Tag Archives: mechanics

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/

Laws of biology?

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daisyMany people are familiar with Newton’s Laws of Motion and, perhaps aware of the existence of the laws of thermodynamics. These are fundamental laws of physics upon which much of our engineered world is built. But, are there corresponding fundamental laws of biology? The question is important because we need to understand the interaction of engineered products and services with the biological world (including us) because, as John Caputo has suggested, a post-humanist world is coming into existence as the boundary between humans and technology is eroded.

So, back to laws of biology.  It is challenging to identify predictive statements about the biological world that are generally applicable. Elliott Sober argued that there are no exceptionless laws in biology. However, others would point to Dollo’s law that states evolution is irreversible, which sounds like a form of the second law of thermodynamics: entropy increases in all real processes. Indeed, McShea and Brandon have written a book entitled ‘Biology’s First Law: the tendency for diversity and complexity to increase in evolutionary systems’ which sounds even more like the second law of thermodynamics.

There are other candidates such as the Hardy-Weinberg law that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences; maybe this is corollary of Dollo’s law?   Or, the Michaelis-Menten rate law that governs enzymatic reactions. But, are there any biological laws that are sufficiently general to apply beyond the context of life on Earth?  Answers via comments, please!

Sources:

Caputo JD. Truth: philosophy in transit. London: Penguin, 2013.

Sober, E., Philosophy of biology, Boulder CO: Westview Press, 1993.

Sober, E., Philosophy in biology, in the Blackwell Companion to Philosophy, 2nd edition, edited by Nicholas Bunnin & E.P. Tsui-James, Blackwell Publishers Ltd, 2006.

McShea, D.W. & Brandon, R., Biology’s first law: the tendency for diversity and complexity to increase in evolutionary systems, Chicago: Chicago University Press, 2010.

Insidious damage

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bikeRecently, my son bought a carbon-fibre framed bike for his commute to work. He talked to me about it before he made the decision to go ahead because he was worried about the susceptibility of carbon-fibre to impact damage. The aircraft industry worries about barely visible impact damage (BVID) because while the damage might be barely visible on the accessible face that received the impact, within the carbon-fibre component there can be substantial life-shortening damage. I reassured my son that it is unlikely a road bike would receive impacts of sufficient energy to induce life-shortening damage, at least in ordinary use. However, such impacts are not unusual in aircraft structures which means that they have to be inspected for hidden, insidious damage. The most common method of inspection is based on ultrasound that is reflected preferentially by the damaged areas so that the shape and extent of damage can be mapped. It is difficult to predict the effect on the structural performance of the component from this morphology information so that, when damage is found, the component is usually repaired or replaced immediately. In my research group we have been exploring the use of strain measurements to locate and assess damage by comparing the strain distributions in as-manufactured and in-service components. We can measure the strain fields in components using a number of techniques including digital image correlation (see my post entitled ‘256 shades of grey’) and thermoelastic stress analysis (see my post entitled ‘Counting photons to measure stress‘). The comparison is performed using feature vectors that represent the strain fields, see my post of a few weeks ago entitled ‘Recognising strain’. The guiding principle is that if damage is present but does not change the strain field then the structural performance of the component is unchanged; however when the strain field is changed then it is easier to predict remanent life from strain data than from morphology data. We have demonstrated that these new concepts work in glass-fibre reinforced laminates and are in the process of reproducing the results in carbon-fibre composites.

Sources

Patterson, E.A., Feligiotti, M., Hack, E., 2013, On the integration of validation, quality assurance and non-destructive evaluation, J. Strain Analysis, 48(1):48-59.

Patki, A.S., Patterson, E.A., 2012, Damage assessment of fibre reinforced composites using shape descriptors, J. Strain Analysis, 47(4):244-253.