# Dear Adam: Bizarre Love Triangle

I have extensive experience connecting the heart to the mind, and knows the only thing true love needs to grow is pure, brutal logic. As such, periodically, I will reach into the mailbag and answer your romantic queries. This week, I try to reduce a messy love triangle into a love… line?

Let’s try to turn your Bizarre Love Triangle into a Familiar Line of Affection

I am desperately in love with someone. But lo! There is a competing suitor! Unfortunately, my dear, sweet, conflicted lover can’t decide if my rival or I would be a better partner. “You are both so nice and are so good for me, but for different reasons!” It would appear that my sweet peach needs time to think, and see who will persevere through the indecision longer. Oh Adam, what do I do? How long do I wait? Please help.

Sincerely,

Strung-Along

Dear Strung-Along,

I am sorry to hear about your unfortunate circumstance. Oh, to be in such demand, am I right? Your “sweet peach” (or maybe sour apple?) appears to have their pick of the orchard. But we aren’t talking about fields of trees; love is a battlefield, and what you have here is a war of attrition.

Well, it’s not not true….

Like two starving vultures, you and your rival stare each other down over the steaming carrion that is your love, unwilling to fight directly (a good call, best avoid the Prisoner’s Dilemma), but terrified you will never find love like this again! How long do you wait? At what point have you waited too long? You certainly aren’t getting any younger… Let’s consider your options.

They say time is money, but love don’t cost a thing… but that’s nonsense, and “they” are wrong. Let’s think of your situation as an “all-pay, blind auction”, since I assume you are not on speaking terms with your rival. You both cast your maximum bid of time, and the higher bidder wins the love. However, both parties are still required to pay the lowest of the two bids.

Let’s assume you and your rival are equally desperate, so the value of love is L for both of you. If your bid is b, then losing will results in -b happiness, while winning results in L-b happiness. If you both bid the same amount of time then I assume you will engage in polygamy and end up with a happiness value of (L-b)/2.

Knowing that you can wait forever, but only have to wait as long as your rival does, suggests it may be in your best interest to indeed plan to wait forever. But what if you both decide to wait longer than (L-b)/2?  You and your rival both risking mutually assured destruction, coming out a bitter, disenchanted lover if you win, or dying cold and alone if you lose. Both are negative results, in my professional opinion. We can simplify our problem and hopefully determine our strategy by considering two resolutions:

1. There is a high bidder, and a low bidder. If you think you will be the low bidder, the logical strategy is to quit immediately, insuring you don’t lose anything. If you think you will be the high bidder, you are incentivized to bid the lowest number that still assures victory. So if there is no tie, both parties are pressured to make the lowest possible bid, converging on zero to ensure the maximum possible payout or the minimum possible loss.
2. You will tie. If you think you may tie, you have no reason to bid more than (L-b)/2 for risk of winning but still coming out a loser.

Since we play nice at Dear Adam, we will only consider pure strategies. The only logical choices are to not play (no losses), or to wait up to (L-b)/2, and you must decide now. But who knows what your rival will do? We can make a table of the range of outcomes based on you and your rival’s decision:

 Your Decision Stay between 0 to (L-b)/2 Go Range of Outcomes -(L-b)/2 to L 0

In the wise words of The Clash, “should I stay or should I go, now?”

So what’s it gonna be boy? Will you love me forever? Oops, wrong song.

I’m sorry to say, but there is no way to guarantee you come out of this happy. If you leave now, you can be sure you won’t be unhappy, but there is nothing saying you will come out ahead by staying. You can try to get in the head of your enemy and assign some probabilities to their actions, but that just turns this into gambling. I am sorry but hey, that’s life. My recommendation is to ignore the table and never give up. You might end a winner, you might end a loser, but at least you won’t be a quitter. (This also reduces competition for me by exactly one person: you.)

Illogically yours,

# Outreach Opportunities and Events

This week I have been exploring various science outreach and communication opportunities, events, and jobs, and figured compiling a list would be useful for others. I will try to keep this list updated, so if you have any opportunities you’d like to share, let me know.

## Local (Hamilton, Ontario)

Mathstronauts: An educational outreach platform, bringing science, technology, engineering and math education to middle school students in Hamilton. They are looking for instructors, volunteers, and mentors for their various STEM and programming-based after school programs. These programs run through the school year, and all training material is provided.

Sidewalk Astronomy: Astronomy graduate students from McMaster’s Department of Physics and Astronomy set up a large telescope to hold public viewings of some of the brightest objects (e.g. stars, planets, Andromeda galaxy, etc.) in Hamilton’s night sky. This group provides free, public viewings on McMaster campus.

Science on Tap: Outreach events filled with scientific discussion, trivia, and beer. At Science on Tap, you’ll have the opportunity to interact with researchers in various scientific fields as they present some of science’s most intriguing phenomena. Events happen roughly once per semester, with the next one being scheduled for early August.

YWCA STEM Programaimed at girls from low-income families to help put post-secondary education on their radar. The bi-weekly session will be held at Wesley Urban Ministries’ location at 155 Queen St. N. on Tuesdays and Thursdays, featuring hands-on activities, guest speakers and a year-end showcase.

## National

Let’s Talk Science: Let’s Talk Science is an award-winning, national, charitable organization focused on education and outreach. Let’s Talk Science creates and delivers unique, accessible learning programs and services that engage children, youth and educators in science, technology, engineering and math (STEM). The organization strives to prepare all youth for their future careers and roles as citizens in a world that is increasingly shaped by science and technology. They are always looking for after school program volunteers, writers, editors, translators, interviewers… You name it.

## International

_Bites blogsI’ve written for Softbites, a blog about soft matter physics, but there are many other Bites blogs out there, looking for authors!

The Conversation: The Conversation has a monthly audience of 10.7 million users, and reach of 38.2 million through Creative Commons republication.To be published by The Conversation you must be currently employed as a researcher or academic with a university or research institution. PhD candidates under supervision by an academic can write for us, but we don’t currently publish articles from Masters students.

Pacific Science Center Maker-in-Residence:  Based in Seattle, the Maker in Residence volunteer position at Pacific Science Center’s Tinker Tank is a unique, open-ended role for people with a wide variety of interests including engineering, hardware development, education, and the “Maker Movement”. Akin to an Artist in Residency program, the Maker in Residence position provides space and materials to support individuals looking to develop, expand, and share their skills in science, technology, engineering, design, and tinkering. It is also intended to demonstrate to visitors and volunteers vast possibilities within engineering and the Maker Movement and inspire folks to participate.

# How did humanity exist before air conditioning?

While the temperature doesn’t seem to be rising much in Hamilton, Canada (it’s actually very pleasant lately), I still remember what it’s like to have all of my water weight on the outside of my body. Luckily for me, I will have access to an air conditioner this year.

But how did humanity survive so many summers before inventing air conditioning?

Modern temperature control is mostly reactive, and based on overpowering nature. For example, when you get into your car after it’s been parked in the sun, the first thing you do is crank the AC. If you are clever, you may try to push the hot air out of the vehicle by opening the windows before engaging the air conditioning. Whether you are clever about it or not, battling with nature is not an energy efficient way of beating the heat.

By looking at the architecture of older and even ancient buildings, you see an incredible diversity compared to modern designs. Yet, despite the aesthetic differences of different cultures, some techniques seem to be invented over and over again. These techniques are often solutions to problems created by the local climate, and are of course energy-free. This type of architecture –  that eschews traditional aesthetics to better fit the climate – is known as vernacular architecture, and is fascinating. By studying these structures, one can identify a few fundamental strategies employed in many of the worlds warmer locations that could inspire smart, energy saving design

The basics: Objects are heated as the absorb energy. Energy is transmitted from the Sun to Earth via light. Putting something between you and the Sun will reduce the energy that’s transmitted to you. Therefore, you should put something between the inside of your home and the sun.

The next level of shading is understanding where the energy goes, if not into your home.

Conventional wisdom tells us your black t-shirt is going to be hotter in the sun than your white one because black absorbs more energy. So what you really want is something that doesn’t absorb light to shade your home. Failing that, you can try to keep the blinds far away from the inside of your home as you can, so the heat absorbed by the blinds doesn’t get transmitted to your home.

This was well understood in the Southern United States, whose architecture is well known for featuring giant porches. The porches serve the dual purpose of providing a pseudo room with excellent airflow, while shielding the house’s facade from direct sunlight.

Obviously the home of some Southern high roller. Look at those porches!

But this technique was not reserved for the wealthy. Even small homes could benefit, by pointing your front door East and building out a long awning.

Obviously not the home of some Southern high roller. But they are making due!

(Worth noting, a deep cave provides excellent shading)

## Ventilation

Ventilation serves several purposes. The most obvious is to shuttle hot air out of your house and replace it with cooler air from outside. Another reason is to aid in evaporative cooling, and both of these reasons are linked.

Initially, the walls and roof of your house insulate you from the heat of the day. However, as the day wears on, your walls absorb more and more energy. Eventually the walls and roof become hotter than the air outside (feel a tin roof at noon). This energy radiates inwards, heating the inside of your home and everything in it. Since the walls and roof are hotter than the outside air, if the air inside is unable to escape, and given enough time, the temperature in your home will surpass the temperature outside. What makes matters worse, each wall is radiating heat. This means more energy will eventually be transferred to the air inside your home.

By analogy, the temperature of a lake will be lower than the temperature of a kiddie pool next to the lake. While the lake will absorb energy from above, the kiddie pool will also absorb energy from the plastic walls in addition to the energy from direct sunlight. Additionally, as the molecules of water at the top surface of the lake take on energy, they will pass some off to adjacent molecules, of which there are many. A kidding pool does not have the ability to exchange its water or distribute its absorbed energy very well. The stagnant water – or air – will therefore reach a much higher temperature.

If only we could get a bit more water circulation in here…

As well as distributing energy more evenly, ventilation aids in evaporative cooling. As you and your appliances (like your shower, faucets, etc) sweat, moisture is taken up by the air in your home, increasing the air’s humidity. Increasing the humidity does two things. First, there is a limit to the amount of moisture air can hold based on air pressure and temperature. This means if the air in your home is humid, it will not be able to wick away as much moisture from your body, slowing your body’s best method of cooling. Not only does humidity negatively affect your body’s own cooling mechanism, it also makes it harder for the temperature of the air to be reduced.

Based on the composition of an object, different amounts of energy will be required to raise the temperature any given object. This characteristic is known as a materials thermal capacity. For example, water has a high thermal capacity, making it particularly hard to heat. This is why going to the beach is such a good idea in the summer – the lake will stay cool regardless of season. However, this argument works in reverse too. To cool a mass of water at a specific temperature is difficult. Water is said to have a large “thermal mass”, drawing the analogy between heating and cooling to pushing a weight.

Ventilation is very important to the Malay, an ethnic group occupying locations that are today a part of the modern nations of MalaysiaIndonesiaBruneiSingapore, and southern Thailand.

When hot air is also very humid, it is carrying a lot of energy. Since a significant fraction of the air is made up of water, reducing the temperature of the air will be much harder than if the air was dry. (Now think about why air conditioners spit out water.) So you have two options. You can either attempt to cool this air and all the evaporated water it is carrying (which will be very energy intensive), or with appropriate ventilation, replace the moist air with dry air before cooling it.

It is not surprising, then, to see that warm climate architecture all over the world emphasize the importance of airflow. Large breezy windows, open-concept porches and sleeping rooms, as well as artificial wind-tunnels are all strategies that can be found all over the world. Beautiful examples of artificial wind tunnels, or alleys that collect and funnel air through one channel, can once again be found in the American South.

Oak Alley plantation, LA. This alley of trees funnels air towards the front of the house, where one will likely find a large porch.

Both the “Dogtrot” and “Shotgun” home utilize a unique wind tunnel design to optimize airflow as well. The former having a constant, open channel cutting through the home, and the latter lining up all of its rooms, forcing the breeze to pass through the entire house.

A breeze can be channeled horizontally like in the designs above, or it can be directed upward. Since hot air rises, ceiling ventilation like a good cupola make for an airflow that pulls cool air up and shuttles hot air out.

Large windows in the protruding “cupola” concentrate and release hot air. This creates a negative pressure in the house, sucking air from outside, in.

(Worth noting, a large cave will have plenty of air, like a lake does water, to distribute heat evenly. Not that it would ever really get hot in there.)

## Heat Sinks

As we learned above, some materials are considered to have a large “thermal mass”, which means it requires a lot of energy to raise and lower its temperature. This effect keeps lakes cool, humid air hot, and explains why summer homes are often situated near a body of water. Air passing over the water is cooled, and is mercifully delivered to your property.

Or even “cooler”, you can just live on the water.

This effect can also help determine what materials to construct your house from. Heavy plaster walls, for example, will absorb lots of energy, radiating very little into your home. However, it holds on to this energy, so “night flushing” is required to keep your home cool day-to-day. This process involves keeping your house shut during the day, then opening it up at night to try and pull as much energy out of the walls as possible. This sort of architecture is common in places with large diurnal temperature swings.

Iconic Greek architecture using thick, heavy walls. Very cave-like. I’m into it.

Alternatively, one can take this principle to the extreme and build walls so thick that they won’t absorb enough heat over an entire season, let alone one day, to heat your home.

A very old structure from Mesopotamia. The conical shape also minimizes the surface area to volume ratio, meaning less energy is absorbed or released on the surface compared to the amount of space on the inside.

These structures have the dual purpose of also keeping your home warm in the winter, and are common in places with large seasonal temperature differences. (Worth noting, this can be accomplished by living in a cave or underground)

A seaweed roof in Denmark. Not typically known for their brutal summers, a thick roof will also insulate the home in the winter (heat will try to escape from the roof).

## Modern Cooling

With the advent of air conditioning, a lot of these techniques are disappearing. In a world unconvinced of climate change, where energy and fossil fuels are so inexpensive, why let nature dictate your architecture? However, these designs could be one part of a low energy temperature control strategy in modern buildings. Coupling these smart designs with energy efficient appliances and air conditioning could represent the next step in human comfort.

Or we could all move into caves. That would work too. I vote caves.

# The Hydraulic Press Channel is Awsome, Part 2

Last week we described our experimental apparatus (the hydraulic press) and a technique for characterizing materials. This week we will allow The Hydraulic Press Channel to perform our experiments (crush various materials with a press that has holes cut in the top), and we will analyze the results.

## Results

Several materials were extruded through holes of uniform size via hydraulic press. In this article we will limit our analysis to the orange mystery material, and the crayons. The experiment can be viewed below.

With enough pressure, both materials passed through the holes. After passing through the holes, the extruded crayons took on a long, cylindrical shape while the orange mystery substance fractured dramatically and exploded through the holes. The extruded crayon cylinders were observed to be very fragile and could not be bent without fracturing. The shreds of the orange material that passed through the holes flowed and stick to each other almost instantly, eventually reforming into one continuous medium.

## Discussion

The first observation we can make is how the material behaved before and after being “processed” by the press. The crayons had a well defined shape before they are pressed, and came out as long cylinders that were brittle and could not recombine. This is one of the ways we would expect a solid to behave.

“After” – the crayons stand self-supported.

The orange material appears to fill the cup of the press before it is processed. Liquids tend to flow and take on the shape of their vessel. After the orange material passes through the holes of the press, it appears that the individual bits begin to reform into a single mass – they flow together and combine, much like a very thick liquid would.

“After” – the orange material has begun to reform.

The second observation we can make is the way each material passed through the holes of the press. The crayons appeared to flow through the holes smoothly but the orange mystery material seemed to shatter and shoot through the holes. Based solely on this observation, one may guess the orange material is a solid, while the crayons are a liquid.

These two sets of observations appear to be at odds with each other. The crayons begin solid, then (without altering temperature) flow through the holes. On the other hand, the orange material initially takes on the shape of its vessel and melts back into itself after processing, but fractures like a solid as it passes through the holes. What gives?

Crayons are obviously solid, right? So let’s start from that assumption. Solids that are brittle will fracture. Less brittle solids can “elastically deform” under small stresses, meaning they will return to their original shape when the stress is removed (a traditional bow uses this property to fire an arrow). Under large enough stress, these less brittle materials may snap (like a twig), destroying the material in the process.

A bow being elastically deformed. *swoooon*

Alternatively it may deform permanently, but remain structurally undamaged. The latter is a property of metal and is something your local blacksmith takes advantage of.

A piece of metal being plastically deformed into what looks like a bottle opener.

Note that this is not the same as melting. “Plastic” deformation as described above, requires a large stress. However if one were to melt the steel, it would flow with the smallest of stresses. This technique can be used for casting objects with a mold.

Eh-hem… The One Ring wasn’t forged in Mordor, it was actually cast.

Based on our observations, we know that the crayons aren’t returning to their original shape after being pushed through the holes so the deformation isn’t elastic. Additionally, the crayons are not fracturing and being crushed into a powder like what might happen to a rock under the press; the crayons are not undergoing a destructive process. This suggests the molecules that make up our crayons are able to slip past each other when under enough stress, but are large and dense enough such that they do not flow under normal circumstances.

It turns out crayons are mostly made from paraffin wax, which is a collection of large hydrocarbons between 20 and 40 carbons long. A hydrocarbon is a term for a molecule that consists of some number of carbon atoms linked in a straight line, surrounded by hydrogen bonds. A model of a typical hydrocarbon is shown below.

A 4-carbon hydrocarbon. Butane to be specific

Gasoline, kerosene and diesel are also made of hydrocarbons, though with fewer carbons. These shorter hydrocarbons are liquids because it is easier for smaller molecules to move around each other when they are together in bulk. As we deal with larger and larger molecules randomly assembled in bulk, they become jammed and are no longer able to move past each other as easily. However, with enough stress, these big long hydrocarbons can be forced to align, allowing the molecules to slip past each other easier. Therefore, under higher stress, we see the crayons plastically deform and flow.

Now let’s consider our orange material. We will call our orange material a liquid since, when left alone, it appears to flow like a high viscosity fluid. This means if two pieces of the orange mystery material are left in contact, they will eventually become one. However, as it gets pushed through the holes it begins to act like a solid. It breaks and fractures, then is ejected through the holes. Afterwards, we see that it begins to flow together once more.

Where pushing the crayons through the holes of the press caused the molecules to align and slip, it appears this same processing technique causes the molecules in the orange mystery sample to jam, tangle, and act solid.

It turns out the orange mystery material is a polymer very similar to Silly Putty. Polymers, like hydrocarbons, can be thought of strings of atoms bonded together. However, polymers like Silly Putty are typically much longer than the hydrocarbons that make up waxes, and much more flexible. This means that polymers can act solid as the individual molecules jam and tangle together, but are flexible such that, given enough time, they can wiggle themselves past each other and flow like a liquid.

A common analogy is to consider the molecules that make up Silly Putty to be spaghetti noodles in a pot. If you grab one noodle and slowly pull it out of the pot, it will slip past the other noodles, no problem. But if you grab a single noodle and try to pull it out of the pot quickly, you may pull the rest of the noodles out with you or snap the noodle. Pulling the noodle slowly allows it to flow like a liquid. Pull the noodle quickly, and you have a solid mass of noodles.

Pushing the orange material through the small holes of the press with such high force is like grabbing a few noodles and ripping them out of the bowl. The orange material will not flow nicely though the whole and instead fracture. Leaving the fractured bits alone for some time allows them to flow back together.

## Conclusion

By crushing these materials and observing the carnage, it is possible to make some well informed guesses about what these materials are made of. Knowing what a material is made of and how it behaves in model experiments can allow material scientists to select the correct materials for specific applications, which is an important task for chemical companies that supply plastic and rubber materials to manufacturers. This type of science is also very important in the cosmetic industry and (my favorite), food science.

Consumer: I need a cheese that appears solid, but can be jarred and spread with a knife

# The Hydraulic Press Channel is Awesome, Part 1

Finnish factory owners Lauri and Anni have a hydraulic press and use for the best possible purpose: crush things for fun.

“The first and original Hydraulic Press Channel! Wanna see stuff getting crushed by hydraulic press? This is the right channel for you.”

Pressing non-Newtonian Fluids

I encourage you to fall down the youtube rabbit hole, this is senseless destruction at its finest

Or is it?

Everything is a science demo, so let’s learn something from this.

One of the important roles of material sciences (typically a mix of chemistry, physics and engineering) is to develop new materials for specific applications. For example, when Charles Goodyear learned to vulcanize rubber, he invented an elastic, deformable, but structurally durable material that was ideal for revolutionizing the wheel. Since then, materials scientists have developed synthetic materials (usually plastics) for an incredibly wide variety of applications. Like the bronze age and, iron age are used to define the technological periods of humanity, it is no exaggeration to say the 1950’s were the advent of the age of plastic.

Materials scientists can produce thousands upon thousands of different compounds, but obviously prototyping a product with every compound and deciding which performs best would be absurd. To narrow down the usable materials, they need to characterize their compounds.

What is amusing about characterizing compounds is often tests are as simple as squishing, stretching, shearing, and otherwise playing with them like one would play with Silly Putty. The complicated part comes from determining what to measure. Typically a device will apply a force to the material, and according to Newton, the material will react. In general, it’s this reaction that’s measured – the details will vary, but this is the general principle in characterizing a material.

Not all characterization requires a complicated force measurement, though. One of my favorite devices I used when I worked for a rubber company (supplying butyl rubber for tires and shoe soles, mostly) was the extruder.

The extruder was a thin metal tube with different types of nozzles at the bottom. A material was first loaded into the tube, and then the tube was heated to a temperature specific to the given experiment. Finally, the material was pushed through the nozzle with a piston. Forces applied by the piston could be recorded, as well as the forces on the walls of the tube and on the nozzle, but just by looking at the extruded material, a trained scientist could determine some important properties of the compound. An example of one of the visual cues that tell about the material properties during an extrusion experiment is shown below. Notice how the material comes out smooth, then transitions to a rough, “shark skin”. This can mean that the temperature of the tube is too low or that the material is being pushed out too fast.

Does the extruder sounds a bit like our little hydraulic press? So this is a science demo after all! In part one we will examine the “Experimental Techniques” section of our science demo, since the way a hydraulic press achieves its massive crushing power is actually pretty cool. In part two, we will present some results provided by the Hydraulic Press Channel and discuss what they tell us about the materials.

## Experimental Techniques: The Hydraulic Press

A hydraulic press was invented by Joseph Bramah and patented in 1795. While putting significant effort into developing the modern toilet, Bramah realized he could create a hydraulic equivalent to a classic lever.

A famous Greek dude from Syracuse University once said, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Don’t say I won’t do it either, because I totally will.” Practical concerns like “where do I place the fulcrum?” aside, the principle is sound. When you place an object on one end of a lever and apply a force to the other side, the torque you put on the lever is transferred to the object on the other side. Since torque is the product of force and the distance the force is from the fulcrum (which is why it is easier to hold a grocery bag at your side than with your arms outstretched), a sufficiently long lever with a properly placed fulcrum should allow you to “balance the teeter-totter” with two arbitrarily-sized objects.

A Greek dude from Syracuse University

So how does this relate to the hydraulic press?

The cartoon below is a schematic of a basic hydraulic lift. A force $F1$ is applied to a Piston 1 with an area of $A1$. The force from Piston 1 creates pressure in a volume of liquid, which is sealed water-tight at the other end by Piston 2 which has an area $A2$. Assuming the liquid is incompressible (this is an interesting assumption unto itself, but we will not dig into it here – just know that it’s a good assumption), then the pressure caused by Piston 1 will be equal to the pressure on Piston 2.

A simple schematic of a hydraulic press in equilibrium (neither side is moving up or down). From wiki.

So how do we determine the lifting force (or crushing force, just flip the schematic upside down) of Piston 2?

Pressure is define as a Force per unit Area. That means the pressure caused by Piston 1 is $F1$ distributed over $A1$ which is written: $P = F1/A1$. A higher force or smaller area leads to a higher pressure. Since the pressure is transmitted from Piston 1 to Piston 2 via the fluid, $P = F1/A1 = F2/A2$ . So if $A2$ is larger than $A1$ and the fluid transmits equal pressure to the other piston, then $F2 > F1$, and we can calculate by exactly how much $F2 > F1$:

$F1 = F2 (A2/A1)$ , so $F2$ is $A2/A1$-times larger than $F1$.

This may sound familiar to our lever. The similarity is that with a lever, torque is equal on both sides (if the system is stationary), while a hydraulic press has a pressure which is equal on both sides. The important part is the ratio between lengths on each end of the fulcrum and area of each piston. Note, that Torque=Force*Length and Pressure=Force/Area, so Archemedes would want a long lever on his side while Bramah would want to apply his force to the small piston.

Using this technique of focusing force into a smaller area, a hydraulic press is able to deliver an incredible amount of crushing with a reasonable amount of applied force on the small piston. For example, presses can reach in the ballpark of 9000 psi (pounds per square inch).

We can now use this device to wreak havoc on learn about the physical properties of various materials. Next week we will discuss what we can learn about materials by how they respond to crushing.

# Science for everyone – Pint of Science comes to Hamilton

Science took over the world last week.

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Pint of Science, a global science-for-everyone festival that spans three days in May, made its debut in Hamilton last week. The festival is run predominantly by volunteers and aims to bring science to the people through engaging, digestible public lectures – often in a bar or pub.

If this sounds familiar, it is very much like the Science on Tap event I wrote about earlier this year. While Pint of Science made its debut this year in Hamilton, it is actually a long standing event originating in just three UK cities in 2013. Pint of Science has since spread to over 300 cities across 21 countries.

For its first year in Hamilton, we were treated to three days of two simultaneous lectures at two local bars – The Phoenix on McMaster campus and West Town bar. Topics focused on astronomy, light, and neuroscience and featured researchers from McMaster and their graduate students.

Lots of fun to be had in Hamilton last week.

All of these lectures looked good, so I decided where to go based on beer list.

Welcome to The Phoenix. They claim they have the largest beer selection and patio in Hamilton.

The first day I got to see Dr. Alan Chen and his graduate student (and my roommate) Johnson Liang talk about where all the big elements come from. In short, during their average life cycle, stars will produce elements as large as Iron via nuclear fusion. To make anything larger requires a star to go through a rare life event like going supernova, which partially explains the high abundance of smaller elements in the universe, and the scarcity of heavy metals.

The following evening featured Dr. Laurel Trainor and her graduate student Andrew Chang of the Department of Psychology, Neuroscience & Behaviour at McMaster University. Their research focuses on musical and rhythmic development in infants and children, and how the study of music on the human brain can help us understand our own interpersonal communication.

Some of their research is done in McMaster’s LIVElab, one of the coolest “venues” I’ve ever heard of. I say venue, because it is a mix of concert hall and laboratory. It’s so cool that I promise to do an article on it soon. To quote the lab’s website,

The LIVE (Large Interactive Virtual Environment) Lab is a unique 106-seat Research Performance Hall designed to investigate the experience of music, dance, multimedia presentations, and human interaction.

The space includes Active Acoustic Control; Sound Recording Equipment; and measurement of Behavioral Responses (96 tablets), Movement (motion capture), Brain Responses (EEG), Muscle Tension (EMG), Heart Rate, Breathing Rate, and Sweating Responses (GSR).

The final day featured Dr. Kalai Saravanamuttu from the Department of Chemistry at McMaster University and graduate student  Kathryn Benincasa speaking about their work on light. What makes their light interesting is how they can focus it and keep it coherent over long distances.

Typically light will disperse over long distances, meaning a tight laser beam, or the light from a flashlight for that matter, will spread and become weaker as it travels. Dr. Saravanamuttu’s lab uses techniques to keep the light from dispersing, and is exploring applications for these types of long-range, coherent beams. One particularly interesting application is to give solar panels bug eyes.

Picture the honey-comb-like eye of an insect. By multiple facets over a lens allows them to focus light over nearly 180-degrees. For a bug, that means it can see everything and have a minimal blind spot. For a solar panel, this means it can absorb light from all directions at once. This requires a system of keeping light focused and coherent (check), in a geometry similar to a bug’s eye, that can coat a solar panel. By making these thin, specially designed coatings for solar panels, the researchers hope to increase the efficiency of solar panels making them more economically viable.

Imagine building this structure so the straws point outward over a full 180-degrees. Then shrink it down so you can paint it over a solar panel. You would get light from every direction focusing onto your solar panel.

The best thing about all of these lectures is that they were all completely free to attend. I have written about how important it is for scientists to keep the public informed about their work, and seeing how successful these public lecture events are suggests there is a strong desire for more of them. If you are interested in this sort of thing, keep an eye on this facebook page. There will be some very exciting news in the near future.

# Elastogranularity and how soil shapes the roots of plants, continued

This week a short article of mine was posted on Softbites, a blog “run by a group of young scientists who want to attract a wider audience to the beautiful world of soft matter.” To quote their homepage,

## “Softbites brings you digestible summaries of the latest research in soft matter.

If you have a soft spot for the science of bubbles, liquid crystals and other squishy materials you might have heard of soft matter! If you have not, this branch of physics is a fascinating interdisciplinary field studying various kinds of materials from gels to biological systems. They all share the fact that they are soft, which means they are not exactly solid nor liquid. For instance, if you poke a bit of foam, it will resist like a solid at short times, but it will flow at longer times.”

I wrote about a paper recently published in Physical Review Letters (but also available for free on the arXiv) by DJ Schunter Jr of the Douglas Holmes Group at Boston University. In this paper they take two existing, well understood systems and combine them to create something new and exciting. In particular, they take buckling of beams and combine it with granular rearrangement.

This post is a more technical article and is an addendum to my article on Softbites. I will be diving into some specifics of the analysis of the experiment, and is intended for those who have read the article on Softbites (here) and want more details. I encourage you to please go and read the Soft bites article before continuing below.

## Exploring the difference in buckling as a function of packing fraction

Recall the difference in buckling behavior for different packing fraction $\phi_{0}$, demonstrated in Figure 1:

Figure 1. An elastic beam in inserted into a rigid box filled with beads. Depending on the packing fraction,  $\phi_{0}$, of the beads, the beam exhibits one or two buckles. The curvature of these buckles are affected by $\phi_{0}$.

To quantify the difference in buckling that happens at different packing fractions, the increase in amplitude relative to wavelength of the buckles, $A_{0}/\lambda$, is plotted as a function of the length of insertion relative to initial beam length, $\sqrt{\Delta/L}$. For small values of $\Delta$, the curvature of the buckle is small and can be approximated as a triangle with height $A_{0}$ and base $\lambda = 2L_{0}$. As $\Delta$ increases, the height of the buckle increases according to $A_{0}/\lambda \propto \sqrt{\Delta/L}$. This is shown by the black dashed line in Figure 4, and experiments at both high and low $\phi_{0}$ (red and blue dots respectively) follow this relationship for small $\Delta$. As $\Delta$ increases, even in the absence of beads, the analytic solution for the beam’s buckling (shown by the blue curve) begins to deviate from this approximation. For intermediate values of $\Delta$, experiments at both high and low $\phi_{0}$ are shown to follow the analytic solution of a beam bending in the absence of beads. This suggests the beads are not yet confining the beam in any meaningful way. At even higher $\Delta$, low $\phi_{0}$ experiments continue following the behavior of a free beam but high $\phi_{0}$ begins to deviate rapidly. This deviation shows that confinement due to the beads has a strong effect on the geometry of the buckles in these cases, and the results are consistent with the numerically calculated solution for buckling in the presence of beads (red line).

Figure 2.  Increase in relative amplitude $A_{0}/\lambda$ as a function of $\sqrt{\Delta/L}$. Solutions for small buckles (dashed line), buckling in the absence of beads (blue line), and buckling accounting for beads (red line) are shown. Experimental data for small $\phi_{0}$ (blue dots) and large $\phi_{0}$ (red dots) show good agreement with each of their corresponding solutions.

## Local curvature and bead dislodging

So far we have seen that the nature of buckling is highly dependent on the bead packing fraction $\phi_{0}$. At low $\phi_{0}$, the beam buckles as if the beads were not present. At high $\phi_{0}$, the buckles become highly confined. Confining the buckles forces them to take on a higher curvature – the extra length of beam has less area to spread out in. This forces the beam into an unfavorable shape and effectively stores excess energy in the beam like compressing a spring would store energy within the coils of the spring. Like a spring, if you were to suddenly remove beads from the box (or the compression on the spring), the beam would suddenly pop into a more straight, less curved shape. What we can take away from this observation is that the higher the local curvature of the beam, the more stored energy there is within the beam, and the more the beam is pushing back on the beads in the area of high curvature. Eventually the pressure on the beads will be too great, and one will be forced to pop out of plane, on top of the rest of the beads.

The plot in Figure 3 shows maximum curvature $\kappa$ multiplied by beam thickness $h$ ($\kappa$ ~ compression of the spring, $h$ ~ stiffness of the spring) plotted against $\phi_{0}$ for higher and lower insertion lengths $\Delta/L$ (light blue and dark blue dots, respectively). The plot shows that higher $\phi_{0}$ leads to higher maximum curvature in the beam, as does larger insertion lengths. The plot also shows experiments where a bead becomes dislodged (red squares). This happens more frequently for highly curved and thick beams. The additional images in Figure 3 shows examples of bead movement for systems at various points on the plot. Longer arrows represent larger bead movement, and red circles represent a bead which dislodges from the rest of the beads. Also, notice the direction the beads move in Figure 3 (I). The arrows show how the beads would be pressing into the beam, and help explain why the buckles would move together at high packing fractions.

Figure 3. Beam curvature $\kappa$ normalized by beam thickness$h$ as a function of packing fraction $\phi_{0}$ for normalized insertion lengths $\Delta/L = 0.1$ (light blue) and $\Delta/L = 0.4$. $\kappa h$ is shown to increase for larger $\phi_{0}$. To the right of the plot are examples of bead movement (arrows) for experiments corresponding to regions within the plot. Dislocated beads are shown in red.

This is a unique experiment, and one that I found very satisfying to write about. What I like most about this work is how well quantified each observation is. In many papers, authors will present a system, show off some interesting observations and leave it at that. However, DJ Schunter Jr et al. take this neat experiment and quantitatively explain so much about it, including the spontaneous disloging of beads from the system. The experiment is not too hard to understand qualitatively, but being able to make actual predictions about a system requires a quantitative explanation. When you can predict exactly how a system will behave, it is then possible to use it for something constructive.