PMC

Gradient coil field maps measured with I=1A. The black dashed curve shows the design ROI; the gray dashed line indicates the location of the YZ plane in (a) and (c). (a) G_y coil; YZ plane. (b) G_y coil; XY plane. (c) G_z coil; YZ plane. (d) G_z coil; XZ plane.

Spacecraft location and magnetic field model field lines from the T89 model at 10:00 UT on August 10, 2016, and location of SCW. a Location of VAA and VAB (red and green); GOES 13, 14, and 15 (green, purple, and black); MMS (red), Cluster 1 (light green); Geotail (dark blue) and b MMS, GOES 14 and 15, Geotail, and traced field lines using the T89 model projected in a GSM X–Y plane. c Total current of the SCW and d magnetic local time of the SCW and spacecraft obtained using the SCW model (Sergeev et al. ). Location of MMS, GOES 14, 15, Geotail, and traced field lines using T89 model projected (e) in the GSM X–Z plane and f in the GSM Y–Z plane. The location of the equator is denoted by “e”. The dotted line in e indicates the location of the equatorial plane in the midnight meridian (Y = 0), whereas those in f show the equatorial plane at X = −10 R _E (upper curve) and X = −7 R _E (lower curve)

Extrema in density and dynamic properties. Location in the pressure–temperature plane of the extrema along isotherms for viscosity (full red curve), self-diffusion coefficient (short-dashed blue curve), rotational correlation time (long-dashed green curve), and density (dash-dotted black curve). The gray dotted curve shows the melting lines of ice Ih and ice III ().

Bifurcation diagram in the (u, p) parameter plane showing Hopf curve (thick, solid curve) and the location of the chosen Hopf bifurcation points H1, H2, and H3 on this curve. A generalized Hopf bifurcation (GH) marks the transition from subcritical Hopf points (the curve below GH) to supercritical Hopf points (the curve continuing beyond GH). Regions where p < 0 or u < 0 are non-physical. Below the Hopf curve (regions I and II) a stable fixed point exists, which gradually loses linear stability as the curve is approached. Above the Hopf curve (region III) this point has lost linear stability and become a stable limit cycle. The dashed line is a curve of fold bifurcation points. In region II a single stable fixed point exists. In region I the system is bistable with a second stable fixed point also existing, at lower excitation.