824 research outputs found
Consimilarity and quaternion matrix equations ,
L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a
quaternion matrix with respect to consimilarity transformations
in which is a nonsingular quaternion matrix and
for each quaternion . We give an
analogous canonical form of a quaternion matrix with respect to consimilarity
transformations in which is an arbitrary
involutive automorphism of the skew field of quaternions. We apply the obtained
canonical form to the quaternion matrix equations and
Signatures of Steady Heating in Time Lag Analysis of Coronal Emission
Among the many ways of investigating coronal heating, the time lag method of
Viall & Klimchuk (2012) is becoming increasingly prevalent as an analysis
technique complementary to those traditionally used. The time lag method cross
correlates light curves at a given spatial location obtained in spectral bands
that sample different temperature plasmas. It has been used most extensively
with data from the Atmospheric Imaging Assembly on the Solar Dynamics
Observatory. We have previously applied the time lag method to entire active
regions and surrounding quiet Sun and create maps of the results (Viall &
Klimchuk 2012; Viall & Klimchuk 2015). We find that the majority of time lags
are consistent with the cooling of coronal plasma that has been impulsively
heated. Additionally, a significant fraction of the map area has a time lag of
zero. This does not indicate a lack of variability. Rather, strong variability
must be present, and it must occur in phase in the different channels. We have
shown previously that these zero time lags are consistent with the transition
region response to coronal nanoflares (Viall & Klimchuk 2015; Bradshaw & Viall
2016), but other explanations are possible. A common misconception is that the
zero time lag indicates steady emission resulting from steady heating. Using
simulated and observed light curves, we demonstrate here that highly correlated
light curves at zero time lag are not compatible with equilibrium solutions.
Such light curves can only be created by evolution.Comment: 10 pages, 3 figures. Accepted to ApJ July 5 201
- β¦