Higher-order gravitational potential gradients by tensor analysis in spherical coordinates

2021 ◽  
Vol 95 (7) ◽  
Author(s):  
Xiao-Le Deng ◽  
Jiangjun Ran
Keyword(s):  
Gravitational Potential ◽  
Higher Order ◽  
Tensor Analysis ◽  
Spherical Coordinates ◽  
Potential Gradients

Higher-order gravitational potential gradients for geoscientific applications

2019 ◽  
Vol 198 ◽  
pp. 102937 ◽  
Author(s):  
Pavel Novák ◽  
Martin Pitoňák ◽  
Michal Šprlák ◽  
Robert Tenzer
Keyword(s):  
Gravitational Potential ◽  
Higher Order ◽  
Potential Gradients

scholarly journals Long-term observations of pulsars in the globular clusters 47 Tucanae and M15

2017 ◽  
Vol 13 (S337) ◽  
pp. 251-254
Author(s):  
A. Ridolfi ◽  
P. C. C. Freire ◽  
M. Kramer ◽  
C. G. Bassa ◽  
F. Camilo ◽  
...  
Keyword(s):  
Gravitational Potential ◽  
Globular Clusters ◽  
Higher Order ◽  
The Other ◽  
Line Of Sight ◽  
Physical Parameters ◽  
Spin Period ◽  
Emission Beam ◽  
System Geometry

AbstractMulti-decade observing campaigns of the globular clusters 47 Tucanae and M15 have led to an outstanding number of discoveries. Here, we report on the latest results of the long-term observations of the pulsars in these two clusters. For most of the pulsars in 47 Tucanae we have measured, among other things, their higher-order spin period derivatives, which have in turn provided stringent constraints on the physical parameters of the cluster, such as its distance and gravitational potential. For M15, we have studied the relativistic spin precession effect in PSR B2127+11C. We have used full-Stokes observations to model the precession effect, and to constrain the system geometry. We find that the visible beam of the pulsar is swiftly moving away from our line of sight and may very soon become undetectable. On the other hand, we expect to see the opposite emission beam sometime between 2041 and 2053.

scholarly journals Coordinate Condition and Higher Order Gravitational Potential in Canonical Formalism

1974 ◽  
Vol 51 (5) ◽  
pp. 1598-1612 ◽  
Author(s):  
T. Ohta ◽  
H. Okamura ◽  
T. Kimura ◽  
K. Hiida
Keyword(s):  
Gravitational Potential ◽  
Canonical Formalism ◽  
Higher Order ◽  
Coordinate Condition

Robust endocytoscopic image classification based on higher-order symmetric tensor analysis and multi-scale topological statistics

2020 ◽  
Vol 15 (12) ◽  
pp. 2049-2059
Author(s):  
Hayato Itoh ◽  
Yukitaka Nimura ◽  
Yuichi Mori ◽  
Masashi Misawa ◽  
Shin-Ei Kudo ◽  
...  
Keyword(s):  
Image Classification ◽  
Symmetric Tensor ◽  
Higher Order ◽  
Tensor Analysis ◽  
Multi Scale

Tesseroids: Forward-modeling gravitational fields in spherical coordinates

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. F41-F48 ◽  
Author(s):  
Leonardo Uieda ◽  
Valéria C. F. Barbosa ◽  
Carla Braitenberg
Keyword(s):  
Gravitational Potential ◽  
Computation Time ◽  
Forward Modeling ◽  
Gravity Gradient ◽  
Maximum Relative Error ◽  
Gravitational Acceleration ◽  
Spherical Coordinates ◽  
Gravity Gradients ◽  
Gravitational Fields ◽  
Adaptive Discretization

We have developed the open-source software Tesseroids, a set of command-line programs to perform forward modeling of gravitational fields in spherical coordinates. The software is implemented in the C programming language and uses tesseroids (spherical prisms) for the discretization of the subsurface mass distribution. The gravitational fields of tesseroids are calculated numerically using the Gauss-Legendre quadrature (GLQ). We have improved upon an adaptive discretization algorithm to guarantee the accuracy of the GLQ integration. Our implementation of adaptive discretization uses a “stack-based” algorithm instead of recursion to achieve more control over execution errors and corner cases. The algorithm is controlled by a scalar value called the distance-size ratio ([Formula: see text]) that determines the accuracy of the integration as well as the computation time. We have determined optimal values of [Formula: see text] for the gravitational potential, gravitational acceleration, and gravity gradient tensor by comparing the computed tesseroids effects with those of a homogenous spherical shell. The values required for a maximum relative error of 0.1% of the shell effects are [Formula: see text] for the gravitational potential, [Formula: see text] for the gravitational acceleration, and [Formula: see text] for the gravity gradients. Contrary to previous assumptions, our results show that the potential and its first and second derivatives require different values of [Formula: see text] to achieve the same accuracy. These values were incorporated as defaults in the software.

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