scholarly journals A numerical approach to space-time finite elements for the wave equation

2007 ◽  
Vol 226 (1) ◽  
pp. 466-476 ◽  
Author(s):  
Matthew Anderson ◽  
Jung-Han Kimn
2013 ◽  
Vol 34 (1) ◽  
pp. 390-434 ◽  
Author(s):  
S. Falletta ◽  
G. Monegato ◽  
L. Scuderi

Author(s):  
Timo Saksala ◽  
Reijo Kouhia ◽  
Ahmad Mardoukhi ◽  
Mikko Hokka

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.


Author(s):  
Espen Haug

We have recently presented a unified quantum gravity theory [1]. Here we extend on that work and present an even simpler version of that theory. For about hundred years, modern physics has not been able to build a bridge between quantum mechanics and gravity. However, a solution may be found here; we present our quantum gravity theory, which is rooted in indivisible particles where matter and gravity are related to collisions and can be described by collision space-time. In this paper, we also show that we can formulate a quantum wave equation rooted in collision space-time, which is equivalent to mass and energy.The beauty of our theory is that most of the main equations that currently exist in physics are not changed (in terms of predictions), except at the Planck scale. The Planck scale is directly linked to gravity and gravity is, surprisingly, actually a Lorentz symmetry as well as a form of Heisenberg uncertainty break down at the Planck scale. Our theory gives a dramatic simplification of many physics formulas without altering the output predictions. The relativistic wave equation, the relativistic energy momentum relation, and Minkowski space can all be represented by simpler equations when we understand mass at a deeper level. This not attained at a cost, but rather a reflection of the benefit in having gravity and electromagnetism unified under the same theory.


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