Congratulations to Oxford Mathematicians Martin Bridson, Marcus du Sautoy and Artur Ekert who have been elected Fellows of the Royal Society. Martin is Whitehead Professor of Pure Mathematics, a Fellow of Magdalen College and Head of the Mathematical Institute in Oxford. He has been elected for his many distinguished contributions to group theory and topology. Marcus is Charles Simonyi Professor for the Public Understanding of Science and a Fellow of New College and has been elected for his outstanding achievements in promoting the understanding of science and mathematics to a global audience and for eminent research that has completely transformed the study of zeta functions of groups. Artur is Professor of Quantum Physics at the Mathematical Institute and a Fellow of Merton College. Artur has been elected FRS for his work on quantum physics, quantum computation and cryptography.
|Friday, 29 April 2016||
|Thursday, 21 April 2016||
The chameleon's tongue is said to unravel at the sort of speed that would see a car go from 0-60 mph in one hundredth of a second – and it can extend up to 2.5 body lengths when catching insects. Oxford Mathematicans Derek Moulton and Alain Goriely have built a mathematical model to explain its secrets.
The researchers (working in collaboration with Tufts University in the US) derived a system of differential equations to capture the mechanics of the energy build-up and 'extreme acceleration' of the reptile's tongue.
Derek Moulton, Associate Professor of Mathematical Biology at Oxford, said: 'if you are looking at the equations they might look complex, but at the heart of all of this is Newton's Second Law – the sort of thing that kids are learning in A-levels, which is simply that you're balancing forces with accelerations.
'In mathematical terms, what we've done is used the theory of non-linear elasticity to describe the energy in the various tongue layers and then passed that potential energy to a model of kinetic energy for the tongue dynamics.'
Special collagenous tissue within the chameleon's tongue is one of the secrets behind its effectiveness. This tissue surrounds a bone at the core of the tongue and is surrounded itself by a muscle. Professor Moulton added: 'the muscle – the outermost layer – contracts to set the whole thing in motion. We’ve modelled the mechanics of the whole process, the build up and release of energy.'
The researchers say the insights will be useful in biomimetics – copying from nature in engineering and design - for example in developing soft, elastic materials for robotics. They add that they also did the research because it was interesting and fun. Both pretty good reasons to study mathematics.
|Thursday, 21 April 2016||
The use of mathematical models to describe the motion of a variety of biological organisms has been the subject of much research interest for several decades. If we are able to predict the future locations of bacteria, cells or animals, and then we subsequently observe differences between the predictions and the experiments, we would have grounds to suggest that the local environment has changed, either on a chemical or protein scale, or on a larger scale, e.g. weather patterns or changing distributions of predators/prey.
Early approaches were predominantly centred on the position jump model of motion, where agents undergo instantaneous changes of position according to a distribution kernel interspersed with waiting periods of stochastic length. To clarify, after a random period of time, the organism in question disappears in one location, and reappears in another nearby location. Equations for the probability that a particle is located in a position in space are called drift-diffusion equations - which are usually easy to solve numerically.
(the image above shows the pattern of seagulls above the UK).
|Wednesday, 20 April 2016||
Appearing everywhere from state-of-the-art cryptosystems to the proof of Fermat's Last Theorem, elliptic curves play an important role in modern society and are the subject of much research in number theory today. Jennifer Balakrishnan, a researcher working in number theory, explains more in the latest in our Oxford Mathematics Alphabet.
|Thursday, 14 April 2016||
Oxford Mathematician Rob Style has been awarded the 2016 Adhesion Society Young Scientist Award, sponsored by the Adhesion and Sealant Council, for his fundamental contributions to our understanding of the coupling of surfaces tension to elastic deformation. Rob researches the mechanics of very soft solids like gels and rubber, in particular investigating why they don’t obey the same rules as hard materials that are more traditionally used by engineers.
|Thursday, 14 April 2016||
Oxford Mathematician Jake Taylor King has won the Lee Segel Prize for Best Student Paper for his paper 'From birds to bacteria: Generalised velocity jump processes with resting states.' Jake worked on his research with Professor Jon Chapman. The prize is awarded annually by the Society for Mathematical Biology. One of Jake's co-authors on the paper, Gabs Rosser, previously also studied Mathematics at Oxford in the Wolfson Centre for Mathematical Biology.
|Wednesday, 13 April 2016||
Oxford Mathematician Linus Schumacher has won the prestigious Reinhart Heinrich Doctoral Thesis Award. The award is presented annually to the student submitting the best doctoral thesis in any area of Mathematical and Theoretical Biology.
In the judges' view "Linus' thesis is an outstanding example of how mathematical modelling and analysis that is kept close to the experimental system can contribute efficiently to advance the understanding of complex biological questions. The roles of cellular heterogeneity, microenvironmental cues and cell-to-cell interactions, which are common themes in the study of biomedical systems, are skillfully dissected and analysed in relevant experimental model systems, leading to significant advances in the current understanding of said systems."
The judges concluded: "the modelling aims to derive generic, theoretical insights from specific, biological questions. The work has led to a number of excellent publications."
|Friday, 8 April 2016||
If effectively harnessed, increased uptake of renewable generation, and the electrification of heating and transport, will form the bedrock of a low carbon future. Unfortunately, these technologies may have undesirable consequences for the electricity networks supplying our homes and businesses. The possible plethora of low carbon technologies, like electric vehicles, heat pumps and photovoltaics, will lead to increased pressure on the local electricity networks from larger and less predictable demands.
Stephen Haben and colleagues from the University of Oxford and colleagues from the University of Reading are working with the distribution network operator (DNO) Scottish and Southern Energy Power Distribution on the £30m Thames Valley Vision project. The aim is to develop sophisticated modelling techniques to help DNOs avoid expensive network reinforcement as the UK moves toward a low carbon economy. In other words, what are some of the smart alternatives to “keeping the lights on” without simply digging up the road and laying bigger cables?
With recent advanced monitoring infrastructures (such as smart meters) we can now start using mathematical and statistical techniques to better understand, anticipate and support local electricity networks. The team has been analysing smart meter data and employing clustering methods to better understand household energy usage and discover how many different types of behaviours exist. This is turn can lead to improvements in demand modelling, designing tariffs and other energy efficiency strategies (e.g. demand side response). The researchers found different types of behaviour with varying degrees of intra-day demand, seasonal variability and volatility. Each of these therefore has different types of possible strategies in terms of reducing energy and costs. An important discovery is that energy behavioural use has very weak links with the socio-demographics, tariffs or houses size. Hence to really understand your energy demand requires the monitoring of data available through smart meters.
Forecasts can help DNOs manage and plan the networks in many ways, in particular by anticipating extremes in demand (e.g. large amounts of local generation on a sunny day). The researchers have developed a range of point and probabilistic forecasts for a wide number of relevant applications. Long term, scenario forecasts are generated using agent based models to simulate the impact of low carbon technologies. Shorter term forecasts have been developed to estimate daily demands and thus create appropriate plans for the charging and discharging cycles of batteries, helping to reduce peak overloads. These algorithms have been successfully used in silico and will soon be deployed and tested on real storage devices on the network.
Most recently the team are working on understanding limits to their models when monitoring data is unavailable or sparse. This is desirable since acquiring data and installing monitoring equipment is expensive. Can households be accurately modelled with only limited access to monitored data? If so, how much monitoring is really necessary? They have found that local energy demand is very dependent on the number and proportion of commercial and domestic properties. Such insights will be used to device workable solutions so that a DNO can choose the most appropriate (i.e. least disruptive but most cost effective) solution for different network types. Whether, for example, that is installing batteries, introducing monitoring or investing in infrastructure upgrades.
In summary, the extra visibility of household level demand through higher resolution monitoring equipment has created new opportunities for better understanding energy behavioural usage and highlighted the need for novel analytics. Demand at the individual customer level is irregular and volatile in contrast to the high voltage demands that has traditionally been investigated and thus current methods may not be applicable. The methods necessary to reduce energy demand and promote energy efficiency sit in many areas of applied mathematics, data science and statistics. This requires mathematicians to be at the forefront of designing and creating new methods and techniques for the future energy networks.
|Wednesday, 6 April 2016||
The Society for Industrial and Applied Mathematics (SIAM) has announced that Professors Xunyu Zhou and Endre Suli from Oxford Mathematics are among its newly elected Fellows for 2016.
SIAM exists to ensure the strongest interactions between mathematics and other scientific and technological communities through membership activities, publication of journals and books, and conferences.
|Saturday, 26 March 2016||
A diophantine equation is an algebraic equation, or system of equations, in several unknowns and with integer (or rational) coefficients, which one seeks to solve in integers (or rational numbers). The study of such equations goes back to antiquity. Their name derives from the mathematician Diophantus of Alexandria, who wrote a treatise on the subject, entitled Arithmetica.
The most famous example of a diophantine equation appears in Fermat’s Last Theorem. This is the statement, asserted by Fermat in 1637 without proof, that the diophantine equation has no solutions in whole numbers when n is at least 3, other than the 'trivial solutions' which arise when XYZ = 0. The study of this equation stimulated many developments in number theory. A proof of the theorem was finally given by Andrew Wiles in 1995.
The basic question one would like to answer is: does a given system of equations have solutions? And if it does have solutions, how can we find or describe them? While the Fermat equation has no (non-trivial) solutions, similar equations (for example ) do have non-trivial solutions. One of the problems on Hilbert’s famous list from 1900 was to give an algorithm to decide whether a given system of diophantine equations has a solution in whole numbers. In effect this is asking whether the solvability can be checked by a computer programme. Work of Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson, culminating in 1970, showed that there is no such algorithm. It is still unknown whether the corresponding problem for rational solutions is decidable, even for plane cubic curves. This last problem is connected with one of the Millennium Problems of the Clay Mathematics Institute (with a million dollar prize): the Birch Swinnerton Dyer Conjecture.
To find out more about diophantine problems read Professor Jonathan Pila's latest addition to our Oxford Mathematics Alphabet.