Since googling up NASA’s online VLF receiver mp3 stream (seems to be defunct now, fortunately there are other streams available.. see http://abelian.org/vlf/) I wanted to try to receive these signals myself. So I came up with some schematics on the internet for a basic vlf receiver and built and tested a couple of these.
The sferics are crisp, loud and clear, the circuits work very well if the conditions are right. Small enough to fit a pocket, it’s interesting to walk aroud the area I live and listen in to the various weird signals eminating from all sorts of electronics and machinery. I’ve yet to record auroral activity, but that is next on the agenda.
I want to write a little bit more about my studies on waves and automata models. I wrote a vastly improved TLM code on MATLAB which now includes for example first order absorbing boundaries. It is important to distinct this approach from a mathematical model, this is a analogous physical system to wave propagation. You could think of it as using computer memory element grid as an discrete analogy to the vacuum.
This sort of physical modelling and computation was first used by a Hungary born mathematician and electrical engineer Dr. Gabriel Kron in 1943 while working for General Electric (see paper called ‘Equivalent Circuits to Represent the Electromagnetic Field Equations’ on Physical Review Vol.64 Numbers 3-4 1943.) The approach involved analog computing in the form of a RLC network. The approach was then picked up by P.B. Johns and R.L. Beurle (see paper ‘Numerical solution of 2-dimensional scattering problems using a transmission-line matrix’ on Proc. IEE, Vol. 118, No. 9, 1971, pp. 1203-1208) applied to ‘computors’ as they were then called.
The Johns and Beurle numerical method involves applying a simple scattering automata rule to a discrete node grid. This doesn’t exactly involve integration in the sense that a discretisized mathematical model would; only arithmetic needed is addition (floating or fixed-point) for summing up the node incidence and reflection time-step impulses involved in the scattering rule (which are directly derivable from normalized unitary impedance electrical node network.)
The simple TLM here is configured for the classic Young double slit experiment. Although this particular setup could be thought to just propagate the electric field, the corresponding magnetic field can be derived aswell together with different permittivity and permeability coefficients to model material properties.
Studying wave equation discretization has personally led me to understand and appreciate the physics which rely heavily on this mathematics, namely electrodynamics and field theories. I think this sort of ‘visual intuition’ is a important part of learning when dealing with dynamics which can be extremely complicated and complex, at least it has been exactly that for me. Studying the computability of these equations has definetly paved some way in these theoretically dense subjects.
I recently made few basic computer models of the Schrödinger wave equation with MATLAB for computational physics course work.
Here is a two dimensional version of the discretisized time-dependent wave equation calculated using a clever leapfrog integration algorithm scheme by Visscher.
Things start to get visually more interesting when integrating the time-dependant equation in three dimensions.
Here is another run with a slightly different value for the momentum of the wavepacket.
Unfortunately MATLAB seriously lacks in the volumetric plotting department so we’ll have to do with phong shaded isosurfaces instead of a more appropriate voxel based plot. Don’t worry, this will not end up forming black holes and destroying Vulcan.