As with the AD solutions, the positive entropy gradient in the immediate post-shock ﬂow, S ∝ (r/rvir )p with p ≈ 1, is due to the increasing strength of the accretion shock with cosmic time (Tozzi & Norman 2000).
Entropy Evolution in Galaxy Groups and Clusters; A Comparison of External and Internal Heating
For post heights h ≥ Lc , the gradient of both curves increases appreciably so that ǫ1 and ǫ3 grow relatively quickly with post height.
Topology and Bistability in liquid crystal devices
It might be helpful for the reader to look at the ﬁrst version of posted in the arxiv where the authors gave a more transparent proof of a weaker upper bound C e−cR√log R in the long gradient curve theorem.
Random Complex Zeroes and Random Nodal Lines
They travel down the surface-density gradient, so there is no danger that the post-front Σ will not be larger than Σmin .
The disc instability model of dwarf-novae and low-mass X-ray binary transients
We expect that the spatial gradient terms in the ﬁelds will become large, and they must be included if we are are to make quantitative predictions about the role of chaos in the post-inﬂationary universe.
Chaos after Two-Field Inflation