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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-06-20 08:04:44 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-06-20 08:04:44 +0200
commit95a311392775786d4cafc10d8ec424a7f3a0d09f (patch)
tree01c6da62b2deb718807af90f473b0427e11c44fa
parent32f23e83eb092c07a898a57354eecf510e5681d4 (diff)
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Small tweaks.
-rw-r--r--2-point.tex4
1 files changed, 2 insertions, 2 deletions
diff --git a/2-point.tex b/2-point.tex
index b596e3b..22cce5b 100644
--- a/2-point.tex
+++ b/2-point.tex
@@ -962,7 +962,7 @@ m)=E_\mathrm{th}$, the threshold energy is also the pivot around which the
points asymptotically nearby marginal minima change their properties.
To examine better the population of marginal points, it is necessary to look at
-the next term in the series of the complexity with $\delta q$, since the linear
+the next term in the series of the complexity with $\Delta q$, since the linear
coefficient becomes zero at the marginal line. This tells us something
intuitive: stable minima have an effective repulsion between points, and one
always finds a sufficiently small $\Delta q$ that no stationary points are
@@ -988,7 +988,7 @@ where $\delta\mu_1$ is given by the coefficient in \eqref{eq:expansion.mu.1}
and
\begin{equation}
\delta\mu_2=\frac{v_f}{f'(1)f''(1)^{3/4}}\sqrt{
- \frac{E_0-E_\mathrm{th}}2\frac{f'(1)\big(f'''(1)-2f''(1)\big)+2f''(1)^2}{u_f}
+ \frac{E_0-E_\mathrm{th}}2\frac{2f''(1)\big(f''(1)-f'(1)\big)+f'(1)f'''(1)}{u_f}
}
\end{equation}
Similarly, one finds that the energy lies in the range $E_1=E_0+\delta