SIPS2022 Volume 3 Horstemeyer Intl.Symp. Multiscale Materials Mechanics & Applications

Editors: | F. Kongoli,E. Aifantis, A, Konstantinidis, D, Bammann, J. Boumgardner, K, Johnson, N, Morgan, R. Prabhu, A. Rajendran |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2022 |

Pages: | 382 pages |

ISBN: | 978-1-989820-38-4(CD) |

ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |

We introduce a computational framework for performing numerical experiments in weak gravity dynamics under the conditions of non-flat inherent geometry of space. It

is a generalization of the Particle Mesh method for the case of non-Euclidean geometry. As such, it includes a solver for the Poisson Equation and particle accelerations

for the general case of a non-flat three-dimensional space. The framework is useful for performing numerical experiments to investigate the Inherent Structure Hypothesis

explanation of the dark matter effect described in earlier work by Tenev and Horstemeyer (2019). It assumes weak gravity and nearly static gravitational fields,

which are valid assumptions for our common experience of gravity and are consistent with the conditions under which the Dark Matter effect has been observed. The

inputs to the framework are: 1) a displacement function into a transverse fourth dimensions used to specify the inherent curvature of space, 2) a fixed mass density

field, and 3) a collection of point particles that only interact through their contribution to the gravitational field. The framework was implemented in MATLAB R and was validated by using it to compute the Sun’s gravitational field and comparing the result to the theoretical prediction.