Custom Electric Potential

I would like an electric potential with specific qualities, namely, quadratic in two dimensions. On the one hand, I could try and do a little thought experiment, as to which boundary gives the desired properties. Realistically though on the length scale I need it, the odds of producing the boundary are zilch. Much easier in terms of the multipole expansion. With this in mind, and knowing that copper wire along a cylinder makes for an easy setup, and that at least four terms are required for a quadratic potential, the following should work: V(x=0,z=a)=k, V(x=0,z=-a)=k, V(x=-a,z=0)=-k, V(x=a,z=0)=-k, with each wire along y. Assuming long wires, the potential for all four in the x/z plane is:

To confirm this has the desired behavior near the origin (and hopefully over some reasonable distance), I turn to the Taylor multi-variable expansion. Example partial derivatives:

Substituting into the expansion:

does indeed reveal that V ~ (2/{a*a})[z*z-x*x], as desired:

CUDA part I

NMR can provide unparalleled insight into local atomic structural details, although in the solid state interpretation of lineshapes is hindered by anisotropic broadening, eg., the attached MQMAS spectra of two distinct chemical sites. The situation grows much worse for disordered materials where parameters take on a stochastic nature. I’ve developed some HPC software to enable the simulation of MQMAS spectra for these scenarios, and now my attention is turned to implementation using general purpose graphical processor unit (GPGPU) programming. For the paltry sum of 70USD you can have a little super computer of your own in the form the NVIDIA GeForce 8400 GPU. I installed today and have started playing…

honours thesis

I completed this at UQ physics in 1999, here’s the abstract and the document itself. The device I constructed was originally intended for use with the scramjet project, although in my time was tested (successfully) on a small shock tunnel in the basement of Hawken. The shadowgraph images produced were spectacular although they seem to be MIA right now

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Time resolved imaging in compressible flows using a Cranz-Schardin Camera

A Cranz-Schardin camera arrangement was devised and constructed to obtain time resolved shadowgraphs of the flow over a cylinder. Detached shock waves are clearly visible as well as some three dimensional effects. The camera system uses a high power AlInGaP light emitting diode (LED), the model HLMP-DG08 by Hewlett Packard. The diode has a narrow viewing angle (6^o), high luminous intensity (6500mcd @ 20mA), with peak emission at 626nm and a FWHM¹ of 17nm. Within the camera system, the LED is pulsed rapidly at high currents, serving as both shutter and light source. These pulses are separated temporally and spatially, back-lighting the object which is subsequently imaged onto the film plane. Generation of pulsed input to the sources is provided by CMOS² circuitry coupled with an analogue driver stage for each channel, producing high current gain. The maximum output of the analogue driver stages was in the vicinity of 5 amps, producing sufficient light intensity in the LED’s to saturate a CCD³ camera. The light emitting diode is advantageous over lasers in this application for a number of reasons. Besides the obvious reduction in cost, LED’s are responsive (tau_res = 20ns) may be switched rapidly and have a fairly good signal to noise ratio for such a small, inexpensive device. The camera overall promises to be an invaluable diagnostic tool, at least in situations where competing luminosity can be reduced.

1. Full Width (at) Half Maximum (intensity).
2. Complementary Metal Oxide Semiconductor.
3. Charge Coupled Device.

thesis