Bleicher at 08:04, 10 May 2021

2021-05-10T08:04:46Z

Tomasik: Created page with "Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for t..."

2018-10-29T21:43:30Z

Created page with "Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for t..."

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Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for the description of fireball expansion in heavy-ion collisions.

← Older revision		Revision as of 08:04, 10 May 2021
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		+	A '''transport coefficient''' <math>\gamma</math> measures how rapidly a perturbed system returns to equilibrium.
		+
		+	The transport coefficients occur in [[transport phenomenon]] with transport laws
		+	<math> {\mathbf{J} {_k}} \, = \, \gamma_k \, \mathbf{X} {_k}</math>
		+	where:
		+	: <math> {\mathbf{J}{_k}} </math> is a flux of the property <math> k </math>
		+	: the transport coefficient <math> \gamma _k </math> of this property <math> k </math>
		+	: <math> {\mathbf{X}{_k}} </math>, the gradient force which acts on the property <math> k </math>.
		+
		+	Transport coefficients can be expressed via a [[Green–Kubo relations\|Green–Kubo relation]]:
		+
		+	:<math>\gamma= \int_0^\infty \langle \dot{A}(t) \dot{A}(0) \rangle \, dt,</math>
		+
		+	where <math>A</math> is an observable occurring in a perturbed Hamiltonian, <math>\langle \cdot \rangle</math> is an ensemble average and the dot above the ''A'' denotes the time derivative.<ref>Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, {{ISBN\|9789810224516}}, p. 80, [https://books.google.com/books?id=FHEh1C4GuZcC&lpg=PA80&dq=ficks%20law%20%22transport%20coefficient%22&pg=PA80#v=onepage&q=ficks%20law%20%22transport%20coefficient%22&f=false Google Books]</ref>
		+	For times <math>t</math> that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized [[Einstein relation (kinetic theory)\|Einstein relation]]:
		+
		+	:<math>2t\gamma=\langle \|A(t)-A(0)\|^2 \rangle.</math>
		+
		+	In general a transport coefficient is a tensor.
		+
	Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for the description of fireball expansion in heavy-ion collisions.		Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for the description of fireball expansion in heavy-ion collisions.
		+
		+
		+	== Examples ==
		+	* [[Diffusion constant]], relates the flux of particles with the negative gradient of the concentration (see [[Fick's laws of diffusion]])
		+	* [[Thermal conductivity]] (see [[Fourier's law]])
		+	* [[Mass transfer coefficient\|Mass transport coefficient]]
		+	* [[Shear viscosity]] <math>\eta = \frac{1}{k_BT V} \int_0^\infty dt \, \langle \sigma_{xy}(0) \sigma_{xy} (t) \rangle</math>, where <math>\sigma</math> is the [[viscous stress tensor]] (see [[Newtonian fluid]])
		+	* [[Electrical conductivity]]
		+
		+	== See also ==
		+	*[[Linear response theory]]
		+	*[[Onsager reciprocal relations]]
		+
		+	== References ==
		+	<references />
		+
		+	[[Category:Thermodynamics]]
		+	[[Category:Statistical mechanics]]

Transport coefficients - Revision history

Bleicher at 08:04, 10 May 2021

Tomasik: Created page with "Transport coefficients, like [https://en.wikipedia.org/wiki/Viscosity shear viscosity] and [https://en.wikipedia.org/wiki/Volume_viscosity bulk viscosity], are important for t..."