A three‐parameter markov model for sedimentation

Considering velocity perturbations as white noise and assuming exponential decay of velocities to the mean velocity μ, we obtain a two-parameter Langevin equation. The conditional and steady-state probability density functions for instantaneous velocity are used to develop theoretical expressions for variables which can be measured experimentally. Support for the model is adduced from published data and our own experimental results. The parameter μ is obtained from the mean of the distance travelled in time T during steady state and the two Langevin parameters from its correlation coefficient and variance. Precision and bias in experimentation are discussed. Si l'on considere les perturbations des vitesses comme un bruit bizarre et qu'on suppose qu'il se produit une decroissance exponentielle des vitesses jusqu'a la vitesse moyenne μ, on obtient une equation de Langevin a deux parametres. On emploie les fonctions des densites de probabilites conditionnelles et stables pour la vitesse instantanee, afin de mettre au point des expressions theoriques pour des variables qu'on peut mesurer experimentalement Les donnees publiees et les resultats experimentaux de l'auteur du present travail militent en faveur du modele. On obtient le parametre μ a partir de la moyenne de la distance parcourue en temps T lors du regime stable, ainsi que les deux parametres de Langevin a partir de son coefficient de correlation et de sa variation. On discute la precision et la polarisation dans le travail experimental.

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