Applications are now being accepted for two fully-funded PhD studentships (1 x experimental, and 1 x theory/modelling) to study novel emergent properties of soft matter. Review of applications will begin immediately and continue until the position is filled, with a goal of commencing work in or before February 2017.

Simple soft matter systems can give rise to complex emergent properties such as gelation, and phase transitions, described using elegant theories such as percolation and reptation. With slightly more complex building blocks, we can obtain self-assembled micelles, rods, and bilayers, or produce active matter which is likened to biological swarms. In the era of nanotechnology, micro- and nanoparticles can be designed and engineered to probe further possibilities. This project will use nanotech capabilities, alongside theoretical work, to design, make, and study forms of soft matter with new emergent properties.

One (experimental) student will use various capabilities (e.g. microfabrication, protein engineering, surface chemistry) to produce particles in solution which assemble and cluster in unconventional ways. Candidate materials could include: (i) Materials with memory, analogous to collections of pedestrians (Figure, left); (ii) Interacting mobile particles, including asymmetric Janus spheres (Figure, right); (iii) Metastable materials which enable switchable transitions. The student will be trained in a wide range of nanotechnology techniques.

Figure: Left (from [1]), pedestrians travelling up (blue) and down (red) learn to separate over time. Middle and right, TEM images of Janus particles – gold evaporated on to silica – fabricated at UoA (images: Anupama Rao Gulur Srinivas).

Another student will use theoretical and modelling approaches (e.g. molecular dynamics) to understand emergent phenomena observed in the experimental work. This work will also guide the experiments by exploring the possibilities arising from specific particle designs. Universality is a particularly exciting aspect here: analogous systems could be identified within social, ecological, economic, and other complex systems. Computational work will draw upon the University of Auckland’s high performance computing resources.

Projects will be academically challenging, requiring applicants with a strong background in a physical sciences discipline and excellent command of written and spoken English. For the experimental project, laboratory research experience would be an advantage. For the theoretical project, familiarity with collective phenomena and/or high performance computing would be an advantage.

The projects are based in the Departments of Physics and Chemistry at the University of Auckland. Students will benefit from extensive collaborations and thriving postgraduate communities within two of New Zealand’s Centres of Research Excellence: The MacDiarmid Institute for Advanced Materials and Nanotechnology (www.macdiarmid.ac.nz), and Te Punaha Matatini (www.tepunahamatatini.ac.nz). Each student will receive a stipend of $27,000 per annum in addition to course fees.

Applications should include a CV, academic transcripts, and a brief (1 page max) statement of research experience. Applicants must fulfil the University’s English language requirements (www.auckland.ac.nz/en/for/international-students/is-entry-requirements/is-english-language-requirements.html) and should provide the names of at least two people who can provide personal letters of reference.

Contact:
Dr Geoff Willmott
g.willmott@auckland.ac.nz

[1] Morton, N.A. and S.C. Hendy, Symmetry Breaking in Pedestrian Dynamics. 2016: arXiv:1605.05437.

The World Cup Final is just one and a half fitful sleeps away, so it must be time to wrap up this blog series (for now 🙂 ). There is a bundle of other topics that could be discussed, so I’m just going to list a few ideas (from high school physics, to interdisciplinary research, and to science fiction) that will hopefully get you thinking. They’re all areas where the skills we learn in physics classes can play a role. I reckon a good keen physicist could even get their teeth into some of the social science topics that have been highlighted by Massey University researchers.

So here goes, the final round-up:

• The Julian Savea collision topic ended up going a little bit viral (“cultural”?) … well, at least it replicated a few times. Fans of that topic, and school teachers, will be happy to hear that English physicist John Biggins has gone retro and analysed the Lomu collisions from the 1995 World Cup semi-final. The question sheet here has been posted by Isaac Physics, which is a really good (and fast-growing) resource bank for secondary school physics.
• The lineout is another rich source of mechanics and dynamics problems, if you need one. A player jumping for the ball has to reach as high as possible, as quickly as possible, while supported by two team-mates, one at the front and one at the back. The thrower needs to deliver the ball on the right trajectory so that it intersects with the lifted player at the top of his jump. And this has to happen at the right time!

Figure: Physicist’s impression of an All Black lineout.

• Famously, the bounce of  rugby ball is seemingly irregular and unpredictable. However, it is possible to think about how the ball will bounce based on the angle at which is hits the ground. Of course, this problem is much simpler if the ball doesn’t deform during impact … but this isn’t the case. The collision is inelastic and the coefficient of restitution tells us about the ball’s energy loss.

Figure: The ellipsoidal ball (image from World Rugby Laws) might land vertically (red arrow) but so that the reaction force does not act through the centre of mass.

• Following on from that link in the last point, there’s been far more slow-motion photography in sports coverage over the past few years, bringing new perspectives to high velocity ball sports like cricket and tennis. One important reason for cheaper and cheaper cameras is that researchers are continuously improving the efficiency of CCD detectors (which collect the light and form an electronic image).
• It seems inevitable that rugby will come under increasing pressure to adopt technologies similar to the ‘hawkeye’ systems used in cricket and tennis. These systems use images from several cameras at different angles to triangulate the position of a ball. In rugby, the ball is sometimes hidden under a pile of bodies, so something similar to the magnetic sensors now used for goal line technologies in soccer may prove useful. Good old radio waves are the favoured means of communication for referees and their assistants, although ensuring the reliability of these transmissions is an interesting challenge – at least for those involved in club rugby.
• Advances in materials science play a key role in modern rugby jerseys, as highlighted by Michelle Dickinson in her latest column.
• The thrill of the chase: if a lucky Australian picks up an intercept on Sunday morning, someone like Ben Smith has the task of trying to chase them down. We’re lucky that ‘Ben from Accounts’ has good skills with a calculator, because it turns out that figuring out the best speed and direction for chasing a moving object is a complicated mathematical problem. Should he go towards the ball, or head towards the corner post? The latter gives him the best chance of stopping a try, but the former (or half way in between) might gain him more territory. What is the optimal running line for a flanker from the set piece? Where should the ref go to see the next phase most clearly?

Figure: As tweeted by @JayReeve.

• For my colleagues down the hall at Te Punaha Matatini, I have to mention data science.There is a good reason that Steve Hansen and co. have laptops propped up in front of them while they’re watching the game – a huge amount of data can now be extracted from rugby games in order to analyse a team and their opposition. This is used by people like Wayne Smith (aka ‘the nutty professor‘) to form tactical strategies. Dealing effectively with large and complex data sets is a very modern problem, and one which can take some lessons from physics. Of course, physicists learn to deal with lots of data, and are skilled with numbers and computers. There are also concepts that might be transferred from fields such as condensed matter physics, in which we try to explain how simple properties of matter emerge from a large number of interacting bodies (like, really large, such as atoms or molecules).
• Related to this, Trevor Lispcombe’s book (source note below) has an interesting section comparing tacklers to gas molecules (!). You can figure out the mean free path for a ball-carrier trying to run past opponents. When a team is defending close to their line, it’s as if the gas is compressed. The players are all confined to a relatively small space between the goal line and the ball. If they were gas molecules, we would say that the pressure is higher – the pressure might be reduced a little if someone is in the sin-bin! Trevor therefore thinks that it is easier to run through a defence when the ball is further from the line, which is food for thought.
• … and finally, of course, time travel. I suggest we set the dial for Johannesburg, 1995.

A last thought is that rugby is a sport in which players and teams that rise to the top are persistently innovative, highly analytical, and base their analysis on a strong evidence base. This definitely how the All Blacks operate, and these are also key traits of high-quality science. As scientists in New Zealand, there are certainly things we can learn from our successes on the rugby pitch – if not from talkback radio!

You can leave questions / comments / suggestions here or @GeoffWillmott. Source note: some material is based on the book “The Physics of Rugby” by Trevor Davis Lipscombe (Nottingham University Press).

This penultimate (semi-final?) RWC blog takes its name from a regular Friday night feature on The Crowd Goes Wild. Smashed ’em Bro is a countdown of the most spectacular collisions from the week’s sports coverage. In a happy coincidence, Stuff.co.nz got in touch this week to ask about trying to tackle Julian Savea.* You can read about some calculations from last Sunday’s demolition of the French at that link.

When making a tackle, first and foremost let’s make sure that it’s safe. Anyone taking part in a rugby game in New Zealand (playing, coaching, or refereeing) needs to watch Rugby Smart. We have to grasp the player with our arms below the line of their shoulders, and we can’t lift or tip them over so their head or shoulders hit the ground first. The person being tackled must not be jumping in the air, and they must be carrying the ball. If we don’t follow these rules, the next blog will have to be about the optical spectrum of cards in the ref’s pocket.

To get on to the countdown, what we need is drastic change in the speed and/or direction of motion. We can explain most of what goes on in a collision using conservation of momentum: the total momentum after the collision is equal to the total momentum before the collision. From previous blogs, we might remember that p = mv. Momentum is just mass times velocity, and velocity is a vector. So, momentum is also a vector. Here we’re putting vectors in bold type. Momentum points in the same direction as velocity, but its magnitude (arrow length) is multiplied by m.

In the Figure (bird’s eye view), we have three cases in which Springbok legend Bryan Habana (H) is running along with a certain velocity (green arrows), and collides with All Black loosie Jerome Kaino (K, black arrows). Initially, we have p = m_H v_H + m_K v_K . This is vector addition, so we have to put the arrows representing m_H v_H and m_K v_K head-to-tail to find the resultant p. After the collision, Kaino and Habana stick together, because Kaino has correctly grasped his opponent. So, the total mass is m_H + m_K, and the final velocity is v = p / (m_H + m_K).

In case A, Jerome is standing still when he makes the tackle (v_K = 0), so p points in the direction that Bryan was running, and afterwards the players move off in that direction. The (blue) velocity arrow is shorter than before the collision, because the mass of both players is greater than the mass of Habana on his own. This is what happens in most tackles, especially in amateur rugby.

In case B, Jerome runs into Bryan at the same velocity, but in the opposite direction. Kaino’s momentum is slightly greater because he’s a forward, so he’s a bit heavier than Habana. When we add the momentum vectors, there is a small resultant from right to left, and the two move in that direction after the collision. This represents a decent change in velocity for Habana, and the collision might make the Friday night countdown.

In case C, Jerome runs towards Bryan at a 90 degree angle. We have to draw a triangle and use some trigonometry to figure out p. The magnitude of p (from Pythagoras) is larger than cases A and B, so the velocity is relatively large following the collision, and at an angle to the original direction of Habana’s motion. This type of collision probably produces the most spectacular changes in direction, and it’s one reason why rugby coaches tell you not to run across-field.

So, collisions will produce large changes in velocity when the two colliding ‘bodies’ are moving fast (running quickly), and have large mass (are big and muscle-y). But the momentum of a collision can be altered by applying forces  – see Newton’s 2nd Law.

This picture shows several players in a scrum, trying to push from right to left. What you might notice is that all the boots are on an angle. To exert a force sideways on the scrum, the players have to sink their boots into the turf so that they can push against the ground sideways.** The same is true at a tackle. A player can change p if they arrange their footwork so that they can push sideways off the ground. Players need to retain their balance: there’s no point pushing strongly while you’re lying flat on your face. Of course, in a tackle everything happens quickly. If players get into a position where they are unable to use their feet to exert a sideways force, they are at the mercy of their opponent.

To make a spectacular hit, you can now start to think about whether the tackler wants to make contact high or low (if you know about torque, you can throw that in the mix), and whether the ball carrier is better off with their feet on or off the ground. Once you’ve got it all sorted, you can analyse this.

You can leave questions / comments / suggestions here or @GeoffWillmott. Source note: some material is based on the book “The Physics of Rugby” by Trevor Davis Lipscombe (Nottingham University Press).

* Although Stuff is motivated by scaremongering, it’s good that Doug King gets a plug in that article for his excellent work on concussion in rugby.

** This is why forwards have longer studs on their boots than backs. It might slow them down a little when they are running, but it is more important that they are able to grip and push in the scrums.

I’m more than a little bit edgy about the quarter-final against France tomorrow morning, so this post is going to concentrate on a couple of distinctive aspects of Forsyth-Barr Stadium in Dunedin, which is just about as far away from Cardiff as possible.* It’s also a bit of a follow-up to the previous post on kicking.

Forsyth-Barr Stadium (completed August 2011) has a roof, which comes in pretty handy during the Otago winter. When a stadium has a roof, the first thing that springs to mind (for me, anyway) is whether the ball can be kicked high enough to hit the roof. If you’re ever out on a field under a roof holding a rugby ball, hitting the roof is probably the first thing you’d try.

We can use kinematic equations to figure out the trajectory of your kick. If the ball goes straight up with an initial velocity (v), we know that an gravitational acceleration (g) acts straight down on the ball, so the vertical height it will reach before stopping (h) is given by

Now, the roof of Forsyth-Barr is on a bit of a slope, and the height near the edge of the field is reportedly around 30 m. Using the equation, we find that the ball has to be travelling at 24.3 metres per second when it leaves your boot if it is to hit the roof. How fast is this? In rugby terms, we might think about how far the same kick might go when it is directed downfield. You can figure out that if you kick the ball at some angle to the ground (x), then it will follow a parabolic arc, and the maximum horizontal distance travelled (d) is given by d = v² / g (which is the same as 2h in this case). For this maximum distance, x = 45 degrees.

So, we find that the kick that would reach the roof of Forsyth-Barr Stadium could travel 60 m on the full if kicked downfield. That’s a very long kick indeed, although I don’t think it’s impossible. To be fair to the Stadium designers, the roof height near the middle of the field is closer to 37 m, so the kicker would need to be able to kick the ball 74 m downfield, on the full, to be able to hit the roof at this point. The stadium’s website reckons that the highest observed kick of a rugby ball is 29.4 m.**

[If you want a harder trajectories problem, try adding some wind speed or some posts that need to be cleared.]

We’re not finished with Dunedin yet, because I’d like to draw your attention to a conundrum for goal-kickers at Forsyth-Barr. Shortly after the Stadium was built, and during the 2011 World Cup, it was noticed that goal-kickers weren’t having a great time in Dunedin. Internationally renowned aces Johnny Wilkinson (England) and Morne Steyn (South Africa) had sub-par outings there, and overall statistics were a little low.

In 2011, Brian Wilkins from NIWA in Wellington gave an explanation in press reports, suggesting that any swerve on the ball due to spin is accentuated by the roof because the air is relatively still, and non-turbulent. This explanation is based on the Magnus Effect, as discussed in the previous RWC Physics post. There are a couple of other ideas to throw into the mix:

1. The knuckleball effect, which takes its name from baseball, but is also used in (for example) soccer. The idea is that, if the spin on the ball is minimal, then different flows over different parts of the ball cause swerve (as in the Magnus Effect), but that the direction of swerve is unpredictable and erratic. Knuckleballs will be different for different types of balls (here is a video of some guys comparing different soccer balls against some fairly average goalkeeping) because the flow over the seams of the ball is important. The properties of the air should also make knuckleballs more or less prominent.

Erratic motion is great if you’re trying to throw a strike or beat the goalie, but not so good for a goal-kicker. From a rugby point of view, different types of kicker may be more (or less) affected. Morne Steyn, an excellent goalkicker, learned his trade on the high veldt in South Africa, where the atmosphere is thin and the ball flies straight and true. It’s quite possible that this kicking style meant that he was vulnerable to knuckleball effects at Forsyth-Barr.

2. Kickers get to practice on the field, with the roof on, before the match. Also, similar low kicking percentages aren’t observed at other covered stadiums. This leads me to think that the aerodynamics might be affected by changes in air temperature or humidity that only happen once a big crowd turns up in Dunedin.

*Oh OK you can think about Cardiff if you want: the Millenium Stadium roof is 33 m high.

**Here we’ve ignored that the ball is kicked from a little way above the ground, and that there are aerodynamic advantages to spiral kicks as discussed previously.

What goes on when a rugby ball is kicked? This is actually a pretty tricky question, and not just because the ball isn’t round! We’ll narrow it down a bit and talk about the spiral and the swerve.

The Spiral

Any budding young first five-eighth learns the spiral punt at an early age. They kick the ball with the outside of their foot so that it spins (purple arrow) around its long axis (black arrow), while travelling in the direction of that axis. Pretty soon these mini-Dan Carters figure out that this style of kick helps them to kick the ball further.*

The ball travels further because the air resistance on the ball is relatively small. Air resistance is like the ‘wind’ you feel when you’re riding a bike. It produces a drag force which slows you down, or makes it harder to maintain a constant speed. The size of the force felt by a particular object depends on its shape – generally, if less surface area is facing the direction of movement, then the force is weaker. This is why you hunch over your handlebars when you want to ride your bike quickly, and why the rugby ball travels further if it stays end-on into the wind, rather than side-on. In the picture above, the area of the ball that you see is much smaller when the ball is end-on to your viewpoint.

If you’ve kicked it right, the punted ball stays with its long axis pointing in the direction of motion as it flies downfield. This position is held stable by gyroscopic forces – the same phenomenon which keeps a spinning top upright. A spinning top looks like it should fall over, but stays upright; in the same way, a spinning rugby ball is prevented from tumbling end-over-end.

The trick to understanding a gyroscope** is angular momentum. Just like any moving object has (normal, or ‘linear’) momentum, any spinning object has angular momentum, and to show it we use a vector pointing in the direction of the spinning axis. In the figure above, the angular momentum vector points along the black axis. To start the ball tumbling end-over-end, angular momentum must be provided in a different direction (in the figure above, the vector might point in or out of the page). The interaction between these two vectors which point in different directions produces a gyroscopic force. This prevents the ball from tumbling, and the spin associated with the spiral punt is preserved.

The Swerve

All kinds of sports fans will be familiar with balls swinging around in flight. Whether it’s Roberto Carlos bending a soccer ball around the wall, a swinging ace at Wimbledon, Shane Warne’s dipping flipper, or a weekend hacker slicing and hooking their golf ball from bunker to rough, the same principle applies. It affects kicks in rugby, and this week it would be wrong to go any further without also mentioning the newly crowned NRL premiership winner Johnathan Thurston and his banana kicks at goal.

Most of the time, the swerve on a spinning ball is caused by the Magnus effect, which sends the ball sideways because of a difference of pressure on the two sides of the ball. The idea (called Bernoulli’s principle) is that the air pressure is lower where air is moving with higher speed. This applies to aeroplane wings, which are shaped so that the wind speed is greater above the wing, and the pressure difference on either side of the wing forces the plane upwards (phew). The flow of air past a spinning ball is disrupted on the side of the ball which is moving against the oncoming air. There is more turbulence on that side of the ball. There’s a round ball in this picture for simplicity, and the grey area shows where there is slow-moving, high-pressure turbulent air.

The direction of the Magnus force for the spinning ball can be predicted using a right hand rule. For this, we need two vectors. The first is that angular momentum vector caused by the ball spinning, which points out of the page in the figure above. The second vector is the direction of the ball’s motion – here, pointing from left to right. If we take our right hand and curl the fingers so that they turn from the angular momentum vector to the velocity vector, then our thumb will point in the direction of the Magnus force. That means that you’re curling your fingers from a vector pointing out of the page into a vector pointing towards the right, and your thumb points upwards. This is the direction of the Magnus force, and the direction in which the ball will swerve.

* The same is true of the spiral pass, although in that case you also want to consider that your team-mate has to catch the pass … for similar reasons the spiral punt is never really used in Australian rules football.

** Smartphones have very small gyroscopes which act as sensors. These sensors are what tells the phone that it is sitting on its side or being waved around, so that the screen can react accordingly.

When physics and rugby appear in the same conversation, it usually goes like this:

etc.

To some readers this chat might sound odd, but let me assure you that similar conversations are not at all uncommon! You’ll hear them at the rugby club, on the bus, in the back row at a funeral, or in media commentaries.

What is happening here is that a player has been running towards the opponent’s goal line, and passed the ball to a team-mate. The forward pass (or not) decision can be crucial; if you asked a rugby-following New Zealander to name a forward pass from history, I’d wager that most of them would immediately name one particularly traumatic example from 2007.

As for the rugby, and the stationary spectator (in the field’s frame of reference) is like the observer on the train platform. They see the passer running with some velocity (blue arrow) and the ball going forwards (red arrow). We can switch to the passer’s frame of reference by subtracting a vector representing the velocity difference between the two frames: we turn around the blue arrow. The resulting green arrow goes backwards. The accepted interpretation (as in the video) is that the ball must go backwards in the passer’s frame of reference, which means it can travel forwards relative to the field.

To summarise, the advice to “watch the passer’s hands” is good, and the motion of the ball relative to lines on the field is irrelevant.

Comments are welcome here or @GeoffWillmott

Update: nice to find that Matthew Collett, my colleague in the physics department, talked to the Herald about this topic in 2011

* It was a Youtube video much like this which enabled a consistent refereeing interpretation to develop. I believe the original video was made and posted by referees in Queensland. So a proper discussion is a product of the Youtube era, and I guess we have one thing for which to thank the Aussies.

Enthusiasm for the Rugby World Cup is reaching fever pitch. Laws have been passed to allow breakfast-time trips to the pub, Fonterra has gone next-level ‘innovative’ and ‘value-added’ with their black milk, and here in Auckland’s Department of Physics we are dealing with nationalistic fervour resulting from a $2 sweepstake draw.

So, in a blatant display of personal* and professional opportunism, I’m going discuss how physics crops up on a rugby paddock. I’m not aiming high: just something better than the Herald sports section. Maybe it will contribute to a coffee table discussion, or a lesson plan. For the first instalment, we need to talk about Keven.

The coolest TV innovation that emerged during the 2011 World Cup was probably the use of the Spidercam. Specifically, the top-down view of the scrum literally added another dimension to the way we watch this aspect of the game.

If you haven’t spent the last 15 years under a rock, without any access to Weet-Bix, then you’ll know that 127-test All Black Keven Mealamu is wearing black with a number 2 on his back. Both the All Blacks (wearing, er, black) and France (wearing white, known as Les Bleus, c’est la vie) want to push their opponents backwards (left to right). Here you can spend 7 minutes reliving every scrum from THAT 8-7 final at Eden Park. Scrums are awesome.

All I want to do here is talk about the vector diagram of forces acting on a front-rower. We represent a force by a vector: an arrow with length proportional to the strength of the force, pointing in the direction of the force. When more than one force acts on the same object, the total force can be found by joining all the arrows base-to-tip in succession, then finding the ‘resultant’ arrow from the base of the first arrow to the tip of the last.

Figure A shows the forces acting on Keven, including the force he’s providing by pushing himself. There’s a force pushing him from behind, and une force bleu pushing in the other direction. Putting the force vectors base-to-tip, the sum is about zero (Figure B). Newton’s first law (an object which is at rest will remain at rest, unless acted upon by an external force) tells us that we need some total force to move (accelerate) Keven, so we can tell that Keven is not about to move very quickly to the left or the right. This is what we’d expect, because scrums don’t go anywhere in a hurry.

However, Keven certainly feels the forces acting on him. We can figure out the pressure (force per area) acting on his shoulders by estimating the forces applied by the opposition. There’s 3 or 4 French players directly in front of Keven, pushing on his shoulders, so I reckon that if they can generate 3 or 4 body-weights worth of force, that will be about 20 MPa pressure. (Have I got it right? How big are Keven’s shoulders anyway?). This is about 200 times atmospheric pressure, equivalent to the pressure inside a scuba tank, or under a stiletto high heel. So Keven, who is 1.81 m tall, isn’t getting any taller in a hurry.

If one of the forces acts a little bit sideways (say, 5 degrees), then the vector sum points sideways (red, Figure C). Now there is an unbalanced force, and Keven will accelerate in the direction of the red arrow. The message here is that the scrum is easily destabilized: the players mostly concentrate on pushing from left to right, so they are not positioned well to oppose the red vector. Players, in particular props, can easily upset the scrum by slightly tweaking their body position, their grip, or the position of their feet. An opponent must be very strong and skilled if they want to keep the scrum stable.

Keven is slightly protected by the two players alongside him, but stability is an even bigger problem when you watch the scrum from the usual viewpoint (side-on). Now, each front-rower has to hold themselves up without having two mates buffering the motion in that direction. Also gravity joins the force diagram. This is why scrums are so easily collapsed, and there’s a rule that the front-rowers have to enter the scrum with shoulders elevated above their hips.

Where do these pushing forces come from? In upcoming posts I hope to discuss how players can choose the length of their sprigs to provide the most force, along with forward passes, spiral kicks, etc. So watch this space and please leave questions / comments / suggestions here or @GeoffWillmott

Source note: My RWC material serializes a Café Scientifique talk first delivered to an enraptured audience of approximately 10 pensioners at Wholly Bagels Lower Hutt during the 2011 World Cup. Much of the material is based on the book “The Physics of Rugby” by Trevor Davis Lipscombe (Nottingham University Press).

* I’m a rugby ref with the Auckland Rugby Referees’ Association.

Prof Sir Sam Edwards passed away earlier this month. Notable obituaries have been written by Cavendish Laboratory colleagues of Edwards, Prof Athene Donald (here and here), and Prof Malcolm Longair (here).

Reading some of the tributes to Edwards, it occurred to me that his work has had more influence on me more than I had thought. He was a mentor to some of my mentors – in New Zealand we might call this academic whakapapa. His ideas figured heavily in my undergraduate literature review on spin glasses, in an honours course I took on theoretical methods, and most recently in the polymer physics I teach at Auckland. I thought I’d record a couple of reflections on Edwards’ work as I have come across it.

Edwards is most well-known for his work in Soft Matter Physics, an area which superficially appears …. well, tricky. Physics students (broadly) progress from considering single items and phenomena, to well-ordered crystals with many atoms, and to continuous gases and liquids. In Soft Matter Physics we describe milk, snot, rubber, plastics and food: systems with disordered microscopic components (like a fluid) which may interact strongly (like a solid). Our PHYS354 course includes a module on Soft Matter Physics, and this area stands to play a significant role in continuing research here at Auckland and within the MacDiarmid Institute.

A key example of Edwards’ work is the rheology (or, mechanical properties) of polymers. Unlike elastic solids, polymers do not return to their original positions after being strained. They do not flow freely like a simple liquid (e.g. water). Their mechanical properties depend on how they have been strained previously, and how fast they have been strained; they are viscoelastic and non-Newtonian. The theory of reptation, which can be used to explain how polymers deform, is most easily associated with 1991 Nobel laureate in physics, Pierre Gilles de Gennes – particularly as the theory is so elegant that it appears stereotypically French! However the credit is shared principally with Edwards (who was Welsh) and Masao Doi (who is Japanese).

Polymer molecules are long and thin, so that a mixture can be thought of as a plate of spaghetti (or perhaps a can of worms). In reptation, each polymer strand is confined to a tube formed by the other strands, and theoretical approaches can progress from there.

[Images from R.A.L. Jones, Soft Condensed Matter, Oxford University Press (2002).]*

As an example of one of the ways this is expressed mathematically, consider the following equation, which can be used to calculate the probability P that a polymer strand (a chain with N links of length a) has an end-to-end vector r:

This calculation known as a path integral; the notation “Dr” represents an integral over all the possible ways of obtaining the vector r between the start and end of the chain.

Edwards introduced this path integral approach to polymer physics in a series of papers through the 1960s. The remarkable part is that the theory is borrowed from a field-theory approach to particle physics: the same calculation will find the probability that a quantum mechanical particle goes between particular initial and final states. All you have to do is replace the chain length Na with a length of time T, and change the constants in the exponent to include a particle’s mass and Planck’s constant. Applying this technique to polymer physics is powerful:

• Path integrals can be represented by intuitive diagrams. In particle physics, these are known as Feynman diagrams, and Edwards extended their use to soft matter.
• Further tools from particle physics (especially application of fields to the particle) can be imitated in order to represent the interactions between polymer strands, as in reptation.

The use of an idea developed for one purpose to describe a completely different problem plays an important role in physics, and has been called universality.** There is another nice example of universality from Edwards’ work, this time relating to his development (with Philip Anderson in the 1970s) of theory relating to a class of material called spin glasses.

In spin glasses, atoms are spatially arranged in a nice ordered crystal lattice, but the arrangement of their magnetic spins is the tricky part. Each atom has a spin that can be thought of as a little arrow pointing in a particular direction. Interactions between neighbouring atoms give rise to rules, for example, “if the atom next to me has spin pointing up, then I should have spin pointing down, and vice versa.” Spin glasses arise when the atoms are arranged so that the rules can’t be followed – for the example above, if I am an atom placed next to two neighbours with spins pointing up and down, what am I to do?

This phenomenon has a most apt and evocative name – it is said that the spins are frustrated. For large collections of atoms, the problem can be approached by arranging the spins to minimise the energy (the amount of frustration) in the system. This is a difficult problem, because many different arrangements of the spins have low energy, but it is not clear which has the lowest. Physicists often talk of an energy landscape: a rolling plain in which there are many hills and valleys, but the plain is so large that it is difficult to tell where the lowest point is. This problem, and Edwards’ approach to it, also has strong universality, and can be applied to problems as diverse as neural networks and the travelling salesman problem.***

So that’s a couple of examples from the work of Prof Sir Sam Edwards, who is known for application of field theories to soft matter, development of a theory for polymers in particular, and introducing us to spin glasses. For more about Edwards’ scientific contributions, there’s a book called Stealing the Gold. If you are looking for the copy in the University of Auckland General Library, you might have to wait a little while.

* This is our PHYS354 textbook. Jones, who studied with Edwards at Cambridge, is now Professor of Physics and Pro-Vice Chancellor at The University of Sheffield.

** Universality is an important aspect of complex systems, a field being studied by Te Pūnaha Matatini, which is based here in the Department of Physics at Auckland.

*** If a salesman must visit every house in a neighbourhood, which is the shortest route to take? Solving this problem efficiently is an important problem in maths and computer science.

For the first couple of weeks in 2015 we have the pleasure of hosting Vaihola Mausa (Auckland Girls’ Grammar School) and Andrew Fatialofa (Marcellin College) as MacDiarmid Institute Discovery Awards students. They have been working hands-on in the labs run by myself, Bryon Wright and Duncan MacGillivray in the Department of Physics and the School of Chemistry. In my lab, they did a wide variety of high-speed photography, and made the new compilation that’s up on our Youtube channel. It’s all their own work, and in particular I take no responsibility for the music. Here are some stills:

Here’s Vaihola and Andrew in my lab setting up an experiment with Conor Seo (with goggles), a summer student with Michelle Dickinson in engineering. We need the bright LED light to get enough light into the camera during a short exposure time. On the right two colleagues in the Department of Physics (Dion O’Neale and Nick Rattenbury) are trying to build a cloud chamber … no movies yet! People who attended the MacDiarmid Institute Students and Postdocs Symposium in November will recall my comments about selfies and bad hair days.

Here’s microfabrication whiz Hayley Ware showing Andrew and Vaihola how to do profilometry – measuring the roughness or structural profile of a surface. They’re all dressed up because they’re in the School of Chemistry’s microfabrication ‘clean room’ … this is kept free of dust, hair etc. which might interfere with the delicate process of making microstructures.

The MacDiarmid Discovery Awards is a programme designed for year 12 or 13 Māori and Pasifika pupils, who have demonstrated their interest in science. This year, six students are hosted in Wellington, and two each in Canterbury and Auckland. One former Discovery Awards student (Shem Harris, Horewhenua College) won the presitigious Douglas Myers Scholarship for undergraduate study at Cambridge University in 2014.

One of the problems in this year’s International Young Physicists’ Tournament (IYPT), called “Water Bombs”, was as follows:

Some students are ineffective in water balloon fights as the balloons they throw rebound without bursting. Investigate the motion, deformation, and rebound of a balloon filled with fluid. Under what circumstances does the balloon burst?

In one of the New Zealand selection rounds, Stan Sarkies (Wellington High School) approached us to use our high speed camera for experimental work on this problem. Stan was eventually part of the New Zealand team of 5 students who won a silver medal at the IYPT main event in Shrewsbury, England.

These experiments were a little bit messier than we thought they would be, because it turns out that your average Warehouse water balloon is pretty tough. A vertical drop of 2 metres wasn’t usually enough to break one, and then there is the problem of hitting the target, especially from an angle … anyway, click for a movie:

This sort of movie is pretty similar to some water drop experiments we’ve seen before: drops in space and bouncing from a superhydrophobic surface. The similarity in terms of the overall drop behaviour (and some of the surface waves) goes to show how important surface tension is to a water drop – the surface of a drop basically acts like a stretchy piece of elastic, although not as strong as a balloon.

Keen observers will have noticed that the shape of the balloons is slightly more complicated than that of a drop in the first moments after impact. The differences are that there is a mismatched boundary between the elastic and the water, that liquids (unlike solids) do not support shear waves, and that there are bubbles and water pockets in the balloons.

When a water balloon impacts with enough kinetic energy or inertia (the ‘oomph’ it has when it hits the surface), the surface tension is overcome, and the balloon bursts. We can see that it fractures (cracks) where the tension is greatest, in a ring around the edge of the spreading rim. With the tension released, the water escapes through this fracture.

We see the same effect with water drops, where a drop spreads and the pressure build-up overcomes the surface tension. Because there is no solid surface, there is no fracture and and water escapes in many little droplets – a splash. It is actually pretty difficult to get a drop to bounce off a surface without splashing. The surface has to be smooth and water-repellent and the drop height has to be just right so that the surface tension is not overcome, but the drop still has enough energy to bounce.

As always with high-speed photography, some of still images are pretty strange.