An OGH curve is not only mathematically smooth, i.e., with minimum strain energy, but also geometrically smooth, i.e., loop-, cusp- and fold-free if the geometric smoothness conditions and the tangent direction preserving conditions on the tangent angles are satisfied.
The long duration field tests, conducted over 10 days using two icebreakers, show the virtual drilling rig was maintained within the managed ice channel in complex ice drift conditions that included multiple ice drift loops, cusps, and reversals.
As Pollock increased his lateral speed, the lines he created progressed from loops to cusps to undulating sinusoids.
This pattern is a sigmoid (an S- or inverse S-shaped structure) that changes into a cusp-shaped loop structure after the flare occurs.
The package manual provides some pedagogical examples and the computation of all ladder diagrams at three-loop relevant for the cusp anomalous dimension in ABJ(M).
The left panel shows the whole sun; the upper and lower right panels show the sigmoid and cusp-loop structures, observed before and after the flare, respectively.
On 11 May 1998, at about 8 UT, the sigmoid underwent eruption evidenced by expanding elongated EUV loops, dimmings and formation of a cusp.
Long et al. [27] obtained the loop soliton solution and periodic loop soliton solution [28], solitary wave solution and solitary cusp wave solution and smooth periodic wave solution and nonsmooth periodic wave solution of (1.1) and also discussed their dynamic characters and relations by the integral bifurcation method.
Hysteresis-loop and slow-wave paths for A the saddle case, time forward; B the cusp case, time reversed; C the saddle case, time reversed, and D the cusp case, time forward.
Within the cusp region there are three equilibria including a saddle which is necessary to form a homoclinic loop.
One variant of the simple cycloid is the curtate cycloid, for which the curve falls below the line at the cusps, making retrograde loops in which the curve moves in the direction opposite to that of the rolling circle.
