We derive the asymptotic winding law for a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges to an inverse Gamma distribution. For winding around a disk, the angle converges to a distribution given by an elliptic theta function. For winding in an annulus, the winding angle is asymptotically Gaussian with a linear drift term. We validate our results with numerical simulations.
An auxiliary device for rotating alfalfa in air flow with waste air recycling was designed in this study. The motion characteristics of rotating alfalfa in air flow and the new crafts of herbage drying for drying homogeneity were studied. An aerodynamic model of alfalfa segments was established based on the result of the experiment on alfalfa rotation in air flow. The movement of alfalfa segments was analyzed using kinematic simulation. The movement trail and the behavior of alfalfa rotation in air flow were tested and verified. Experimental results revealed that the effect of alfalfa rotation in air flow depends on the air flow parameters and the mechanism of the new device. The influence of drying air flow velocity, initial velocity, and air flow angle were analyzed using a nonlinear regression orthogonal design and rotating alfalfa in air flow and building mathematical models of rotating alfalfa parameters on experimental criteria to optimize the parameters of alfalfa drying homogeneity. MATLAB was used for single-target optimization and experimental verification. Optimized drying parameters were ascertained (i.e., air flow velocity, 2.82 m/s; initial velocity, 0.05 m/s; air flow angle, 5.0 to 5.5 ) based on the simulation of the alfalfa drying study and experimental result.
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