Related papers: Mathematics and explanation in astronomy and astro…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
Spirals in galaxies have long been thought to be caused by gravitational instability in the stellar component of the disk, but discerning the precise mechanism had proved elusive. Tidal interactions, and perhaps bars, may provoke some…
In a series of papers, we propose a theory to explain the formation and properties of rings and spirals in barred galaxies. The building blocks of these structures are orbits guided by the manifolds emanating from the unstable Lagrangian…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
Scientific articles, for instance in the field of astrophysics, are often filled with a variety of images. In philosophical studies, these images are usually analyzed in terms of their function within the scientific argument presented in…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
The dust in galaxies makes radiation transport calculations in them absolutely necessary. It is not only common practice in Astrophysics, but also wisdom, to try to make as simple models as possible to simulate physical systems. For spiral…
During the last few decades, great effort has been made towards understanding hydrodynamical processes which determine the structure and evolution of stars. Up to now, the most stringent constraints have been provided by helioseismology and…
The Sun provides a critical benchmark for the general study of stellar structure and evolution. Also, knowledge about the internal properties of the Sun is important for the understanding of solar atmospheric phenomena, including the solar…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
We summarize some of the compelling new scientific opportunities for understanding stars and stellar systems that can be enabled by sub-milliarcsec (sub-mas) angular resolution, UV-Optical spectral imaging observations, which can reveal the…
The mathematical universe discussed here gives models of possible structures our physical universe can have.
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
The disciplines of asteroseismology and extrasolar planet science overlap methodically in the branch of high-precision photometric time series observations. Light curves are, amongst others, useful to measure intrinsic stellar variability…
The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic…
The study of the Universe and all its contents, the physical phenomena and the evolution of the sky objects has always attracted the Humanity. The Astronomy begins to try to explain these things, others sciences too. Therefore, we think a…
We commonly think of mathematics as bringing precision to application domains, but its relationship with computer science is more complex. This experience report on the use of Racket and Haskell to teach a required first university CS…