Repost: The varied and graphically-intensive world of nomograms March 3, 2013
Posted by mareserinitatis in electromagnetics, engineering, geology, geophysics, grad school.Tags: electrical engineering, geology, geophysics, magnetic fields, nomograms, smith chart
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I spent a good chunk of time yesterday dealing with Smith charts, and I remembered in the recesses of my brain that I had once posted something about them in the old blog. Sadly, it wasn’t as technically intensive as it could have been, but I still decided it was fun enough for a repost. If you would like to read something with a bit more technical content, you can check out Fluxor’s post on Smith charts at EngineerBlogs.
A nomogram is an incredibly useful tool. It is a visual “solution” to an equation. Usually it is some sort of chart or plot that allows you to figure out “what you’ve got” and you can move from there to “what you need”.
Anyone who works on the analog side of electrical engineering often gets to play with Smith charts, which were of course invented by Baker*. They’re rather confusing looking things:
The usefulness in Smith charts is that they can allow you to determine things like how much more transmission line you need to get an impedance match in your device. Rather than trying to solve an equation using complex values, you can just move along the curve in a Smith chart. (Disclaimer: While I learned how to use Smith charts in my microwave engineering course, I unfortunately would need to spend some time with my buddy Pozar to remember how to do it now.) I’m also aided in my negligence by the fact that there are a lot of nifty software programs that will compute the necessary values, reducing the necessity of using a Smith chart. (Thank goodness for computers. If it weren’t for computers, I’d probably have to learn how to use a slide rule, too.)
What brought this up is that I was introduced to a nomogram used by scientists in the field of paleomagnetism. The nomograms in this case showed relationships in demagnetization of magnetic minerals. For instance, if you have a mineral that has been exposed to a temperature of 400°C for 1000 seconds in the lab, you can follow the line on the nomogram and discover that the same amount of demagnetization could be caused by sitting in a temperature of 350°C for 100 million years.
So why do I spend time mentioning this on my LJ? Could it be because knowing that there are graphical methods to approximate solutions to problems is good to know? It is good to know, but it’s not why I bring it up. The reason I felt the need to post about it is because I had an entirely different picture of nomograms when I was sitting in class:
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*Just kidding. It was developed by Phillip H. Smith.
It’s freezing; no wait, it’s melting… May 23, 2011
Posted by mareserinitatis in engineerblogs.org, geophysics, papers, research, science.Tags: geodynamo, inner core, magnetic fields, outer core
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First order of business is to send you to EngineerBlogs.org where I posted today on how engineers who do simulation are not, in fact, inept experimentalists. Just come back after you’ve read it (and commented!).
Are you done yet?
The other thing I wanted to mention was that I came across an article on LabSpaces about how Earth’s core may be continually freezing and melting. I am interested because of implications for the geodynamo. (As a side note, I haven’t read the paper directly, just commenting on the LabSpaces post.)
Earth’s outer core is composed primarily of molten iron, but there are some lighter elements in there. The generally accepted theory is that most of the energy to power the geodynamo (which generates Earth’s magnetic field) comes from the freezing of the outer core. It’s still really hot down there, but the pressure is so high that the iron can become solid. As the iron freezes out, it releases energy. Another source of energy is the rising of the lighter elements as they don’t freeze out.
There are some problems with this theory. First is that the iron isn’t freezing out at a rate to produce sufficient amounts of energy to power the geodynamo. That is, it provides some of the energy, but not all of it. If this freezing out process were to produce the amount of energy needed to power the geodynamo entirely, it would have entirely solidified in about a billion years. The planet has been here for about 4 billion, so obviously that’s not what’s going. Second, the amount of energy generated by the inner core is proportional to its surface area. This means that you would expect Earth’s magnetic field to increase over time as the inner core grew. Experimental evidence suggests that Earth’s magnetic field strength was about the same, even 3 billion years ago.
The theory that the inner core is continually freezing and melting again might change some of the perspective on this. If the core freezes and generates energy and then melts again, this could potentially explain why the core hasn’t frozen out and may lead one to believe the core may have been growing for longer than anticipated. On the other hand, if the remelting process consumes a significant amount of energy, it could definitely not help with the energy balance issues. If this process is consuming a lot of energy, then that may actually exacerbate the problem because that means more energy may need to come from some other mechanism.
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