Category Archives: mechanics

Popping balloons

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Balloons ready for popping

Balloons ripe for popping!

Each year in my thermodynamics class I have some fun popping balloons and talking about irreversibilities that occur in order to satisfy the second law of thermodynamics.  The popping balloon represents the unconstrained expansion of a gas and is one form of irreversibility.  Other irreversibilities, including friction and heat transfer, are discussed in the video clip on Entropy in our MOOC on Energy: Thermodynamics in Everyday Life which will rerun from October 3rd, 2016.

Last week I was in Florida at the Annual Conference of the Society for Experimental Mechanics (SEM) and Clive Siviour, in his JSA Young Investigator Lecture, used balloon popping to illustrate something completely different.  He was talking about the way high-speed photography allows us to see events that are invisible to the naked eye.  This is similar to the way a microscope reveals the form and structure of objects that are also invisible to the naked eye.  In other words, a high-speed camera allows us to observe events in the temporal domain and a microscope enables us to observe structure in the spatial domain.  Of course you can combine the two technologies together to observe the very small moving very fast, for instance blood flow in capillaries.

Clive’s lecture was on ‘Techniques for High Rate Properties of Polymers’ and of course balloons are polymers and experience high rates of deformation when popped.  He went on to talk about measuring properties of polymers and their application in objects as diverse as cycle helmets and mobile phones.

Credibility is in the eye of the beholder

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Picture1Last month I described how computational models were used as more than fables in many areas of applied science, including engineering and precision medicine [‘Models as fables’ on March 16th, 2016].  When people need to make decisions with socioeconomic and, or personal costs, based on the predictions from these models, then the models need to be credible.  Credibility is like beauty, it is in the eye of the beholder.   It is a challenging problem to convince decision-makers, who are often not expert in the technology or modelling techniques, that the predictions are reliable and accurate.  After all, a model that is reliable and accurate but in which decision-makers have no confidence is almost useless.  In my research we are interested in the credibility of computational mechanics models that are used to optimise the design of load-bearing structures, whether it is the frame of a building, the wing of an aircraft or a hip prosthesis.  We have techniques that allow us to characterise maps of strain using feature vectors [see my post entitled ‘Recognising strain‘ on October 28th, 2015] and then to compare the ‘distances’ between the vectors representing the predictions and measurements.  If the predicted map of strain  is an perfect representation of the map measured in a physical prototype, then this ‘distance’ will be zero.  Of course, this never happens because there is noise in the measured data and our models are never perfect because they contain simplifying assumptions that make the modelling viable.  The difficult question is how much difference is acceptable between the predictions and measurements .  The public expect certainty with respect to the performance of an engineering structure whereas engineers know that there is always some uncertainty – we can reduce it but that costs money.  Money for more sophisticated models, for more computational resources to execute the models, and for more and better quality measurements.

Models as fables

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moel arthurIn his book, ‘Economic Rules – Why economics works, when it fails and how to tell the difference‘, Dani Rodrik describes models as fables – short stories that revolve around a few principal characters who live in an unnamed generic place and whose behaviour and interaction produce an outcome that serves as a lesson of sorts.  This seems to me to be a healthy perspective compared to the almost slavish belief in computational models that is common today in many quarters.  However, in engineering and increasingly in precision medicine, we use computational models as reliable and detailed predictors of the performance of specific systems.  Quantifying this reliability in a way that is useful to non-expert decision-makers is a current area of my research.  This work originated in aerospace engineering where it is possible, though expensive, to acquire comprehensive and information-rich data from experiments and then to validate models by comparing their predictions to measurements.  We have progressed to nuclear power engineering in which the extreme conditions and time-scales lead to sparse or incomplete data that make it more challenging to assess the reliability of computational models.  Now, we are just starting to consider models in computational biology where the inherent variability of biological data and our inability to control the real world present even bigger challenges to establishing model reliability.

Sources:

Dani Rodrik, Economic Rules: Why economics works, when it fails and how to tell the difference, Oxford University Press, 2015

Patterson, E.A., Taylor, R.J. & Bankhead, M., A framework for an integrated nuclear digital environment, Progress in Nuclear Energy, 87:97-103, 2016

Hack, E., Lampeas, G. & Patterson, E.A., An evaluation of a protocol for the validation of computational solid mechanics models, J. Strain Analysis, 51(1):5-13, 2016.

Patterson, E.A., Challenges in experimental strain analysis: interfaces and temperature extremes, J. Strain Analysis, 50(5): 282-3, 2015

Patterson, E.A., On the credibility of engineering models and meta-models, J. Strain Analysis, 50(4):218-220, 2015

Undermining axioms at the speed of light

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International Prototype of the Kilogram (IPK)

International Prototype of the Kilogram (IPK)

An axiom is a statement so evident or well-established that it is accepted without controversy or question.  However, in his review of Sokal’s Hoax, Steven Weinberg has suggested that ‘none of the laws of physics known today (with the possible exception of the general principles of quantum mechanics) are exactly and universally valid’.  This propels physics to the same status as biology (see my post entitled ‘Laws of biology?‘ on January 13th 2016) – in lack exactly and universally valid laws and it suggests that there are no scientific axioms. 

‘Things that are equal to the same things are equal to each other’ is Euclid’s first axiom and in thermodynamics leads to the Zeroth Law: ‘Two things each in thermal equilibrium with a third are also in thermal equilibrium with each other’ (see my posts entitled ‘All things being equal‘ on December 3rd, 2014 on ‘Lincoln on equality‘ on February 6th, 2013).   Thermal equilibrium means that there is no transfer of thermal energy or heat between the two things, this leads to the concept of temperature because when two things are in thermal equilibrium we say that they are at the same temperature.   Last week I explained these ideas in both my first year undergraduate class on thermodynamics and my on-going MOOC.  This week, I have challenged MOOC participants to try to identify other measurement systems, besides temperature, that are based on Euclid’s first axiom.

For instance, its application to mechanical equilibrium leads to Newton’s laws and from there to mass as a measure of a body’s inertia.  We use Euclid’s axiom to evaluate the mass of things through a chain of comparisons that leads ultimately to the international kilogram at the Bureau International des Poids et Mesures in France.  Similarly, we measure time by comparing our time-pieces to an international standard for a second, which is the duration of  9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 

However, given Weinberg’s statement perhaps I can give you a harder challenge than MOOC participants: can you identify exceptions to Euclid’s first axiom?

I think I can identify one: if you calibrated two very accurate timepieces against a cesium 133 clock and then took one on a journey through space travelling at the speed of light while the other remained on Earth, when you brought the two together again on Earth they would not agree, based on Einstein’s theory of relativity, or what he called relativity of simultaneity.  Now see what you can come up with!

Sources:

Steven Weinberg, ‘Sokal’s Hoax’, NY review of Books, 43(13):11-15, August 1996.

Oliver Byrne, First Six Books of the Elements of Euclid, London: William Pickering, 1847

Joseph Schwartz & Michael McGuinness, Einstein for Beginners, London: Writers and Readeres Publishing Cooperative, 1979 & Penguin Random House, 2013.

Albert Einstein, Relativity: The Special and the General Theory, (translated by Robert W. Lawson), London: Methuen & Co Ltd., 1979 & on-line at www.bartleby.com/173/