RAPID COMPUTATION OF GRAVITATIONAL ATTRACTION OF THREE‐DIMENSIONAL BODIES OF ARBITRARY SHAPE

Geophysics ◽  
1960 ◽  
Vol 25 (1) ◽  
pp. 203-225 ◽  
Author(s):  
Manik Talwani ◽  
Maurice Ewing
Keyword(s):  
Gravity Anomaly ◽  
Arbitrary Shape ◽  
High Speed ◽  
Three Dimensional ◽  
Isostatic Compensation ◽  
External Point ◽  
Spherical Earth ◽  
Terrain Corrections ◽  
High Degree ◽  
Special Case

An expression is derived for the gravity anomaly at an external point caused by a horizontal lamina with the boundary of an irregular polygon. This expression is put in a form suitable for computation by a high speed digital computer. By making the number of sides of the polygon sufficiently large, any irregular outline can be closely approximated. Any three dimensional body can be represented by contours. By replacing each contour by a polygonal lamina, the anomaly caused by it can be obtained at any external point. By a system of interpolation between contours combined with a numerical integration the gravity anomaly caused by the three‐dimensional body can be calculated to a high degree of precision. This method may also be used for rapidly computing terrain corrections on a flat earth. By making a small modification it can further be adopted for computing the terrain correction as well as local isostatic compensation on the Airy system up to the external radius of Hayford zone O on a spherical earth. The expression for the anomaly caused by a horizontal polygonal lamina is also obtained for the special case when the sides of the polygon are alternately parallel to the x- and y-axes, that is, the polygonal lamina can be divided into a number of rectangular laminae. A chart is provided for the hand computation of the gravity anomaly in this case.

scholarly journals WAVE SCATTERING BY PERMEABLE AND IMPERMEABLE BREAKWATER OF ARBITRARY SHAPE

1974 ◽  
Vol 1 (14) ◽  
pp. 110
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Yasu Yumura
Keyword(s):  
Arbitrary Shape ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Floating Body ◽  
Wave Forces ◽  
Method Of Calculation ◽  
Wave Channel ◽  
Method Of Solution ◽  
Special Case

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method. The method described here is the extension of the author's method of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions. Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel. The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary.

scholarly journals Power mode of axisymmetric high-speed combined extrusion of bimetallic road milling picks

2021 ◽  
Vol 66 (4) ◽  
pp. 411-419
Author(s):  
K. Yu. Bykov ◽  
I. V. Kachanov ◽  
I. M. Shatalov
Keyword(s):  
High Speed ◽  
Axisymmetric Deformation ◽  
Stage Model ◽  
Equal Area ◽  
Second Stage ◽  
Industrial Implementation ◽  
Third Stage ◽  
Power Mode ◽  
High Degree ◽  
Special Case

The article presents a simplified three-stage model of the transition from a flat to axisymmetric deformation during high-speed, combined extrusion of bimetallic road milling picks. The transition is based on the principle of equality of areas, according to which the area of a figure during a flat deformation is replaced by an equal area of a circle. In this case, it is assumed that the kinematically possible field of the slip lines remains unchanged. This approach makes it possible to reduce the number of necessary calculations and at the same time maintain a high degree of correctness of the obtained equations. The first stage shows the transition to a special case of a flat problem, in which a stepped rectangular part is extruded from the original square blank, in which one of the sides is equal to the square side of the original blank. At the second stage of the transition, a flat-step part having square sections along its entire length is extruded from the original square-section blank. Directly at the third stage, the final transition to the axisymmetric deformation of the cutter is formed, in which the area of the square is replaced by the equal area of the circle. The dependences obtained because of solving the axisymmetric problem can be recommended for calculations in the industrial implementation of the technology of high-speed combined extrusion of bimetallic milling picks.

A method for computing the geoid height contribution of three‐dimensional bodies within a spherical earth

Geophysics ◽  
1983 ◽  
Vol 48 (12) ◽  
pp. 1665-1670 ◽  
Author(s):  
S. J. Hellinger
Keyword(s):  
Gravitational Potential ◽  
Arbitrary Shape ◽  
Three Dimensional ◽  
Geoid Height ◽  
Observation Point ◽  
Simple Shape ◽  
Digital Computation ◽  
Anomalous Body ◽  
Anomalous Density ◽  
Spherical Earth

A method is presented for calculating the geoid height associated with three‐dimensional bodies of arbitrary shape and anomalous density within a spherical earth. Each three‐dimensional body is specified by giving its shape and anomalous density at a number of successive depths. The method calculates the anomalous gravitational potential due to such bodies and then obtains the geoid height using Bruns’ formula. The calculation utilizes the portion of the density model that lies in a hemisphere centered at the observation point. The method is partly analytical and partly numerical, and it is designed for digital computation. Use of the method to compute the anomalous potential in the vicinity of an anomalous body of simple shape shows that the method can give very accurate results.

High-speed brightfield 3-D imaging and 3-D image analysis of thick and overlapped cell clusters in cytological preparations

1994 ◽  
Vol 52 ◽  
pp. 218-219
Author(s):  
Robert W. Mackin
Keyword(s):  
Image Analysis ◽  
High Speed ◽  
Three Dimensional ◽  
Image Data ◽  
Ccd Camera ◽  
Objective Lens ◽  
Array Processor ◽  
Vaginal Smears ◽  
Low Contrast ◽  
Computer Controlled

This paper presents two advances towards the automated three-dimensional (3-D) analysis of thick and heavily-overlapped regions in cytological preparations such as cervical/vaginal smears. First, a high speed 3-D brightfield microscope has been developed, allowing the acquisition of image data at speeds approaching 30 optical slices per second. Second, algorithms have been developed to detect and segment nuclei in spite of the extremely high image variability and low contrast typical of such regions. The analysis of such regions is inherently a 3-D problem that cannot be solved reliably with conventional 2-D imaging and image analysis methods.High-Speed 3-D imaging of the specimen is accomplished by moving the specimen axially relative to the objective lens of a standard microscope (Zeiss) at a speed of 30 steps per second, where the stepsize is adjustable from 0.2 - 5μm. The specimen is mounted on a computer-controlled, piezoelectric microstage (Burleigh PZS-100, 68/μm displacement). At each step, an optical slice is acquired using a CCD camera (SONY XC-11/71 IP, Dalsa CA-D1-0256, and CA-D2-0512 have been used) connected to a 4-node array processor system based on the Intel i860 chip.

Effects of Three-Dimensional Pressure Gradients on High-Speed Turbulent Boundary Layers

2021 ◽  
Author(s):  
Scott J. Peltier ◽  
Brian E. Rice ◽  
Ethan Johnson ◽  
Venkateswaran Narayanaswamy ◽  
Marvin E. Sellers
Keyword(s):  
Boundary Layers ◽  
High Speed ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients

Three-Dimensional Imaging through Shock-Waves at Ultra-High Speed.

2018 ◽  
Author(s):  
Yi Chen Mazumdar ◽  
Michael E. Smyser ◽  
Jeffery Dean Heyborne ◽  
Daniel Robert Guildenbecher
Keyword(s):  
Shock Waves ◽  
High Speed ◽  
Three Dimensional ◽  
Three Dimensional Imaging ◽  
Ultra High Speed

scholarly journals High-speed volumetric two-photon fluorescence imaging of neurovascular dynamics

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Jiang Lan Fan ◽  
Jose A. Rivera ◽  
Wei Sun ◽  
John Peterson ◽  
Henry Haeberle ◽  
...  
Keyword(s):  
Blood Flow ◽  
High Speed ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Microscopy ◽  
Fluorescence Signal ◽  
Imaging Method ◽  
Spatiotemporal Resolution ◽  
Two Photon

AbstractUnderstanding the structure and function of vasculature in the brain requires us to monitor distributed hemodynamics at high spatial and temporal resolution in three-dimensional (3D) volumes in vivo. Currently, a volumetric vasculature imaging method with sub-capillary spatial resolution and blood flow-resolving speed is lacking. Here, using two-photon laser scanning microscopy (TPLSM) with an axially extended Bessel focus, we capture volumetric hemodynamics in the awake mouse brain at a spatiotemporal resolution sufficient for measuring capillary size and blood flow. With Bessel TPLSM, the fluorescence signal of a vessel becomes proportional to its size, which enables convenient intensity-based analysis of vessel dilation and constriction dynamics in large volumes. We observe entrainment of vasodilation and vasoconstriction with pupil diameter and measure 3D blood flow at 99 volumes/second. Demonstrating high-throughput monitoring of hemodynamics in the awake brain, we expect Bessel TPLSM to make broad impacts on neurovasculature research.

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