From 7e02d2c027a7fdc6e00500e5bbe8c8ae5bfd3906 Mon Sep 17 00:00:00 2001 From: Nico Dirkes Date: Wed, 20 Mar 2024 09:19:55 +0100 Subject: [PATCH] Update tank-treading model in background.rst --- docs/background.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/background.rst b/docs/background.rst index 92ca1c8..92ec443 100644 --- a/docs/background.rst +++ b/docs/background.rst @@ -56,7 +56,7 @@ This is implemented as :class:`hemtracer.rbc_model.strain_based.AroraSimplified` Tank-treading model ^^^^^^^^^^^^^^^^^^^ -This model was derived by Dirkes et al. :cite:p:`dirkesEulerianFormulationTensorBased` by replacing the differential equation for the orientation tensor Q by an algebraic equation for steady orientation. The model is generally more efficient than the full Eulerian reformulation and more robust, as it contains only the eigenvalues (3 DoF's). The governing equations are +This model was derived by Dirkes et al. :cite:p:`dirkesEulerianFormulationTensorBased` by replacing the differential equation for the orientation tensor Q by an algebraic equation for equilibrium orientation. The model is generally more efficient than the full Eulerian reformulation and more robust, as it contains only the eigenvalues (3 DoF's). The governing equations are .. math:: :nowrap: @@ -66,8 +66,8 @@ This model was derived by Dirkes et al. :cite:p:`dirkesEulerianFormulationTensor \\ \mathbf Q & = & \begin{cases} - \mathbf Q^\mathrm{steady} & \text{if cell is tank-treading} \\ - \mathbf 0 & \text{if cell is tumbling} + \mathbf Q_\star & \text{tank-treading} \\ + \mathbf 0 & \text{tumbling} \end{cases} \, , \qquad \mathrm{with} \quad \tilde{\mathbf{E}} = \mathbf{Q}^\mathrm{T} \mathbf{E} \mathbf{Q} \, , \end{eqnarray}