diff --git a/docs/passive_cable/cable_computation.tex b/docs/passive_cable/cable_computation.tex
index 39a372196c006c7c67837f039df88c903cb439b4..888aa8a11890879818e2964ba4644744e434ab79 100644
--- a/docs/passive_cable/cable_computation.tex
+++ b/docs/passive_cable/cable_computation.tex
@@ -54,16 +54,16 @@ is the reversal potential.
\begin{table}[ht]
\centering
\begin{tabular}{lSl}
- \toprule
- Term & {Value} & Property\\
- \midrule
- $d$ & \SI{1.0}{\um} & cable diameter \\
- $L$ & \SI{1.0}{\mm} & cable length \\
- $R_A$ & \SI{1.0}{\ohm\m} & bulk axial resistivity \\
- $R_M$ & \SI{4.0}{\ohm\m\squared} & areal membrane resistivity \\
- $C_M$ & \SI{0.01}{\F\per\m\squared} & areal membrane capacitance \\
- $E_M$ & \SI{-65.0}{\mV} & membrane reversal potential \\
- \bottomrule
+ \toprule
+ Term & {Value} & Property\\
+ \midrule
+ $d$ & \SI{1.0}{\um} & cable diameter \\
+ $L$ & \SI{1.0}{\mm} & cable length \\
+ $R_A$ & \SI{1.0}{\ohm\m} & bulk axial resistivity \\
+ $R_M$ & \SI{4.0}{\ohm\m\squared} & areal membrane resistivity \\
+ $C_M$ & \SI{0.01}{\F\per\m\squared} & areal membrane capacitance \\
+ $E_M$ & \SI{-65.0}{\mV} & membrane reversal potential \\
+ \bottomrule
\end{tabular}
\caption{Cable properties for the Rallpack 1 model.}
\label{tbl:rallpack1}
@@ -87,9 +87,9 @@ and the linear membrane capacitance $c$. These determine $\lambda$ and $\tau$ by
With the model boundary conditions,
\begin{subequations}
\begin{align}
- v(x, 0) &= E, \\
- \left.\frac{\partial v}{\partial x}\right\vert_{x=0} & = -Ir, \\
- \left.\frac{\partial v}{\partial x}\right\vert_{x=L} & = 0,
+ v(x, 0) &= E, \\
+ \left.\frac{\partial v}{\partial x}\right\vert_{x=0} & = -Ir, \\
+ \left.\frac{\partial v}{\partial x}\right\vert_{x=L} & = 0,
\end{align}
\end{subequations}
where $I$ is the injected current and $L$ is the cable length.
@@ -98,18 +98,18 @@ The solution $v(x, t)$ can be expressed in terms of the solution $g(x, t; L)$
to a normalized version of the cable equation,
\begin{subequations}
\begin{align}
- \label{eq:normcable}
- \frac{\partial^2 g}{\partial x^2} & =
- \frac{\partial g}{\partial t} + g,
+ \label{eq:normcable}
+ \frac{\partial^2 g}{\partial x^2} & =
+ \frac{\partial g}{\partial t} + g,
\\
- \label{eq:normcableinitial}
- g(x, 0) &= 0,
- \\
- \label{eq:normcableleft}
- \left.\frac{\partial g}{\partial x}\right\vert_{x=0} & = 1,
- \\
- \label{eq:normcableright}
- \left.\frac{\partial g}{\partial x}\right\vert_{x=L} & = 0
+ \label{eq:normcableinitial}
+ g(x, 0) &= 0,
+ \\
+ \label{eq:normcableleft}
+ \left.\frac{\partial g}{\partial x}\right\vert_{x=0} & = 1,
+ \\
+ \label{eq:normcableright}
+ \left.\frac{\partial g}{\partial x}\right\vert_{x=L} & = 0
\end{align}
\end{subequations}
by
@@ -158,7 +158,7 @@ and thus
Consequently,
\begin{equation}
\begin{aligned}
- G(x, s) &= \frac{1}{ms}\cdot\frac{e^{mx}+e^{2mL-mx}}{1-e^{2mL}}\\
+ G(x, s) &= \frac{1}{ms}\cdot\frac{e^{mx}+e^{2mL-mx}}{1-e^{2mL}}\\
&= - \frac{1}{ms}\cdot\frac{\cosh m(L-x)}{\sinh mL}.
\end{aligned}
\end{equation}
@@ -199,10 +199,10 @@ arising from $m=\sqrt{1+s}$, as letting $m=-\sqrt{1+s}$ leaves $G$ unchanged.
For $|s+1|>\epsilon$,
\begin{equation}
\begin{aligned}
- |s^{3/2}G(x,s)|^2
- & \leq (1+\epsilon)^{-1} \left| \frac{\cosh m(L-x)}{\sinh mL} \right|^2
- \\
- & \leq (1+\epsilon)^{-1} (1+|\coth mL|)^2
+ |s^{3/2}G(x,s)|^2
+ & \leq (1+\epsilon)^{-1} \left| \frac{\cosh m(L-x)}{\sinh mL} \right|^2
+ \\
+ & \leq (1+\epsilon)^{-1} (1+|\coth mL|)^2
\label{eq:gbounds}
\end{aligned}
\end{equation}
@@ -218,8 +218,8 @@ Recalling $m=\sqrt{1+s}$, $m$ and $\sinh mL$ are non-zero in
a neighbourhood of $s=0$, and so the pole is simple and
\begin{equation}
\begin{aligned}
- \Res(G; 0) & = - \frac{1}{m}\cdot\left.\frac{\cosh m(L-x)}{\sinh mL}\right|_{s=0}\\
- & = - \frac{\cosh (L-x)}{\sinh L}.
+ \Res(G; 0) & = - \frac{1}{m}\cdot\left.\frac{\cosh m(L-x)}{\sinh mL}\right|_{s=0}\\
+ & = - \frac{\cosh (L-x)}{\sinh L}.
\end{aligned}
\end{equation}
@@ -235,9 +235,9 @@ Let $G(x,s)=f(x,s)/h(s)$, where
Noting that $dm/ds = \frac{1}{2}m^{-1}$,
\begin{equation}
\begin{aligned}
- h'(s) &= \frac{1}{2}m^{-1}\sinh mL + \frac{1}{2}L\cosh mL \\
- &= \frac{1}{2}L + \frac{1}{2}L + O(m^2) \quad(m\to 0) \\
- &= L + O(s+1) \quad(s\to -1).
+ h'(s) &= \frac{1}{2}m^{-1}\sinh mL + \frac{1}{2}L\cosh mL \\
+ &= \frac{1}{2}L + \frac{1}{2}L + O(m^2) \quad(m\to 0) \\
+ &= L + O(s+1) \quad(s\to -1).
\label{eq:hprime}
\end{aligned}
\end{equation}
@@ -255,11 +255,11 @@ $m_k$ is non-zero for $k\geq 1$ and
Consequently the pole is simple and
\begin{equation}
\begin{aligned}
- \Res(G; s_k)
- & = f(x, s_k)/h'(s_k)\\
- & = -\frac{2}{s_k L}\frac{\cosh m_k(L-x)}{\cosh m_kL} \\
- & = -\frac{2}{s_k L}\frac{\cosh m_kL\cosh m_kx-\sinh m_kL\sinh m_kL}{\cosh m_kL} \\
- & = -\frac{2}{s_k L}\cosh m_k x,
+ \Res(G; s_k)
+ & = f(x, s_k)/h'(s_k)\\
+ & = -\frac{2}{s_k L}\frac{\cosh m_k(L-x)}{\cosh m_kL} \\
+ & = -\frac{2}{s_k L}\frac{\cosh m_kL\cosh m_kx-\sinh m_kL\sinh m_kL}{\cosh m_kL} \\
+ & = -\frac{2}{s_k L}\cosh m_k x,
\end{aligned}
\end{equation}
as $\sinh m_k=0$.
@@ -272,7 +272,7 @@ In terms of $a_k$,
The series exapnsion for $g(x, t)$ therefore is
\begin{equation}
g(x, t) = -\frac{\cosh(L-x)}{\sinh L} + \frac{1}{L}e^{-t}\left\{
- 1+2\sum_{k=1}^\infty \frac{e^{-ta_k^2}}{1+a_k^2}\cos a_k x\right\}.
+ 1+2\sum_{k=1}^\infty \frac{e^{-ta_k^2}}{1+a_k^2}\cos a_k x\right\}.
\label{eq:theg}
\end{equation}
@@ -285,16 +285,16 @@ of stopping criteria for a given tolerance.
Let $g_n$ be the partial sum
\begin{equation}
g_n(x, t) = -\frac{\cosh(L-x)}{\sinh L} + \frac{1}{L}e^{-t}\left\{
- 1+2\sum_{k=1}^n \frac{e^{-ta_k^2}}{1+a_k^2}\cos a_k x\right\}.
+ 1+2\sum_{k=1}^n \frac{e^{-ta_k^2}}{1+a_k^2}\cos a_k x\right\}.
\end{equation}
so that $g(x, t) =\lim_{n\to\infty} g_n(x,t)$. Let $\bar{g}_n = |g-g_n|$ be the
residual. The $a_k$ form an increasing sequence, so
\begin{equation}
\begin{aligned}
- \bar{g}_n(x,t)
- & \leq \frac{2}{L}e^{-t}\sum_{n+1}^\infty\frac{e^{-ta_k^2}}{1+a_k^2}\\
- & \leq \frac{2}{L}e^{-t}\int_{a_n}^\infty \frac{e^{-tu^2}}{1+u^2}\,du\\
- & < \frac{2}{L}e^{-t}\int_{a_n}^\infty \frac{e^{-tu^2}}{u^2}\,du.
+ \bar{g}_n(x,t)
+ & \leq \frac{2}{L}e^{-t}\sum_{n+1}^\infty\frac{e^{-ta_k^2}}{1+a_k^2}\\
+ & \leq \frac{2}{L}e^{-t}\int_{a_n}^\infty \frac{e^{-tu^2}}{1+u^2}\,du\\
+ & < \frac{2}{L}e^{-t}\int_{a_n}^\infty \frac{e^{-tu^2}}{u^2}\,du.
\end{aligned}
\label{eq:gbar}
\end{equation}
@@ -313,9 +313,9 @@ For real $\alpha<1$ and $z>0$, \textcite[][Theorem 2.3]{borwein2009} give the up
Substituting into \eqref{eq:gbar} gives
\begin{equation}
\begin{aligned}
- \bar{g}_n(x,t)
- & < \frac{1}{L}e^{-t}\sqrt{t}\,\Gamma(-\frac{1}{2},a_n^2 t) \\
- & \leq \frac{1}{L}e^{-t}\sqrt{t}\,(a_n^2 t)^{-\frac{3}{2}}e^{-a_n^2t} \\
+ \bar{g}_n(x,t)
+ & < \frac{1}{L}e^{-t}\sqrt{t}\,\Gamma(-\frac{1}{2},a_n^2 t) \\
+ & \leq \frac{1}{L}e^{-t}\sqrt{t}\,(a_n^2 t)^{-\frac{3}{2}}e^{-a_n^2t} \\
& = \frac{e^{-t(1+a_n^2)}}{L t a_n^3}.
\end{aligned}
\end{equation}
diff --git a/tests/validation/CMakeLists.txt b/tests/validation/CMakeLists.txt
index a38ae3e23291aff01b8955d3717c63144f1bf940..783ef00321a34313ea36d90d17d9ec3862afa148 100644
--- a/tests/validation/CMakeLists.txt
+++ b/tests/validation/CMakeLists.txt
@@ -38,7 +38,7 @@ foreach(target ${TARGETS})
)
if(BUILD_VALIDATION_DATA)
- add_dependencies(${target} validation_data)
+ add_dependencies(${target} validation_data)
endif()
endforeach()
diff --git a/validation/CMakeLists.txt b/validation/CMakeLists.txt
index 009a27aa43ce8974b154ce265e6dd6c75b990f52..99b4bec969a87219693dfe0bbd05591e1acfd6c2 100644
--- a/validation/CMakeLists.txt
+++ b/validation/CMakeLists.txt
@@ -31,10 +31,10 @@ function(add_validation_data)
set(out "${VALIDATION_DATA_DIR}/${ADD_VALIDATION_DATA_OUTPUT}")
string(REGEX REPLACE "([^;]+)" "${CMAKE_CURRENT_SOURCE_DIR}/\\1" deps "${ADD_VALIDATION_DATA_DEPENDS}")
add_custom_command(
- OUTPUT "${out}"
+ OUTPUT "${out}"
DEPENDS ${deps}
- WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
- COMMAND ${ADD_VALIDATION_DATA_COMMAND} > "${out}")
+ WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}"
+ COMMAND ${ADD_VALIDATION_DATA_COMMAND} > "${out}")
# Cmake, why can't we just write add_dependencies(validation_data "${out}")?!
make_unique_target_name(ffs_cmake "${out}")
diff --git a/validation/ref/neuron/CMakeLists.txt b/validation/ref/neuron/CMakeLists.txt
index 570d3f7234b2fab135b97dde9462884caa23523e..4df17dc38d23b59c935dad9e02ca0eb19d2b793f 100644
--- a/validation/ref/neuron/CMakeLists.txt
+++ b/validation/ref/neuron/CMakeLists.txt
@@ -11,7 +11,7 @@ set(models
foreach(model ${models})
set(script "${model}.py")
add_validation_data(
- OUTPUT "neuron_${model}.json"
+ OUTPUT "neuron_${model}.json"
DEPENDS "${script}" "nrn_validation.py"
COMMAND ${NRNIV_BIN} -nobanner -python "${script}")
endforeach()