‘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.
Can a robot pick up an egg or a baby cactus without damaging either? If it is a conventional ‘hard’ robot then the answer is almost certainly ‘no’. But if it is a ‘soft’ robot then the answer is definitely ‘yes’. They can pick ripe tomatoes from the plant, too. And play the piano with a light touch.
Professor Whitesides’ ingenious robots have ‘fingers’ built from the same soft rubber that is used in implants. They are constructed with a solid layer on one face that is curled around the object being picked up by the inflation of compartments on the reverse face. The inflation of the compartments on the reverse face cause the face to lengthen and the ‘finger’ bends to accommodate the change in length. Careful design of the inflated compartments allows the fingers to conform to the shape being picked up and the use of microfluidics ensures it is not damaged.
Professor Whiteside identified star fish as the source of inspiration for the design of his soft robots. I don’t feel that this short piece has done justice to his work. If, nevertheless, you feel inspired to work for him then there’s probably a queue and since he is professor at Harvard it is almost certainly a long one. His research group has also spun out a company, Soft Robotics Inc. so you could buy some soft robots and explore their capabilities…
Track of the Brownian motion of a 50 nanometre diameter particle in a fluid.
Nanoparticles are being used in a myriad of applications including sunscreen creams, sports equipment and even to study the stickiness of snot! By definition, nanoparticles should have one dimension less than 100 nanometres, which is one thousandth of the thickness of a human hair. Some nanoparticles are toxic to humans and so scientists are studying the interaction of nanoparticles with human cells. However, a spherical nanoparticle is smaller than the wavelength length of visible light and so is invisible in a conventional optical microscope used by biologists. We can view nanoparticles using a scanning electron microscope but the electron beam damages living cells so this is not a good solution. An alternative is to adjust an optical microscope so that the nanoparticles produce caustics [see post entitled ‘Caustics’ on October 15th, 2014] many times the size of the particle. These ‘adjustments’ involve closing an aperture to produce a pin-hole source of illumination and introducing a filter that only allows through a narrow band of light wavelengths. An optical microscope adjusted in this way is called a ‘nanoscope’ and with the addition of a small oscillator on the microscope objective lens can be used to track nanoparticles using the technique described in last week’s post entitled ‘Holes in liquid‘.
The smallest particles that we have managed to observe using this technique were gold particles of diameter 3 nanometres , or about 1o atoms in diameter dispersed in a liquid.
Image of 3nm diameter gold particle in a conventional optical microscope (top right), in a nanoscope (bottom right) and composite images in the z-direction of the caustic formed in the nanoscope (left).
Out-of-focus image from optical microscope of 10 micron diameter polystyrene spheres in water
The holes that I wrote about last week and the week before (post entitled ‘Holes‘ on October 8th)were essentially air-filled holes in a solid plate. When an in-plane load is applied to the plate it deforms and its surface around the hole becomes curved due to the concentration of stress and light passing through the curved surfaces is deviated to form the caustic. If you didn’t follow that quick recap on last week then you might want flip back to last week’s post before pressing on!
The reverse situation is a solid in a fluid. It is difficult to induce stress in a fluid so instead we can use a three-dimensional hole, i.e. a sphere, to generate the curve surface for light to pass through and be deviated. This is quite an easy experiment to do in an optical microscope with some polystyrene spheres floating in distilled water with the microscope slightly out of focus you get bright caustics. And if you take a series of photographs (the x-y plane) with the microscope objective lens at different heights (z-value) it is possible to reconstruct the three-dimensional shape of the caustic by taking the intensity or greyscale values along the centre line of each image and using them all to create new image of the x-z and, or y-z plane, as shown in the picture.
Well done if you have got this far and are still with me! I hope you can at least enjoy the pictures. By the way the particle in the images is about the same diameter as a human hair.
Image in optical microscope of polystyrene particle in water (left), series of images at different positions of microscope objective (centre) and artificial image created from greyscale data along centre-lines of image series (right).