First a description of the Bragg reflection in polar coordinates is developed. Subsequently this formalism is applied to describe diffraction for mosaic crystals, gradient crystals and to include the Doppler effect on moving crystals. Within this framework the performance of a powder diffractometer as ...
The stress distribution near the open hole in polar coordinates under plane stress [6] can be presented as [6.1]σr/σo=12[(1−a2r2)+(1+3a4r4−4a2r2)cos2θ]σθ/σo=12[(1+a2r2)−(1+3a4r4)cos2θ], where a is the hole radius, σo is the nominal stress induced by ...
Bottom: The angles between the displacement vector (initial to final centroid position) and the stimulation axis for each cell are represented in polar coordinates. Scale bars: 20 µm Full size image Cdc42 provides directionality while Rac1 provides speed In order to assess the quantitative ...
Polar Coordinates 24.7 - from the file “Standard MultiPlugin.8bf”Portable Bit Map 24.7 - from the file “PBM.8bi”Poster Edges 24.7 - from the file “Filter Gallery.8bf”Radial Blur 24.7 - from the file “Standard MultiPlugin.8bf”Radiance 24.7 - from the file “Radiance.8bi”Range ...
Polar Coordinates 23.0 - from the file “Standard MultiPlugin.8bf”Portable Bit Map 23.0 - from the file “PBM.8bi”PortraitPro 3.1.0 - from the file “PortraitProPSFilter64.8bf”PortraitPro Body 3.1.0 - from the file “PortraitProBodyPSFilter64.8bf”Portraiture 3 3.0.2.7 - from t...
At each step of the algorithm, we want ||∇f(Xn)||2, the sum of the squares of the elements in the gradient, to get smaller and converge to zero. One way to achieve this is to find the value ofαnwhich minimizesXn– αn∇f(Xn). We then setXn+1=Xn– αn∇f(Xn). Th...
We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of...
to get the solution of a pipe (similar to the example 1 in FLUENT document :laminar flow in pipe). Now I am confused that if I could get the right gradient of velocity in x direction when I use C_U_G. Should I consider the difference of Polar Coordinates amd Cartesian Coordinates?
In the polar coordinates, the areal element on a sphere of radius R is(13)R2dσ=sdsdαwhere s and α are the distance and azimuth from P to P's neighboring point. Around the neighborhood of P, the geoid height N can be expanded into a Taylor series as:(14)N=NP+xNx+yNy+12!x2...
in polar coordinates to allow the use of a radial envelope function, which is the key to limiting the radial extent of the gradient coil. Moreover, this approach allows a theoretically correct solution for the shield coil layer similarly limited in radial extent and easily extended to shim ...