Tag Archives: Royal Society

Million to one

‘All models are wrong, but some are useful’ is a quote, usually attributed to George Box, that is often cited in the context of computer models and simulations.  Working out which models are useful can be difficult and it is essential to get it right when a model is to be used to design an aircraft, support the safety case for a nuclear power station or inform regulatory risk assessment on a new chemical.  One way to identify a useful model to assess its predictions against measurements made in the real-world [see ‘Model validation’ on September 18th, 2012].  Many people have worked on validation metrics that allow predicted and measured signals to be compared; and, some result in a statement of the probability that the predicted and measured signal belong to the same population.  This works well if the predictions and measurements are, for example, the temperature measured at a single weather station over a period of time; however, these validation metrics cannot handle fields of data, for instance the map of temperature, measured with an infrared camera, in a power station during start-up.  We have been working on resolving this issue and we have recently published a paper on ‘A probabilistic metric for the validation of computational models’.  We reduce the dimensionality of a field of data, represented by values in a matrix, to a vector using orthogonal decomposition [see ‘Recognizing strain’ on October 28th, 2015].  The data field could be a map of temperature, the strain field in an aircraft wing or the topology of a landscape – it does not matter.  The decomposition is performed separately and identically on the predicted and measured data fields to create to two vectors – one each for the predictions and measurements.  We look at the differences in these two vectors and compare them against the uncertainty in the measurements to arrive at a probability that the predictions belong to the same population as the measurements.  There are subtleties in the process that I have omitted but essentially, we can take two data fields composed of millions of values and arrive at a single number to describe the usefulness of the model’s predictions.

Our paper was published by the Royal Society with a press release but in the same week as the proposed Brexit agreement and so I would like to think that it was ignored due to the overwhelming interest in the political storm around Brexit rather than its esoteric nature.


Dvurecenska K, Graham S, Patelli E & Patterson EA, A probabilistic metric for the validation of computational models, Royal Society Open Science, 5:1180687, 2018.

Third time lucky

At the end of last year my research group had articles published by the Royal Society’s journal  Open Science in two successive months [see ‘Press Release!‘ on November 15th, 2017 and ‘Slow moving nanoparticles‘ on December 13th, 2017].  I was excited about both publications because I had only had one article published before by the Royal Society and because the Royal Society issues a press release whenever it publishes a new piece of science.  However, neither press release generated any interest from anyone; probably because science does not sell newspapers (or attract viewers) unless it is bad news or potentially life-changing.  And our work on residual stress around manufactured holes in aircraft or on the motion of nanoparticles does not match either of these criteria.

Last month, we did it again with an article on ‘An experimental study on the manufacture and characterization of in-plane fibre-waviness defects in composites‘.  Third time lucky, because this time our University press office were interested enough to write a piece for the news page of the University website, entitled ‘Engineers develop new method to recreate fibre waviness defects in lab‘.  Fibre waviness is an issue in the manufacture of structural components of aircraft using carbon fibre reinforced composites because kinks or waves in the fibres can cause structural weaknesses.  As part of his PhD, supported by Airbus and the UK Engineering and Physical Sciences Research Council (EPSRC), Will Christian developed an innovative technique to generate defects in our lab so that we can gain a better understanding of them. Read the article or the press release to find out more!

Image shows fracture through a waviness-defect in the top-ply of a carbon-fibre laminate observed in a microscope following sectioning after failure.


Christian WJR, DiazDelaO FA, Atherton K & Patterson EA, An experimental study on the manufacture and characterisation of in-plane fibre-waviness defects in composites, R. Soc. open sci. 5:180082, 2018.

Slow moving nanoparticles

Random track of a nanoparticle superimposed on its image generated in the microscope using a pin-hole and narrowband filter.

A couple of weeks ago I bragged about research from my group being included in a press release from the Royal Society [see post entitled ‘Press Release!‘ on November 15th, 2017].  I hate to be boring but it’s happened again.  Some research that we have been performing with the European Union’s Joint Research Centre in Ispra [see my post entitled ‘Toxic nanoparticles‘ on November 13th, 2013] has been published this morning by the Royal Society Open Science.

Our experimental measurements of the free motion of small nanoparticles in a fluid have shown that they move slower than expected.  At low concentrations, unexpectedly large groups of molecules in the form of nanoparticles up to 150-300nm in diameter behave more like an individual molecule than a particle.  Our experiments support predictions from computer simulations by other researchers, which suggest that at low concentrations the motion of small nanoparticles in a fluid might be dominated by van der Waals forces rather the thermal motion of the surrounding molecules.  At the nanoscale there is still much that we do not understand and so these findings will have potential implications for predicting nanoparticle transport, for instance in drug delivery [e.g., via the nasal passage to the central nervous system], and for understanding enhanced heat transfer in nanofluids, which is important in designing systems such as cooling for electronics, solar collectors and nuclear reactors.

Our article’s title is ‘Transition from fractional to classical Stokes-Einstein behaviour in simple fluids‘ which does not reveal much unless you are familiar with the behaviour of particles and molecules.  So, here’s a quick explanation: Robert Brown gave his name to the motion of particles suspended in a fluid after reporting the random motion or diffusion of pollen particles in water in 1828.  In 1906, Einstein postulated that the motion of a suspended particle is generated by the thermal motion of the surrounding fluid molecules.  While Stokes law relates the drag force on the particle to its size and fluid viscosity.  Hence, the Brownian motion of a particle can be described by the combined Stokes-Einstein relationship.  However, at the molecular scale, the motion of individual molecules in a fluid is dominated by van der Waals forces, which results in the size of the molecule being unimportant and the diffusion of the molecule being inversely proportional to a fractional power of the fluid viscosity; hence the term fractional Stokes-Einstein behaviour.  Nanoparticles that approach the size of large molecules are not visible in an optical microscope and so we have tracked them using a special technique based on imaging their shadow [see my post ‘Seeing the invisible‘ on October 29th, 2014].


Coglitore D, Edwardson SP, Macko P, Patterson EA, Whelan MP, Transition from fractional to classical Stokes-Einstein behaviour in simple fluids, Royal Society Open Science, 4:170507, 2017. doi:

Press release!

A jumbo jet has about six million parts of which roughly half are fasteners – that’s a lot of holes.

It is very rare for one of my research papers to be included in a press release on its publication.  But that’s what has happened this month as a consequence of a paper being included in the latest series published by the Royal Society.  The contents of the paper are not earth shattering in terms of their consequences for humanity; however, we have resolved a long-standing controversy about why cracks grow from small holes in structures [see post entitled ‘Alan Arnold Griffith‘ on  April 26th, 2017] that are meant to be protected from such events by beneficial residual stresses around the hole.  This is important for aircraft structures since a civilian airliner can have millions of holes that contain rivets and bolts which hold the structure together.

We have used mechanical tests to assess fatigue life, thermoelastic stress analysis to measure stress distributions [see post entitled ‘Counting photons to measure stress‘ on November 18th, 2015], synchrotron x-ray diffraction to evaluate residual stress inside the metal and microscopy to examine failure surfaces [see post entitled ‘Forensic engineering‘ on July 22nd, 2015].  The data from this diverse set of experiments is integrated in the paper to provide a mechanistic explanation of how cracks exploit imperfections in the beneficial residual stress field introduced by the manufacturing process and can be aided in their growth by occasional but modest overloads, which might occur during a difficult landing or take-off.

The success of this research is particularly satisfying because at its heart is a PhD student supported by a dual PhD programme between the University of Liverpool and National Tsing Hua University in Taiwan.  This programme, which supported by the two partner universities, is in its sixth year of operation with a steady state of about two dozen PhD students enrolled, who divide their time between Liverpool, England and Hsinchu, Taiwan.  The synchrotron diffraction measurements were performed, with a colleague from Sheffield Hallam University, at the European Synchrotron Research Facility (ESRF) in Grenoble, France; thus making this a truly international collaboration.


Amjad K, Asquith D, Patterson EA, Sebastian CM & Wang WC, The interaction of fatigue cracks with a residual stress field using thermoelastic stress analysis and synchrotron x-ray diffraction experiments, R. Soc. Open Sci. 4:171100.