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Fig. 3. Two-pitches model of the transverse flagellar wave. (A)
0
(broken line) and
(solid line) which alternate between
1 and
2. (B) cos
(solid line) and
sin
(broken line).
indicates the phase of this wave and it
switches between
1 and
2.
1=
0/2p is the equation for
when 0<
0<2
, and
2=(
0-2
)/2(1-p) is the equation
for
when 2
p''
0<2
, where
p is the ratio of a half pitch corresponding to the remote part of
the antero-posterior axis of the cell to a wavelength and
0
is the minimum non-negative value for
2
(ftt-s/
t)-2
m,
where t, s, ft,
t and m are
time, length along the circle where the transverse flagellum wave propagates,
the frequency and wavelength of the helical wave and a positive integer that
minimizes
0(s,t), respectively.