appendices:a8
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appendices:a8 [2024/06/17 11:21] arthur |
appendices:a8 [2025/08/12 13:48] (current) arthur |
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| The hysteresis is then defined by: | The hysteresis is then defined by: | ||
| - | \[\frac{\partial S_{es}}{\partial s} (\text{wetting}) = \left(\frac{s_w}{s}\right)^b\left(\frac{\partial S_{ew}}{\partial s}\right) \text{ with } s_w = a_w \left(S_e^{-1/m_w}\right)^{1/n_w}\] | + | \[\frac{\partial S_{es}}{\partial s} (\text{wetting}) = \left(\frac{s_w}{s}\right)^b\left(\frac{\partial S_{ew}}{\partial s}\right) \text{ with } s_w = a_w \left(S_e^{-1/m_w}-1\right)^{1/n_w}\] |
| - | \[\frac{\partial S_{es}}{\partial s} (\text{drying}) = \left(\frac{s_d}{s}\right)^{-b}\left(\frac{\partial S_{ed}}{\partial s}\right) \text{ with } s_d = a_d \left(S_e^{-1/m_d}\right)^{1/n_d}\] | + | \[\frac{\partial S_{es}}{\partial s} (\text{drying}) = \left(\frac{s_d}{s}\right)^{-b}\left(\frac{\partial S_{ed}}{\partial s}\right) \text{ with } s_d = a_d \left(S_e^{-1/m_d}-1\right)^{1/n_d}\] |
| And therefore: \[S_e^{t+1} = S_e^t + \left(\frac{\partial S_{es}}{\partial s}\right)\times ds\] | And therefore: \[S_e^{t+1} = S_e^t + \left(\frac{\partial S_{es}}{\partial s}\right)\times ds\] | ||
appendices/a8.txt · Last modified: 2025/08/12 13:48 by arthur
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