Entropy analysis for local structure of granular matter

Authors: Gerasymov O. I.

Year: 2017

Issue: 22

Pages: 102-106

Abstract

We apply phenomenological approach based on statistical mechanical concept in the form of Kirkwood-Buff arguments to describe the structural parameters of 2D binary granular mixture. By use of the scale-invariant model for radial distribution function first introduced in [1], we derive expression for correlational integrals which necessarily include geometrical parameters which characterize the properties of the local structure. In particular, expression for the packing fraction has been obtained analytically. We have also obtained the relation between macroscopic properties, such as entropy excess, and parameters of local structure, namely the packing fraction. Entropy excess and entropy difference for states spanning an interval of η = [0.8175 – 0.8380] has been performed and analyzed by means of contrast mapping. Calculations demonstrate nonmonotonic behavior of the entropy excess and, in particular, shows presence of the minimum of Sexc at η= 0.8209. From the excess entropy difference we estimate the entropy production, associated with the transition between different configurational states with an individual local symmetries. Developed approach (because of the scale invariant character of the model measure of state) has been proposed for use with systems that have an isomorphic morphology of the local structure.

Tags: Entropy; Granular matter; local structure; Statistical mechanics; гранульована матерія; ентропія; локальна структура; статистична механіка

Bibliography

  1. Gerasymov O. I. Scattering of external radiations in statistical systems. Solved models. Odessa: Mayak publishers, 1999. 284 p.
  2. Jaeger H. M., Nagel S. R., Behringer R. P. Rev.Mod. Phys., 1996, no. 68, p. 1259.
  3. Paillusson F., Frenkel D. Phys.Rev. Lett. , 2012, no. 109, p. 2080.
  4. Ribi‘ere Ph., Richard P., Philippe P., Bideau D., Delannay R. On the existence of stationary states during granular compaction. Europ. Phys.J, 2007, no. 22, p. 249.
  5. Daniel I., Harry L. Swinney. Stationary state volume in a granular medium. Phys.Rev.E., 2005, no. 71, p. 1021.
  6. Edwards S. F., Oakeshott R.B.S. Theory of powders. Physica A., 1989, no. 157, p. 1080.
  7. Mehta A., Edwards S. F. Statistical and theoretical physics : Statistical mechanics of powder mixtures. Phys.Rev.Lett., 1989, no. 157, pp. 1091-1100.
  8. Briscoe C., Song C., Wang P., Makse A. Entropy of jammed matter. Phys. Rev. Lett., 2008, no. 101, p. 389.
  9. Asenjo D., Paillusson F., Frenkel D. Numerical Calculation of Granular Entropy.Phys. Rev.Lett., 2014, no. 106, p. 1389.
  10. Blumenfeld R., Jordan J., Sam F. Interdependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems. Phys. Rev. Lett., 2012, no. 109, p. 2304.
  11. Kirkwood J. G., Buff F., Journ.Chem . Phys., 1951, no. 19 p. 1591.
  12. Plimpton S. Fast Parallel Algorithms for Short-Range Molecular Dynamics.J.Comp. Phys., 1995, no. 1 p. 117.
  13. Zhao S., Sidle S., Harry L. Swinney and Matthias Schroeter Correlation between Voronoi volumes in disc packings. EPL., 2008, no. 97 p. 2400.
Download full text (PDF)