2.5 Particle Velocimetry Measurements
99
nonmatching probability after certain iterations, correct linking has a high probability and incorrect ones show low probabilities. Finally, the most probable match l i j
will be found with the largest match probability.
2.5.4.3 Arch Identification
The definition of a pebble arch is a collection of mutually stable particles that requires
the information of particles sustaining each other in a granular packing [27]. If a
particle within an arch is not in contact with the base particle, it may be supported
by the other two particles in the arch. Conversely, it contributes to the stabilization
of these two particles too. The examples of 2D arches are shown in Fig. 2.33, which
shows a chain of particles supported by two base particles (particles b and c in the
arching abc). The two base particles do not need the arch particle to stabilize them.
They are stabilized by the other particles in the assembly [51].
To identify arches, at first, one needs to identify the supporting particles of each
bed in the packing [52]. The weighting vector of the candidate stable particle should
pass between the centers of the supporting particles or base particles [53]. Also,
some of these supporting contacts may be provided by the vessel walls [54]. Then,
all mutually stable particles can be identified. Two pebbles A and B are mutually
stable if A supports B and B supports A. Arches are defined as sets of particles
connected through mutually stabilizing contacts. This definition guarantees that a
pebble in the packing belongs to a unique bridge. Finally, the arches can be detected
by making a list of mutually stable pairs of particles and then applying the standard
cluster counting algorithm [55] to separate the system into separated sets of connected
particles.
The arch size s can be defined by the number of particles forming the arch excluding the two base particles. Moreover, the horizontal span or lateral extension n s (x)
is defined as the projection onto the horizontal axis of the segment that joins the
Fig. 2.33 The bulking arch
illustration in a window with
the center at H = 70d,
X = 24d.The blue dashed
lines indicate contacts
between particles and thick
red lines indicate the arches
99
nonmatching probability after certain iterations, correct linking has a high probability and incorrect ones show low probabilities. Finally, the most probable match l i j
will be found with the largest match probability.
2.5.4.3 Arch Identification
The definition of a pebble arch is a collection of mutually stable particles that requires
the information of particles sustaining each other in a granular packing [27]. If a
particle within an arch is not in contact with the base particle, it may be supported
by the other two particles in the arch. Conversely, it contributes to the stabilization
of these two particles too. The examples of 2D arches are shown in Fig. 2.33, which
shows a chain of particles supported by two base particles (particles b and c in the
arching abc). The two base particles do not need the arch particle to stabilize them.
They are stabilized by the other particles in the assembly [51].
To identify arches, at first, one needs to identify the supporting particles of each
bed in the packing [52]. The weighting vector of the candidate stable particle should
pass between the centers of the supporting particles or base particles [53]. Also,
some of these supporting contacts may be provided by the vessel walls [54]. Then,
all mutually stable particles can be identified. Two pebbles A and B are mutually
stable if A supports B and B supports A. Arches are defined as sets of particles
connected through mutually stabilizing contacts. This definition guarantees that a
pebble in the packing belongs to a unique bridge. Finally, the arches can be detected
by making a list of mutually stable pairs of particles and then applying the standard
cluster counting algorithm [55] to separate the system into separated sets of connected
particles.
The arch size s can be defined by the number of particles forming the arch excluding the two base particles. Moreover, the horizontal span or lateral extension n s (x)
is defined as the projection onto the horizontal axis of the segment that joins the
Fig. 2.33 The bulking arch
illustration in a window with
the center at H = 70d,
X = 24d.The blue dashed
lines indicate contacts
between particles and thick
red lines indicate the arches