is nonsingular and continuous in ''θ''.
</ol>
If conditions (i)−(iii) hold then the parametric model is regular.

<li>[[Local asymptotic normality]].

<li>If the regular parametric model is identifiable then there exists a uniformly <math>\scriptstyle \sqrt{n}</math>-consistent and efficient estimator of its parameter ''θ''.<ref>{{harvnb|Bickel|1998}}, Theorems 2.5.1, 2.5.2</ref>
</ul>

== See also ==

* [[Statistical model]]
* [[Parametric family]]
* [[Parametrization]] (i.e., [[coordinate system]])
* [[Parsimony]] (with regards to the trade-off of many or few parameters in data fitting)

==Notes==
{{Reflist}}

==References==

{{refbegin}}
* {{cite book
| author = Bickel, Peter J. and Doksum, Kjell A.
| title = Mathematical Statistics: Basic and Selected Topics, Volume 1.
| volume =
| edition = Second (updated printing 2007)
| year = 2001
| publisher = Pearson Prentice-Hall
}}
* {{cite book
| authors = Bickel, Peter J.; Klaassen, Chris A.J.; Ritov, Ya’acov; Wellner Jon A.
| title = Efficient and adaptive estimation for semiparametric models
| publisher = Springer: New York
| year = 1998
| isbn = 0-387-98473-9
| ref = CITEREFBickel1998
}}
* {{cite book
| last = Davidson
| first = A.C.
| title = Statistical Models
| publisher = Cambridge University Press
| year = 2003
}}
* {{cite book
| author = [[David Freedman (statistician)|Freedman, David A.]]
| title = Statistical Models: Theory and Practice
| publisher = [http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521671057 Cambridge University Press]
| isbn = 978-0-521-67105-7
| year = 2009
| edition = Second
}}
* {{cite book
| author = [[Lucien Le Cam|Le Cam, Lucien]]
| coauthors = Lo Yang, Grace
| title = Asymptotics in statistics: some basic concepts
| year = 2000
| publisher = Springer
| isbn = 0-387-95036-2
| ref = CITEREFLeCam2000
}}
* {{cite book
| author = [[Erich Leo Lehmann|Lehmann, Erich]]
| title = Theory of Point Estimation
| year = 1983
}}
* {{cite book
| author = [[Erich Leo Lehmann|Lehmann, Erich]]
| title = Testing Statistical Hypotheses
| year = 1959
}}
* {{cite book
| author = Liese, Friedrich and Miescke, Klaus-J.
| title = Statistical Decision Theory: Estimation, Testing, and Selection
| year = 2008
| publisher = Springer
}}
* {{cite book|title=Parametric Statistical Theory | last1=Pfanzagl | first1=Johann
|authorlink= 
|last2=with the assistance of R. Hamböker
|year=1994|publisher=Walter de Gruyter
|isbn=3-11-013863-8
}} {{MR|1291393}}

{{refend}}

{{DEFAULTSORT:Parametric Model}}
[[Category:Statistical theory]]
[[Category:Statistical models]]

Biaxial nematic

2012-12-19T16:27:26Z

86.173.16.116:

'''Rock magnetism''' is the study of the [[magnetic]] properties of [[Rock (geology)|rocks]], [[sediments]] and [[soils]]. The field arose out of the need in [[paleomagnetism]] to understand how rocks record the Earth's magnetic field. This [[remanence]] is carried by minerals, particularly certain strongly magnetic minerals like [[magnetite]] (the main source of magnetism in [[lodestone]]). An understanding of [[remanence]] helps paleomagnetists to develop methods for measuring the ancient magnetic field and correct for effects like sediment [[compaction (geology)|compaction]] and [[metamorphism]]. Rock magnetic methods are used to get a more detailed picture of the source of distinctive striped pattern in marine [[magnetic anomalies]] that provides important information on [[plate tectonics]]. They are also used to interpret terrestrial magnetic anomalies in [[magnetic surveys]] as well as the strong crustal magnetism on [[Mars]].

Strongly magnetic minerals have properties that depend on the size, shape, defect structure and concentration of the minerals in a rock. Rock magnetism provides non-destructive methods for analyzing these minerals such as [[magnetic hysteresis]] measurements, temperature-dependent [[remanence]] measurements, [[Mössbauer spectroscopy]], [[ferromagnetic resonance]] and so on. With such methods, rock magnetists can measure the effects of past climate change and human impacts on the mineralogy (see [[environmental magnetism]]). In sediments, a lot of the magnetic [[remanence]] is carried by minerals that were created by [[magnetotactic bacteria]], so rock magnetists have made significant contributions to [[biomagnetism]].

== History ==

Until the 20th century, the study of the Earth's field ([[geomagnetism]] and [[paleomagnetism]]) and of magnetic materials (especially [[ferromagnetism]]) developed separately.

Rock magnetism had its start when scientists brought these two fields together in the laboratory.<ref name=Dunlop>{{Harvnb|Dunlop|Özdemir|1997}}</ref> Koenigsberger (1938), Thellier (1938) and Nagata (1943) investigated the origin of [[remanence]] in [[igneous rock]]s.<ref name=Dunlop/> By heating rocks and archeological materials to high temperatures in a magnetic field, they gave the materials a [[thermoremanent magnetization]] (TRM), and they investigated the properties of this magnetization. Thellier developed a series of conditions (the [[Thellier laws]]) that, if fulfilled, would allow the determination of the intensity of the ancient magnetic field to be determined using the [[Thellier-Thellier method]]. In 1949, [[Louis Néel]] developed a theory that explained these observations, showed that the [[Thellier laws]] were satisfied by certain kinds of [[single domain (magnetic)|single-domain]] magnets, and introduced the concept of blocking of TRM.<ref>{{Harvnb|Néel|1949}}</ref>

When paleomagnetic work in the 1950s lent support to the theory of [[continental drift]],<ref>{{Harvnb|Irving|1956}}</ref><ref>{{Harvnb|Runcorn|1956}}</ref> skeptics were quick to question whether rocks could carry a stable [[remanence]] for geological ages.
<ref>For example, [[Sir Harold Jeffreys]], in his influential textbook ''The Earth'', had the following to say about it:
<blockquote>
"When I last did a magnetic experiment (about 1909) we were warned against careless handling of permanent magnets, and the magnetism was liable to change without much carelessness. In studying the magnetism of rocks the specimen has to be broken off with a geological hammer and then carried to the laboratory. It is supposed that in the process its magnetism does not change to any important extent, and though I have often asked how this comes to be the case I have never received any answer.{{harvnb|Jeffreys|1959|p=371}}
</blockquote></ref>
Rock magnetists were able to show that rocks could have more than one component of remanence, some soft (easily removed) and some very stable. To get at the stable part, they took to "cleaning" samples by heating them or exposing them to an alternating field. However, later events, particularly the recognition that many North American rocks had been pervasively remagnetized in the [[Paleozoic]],<ref>{{Harvnb|McCabe|Elmore|1989}}</ref> showed that a single cleaning step was inadequate, and paleomagnetists began to routinely use stepwise demagnetization to strip away the remanence in small bits.

== Fundamentals ==
=== Types of magnetic order ===

The contribution of a mineral to the total magnetism of a rock depends strongly on the type of magnetic order or disorder. Magnetically disordered minerals ([[diamagnets]] and [[paramagnets]]) contribute a weak magnetism and have no [[remanence]]. The more important minerals for rock magnetism are the minerals that can be magnetically ordered, at least at some temperatures. These are the [[ferromagnets]], [[ferrimagnets]] and certain kinds of [[antiferromagnets]]. These minerals have a much stronger response to the field and can have a [[remanence]].

==== Diamagnetism ====

[[Diamagnetism]] is a magnetic response shared by all substances. In response to an applied magnetic field, [[electrons]] precess (see [[Larmor precession]]), and by [[Lenz's law]] they act to shield the interior of a body from the [[magnetic field]]. Thus, the moment produced is in the opposite direction to the field and the [[magnetic susceptibility|susceptibility]] is negative. This effect is weak but independent of temperature. A substance whose only magnetic response is diamagnetism is called a diamagnet.

==== Paramagnetism ====

[[Paramagnetism]] is a weak positive response to a [[magnetic field]] due to rotation of electron [[spin (physics)|spins]]. Paramagnetism occurs in certain kinds of iron-bearing minerals because the iron contains an unpaired electron in one of their shells (see [[Hund's rules]]). Some are paramagnetic down to absolute zero and their [[susceptibility]] is inversely proportional to the temperature (see [[Curie's law]]); others are magnetically ordered below a critical temperature and the susceptibility increases as it approaches that temperature (see [[Curie-Weiss law]]).

==== Ferromagnetism ====

Collectively, strongly magnetic materials are often referred to as [[ferromagnets]]. However, this magnetism can arise as the result of more than one kind of magnetic order. In the strict sense, [[ferromagnetism]] refers to magnetic ordering where neighboring electron spins are aligned by the [[exchange interaction]]. The classic ferromagnet is [[iron]]. Below a critical temperature called the [[Curie temperature]], ferromagnets have a [[spontaneous magnetization]] and there is [[hysteresis]] in their response to a changing magnetic field. Most importantly for rock magnetism, they have [[remanence]], so they can record the Earth's field.

[[Iron]] does not occur widely in its pure form. It is usually incorporated into [[iron oxides]], [[iron(III) oxide-hydroxide|oxyhydroxides]] and [[iron sulfide|sulfides]]. In these compounds, the iron atoms are not close enough for direct exchange, so they are coupled by indirect exchange or superexchange. The result is that the crystal lattice is divided into two or more sublattices with different moments.<ref name=Dunlop/>

==== Ferrimagnetism ====

[[Ferrimagnets]] have two sublattices with opposing moments. One sublattice has a larger moment, so there is a net unbalance. [[Magnetite]], the most important of the magnetic minerals, is a ferrimagnet. Ferrimagnets often behave like [[ferromagnets]], but the temperature dependence of their [[spontaneous magnetization]] can be quite different. [[Louis Néel]] identified four types of temperature dependence, one of which involves a reversal of the magnetization. This phenomenon played a role in controversies over marine [[magnetic anomalies]].

==== Antiferromagnetism ====

[[Antiferromagnets]], like ferrimagnets, have two sublattices with opposing moments, but now the moments are equal in magnitude. If the moments are exactly opposed, the magnet has no [[remanence]]. However, the moments can be tilted ([[spin canting]]), resulting in a moment nearly at right angles to the moments of the sublattices. [[Hematite]] has this kind of magnetism.

== Magnetic mineralogy ==
{{Main|Magnetic mineralogy}}

== Types of remanence ==

Magnetic [[remanence]] is often identified with a particular kind of remanence that is obtained after exposing a magnet to a field at room temperature. However, the Earth's field is not large, and this kind of remanence would be weak and easily overwritten by later fields. A central part of rock magnetism is the study of magnetic remanence, both as [[natural remanent magnetization]] (NRM) in rocks obtained from the field and remanence induced in the laboratory. Below are listed the important natural remanences and some artificially induced kinds.

=== Thermoremanent magnetization (TRM) ===
{{Main|Thermoremanent magnetization}}
When an [[igneous]] rock cools, it acquires a ''thermoremanent magnetization (TRM)'' from the Earth's field. TRM can be much larger than it would be if exposed to the same field at room temperature (see [[remanence#Isothermal remanence|isothermal remanence]]). This remanence can also be very stable, lasting without significant change for millions of years. TRM is the main reason that [[paleomagnetists]] are able to deduce the direction and magnitude of the ancient Earth's field.<ref>{{Harvnb|Stacey|Banerjee|1974}}</ref>

If a rock is later re-heated (as a result of burial, for example), part or all of the TRM can be replaced by a new remanence. If it is only part of the remanence, it is known as ''partial thermoremanent magnetization (pTRM)''. Because numerous experiments have been done modeling different ways of acquiring remanence, pTRM can have other meanings. For example, it can also be acquired in the laboratory by cooling in zero field to a temperature <math>T_1</math> (below the [[Curie temperature]]), applying a magnetic field and cooling to a temperature <math>T_2</math>, then cooling the rest of the way to room temperature in zero field.

The standard model for TRM is as follows. When a mineral such as [[magnetite]] cools below the [[Curie temperature]], it becomes [[ferromagnetic]] but is not immediately capable of carrying a remanence. Instead, it is [[superparamagnetic]], responding reversibly to changes in the magnetic field. For remanence to be possible there must be a strong enough [[magnetic anisotropy]] to keep the magnetization near a stable state; otherwise, [[thermal fluctuations]] make the [[magnetic moment]] wander randomly. As the rock continues to cool, there is a critical temperature at which the magnetic anisotropy becomes large enough to keep the moment from wandering: this temperature is called the ''blocking temperature'' and referred to by the symbol <math>T_B</math>. The magnetization remains in the same state as the rock is cooled to room temperature and becomes a thermoremanent magnetization.

=== Chemical (or crystallization) remanent magnetization (CRM) ===
Magnetic grains may precipitate from a circulating solution, or be formed during chemical reactions, and may record the direction of the magnetic field at the time of mineral formation. The field is said to be recorded by ''chemical remanent magnetization (CRM)''. The mineral recording the field commonly is hematite, another iron oxide. Redbeds, clastic sedimentary rocks (such as sandstones) that are red primarily because of hematite formation during or after sedimentary diagenesis, may have useful CRM signatures, and magnetostratigraphy can be based on such signatures.

=== Depositional remanent magnetization (DRM) ===
Magnetic grains in sediments may align with the magnetic field during or soon after deposition; this is known as detrital remnant magnetization (DRM). If the magnetization is acquired as the grains are deposited, the result is a depositional detrital remanent magnetization (dDRM); if it is acquired soon after deposition, it is a ''post-depositional detrital remanent magnetization (pDRM)''.

=== Viscous remanent magnetization ===
{{Main|Viscous remanent magnetization}}

''Viscous remanent magnetization (VRM)'', also known as viscous magnetization, is [[remanence]] that is acquired by [[ferromagnetic]] [[minerals]] by sitting in a [[magnetic field]] for some time. The [[natural remanent magnetization]] of an [[igneous rock]] can be altered by this process. To remove this component, some form of stepwise demagnetization must be used.<ref name=Dunlop/>

== Applications of rock magnetism ==
* [[magnetic anomaly|magnetic anomalies]]
* [[magnetostratigraphy]]
* [[Paleomagnetic secular variation]]
* [[paleointensity]]
* [[plate tectonics]]
* [[biomagnetism]]
* [[environmental magnetism]]
* [[magnetic fabrics]]

==See also==
*{{books-inline|Geomagnetism}}

== Notes ==
{{Reflist|2}}

== References ==
{{Refbegin}}
*{{cite book
|last1 = Dunlop
|first1 = David J.
|last2 = Özdemir
|first2 = Özden
|title = Rock Magnetism: Fundamentals and Frontiers
|publisher = [[Cambridge Univ. Press]]
|year = 1997
|isbn = 0-521-32514-5
|ref = harv
}}
*{{Cite book
| last = Hunt
| first = Christopher P.
| last2 = Moskowitz
| first2 = Bruce P.
| contribution = Magnetic properties of rocks and minerals
| year = 1995
| editor-last = Ahrens
| editor-first = T. J.
| title = Rock Physics and Phase Relations: A Handbook of Physical Constants
| publication-place = Washington, DC
| publisher = American Geophysical Union
| volume = 3
| pages = 189–204
| ref = harv
| postscript = 
}}
*{{cite journal
|doi = 10.1007/BF02629944
|last = Irving
|first = E.
|year = 1956
|title = Paleomagnetic and palaeoclimatological aspects of polar wandering
|journal = Geofis. Pura. Appl.
|volume = 33
|issue = 1
|pages = 23–41
|ref = harv
|bibcode = 1956GeoPA..33...23I }}
*{{cite book
|last = Jeffreys
|first = Sir Harold
|title = The earth: its origin, history, and physical constitution
|publisher = [[Cambridge Univ. Press]]
|year = 1959
|isbn = 0-521-20648-0
|ref = harv
}}
*{{cite journal
|doi = 10.1029/RG027i004p00471
|last1 = McCabe
|first1 = C.
|last2 = Elmore
|first2 = R. D.
|year = 1989
|title = The occurrence and origin of Late Paleozoic remagnetization in the sedimentary rocks of North America
|journal = [[Reviews of Geophysics]]
|volume = 27
|issue = 4
|pages = 471–494
|ref = harv
|bibcode = 1989RvGeo..27..471M }}
*{{cite journal
|last = Néel
|first = Louis
|year = 1949
|title = Théorie du traînage magnétique des ferromagnétiques en grains fins avec application aux terres cuites
|journal = Ann. Géophys.
|volume = 5
|pages = 99–136
|ref = harv
}}
*{{cite journal
|last = Runcorn
|first = S. K.
|year = 1956
|title = Paleomagnetic comparisons between Europe and North America
|journal = Proc. Geol. Assoc. Canada
|volume = 8
|pages = 77–85
|ref = harv
}}
*{{cite book
|last1 = Stacey
|first1 = Frank D.
|last2 = Banerjee
|first2 = Subir K.
|title = The Physical Principles of Rock Magnetism
|publisher = [[Elsevier]]
|year = 1974
|isbn = 0-444-41084-8
|ref = harv
}}
{{Refend}}

==External links==
* [http://www.irm.umn.edu/IRM/Home.html Institute for Rock Magnetism]
* [http://forc.ucdavis.edu/forc.html UC Davis FORC Group, Introduction to FORC Diagrams]

{{DEFAULTSORT:Rock Magnetism}}
[[Category:Articles with inconsistent citation formats]]
[[Category:Geology]]
[[Category:Geomagnetism]]
[[Category:Geophysics]]

Brake

2012-08-21T15:50:03Z

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