Hard spheres

Hard spheres

Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong repulsion that atoms and spherical molecules experience at very close distances.

Formal definition

Hard spheres of diameter sigma are particles with the following pairwise interaction potential:

:V(mathbf{r}_1,mathbf{r}_2)=left{ egin{matrix}0 & mbox{if}quad |mathbf{r}_1-mathbf{r}_2| geq sigma \ infty & mbox{if}quad|mathbf{r}_1-mathbf{r}_2| < sigma end{matrix} ight.

where mathbf{r}_1 and mathbf{r}_2 are the positions of the two particles.

Virial coefficients

The first three virial coefficients for hard spheres can be determined analytically

:

Higher-order ones can be determined numerically using Monte Carlo integration. We list

:A table of virial coefficients for up to eight dimensions can be found on the page [http://www.sklogwiki.org/SklogWiki/index.php/Hard_sphere:_virial_coefficients Hard sphere: virial coefficients] .

Literature

*J. P. Hansen and I. R. McDonald "Theory of Simple Liquids" Academic Press, London (1986)
* [http://www.sklogwiki.org/SklogWiki/index.php/Hard_sphere_model Hard sphere model] page on SklogWiki.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Hard-core-Prozess — Beispiel eines zweidimensionalen Hard core Punktfeldes. Der Mindestabstand zwischen den Punkten wird durch die einander nicht überlappenden Kreise veranschaulicht; der Durchmesser der Kreise entspricht dem Mindestabstand. Ein Hard core Prozess… …   Deutsch Wikipedia

  • Hard rockert — Musique Allégorie évoquant la musique et les instruments La musique est l art consistant à arranger et ordonner sons et silences au cours du temps : le rythme est le support de cette combinaison dans le temps, la hauteur celle de la… …   Wikipédia en Français

  • Celestial spheres — Not to be confused with celestial sphere. For other uses, see Celestial (disambiguation). Geocentric celestial spheres; Peter Apian s Cosmographia (Antwerp, 1539) …   Wikipedia

  • Klerksdorp Spheres — The Klerksdorp Spheres are small, often spherical to disc shaped, objects, which have been collected by miners and rockhounds from 3.0 billion year old pyrophyllite deposits mined by Wonderstone Ltd., near Ottosdal, South Africa. These objects… …   Wikipedia

  • Van der Waals equation — The van der Waals equation is an equation of state for a fluid composed of particles that have a non zero size and a pairwise attractive inter particle force (such as the van der Waals force.) It was derived by Johannes Diderik van der Waals in… …   Wikipedia

  • gas — gasless, adj. /gas/, n., pl. gases, v., gassed, gassing. n. 1. Physics. a substance possessing perfect molecular mobility and the property of indefinite expansion, as opposed to a solid or liquid. 2. any such fluid or mixture of fluids. 3. any… …   Universalium

  • Aggregate (composite) — Aggregate is the component of a composite material used to resist compressive stress. For efficient filling, aggregate should be much smaller than the finished item, but have a wide variety of sizes. For example, the particles of stone used to… …   Wikipedia

  • Molecular dynamics — (MD) is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms. In the most common version, the trajectories of molecules… …   Wikipedia

  • Colloid — Milk is an emulsified colloid of liquid butterfat globules dispersed within a water based solution. A colloid is a substance microscopically dispersed evenly throughout another substance.[1] A colloidal system consists of two separate phases: a… …   Wikipedia

  • Physics — (Greek: physis φύσις), in everyday terms, is the science of matter [R. P. Feynman, R. B. Leighton, M. Sands (1963), The Feynman Lectures on Physics , ISBN 0 201 02116 1 Hard cover. p.1 1 Feynman begins with the atomic hypothesis.] and its motion …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”