Plotting the power dissipated in a charging RC circuit

This semester I'm teaching the recitation session for the second-year physics course on electricity and magnetism, which is basically an hour a week dedicated to helping students go over the concepts they encountered that week and help work through problems (sort of like a group tutoring session). I also taught it last semester, and we've caught up to an unresolved question I had from the same point in the curriculum.

We've been covering RC circuits, which are simple DC circuits with a resistor (the R) and a capacitor (the C) in line with a driving voltage (a battery, for simplicity). They're wired in such a way that you can move a switch to charge them, and then switch it to discharge; while charging, the charge on the capacitor fills up until its potential difference reaches that of the battery (at which point no more current can flow), and while discharging that charge flows away, dissipating as heat through the resistor. Both follow an exponential curve, which can be adjusted by changing the resistance and capacitance of the system (their product RC has units of seconds, and is known as the time constant of the system, how long it takes for the charge to rise or fall ~63% of the remaining way towards being full or empty).

Anyway, while the textbook we're using had some plots of the charge and current in RC circuits charging and discharging, it also mentioned what the power in the circuit was mathematically (the product of two competing exponential terms) but didn't provide a diagram. I've wanted to plot it myself to see what it looks like since last spring. I could do it using Python and matplotlib, I just never got around to it.

Enter Typst! I've been writing up the problems we cover in the recitation session in Typst so that students have a record they can go back to, and as mentioned in an earlier post it can include diagrams and plots. I started coding up the equations for charge, current, and voltage as a function of time to make some plots to serve as a reminder, and realized I could also encode the equation for the power dissipated in the circuit while charging, which comes out to be

\[P(t) = \left(\frac{V^2}{R}\right)(e^{-t/RC})(1 - e^{-t/RC}).\]

Here's what I included; the third plot shows how the above equation looks.

Anyway, I just wanted to share my discovery. Typst continues to impress me with its ease of use and accessibility. I gave a short introductory talk about it to some of my classes this week, since they're doing a lot of writing of lab reports and it could be useful. Being introduced to \(\LaTeX\) in college was an important milestone in my life and I think learning Typst has the potential to be as revolutionary for them if they're continuing on in STEM fields (or even if they aren't, since Typst can be used for any kind of writing). One of my colleagues even asked me this week if I could do a short presentation on it for his class so they could use it for their (math-heavy) homework. I think it's safe to say I've found my latest obsession at this point, so we'll see where it goes from here. A hui hou!

A new computer! (Sort of)

I was thinking recently that it's been about a year since I moved, only to find when I checked today that it has, in fact, been exactly one year.

It's also been about a month at this point and I haven't mentioned it yet due to being busy, but I'm writing this on a new computer. Well…sort of. A friend of mine recently upgraded his computer out of need (and when it became clear the RAM pricing crisis isn't ending anytime soon), and had a spare motherboard, CPU, and 48 GB of RAM from 2020 which he donated to me. It's DDR4 RAM, which is a generation behind the current standard, but also a generation ahead of the 24 GB of DDR3 RAM I had before. I was just beginning to bump into some constraints with that much RAM, so doubling it has been nice.

It's also an AMD motherboard and CPU (Ryzen 7 5800), in place of my old Intel i5-4690K. I've been intending to switch from Intel to AMD for several years now if I ever had the chance, so this worked out well. While Intel definitely had the advantage in processors for some years, AMD has been steadily closing the gap more recently, especially in areas that mattered to me: AMD processors tend to have more cores and do better at crunching through parallelizable tasks like encoding video. (Both are plenty fast enough for the games I play.) I did do one test where I rendered a short video on my old CPU and the new one, but the photo I took of the time on the old CPU was blurry so I can't say exactly how much faster the new one is (though it is definitely faster; in single-core performance it's rated 4.8 GHz compared to 3.5 GHz for my old CPU).

Near the end of September I took my computer apart and performed the delicate motherboard replacement surgery. It passed mostly without incident, other than needing to make sure various pieces were actually wedged in their sockets good and tight. A CPU cooling fan came along with everything, and since I had no idea if my 2014 watercooling pump would fit in a 2020 motherboard I opted for the fan. One of the four little plastic stand-offs holding the brace for it was missing, so I measured it, went down to my workshop, and cut a new one out of a bit of old dowel with a few minutes' work.

The newly-made part…

…installed and keeping those braces off the motherboard.

As far as I can tell it's doing fine. Not that my computer ever ran particularly loud, but I haven't noticed any big differences in noise – if anything, the new fan might be quieter.

Overall it's been good. I haven't noticed any mind-blowing differences, but things generally do feel a bit snappier. I'll need to get back to video-making or otherwise find some way to stress-test it and see how it performs. We'll see what happens! It's a busy semester for me. A hui hou!

More hurricanes!

The hurricane seasons continues to churn in the Pacific, kicked into overdrive by the strongest El Niño on record. This past Saturday hurricane Nolo swung by south of the islands, bringing some rain but staying far enough away to not bring much wind. Thankfully there wasn't much damage; I think only a few people even lost power. UH Hilo preemptively shut down Thursday and Friday, which – as the AC remains broken in STB – was a welcome opportunity to work from home and catch up on grading homework in some lovely cool weather. In fact this week the word came down that we're to minimize our time in the building, with various classes being temporarily relocated, so I've been working mostly from home the past few days. The AC may be fixed next week, though, so we'll see how that goes. Never boring around here! A hui hou!

More Typsting

It's been a month since I first tried out Typst, and I have quickly fallen in love. I first used it to write up the syllabi for my classes at the beginning of the semester. They were functional, and looked all right, though were a few things I wasn't able to figure out in the limited time I had. Then I found myself going back and fixing those things, adding new features, turning common features into a template to apply, and occasionally sometimes often using it as a way to procrastinate from other important work (like grading lab reports).

Last week I decided to try using it to write out the problems and solutions from my recitation session (for the calculus-based second year electricity and magnetism course PHYS 272). I'd been providing students with photos of my hand-written notes, but those are always terse and limited to what I need as I'm not overfond of writing. With Typst, I can not only recreate them, but trivially expand upon them and provide context for why I'm taking the steps I am towards the solution.

In practice there was a consideration which kept me from doing this sooner, and that's the presence of diagrams. Much of the problem-solving in E&M involves little pictures, diagrams of the simplified problems we're tackling. They aren't usually very complex, but they're a step beyond the pure text and math I was already getting used to writing in Typst.

Fortunately, Typst has a solution for this: the CetZ package, which allows drawing figures and diagrams within a document. \(\LaTeX\) has something similar in the form of the TikZ package (which inspired CetZ), but while I've been aware of TikZ's existence for quite a few years now I've never had enough motivation (or need) to get around to learning it. With how much fun I was having with Typst, I decided that maybe learning CetZ on top would be beneficial.

And while there have been some difficulties along the way, I've been having a lot of fun with it as well! CetZ is, by its own admission, not as mature as TikZ, but it's already plenty powerful for what I need. Within a few hours of reading its tutorial for the first time Wednesday morning I was making simple diagrams, and I've already improved quite a bit in the intervening time. With the addition of CetZ-Plot, a package that adds plotting capabilities to CetZ, I was even able to get the example shown below under “Electric field of a uniformly charged insulating sphere,” where I could plot the actual \(1/r^2\) fall-off of an inverse-square quantity by defining a function and plotting it.

I'm sure everything I've done with CetZ can be done with TikZ as well, but I was seriously impressed at how easy Typst makes things and how quickly I was able to pick it up. Typst's incremental compilation also means that changes to my diagrams are rendered instantly whenever I change anything, which makes it very easy to iterate and figure out why something isn't working like I think. Thankfully, I now have a reason to keep using it each week as I type up my notes! I even feel something of a desire to make a presentation on it to share with people, but we'll see if that goes anywhere*. A hui hou!

*I am teaching a writing intensive class, and it could be beneficial for students to be aware of…

Trying Typst for the first time

I've been meaning to check out Typst for over a year now. The premise was intriguing: what if we rewrote \(\TeX\) (and \(\LaTeX\)) from the ground up, discarding the parts that made sense fifty years ago and taking everything we've learned in the meantime to make a simpler, clearer markup language? (And also wrote it in Rust for blazing speed.)

I've mentioned \(\LaTeX\) and my love for it many times on this blog. I think I was first introduced to it during the spring semester of 2010, and my immediate thought was: where has this been all my life? \(\LaTeX\) is a markup language (built as an extension of the earlier \(\TeX\)) where documents written in it are compiled to output a nicely typeset version (usually in a format like .pdf or .ps). One of its big selling points is its ability to handle complex mathematics; for scientific writing in particular, which may need to include complex equations with highly specific formatting, it's a lifesaver. I've got a Javascript library called MathJax on this blog which lets me use (some) \(\LaTeX\) formatting to display mathematical output such as:

\[\text{Coulomb's Law: } F=k\frac{q_1 q_2}{r^2}\hat{r}\text{ where the Coulomb constant } k=8.988\times10^9\frac{\text{N}\cdot\text{m}^2}{\text{C}^2}.\]

I was initially drawn to \(\LaTeX\) for the beauty of its output. It was also practical: you can write pretty much any kind of document in \(\LaTeX\), and most scientific journals allow (or require) manuscripts to be submitted in it. I wrote my thesis in it, then turned it into two papers for publication.

At the same time, \(\LaTeX\) is not without its weaknesses. The underlying language \(\TeX\) is both very powerful and very complex (\(\LaTeX\) is essentially an addon for \(\TeX\) to make it easier to use), has a famously steep learning curve, doesn't natively handle UTF-8 characters, and even after years of using \(\LaTeX\) I occasionally run into bizarre issues. Perhaps the strangest was discovering that a hyperlink which spanned a page break in my thesis caused the whole document to fail with a very obscure error message – one I actually never found a real fix for despite much searching. The only advice I could find which worked was to adjust the length of the text before the hyperlink such that it no longer crossed two pages!

This is not to disparage \(\LaTeX\) – it's still worth knowing, I think, has been immensely useful for many people around the world, and it still feels a little magical to watch it take a series of abstruse text and turn it into something beautifully formatted. However, I'm cognizant of its flaws, and open to new experiences.

Enter Typst.

There's something of a pattern in software development, where after developing a piece of complex software, sometimes the best way to improve is to start over from scratch using the lessons learned rather than try to continue patching and editing it. Typst is essentially that rewrite for \(\LaTeX\), taking lessons learned from the last forty years and improving upon it (at least in theory).

Over the summer I read through the Typst tutorial, though Hurricane Lala knocking out power for two days the week before the semester started put a crimp in my plans to try writing my syllabi with it. A practical demonstration of Typst is that I sat down Sunday afternoon the day before I was due to begin teaching and attempted to write a syllabus in it (based on an existing \(\LaTeX\) template I had), and within an hour or two I'd created something which mimicked ~95% of the original's look while requiring much less text to pull off. I was seriously impressed, and then hooked.

It's a little hard to show off what Typst can do, since by design it's often used to mimic the look of \(\LaTeX\) documents. What I can say, however, is that it's much easier to use. This morning in some free time I followed the tutorial instruction to turn my syllabi into a template for future syllabi to use, something I've never even attempted in \(\LaTeX\).

It's also a real joy to use due to lightning-fast compilation. With \(\LaTeX\) you have to run a compiling command, which even for relatively short documents often takes a few seconds. Typst compiles incredibly quickly due to an incremental compilation system, allowing you to see the output of what you're typing in basically real time. And coming back to writing \(\LaTeX\) for this post, I find myself appreciating that all the more; it's amazing what a shorter feedback loops does, allowing you to more easily experiment and try things and see the result immediately.

I could wax lyrical about other features of Typst*, but this post is getting long and I have a feeling I'll be talking about it more in the future. I find myself drawn back to it, wanting to experiment and see what else I can get it to do. And that's perhaps the greatest endorsement I can give Typst: using it is fun. I'm reminded of the heady days when I first discovered \(\LaTeX\), and I can hardly wait to write more in Typst and see what interesting and beautiful things I can create with it. Hopefully I can show some off in the future when I've learned more! A hui hou!

*Typst's syntax is generally lighter and simpler than \(\LaTeX\)'s, its error messages when something is broken are extremely helpful in pointing you to the problem, it has a powerful and flexible CSS-like functionality built-in which makes it a snap to style elements, etc.

Hurricanes and (UH) Hilo

Well, it's been an eventful month here. A week-and-a-half ago on the 15th hurricane Lala swept by and knocked out power to 60% of the entire state, the week before the fall semester started. I lost power for ~54 hours from Saturday afternoon through to Monday evening, and there are people who still haven't gotten it back. We didn't actually see too much wind or rain here in Hāmākua, but Puna and especially Kāʻu got slammed. Then tropical storm Moke passed by on Saturday, but thankfully was far enough away not to add much more than a little rain. I definitely learned a few things about disaster preparedness (namely, that having solar and a battery is the way to go, having spoken to multiple people who were able to keep their fridges running for even longer than the two days I was without electricity).

And did I mention the fall semester started at UH Hilo on Monday? I'm back to teaching with a few more classes this semester, though most of them are labs for which we have experiments already prepared. (I will be grading a lot of lab reports, though.) There was a bit of the usual start-of-semester craziness, with the building AC once again not working, the internal network acting up, the laptop I'd been using last semester giving up the ghost over the summer, and me forgetting to put in the list of rooms I needed access to for my key fob until the day before, but things have been working out. (The AC has been halfway repaired, the network seems to have sorted itself, I got my key access before the end of Monday, and the college has a loaner laptop I can use which should come this week.) I also switched up how I'm writing my syllabi in a way which should make it easier to update them (namely, using Typst instead of \(\LaTeX\), but that'll get its own post here shortly.

In brief: no real damage about the place (but hurricane seasons lasts through November), classes have started, and I'll probably get really busy next week as the labs start to kick off. But I do want to talk about Typst now that I've actually gotten around to trying it, so expect a post on that before too long. A hui hou!

Hummingbirds, sea lions, and honey bees, oh my!

I spent the final week of July in California visiting family where I had the opportunity to take a number of pictures of animals I don't see very often. Hummingbirds were active about the feeder, we visited Pier 39 in San Francisco and saw the sea lions there, and there were a lot of thirsty honey bees around in the July heat.

It's difficult to get a good shot of a hummingbird in flight with how fast they move, so my only chance was when they came up to the feeder to eat. I tried on two different days (seen here) and I'm impressed with how clear the wings came out in the first photo considering the blur they were in person. I was also impressed by how close they let me stand to get these photos. Occasionally one would fly over even closer, at about arm's reach, to hover at head-height and regard me quizzically for a few seconds, a delightful (and ever-so-slightly unnerving) experience.

We were fortunate while visiting Pier 39 that there were a number of sea lions there, since it varies. Mostly they were napping in the sun, though there were generally always one or two swimming about, jumping on or off the floating rafts, and occasionally getting into disputes.

And sometime after my last visit, my parents let a commercial beekeeper park some hives on their property. (It's a great location with all the eucalyptus and almond trees around.) I don't think I've ever really mentioned it on this blog, since it happened before I started writing it, but I used to have bees for a few years before moving out to Hawaii. I enjoyed it, though I'm a poor bee-haver; I picked a bad time to start between Varroa mites and Colony Collapse Disorder (and it hasn't exactly gotten better since then), and my hives didn't manage to survive. I figured it best left to the past when I moved, but I've always retained a sort spot for honey bees. When some fell into the pool I was filling up for them I rescued them with a leaf and let them chill on my hand while I did some macro photography. It's always funny to me how matter-of-factly they go about cleaning and drying themselves before taking to the air again.

And that's it for this post. There are plenty of cool critters here in Hawaii (including honey bees), but it's nice to see some that I haven't in a while. A hui hou!

Making custom coasters

Over the summer I've been experimenting with various woodworking projects, and one which I made on something of a whim was a set of coasters. I thought it'd be fun to take some thin strips of different-colored wood, glue them together (laminate them), cut out short pieces, then glue those pieces together in a pin-wheel, like this:

Woods used are whenge (black), jatoba (brown), maple (white), and purpleheart.

Here they are after I leveled out the slight differences in thickness in the wood strips and applied a finish (on top of a few cutting boards I also made):

The mineral oil in the background is for the cutting boards, for these I used a spray-on tung oil finish.

They came out looking pretty good, but I'd underestimated how much wood doing the spiral would take, so from my initial, roughly 24-inch-long piece of laminated wood strips I got a grand total of two coasters. However, they were thick enough that a friend suggested cutting them in half to make four…which I proceeded to do in possibly the dumbest, hardest, least-efficient way by using the reciprocating saw I'd acquired as part of a package deal when I bought my first power tools back in November (and hadn't used until now).

Have I mentioned I don't own a vice?

Though even if had it wouldn't have helped much, as I discovered when I built a Frankenstein-ian contraption of various clamps and pieces of wood to hold the coasters as I cut them. My attempts to secure them usually lasted a couple of seconds before the oscillating action of the reciprocating saw worked them loose resulting in a lot of awkwardly re-clamping coasters, but it somehow – incredibly – resulted in two sets of roughly-equal thickness coasters with a remarkably straight cut across them.

They're definitely not perfect (even after some more sanding and smoothing), and it was mostly a lesson in what not to do, but y'know, sometimes those are helpful. They might still work as coasters (I haven't really tried), they do look pretty, and it was just a spur-of-the-moment project, so it's all good in the end. Just part of the learning process! A hui hou!

On the difference between gasoline and electric chainsaws

Around the time I moved in last year I realized I was going to need a lawn mower, and also that (for the first time in my life) I was in a position where owning power tools made sense. I hate dealing with gasoline and internal combustion engines and the house has solar panels, so electric was the obvious way to go for a lawn mower. After some deliberation I settled on Ryobi, which fit my needs (and budget) as a DIY-er rather than a professional tradesman. I've been pretty happy with the self-propelled mower I got, along with a number of power tools for woodworking.

One thing I didn't have much need for was a chainsaw, due to there not being many large trees on my parents' property. In May, however, someone I know in Puna who'd heard I was getting into woodworking through a mutual friend reached out to say he'd had some trees come down during some stormy weather in March, and asked if I wanted some of the wood if I'd come cut it up. I said yes to free wood, and while I started out using his landlord's gas chainsaw I knew I'd eventually need one of my own to cut the wood further when I got it home. And that's how I became the owner of a 16" Ryobi electric chainsaw, and had opportunity to try both gas and electric saws recently.

The difference in volume is the obvious point of comparison; I've never been fond of what I can only term the aggressively angry whine of a gas chainsaw revved up. The electric version isn't silent, but the noise it produces is primarily from the chain moving around the blade, and it is a lot quieter – you barely need hearing protection at all.

A less obvious difference is how an electric chainsaw is always ‘on,’ essentially. With a gas chainsaw you have to explicitly start it. This can be an involved process if it hasn't been used in a while, and at minimum requires giving the starting pull-cord a couple of pretty good yanks. It's a point of friction, so you'd rather not do it too often – yet once it's running you want to minimize time spent not cutting, since it's burning gas while idling. This inherent tension makes cutting up a fallen tree tricky since it's an iterative process: you usually can only make so many cuts before needing to move the now-separated branches out of the way so you can reach more parts of the tree. (To be fair, this is based what I encountered doing it solo ­– someone to help move branches out of the way would alleviate this somewhat.)

With an electric chainsaw, however, it's trivial to make a single cut, move a branch, make a cut, etc., in ways that would be really inefficient while burning gas. If I were a professional lumberjack or arborist I'd probably still have reason to be using a gas chainsaw, but for occasional home use like cutting up a single downed tree it's a much more pleasant experience.

Anyway, we'll see what comes of all this cypress wood I've acquired. The trees were clearly healthy and just went down in the storm, as they were still sopping wet when I cut them up even months after falling. From what I've read they'll need to dry for some time before I can really use the wood, but I'm looking forward to eventually making use of them. Future projects, perhaps. A hui hou!

Happy Tau Day 2026!

Happy Tau Day everyone! It seems like hardly any time at all since last year's Tau Day, which is probably a reflection of how utterly, overwhelmingly, busy I've been most of the time between now and then, only finally slowing down this past month-and-a-half. This slowdown (and some non-rainy weather at last) has allowed me to finally start getting to some projects around the house and yard that I identified soon after moving in, so that's been nice.

I don't have anything particularly tau-related to discuss, except for the fact that this week I started looking into Typst. Much like its inspiration \(\LaTeX\) Typst seeks to be a mark-up language that can be used for writing pretty much anything, including scientific or technical papers with complex formatting requirements or mathematical equations. I'll have more to say about it in the future when I've had more time to actually try it (so far I've only read through the tutorial), but it looks interesting. I've heard journals are starting to accept manuscripts typeset in Typst, so it seems to be catching on in the broader scientific world.

We'll see where that goes, though. A hui hou!