The root system of plant is a vitally important organ for living plant. One of the major functions of the root system is uptaking water and nutrients from the soil. The present paper analyzes the whole process of water uptake from soil by a steadily growing plant with a single slender root. We start from the basic principles of physics and fluid-dynamics, consider the structure characteristics of the water transport channel formed by the tiny xylems tubes inside plant, and establish a simplified coherent mathematical model to describe the water transport in the complete system consisting of soil, individual plant, including root, stem and leaves-atmosphere, on the basis of the plant physiology. Moreover, we resolve the proposed mathematical model for a simple artificial plant model under a variety of conditions, in terms of the numerical approach as well as analytical approach. It is shown that the results obtained by both approaches are in very good agreement; the theoretical predictions are qualitatively consistent with the practical experi-ences very well. The simplified mathematical model established in the present pa-per may provide a basis for the further investigations on the more sophisticated mathematical model.
The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.
CHEN MingWen1,2, WANG ZiDong2 & XU JianJun3,4 1 School of Applied Sciences, University of Science and Technology Beijing, Beijing 100083, China
