Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical o...Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.展开更多
An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier-Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton＇s equation,...An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier-Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton＇s equation, involving a hard sphere model to describe particle-to-particle and particle-to-wall collisions. The influence of wall characteristics, size distribution of sand particles and boundary layer depth on vertical distribution of sand mass flux and particle mean horizontal velocity is analyzed, suggesting that all these three factors affect sand transport at different levels. In all cases, for small size groups, sand mass flux first increases with height and then decreases while for large size groups, it decreases exponen- tially with height and for middle size groups the behavior is in-between. The mean horizontal velocity for all size groups well fits experimental data, that is, increasing logarithmically with height in the middle height region. Wall characteristics greatly affects particle to wall collision and makes the fiat bed similar to a Gobi surface and the rough bed similar to a sandy surface. Particle size distribution largely affects the sand mass flux and the highest heights they can reach especially for larger particles.展开更多
文摘Let R be r-dimensional Euclidean space with . Denote by the unit sphere in For we denote by (f) its Cesàro means of order for spherical harmonic expansions. The special value of is known as the critical one. For , we set This paper proves that N^co u holds for a,ty f e L,0 (log+ L)2~po (log+ log+ L)'(,0~', forth I > 1.
基金supported by National Natural Science Foundation of China (Grant No. 50823002 and No. 50821064)
文摘An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier-Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton＇s equation, involving a hard sphere model to describe particle-to-particle and particle-to-wall collisions. The influence of wall characteristics, size distribution of sand particles and boundary layer depth on vertical distribution of sand mass flux and particle mean horizontal velocity is analyzed, suggesting that all these three factors affect sand transport at different levels. In all cases, for small size groups, sand mass flux first increases with height and then decreases while for large size groups, it decreases exponen- tially with height and for middle size groups the behavior is in-between. The mean horizontal velocity for all size groups well fits experimental data, that is, increasing logarithmically with height in the middle height region. Wall characteristics greatly affects particle to wall collision and makes the fiat bed similar to a Gobi surface and the rough bed similar to a sandy surface. Particle size distribution largely affects the sand mass flux and the highest heights they can reach especially for larger particles.
