Feb12

## Mathematics of the mosh pit...

Rock music fans are aware of the phenomenon of the mosh pit at concerts — a riotous area, usually close to the stage, where concert-goers, in lieu of learning complicated dance steps, slam violently into each other (and hence an alternative name for moshing is slam dancing). Until now the fascinating mathematics of this emergent property of crowds has been unjustly ignored. However, this has changed with the advance publication on the arXiv Collective Motion of Moshers at Heavy Metal Concerts by Silverberg, Bierbaum, Sterna and Cohen. The abstract states Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. The authors model the behaviour of the mosh pit (and circle pit), provide source code and Java script interactive moshpit The conclusions will be surprising to many: If we increase the self-propulsion coefficient (decrease ), we find the motion, though random, is no longer fit by a Maxwell-Boltzmann distribution. Instead, collisions between active and passive MASHers [Mobile Active Simulated Humanoid] on the boundary of the simulated mosh pit removes energy faster than collisions among active MASHers can rethermalize the system. Consequently, measurements in silico show a radial temperature gradient is established with a higher effective temperature at the core of the simulated mosh pit and a lower effective temperature at the edge A valuable and timely addition to the literature. Ok, let’s...

Oct03

## Criminal Network

I’ve been really busy the last few weeks – the usual effect of the academic year starting! I’m running a new course called Maths at Work which is about how maths gets used in the “real world”. One of the projects for this involves the mathematics of networks, such as Twitter and Facebook. As part of my investigations I came across a use of Steiner trees in fraud detection. The University of Alberta press release called Math tree may help root out fraudsters gives the non-mathematical side of the story, the mathematical side can be found in the paper Social network meets Sherlock Holmes: investigating the missing links of fraud. It would be interesting to see if this actually works! Anybody have any...

Jul04

## New Maths Journals

I’m on holiday at the moment so don’t have much time to write. If you are interested in the recent fuss about academics fighting for reasonably-priced journals, then pop over to Tim Gower’s blog to see this announcement on new journals. There’s also a little bit on Terry Tao’s blog. It looks like this could be...

May15

## Discount for Variational Problems in Differential Geometry Book...

One for researchers. Last year I, with my colleagues Roger Bielawski and Martin Speight, edited a book, Variational Problems in Differential Geometry. There is currently a US promotional offer for this book: Yes, I want 20% off my copy of Variational Problems in Differential Geometry Feel free to send the link on to people you know who might be...

## Willmore Day at Durham...

Last week’s Yorkshire Durham Geometry Day, held at Durham, celebrated the work and life of Tom Willmore. Willmore was a differential geometer who spent most of his academic career at the University of Durham. As I was giving a talk in a school I missed the first two talks of the day which was a shame as the first explained a recent proof of the long-standing Willmore Conjecture. For a surface we can define the notion of curvature in a number of ways. For Willmore surfaces we use mean curvature so let’s define that. At a point of a surface take a normal vector. Any non-zero vector in the line perpendicular to the tangent plane to the surface will do. Next take any plane that contains this normal. The intersection of this plane with the surface is a curve. Take the curvature of this curve at the point , call this curvature . (The curvature of a curve at a point is where is the radius of the circle that best approximates the curve at that point.) Next take the plane containing the normal that is at right angles to the first one. We get another curve and hence another curvature, call it . Take the mean of these two curvatures, . This is the mean curvature at ; we will denote it by . We can do this at every point and so we get a function given by . An alternative viewpoint is given on the Wikipedia page. Now we integrate the square of this function over the whole of the surface. The Willmore energy of a surface , denoted , is the number . That is we integrate over the whole surface the square of the mean curvature. So for every...

Feb08

## Boycott of Elsevier

I’ve mentioned elsewhere that the current system of publishing research is flawed. The government, i.e. taxpayers, pays us to do research, we send the resulting papers to journal publishers, we referee the papers and edit the journals for free and then the publishers sell the research back to us for a high price. The result is that the taxpayers pay twice, we work for free and the commercial publishers get rich. My answer to this was to start charging for my refereeing services. A small change but so far no-one has asked me to referee for something from a commercial publisher so it is really no change! However, a bigger and more effective method of change is coming – an academic boycott against Elsevier, considered by many to be a serious offender in this problem, has been started by Tim Gowers. Read the story over at the Chronicle of Higher Education, home to Prof...