On Line Distributions of Kelvin Sources

The velocity potential for the flow due to point sources distributed arbitrarily along a straight line near to or at a linearized gravitational free surface is obtained in a new form by use of Fourier transforms. Such a method of representing the potential facilitates the determination of its behavior near to the line of singularities; this behavior is derived formally and its physical properties discussed. A brief illustration is given of a method of using this result in o theory for the motion of a slender ship.

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Determination of the velocity potential of liquid with weakly nonspherical bubbles located in line

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2012.1.001 ◽

2012 ◽

Vol 9 (1) ◽

pp. 11-15

Author(s):

A.A. Aganin ◽

A.I. Davletshin

Keyword(s):

Velocity Potential ◽

Spherical Functions ◽

Straight Line ◽

Axis Of Symmetry

The efficiency of the method of reflections and the method of expansion in terms of spherical functions is investigated in determining the potential of the velocity of liquid with two or more weakly-nonspherical bubbles. The bubble centers are on a straight line, which is the axis of symmetry of the problem.

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Fast calibration of CBED patterns for quantitative analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100149209 ◽

1993 ◽

Vol 51 ◽

pp. 674-675

Author(s):

M.A. Gribelyuk ◽

M. Rühle

Keyword(s):

Reciprocal Lattice ◽

Accurate Determination ◽

Incident Beam ◽

Crystal Thickness ◽

Structure Model ◽

Beam Direction ◽

Transmitted Beam ◽

Reciprocal Vector ◽

On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

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