Granular Matter

Lecture course: Introduction to Granular Gases

Homogeneous State of a Granular Gas is Unstable

Granular Gases are dilute systems of particles which collide inelastically.
Being rather simple by their nature, Granular Gases reveal very rich
behaviour: Cluster and vortex formation, characteristic shock waves
and non-Maxwellian velocity distribution may be mentioned as some
representative examples.

My main Publications on Granular Gases

Books:

N.V.Brilliantov and T.Poeschel,
Kinetic Theory of Granular Gases,
Oxford University Press, (2004) in press.

T.Poeschel, and N.V.Brilliantov (Eds.)
Granular Gas Dynamics,
Lecture Notes in Physics, vol. 624, Springer (2003).

Hydrodynamics, Transport Coefficients, Theoretical Methods

N.V.Brilliantov, T. Pöschel,
Hydrodynamics and transport coefficients for Granular Gases,
Phys. Rev. E, 67, (2003), 061304. pdf file

T.Poeschel, and N.V.Brilliantov,
Kinetic Integrals in the Kinetic Theory of dissipative gases,
In: T. Poeschel, N.V. Brilliantov (Eds.) "Granular Gas Dynamics",
Lecture Notes in Physics, vol. 624, Springer (Berlin, 2003), p. 131-162.
pdf file

N.V.Brilliantov and T.Poeschel,
Hydrodynamics of granular gases of viscoelastic particles,
Phil. Trans. R. Soc. Lond. A, 360, (2002) 415-429.

N.V.Brilliantov and T.Poeschel,
Self-diffusion in granular gases,
Phys.Rev. E, 61, (2000) 1716-1721. pdf file

N. V. Brilliantov, T. Poeschel,
Granular Gases with Impact-velocity Dependent Restitution Coefficient,
in "Granular Gases", ed. by S.Luding, and T.Poeschel,
Lecture Notes in Physics Vol. 564, Springer (Berlin, 2000), p. 100.

Velocity Distribution in Granular Gases

N. V. Brilliantov and T. Poeschel,
Deviation from Maxwell Distribution in Granular Gases with Constant Restitution Coefficient.
Phys. Rev. E, 61, (2000) 2809-2812. pdf file

N. V. Brilliantov and T. Poeschel,
Velocity distribution in granular gases of viscoelastic particles,
Phys. Rev. E, 61, (2000) 5573-5587. pdf file

T.Poeschel, N.V. Brilliantov, and T. Schwager,
Violation of Molecular Chaos in dissipative gases,
Int. J. Mod. Phys. C, 13, (2002) 1263-1272.

N.V.Brilliantov and T.Poeschel,
Granular Gases -- the early stage,
in "Coherent Structures in Complex Systems", ed by D. Reguera, L.L. Bonilla, M. Rubi,
Lecture Notes in Physics, Vol.567, Springer (2001) p.408-419

Clustering and pattern formation in Granular Gases

T.Poeschel, N.V. Brilliantov, and T. Schwager,
Long-time behavior of Granular Gases with impact-velocity dependent coefficient of restitution,
Physica A, 325, (2003) 274-283. pdf file

Inelastic Collisions

The theory of a collision of elastic particles was developed by H. Hertz in 1885.
We generalized Hertz's theory for dissipative collisions, using the simplest model
of viscoelastic particles. The generalized collision law allows to derive the main
characteristics of dissipative collisions - the restitution coefficient. It occurs, that
this quantity is not a material parameter, as was assumed previously, but rather
complicated function of elastic and dissipative material constants and of the
impact velocity at a collision.

My main Publications on Inelastic Collisions

Generalization of Hertz's theory

N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Poeschel,
Model for collisions in granular gases
Phys. Rev. E, 53 (1996) 5382-5392. pdf file

N.V.Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Poeschel,
The collisions of particles in granular systems.
Physica A, 231 (1996) 417-424.

J.-M.Hertzsch, F.Spahn, and N.V.Brilliantov,
On low-velocity collisions of viscoelastic particles.
J. de Phys. II France, 5 (1995) 1725 - 1738.

Coefficient of restitution

T. Poeschel and N. V. Brilliantov,
Extremal collision sequences of particles on a line: optimal transmission of kinetic energy,
Phys. Rev. E, 63, (2001) 021505. pdf file

R. Ramírez, T. Poeschel, N. V. Brilliantov, T. Schwager,
Coefficient of restitution of colliding viscoelastic spheres.
Phys. Rev. E, 60, (1999) 4465. pdf file

Rolling Friction

Up to our knowledge there was no first-principle theory which relates the
coefficient of rolling friction to material properties and a size of a rolling body
without any model parameters. We have developed a simple theory
of a rolling of a soft sphere on a hard plane. We observe that rolling motion
may be treated as a "continuing collision". For a simple model of a soft plane
we developed a theory of a rolling of a hard cylinder on a soft plane.

My main Publications on Rolling Friction

N.V.Brilliantov and T.Poeschel,
Rolling friction of a soft sphere on a hard plane.
Europhys. Letters, 42 (1998) 511. pdf file

N. V. Brilliantov, T. Poeschel,
Rolling as a "continuing collision,
Europ. Phys. J. B, 12, (1999) 299. pdf file

T. Poeschel, T. Schwager, and N. V. Brilliantov,
Rolling of a hard cylinder on a viscous plane,
Europ. Phys. J. B, 10, (1999) 169-174. pdf file

Back to my main page