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Might boron carbide perhaps work? Its pretty strong, neutron absorbing, 3,000 K melting temperature, Mohs hardness is around 9.5. Density is around 2.5 g/cm^2. It is also relatively easy to produce.

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Recall that Maxwell's equations (in the absence of losses) require only that $n^2 = \epsilon\mu$. So when you take the square root, you are mathematically allowed to take either the positive or the negative square root. Of course, then the question becomes, why would you want to take the negative square root? Clearly, this is only an issue if $\epsilon\mu ... 1 Poisson's ration for most metals is close to 1/3. That means for a stretch of 1%, you get a reduction in the diameter of 0.33% Adding up the changes in all three dimensions gives you a volume increase of 0.33%. (The "rubber-band" deformation with no volume change corresponds to a Poisson's Ration of 1/2.) 1 The volume changes. In tension, the chemical bonds all get a little bigger, resulting in a larger volume. To a first approximation, the change of volume is linear, as you have shown. A more accurate analysis shows that the wire gets a little narrower, so the increase in volume is a little less than your result predicts. Things are entirely different with ... 1 I can only speak for steel and aluminum which I have had engineering experience with. The answer is that a solid rod is going to be stronger than a stranded one of the same area. There are a few effects to consider, and most of them work against the stranded cables. Geometry Effects. Strands are not straight and so pulling on them causes contact pressure ... 1 I assume the total cross section of the wires in the rope is equal to the cross section of the steel bar. Since there is some space between the fibers, the rope will have a larger diameter. If the fibers in the rope were all straight and you were careful to pull equally on each fiber, the bar and rope should be equally strong. But they typically won't be. ... 0 Because in the bulk, the energy between two dislocations is proportional to the distance between them. This means the dislocations are confined in the bulk. So they can not appear in side the crystal. 4 The surface of the film is a [001] plane through the silicon (or diamond) lattice, space group Fd-3m (#227), 0 Steel balls would be a lot louder, and would have to be painted. The paint would quickly chip off from constant impacts with other (mostly) unyielding steel balls, looking skanky while providing an uneven rolling surface. 17 There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here, but for some reason I am not allowed to link to it normally: http://211.144.68.84:9998/91keshi/Public/File/34/482-7386/pdf/nature10779.pdf) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump ... 0 It's a mathematical trick to factor$\beta$out of an integral.$\mathbf{u}$and$\mathbf{P}$don't depend on temperature, but$\mathbf{\bar{u}}$and$\mathbf{\bar{P}}$do. But the barred versions appear only as dummy variables in an integral, so their dependence on$\beta\$ is immaterial. This simplifies what comes next. I don't see any way of making ...

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The process of transferring charge between two objects by bringing them into contact and/or rubbing them together is known as the triboelectric effect, and is historically, the first recorded observation of an electric phenomenon. Wiki Page on Triboelectric effect In general, there are too many competing factors such that there is little predictive power.

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