Author
Abstract
Recent computer simulation results [Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation ε≡D/(T0λ)=1 between the diffusion D and mobility λ coefficients when the temperature of the gas T is replaced by the temperature of the impurity T0 in the usual Einstein relation. This problem is analyzed in this paper by solving analytically the Boltzmann–Lorentz equation from the Chapman–Enskog method. The gas is heated by the action of an external driving force (thermostat) which does work to compensate for the collisional loss of energy. Two types of thermostats are considered: (a) a deterministic force proportional to the particle velocity (Gaussian thermostat), and (b) a white noise external force (stochastic thermostat). The diffusion and mobility coefficients are given in terms of the solutions of two linear integral equations, which are approximately solved up to the second order in a Sonine polynomial expansion. The results show that the violation of the Einstein relation (ε≠1) is only due to the non-Maxwellian behavior of the impurity velocity distribution function (absence of the Gibbs state). At a quantitative level, the kinetic theory results also show that the deviation of ε from 1 is more significant in the case of the Gaussian thermostat than in the case of the stochastic one, in which case the deviation of the Einstein relation is in general smaller than 1%. This conclusion agrees quite well with the results found in computer simulations.
Suggested Citation
Garzó, Vicente, 2004.
"On the Einstein relation in a heated granular gas,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 105-126.
Handle:
RePEc:eee:phsmap:v:343:y:2004:i:c:p:105-126
DOI: 10.1016/j.physa.2004.05.032
Download full text from publisher
As the access to this document is restricted, you may want to
for a different version of it.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:343:y:2004:i:c:p:105-126. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.