Wetton Numbers

When modelling physical processes (that is, writing down mathematical equations that describe a physical system, at least approximately), many parameters can enter the model. If you consider idealized fluid flow, the parameters are the density, viscosity and speed of the fluid, and the size of the object it is flowing around. Actually, the behaviour of the fluid does not depend on all four of these parameters separately, but just a single combination of them called the Reynolds number (usually abbreviated Re). A situation changed to a fluid twice the viscosity of the original and with flow speed also twice as fast will behave exactly the same (at least, the same to the level that the Navier Stokes equations can accurately describe the flow). The Reynolds number is dimensionless and in words represents the ratio of inertial to viscous forces in the fluid. Flows with a high enough Reynolds number are turbulent. Small Reynolds number flows are laminar.

Around 10 years ago, as I was approaching my fortieth birthday, I was working on a project modelling fuel cell behaviour. Specifically, I was looking at models of how unit fuel cells in a stack affected each other due to electrical coupling through currents in shared current collecting plates (bipolar plates, which sounds kind of funny now that I look at it years later).  I identified a dimensionless parameter in this stetting that is the ratio of bipolar plate electrical resistance to equivalent resistance in the local electrochemical reaction. It could be used to estimate the number of adjacent cells that would be affected by an anomalous cell in the stack through this electrical coupling. In the paper I wrote up, I labelled this parameter W. I hoped that people would refer to it as the Wetton number. This was a bit egotistical, I admit, but it was an important birthday coming up for me. However, while the paper was in draft, I discovered that a very related idea was known in the literature since the 1940s as the Wagner number. Not only did that bastard Wagner steal my number (well OK, he did get there first by quite a large margin), but his number was the inverse of mine, and I had to do the work to change this everywhere that it occurred in my draft.

While working with Jean St Pierre at the Hawaii Natural Energy Institute earlier this year, I identified another candidate for the Wetton number, W1. It is the solubility of a trace gas component (possibly a contaminant) in air, scaled to the fuel cell setting. A high W1 means that the trace component will be almost completely scavenged by the water by fuel cell outlet. You see the "1" on the W1, so you can guess that there is a W2. The second parameter describes a possible, generic first order ionization of the dissolved component. The formation of these ions effectively allows more of the component to enter the water. It is more significant at low concentration levels. Not all gases will ionize significantly in water but there are some interesting ones that do, like sulphur dioxide. The ionization lowers the pH of the water (this effect is one of the contributors to acid rain). Maybe these new candidates will actually be known as Wetton numbers. This would be a nice fiftieth birthday present!

More (semi) Scrap Wood Carpentry

I returned to my scrap wood carpentry hobby the last few weeks. I have looked online at various web sites about carpentry, trying to actually learn something. As I expected, it starts to get pretty complicated as soon as you get past the idea of screwing two boards together. Beyond the construction and finishing techniques, you have to take into account the properties of solid wood, which will expand and contract significantly with temperature and humidity. There seem to be limitless (expensive) tools you need to do any serious carpentry. I am going to try and make do with my circular saw, router, drill and sander (nice ones that my father got me over the years), and the odd hand tool I have already. Somewhere in the back of my mind I had hoped to build up enough skill playing around with scrap wood to be able to do some kitchen renovations we have in mind on my own. I just don't think that will happen now, we'll have to get a professional in. I do have a few things I'd like to make on my own still, for fun - and the higher content of scrap wood the better (you'll see below that I have had to actually buy some wood for my latest projects). I want to at least get to the minimal stage where I can build a few custom things to fit specific spots in our house that don't have nails, screws, or gaps between the boards showing. This seems to be one of the minimal goals of furniture making. I haven't been following plans, a lot of the fun is coming up with the design. 

The two things I made recently are a computer desk that fits in a particular, narrow gap, shown on the left below. On the right is a workbench. I made it with the gap in the middle for long rip cuts and the same height as a commercial bench my parents in law gave me a few years ago, so I can use both for bigger pieces. I may have to tinker with the arrangement of the top boards to allow room for clamps as I start to use it, I just don't have enough experience yet to know where they will be needed while arranging pieces for cutting, routing and assembly. Notice the off centre middle support on the bench. I used ideas from advanced geometry to determine the most aesthetically pleasing location. The tops of both pieces were made of new boards I had to buy for about $30. 

Food Shopping near the Makiki District of Honolulu

I know everyone is waiting for the food shopping entry in the blog for Honolulu (not), and I won't disappoint you. This mathematical army of one definitely marches on its stomach. I had an apartment in the Makiki district of Honolulu, at the corner of Pikoii and Wilder. Honolulu is divided up into relatively small districts (Waikiki is the most well known to tourists). Locals tell me that there is a real local flavour to life on the Islands. It is true that they are not large and traffic is heavy enough that getting around is slow even if you wanted to travel outside your area. So, in my area I shopped for food at three main places:

1. Safeway at the corner of Pikoii and Beretania. This seems pretty dull and in some ways it was. I could use my Safeway card from BC for discounts. What was interesting was that overall food prices were double that in Vancouver. It makes sense when you think that everything has to be shipped out there, and Hawaii is not close. It is interesting that locals praise stores like Safeway and Costco for coming to the Island and making prices "reasonable" to what they were before. If you can't stand patronizing Safeway there is a more local Foodland next door on Beretania with almost identical selection and pricing. 
2. Makiki Farmers Market at the corner of Wilder and Mikiki, Thursday evenings. This was just a few blocks away, on my bus route back from the University. Small market but all kinds of local fresh fruit and vegetables. I tried fresh pineapple, apple bananas, mangoes, long squash, Thai basil, all kinds of lettuce and tomatoes from this market - all great. Prices were not low, but competitive with Safeway and all local and fresh. 
3. Hawaii Farmers Market at the corner of King and Ward (in the parking lot of the Blaisdell centre), Wednesday evenings. This was a bit father away, but on my way home from the fuel cell test facility on the Hawaii Energy Corporation site. This is a larger market, with local coffees and fresh fish (except the week I was planning to get fish there). 

Another place you might want to check out for specialty liquors is Tamuras on Waialae (which seems to be the main street in Honolulu for locals). This is a bit of a trip outside the Makiki district. I stopped there on the way back from the Kahala Mall (which I went to on the city bus) where there is a Whole Foods, which I also recommend as a good place to shop for food.