1,027 research outputs found
Graph quasivarieties
Introduced by C. R. Shallon in 1979, graph algebras establish a useful
connection between graph theory and universal algebra. This makes it possible
to investigate graph varieties and graph quasivarieties, i.e., classes of
graphs described by identities or quasi-identities. In this paper, graph
quasivarieties are characterized as classes of graphs closed under directed
unions of isomorphic copies of finite strong pointed subproducts.Comment: 15 page
Coefficient of tangential restitution for the linear dashpot model
The linear dashpot model for the inelastic normal force between colliding
spheres leads to a constant coefficient of normal restitution,
const., which makes this model very popular for the investigation
of dilute and moderately dense granular systems. For two frequently used models
for the tangential interaction force we determine the coefficient of tangential
restitution , both analytically and by numerical integration of
Newton's equation. Although const. for the linear-dashpot model,
we obtain pronounced and characteristic dependencies of the tangential
coefficient on the impact velocity . The
results may be used for event-driven simulations of granular systems of
frictional particles.Comment: 12 pages, 12 figure
Application of the Gillespie algorithm to a granular intruder particle
We show how the Gillespie algorithm, originally developed to describe coupled
chemical reactions, can be used to perform numerical simulations of a granular
intruder particle colliding with thermalized bath particles. The algorithm
generates a sequence of collision ``events'' separated by variable time
intervals. As input, it requires the position-dependent flux of bath particles
at each point on the surface of the intruder particle. We validate the method
by applying it to a one-dimensional system for which the exact solution of the
homogeneous Boltzmann equation is known and investigate the case where the bath
particle velocity distribution has algebraic tails. We also present an
application to a granular needle in bath of point particles where we
demonstrate the presence of correlations between the translational and
rotational degrees of freedom of the intruder particle. The relationship
between the Gillespie algorithm and the commonly used Direct Simulation Monte
Carlo (DSMC) method is also discussed.Comment: 13 pages, 8 figures, to be published in J. Phys. A Math. Ge
Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery
The coefficient of normal restitution of colliding viscoelastic spheres is
computed as a function of the material properties and the impact velocity. From
simple arguments it becomes clear that in a collision of purely repulsively
interacting particles, the particles loose contact slightly before the distance
of the centers of the spheres reaches the sum of the radii, that is, the
particles recover their shape only after they lose contact with their collision
partner. This effect was neglected in earlier calculations which leads
erroneously to attractive forces and, thus, to an underestimation of the
coefficient of restitution. As a result we find a novel dependence of the
coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure
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