42 research outputs found
Els éssers intel·ligents extraterrestres no existeixen
Un punt de vista científic contrari a l'existència de vida intel·ligent fora de la Terr
General Relativity As an Aether Theory
Most early twentieth century relativists --- Lorentz, Einstein, Eddington,
for examples --- claimed that general relativity was merely a theory of the
aether. We shall confirm this claim by deriving the Einstein equations using
aether theory. We shall use a combination of Lorentz's and Kelvin's conception
of the aether. Our derivation of the Einstein equations will not use the
vanishing of the covariant divergence of the stress-energy tensor, but instead
equate the Ricci tensor to the sum of the usual stress-energy tensor and a
stress-energy tensor for the aether, a tensor based on Kelvin's aether theory.
A crucial first step is generalizing the Cartan formalism of Newtonian gravity
to allow spatial curvature, as conjectured by Gauss and Riemann
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas