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Fig. 3. Two-pitches model of the transverse flagellar wave. (A) {varphi}0 (broken line) and {varphi} (solid line) which alternate between {varphi}1 and {varphi}2. (B) cos{varphi} (solid line) and sin{varphi} (broken line). {varphi} indicates the phase of this wave and it switches between {varphi}1 and {varphi}2. {varphi}1={varphi}0/2p is the equation for {varphi} when 0<{varphi}0<2{pi}, and {varphi}2=({varphi}0-2{pi})/2(1-p) is the equation for {varphi} when 2{pi}p''{varphi}0<2{pi}, 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 {varphi}0 is the minimum non-negative value for 2{pi}(ftt-s/{lambda}t)-2{pi}m, where t, s, ft, {lambda}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 {varphi}0(s,t), respectively.





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