Subsections

The correlation time Hessians of the ellipsoid

τm - τm partial derivative

The second partial derivatives with respect to the geometric parameter τm twice are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{{\partial \tau_m}^2...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-2}. \end{align}\end{subequations}

τm - $ \mathfrak{D}_a$ partial derivative

The second partial derivatives with respect to the geometric parameters τm and $ \mathfrak{D}_a$ are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{\partial \tau_m \cd...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-3}. \end{align}\end{subequations}

τm - $ \mathfrak{D}_r$ partial derivative

The second partial derivatives with respect to the geometric parameters τm and $ \mathfrak{D}_r$ are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{\partial \tau_m \cd...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-3}. \end{align}\end{subequations}

$ \mathfrak{D}_a$ - $ \mathfrak{D}_a$ partial derivative

The second partial derivatives with respect to the geometric parameter $ \mathfrak{D}_a$ twice are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{{\partial \mathfrak...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-3}. \end{align}\end{subequations}

$ \mathfrak{D}_a$ - $ \mathfrak{D}_r$ partial derivative

The second partial derivatives with respect to the geometric parameters $ \mathfrak{D}_a$ and $ \mathfrak{D}_r$ are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{\partial \mathfrak{...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-2}. \end{align}\end{subequations}

$ \mathfrak{D}_r$ - $ \mathfrak{D}_r$ partial derivative

The second partial derivatives with respect to the geometric parameter $ \mathfrak{D}_r$ twice are

\begin{subequations}\begin{align}\frac{\partial^2 \tau_{-2}}{{\partial \mathfrak...
...frak{D}_{iso} + 2\mathfrak{D}_a\mathfrak{R})^{-2}. \end{align}\end{subequations}

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