I wish to be a successful mathematician. I want my papers to be read, enjoyed, even eagerly anticipated. I struggle, however, to write well. Most of my posts are stream of consciousness. They are my thoughts, with only a little reflection thrown in. This I don’t mind. My blog isn’t to advertise myself, allow inclusion …
Category Archive: Academia
A theoretical language to study numerical computation?
I’ve just finished Jörg Frauendiener’s, “On the applicability of constrained symplectic integrators in general relativity”. It’s a readable paper (the necessary background is given in the paper) about numerical integration in Hamiltonian systems. The idea here is that if we have a symplectic manifold modelling the states of some system of ODE’s, along with a …
What do we really know about Dark Energy?
I refer you to Ruth Durrer’s very readable (and short) paper with the same title as above. The main point of the paper is that all evidence for Dark Energy comes from the measurement of luminosity distance as a function of redshift and that energy/matter content of the universe is then inferred from this measurement …
Analytic work on constraint quantities lacking?
The paper provides a general introduction to how to perform analysis of the attractors of some dynamical system (with specified initial conditions) and then applies this to a particular initial value formulation of Einstein’s equations.
Rate of convergence not affected by lower order convergence near boundaries
I’ve just finished up my second reading of Gustafsson’s, “The convergence rate for difference approximations to mixed initial boundary value problems” and I’m still abit confused. The paper is referenced by (what seems to me) almost everyone and their dog as justification that a finite difference scheme can have one order of convergence less on …