25,464 research outputs found
Identification of rolling resistance as a shape parameter in sheared granular media
Using contact dynamics simulations, we compare the effect of rolling
resistance at the contacts in granular systems composed of disks with the
effect of angularity in granular systems composed of regular polygonal
particles. In simple shear conditions, we consider four aspects of the
mechanical behavior of these systems in the steady state: shear strength, solid
fraction, force and fabric anisotropies, and probability distribution of
contact forces. Our main finding is that, based on the energy dissipation
associated with relative rotation between two particles in contact, the effect
of rolling resistance can explicitly be identified with that of the number of
sides in a regular polygonal particle. This finding supports the use of rolling
resistance as a shape parameter accounting for particle angularity and shows
unambiguously that one of the main influencing factors behind the mechanical
behavior of granular systems composed of noncircular particles is the partial
hindrance of rotations as a result of angular particle shape.Comment: Soumis a Physical Review E; Statistical, Nonlinear, and Soft Matter
Physics http://link.aps.org/doi/10.1103/PhysRevE.84.01130
Comparison of the effects of rolling resistance and angularity in sheared granular media
International audienceIn this paper, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. For this purpose, we use contact dynamics simulations. By means of a simple shear numerical device, we investigate the mechanical behavior of these materials in the steady state in terms of shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. We find that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape
Slow relaxation in weakly open vertex-splitting rational polygons
The problem of splitting effects by vertex angles is discussed for
nonintegrable rational polygonal billiards. A statistical analysis of the decay
dynamics in weakly open polygons is given through the orbit survival
probability. Two distinct channels for the late-time relaxation of type
1/t^delta are established. The primary channel, associated with the universal
relaxation of ''regular'' orbits, with delta = 1, is common for both the closed
and open, chaotic and nonchaotic billiards. The secondary relaxation channel,
with delta > 1, is originated from ''irregular'' orbits and is due to the
rationality of vertices.Comment: Key words: Dynamics of systems of particles, control of chaos,
channels of relaxation. 21 pages, 4 figure
On Chaotic Dynamics in Rational Polygonal Billiards
We discuss the interplay between the piece-line regular and vertex-angle
singular boundary effects, related to integrability and chaotic features in
rational polygonal billiards. The approach to controversial issue of regular
and irregular motion in polygons is taken within the alternative deterministic
and stochastic frameworks. The analysis is developed in terms of the
billiard-wall collision distribution and the particle survival probability,
simulated in closed and weakly open polygons, respectively. In the multi-vertex
polygons, the late-time wall-collision events result in the circular-like
regular periodic trajectories (sliding orbits), which, in the open billiard
case are likely transformed into the surviving collective excitations
(vortices). Having no topological analogy with the regular orbits in the
geometrically corresponding circular billiard, sliding orbits and vortices are
well distinguished in the weakly open polygons via the universal and
non-universal relaxation dynamics.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
An n-sided polygonal model to calculate the impact of cyber security events
This paper presents a model to represent graphically the impact of cyber
events (e.g., attacks, countermeasures) in a polygonal systems of n-sides. The
approach considers information about all entities composing an information
system (e.g., users, IP addresses, communication protocols, physical and
logical resources, etc.). Every axis is composed of entities that contribute to
the execution of the security event. Each entity has an associated weighting
factor that measures its contribution using a multi-criteria methodology named
CARVER. The graphical representation of cyber events is depicted as straight
lines (one dimension) or polygons (two or more dimensions). Geometrical
operations are used to compute the size (i.e, length, perimeter, surface area)
and thus the impact of each event. As a result, it is possible to identify and
compare the magnitude of cyber events. A case study with multiple security
events is presented as an illustration on how the model is built and computed.Comment: 16 pages, 5 figures, 2 tables, 11th International Conference on Risks
and Security of Internet and Systems, (CRiSIS 2016), Roscoff, France,
September 201
Connectedness percolation of hard convex polygonal rods and platelets
The properties of polymer composites with nanofiller particles change
drastically above a critical filler density known as the percolation threshold.
Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not
idealized disks and rods but are often modeled as such. Here we investigate the
effect of the shape of the particle cross section on the geometric percolation
threshold. Using connectedness percolation theory and the second-virial
approximation, we analytically calculate the percolation threshold of hard
convex particles in terms of three single-particle measures. We apply this
method to polygonal rods and platelets and find that the universal scaling of
the percolation threshold is lowered by decreasing the number of sides of the
particle cross section. This is caused by the increase of the surface area to
volume ratio with decreasing number of sides.Comment: 7 pages, 3 figures; added references, corrected typo, results
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