# Tagged Questions

Questions involving the laws which are scale invariant, i.e. that apply to different scales equally. Also laws that involve exponential behavior, expressed in terms of certain magnitudes to the power of certain exponents.

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### irrational conformal dimension

I know examples of Conformal Field Theories in which the scaling dimension of certain operators is an integer number or a fractional number. However I do not know any example in which the scaling ...
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### Non-dimensionalizing incompressible Navier-Stokes

I have a question about non-dimensionalization of the incompressible Navier-Stokes (NS) equations. My understanding is that the purpose of non-dimensionalization is to "collapse" solutions onto one ...
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### Scaling dimension in Kerr/CFT

Let's consider the scattering of a scalar field around a Kerr-AdS Black Hole. In terms of the Kerr/CFT correspondence how can I get the relation between the scaling dimension and the mass of the field ...
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### How does a 1,000 mph car maintain vertical stability with tiny front wings?

Formula 1 cars have wings to help keep them on the road during cornering, they don't need them whilst moving in a straight line. And that's ok , they "only" travel at 220 mph. In a different speed ...
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### What is the relationship between scale model size and playback rate that looks normal scale in video?

My son just discovered the 240 FPS slo-mo setting on my iphone6. He used it along with his latest obsession - scale model pullback cars - to make some pretty cool video for a project. Apparently, most ...
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### Criticality and the number of paths on a lattice

In the review "Scaling, universality, and renormalization: Three pillars of modern critical phenomena" by Stanley, he makes the following claim towards the end of the paper, which is neither derived ...
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### Scale-covariant decomposition of capacitance

I'm wondering if there is any good insight of how to evaluate a given capacitive geometry in such a way that it would be expressed as a function that depends only on two components: as a geometric ...
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### How to extract depth of a pixel from an image?

I'll have a few pictures that show the same scene, but only a few things move around a little bit. Now I don't have an information about any size in real life but I'd like to extract a scaling factor ...
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### nuclear fusion scaling with reactor size

Thinking about physics of thermonuclear fusion, I have always intuitive sense, that making fusion feasible is matter of reactor size. In other words I feel like: if the fusion reactor is big enough ...
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### Effect on Q factor and resonant frequency when scaling down a damped oscillator to micro / nano scales

I've always just accepted that as you scale down a mechanical system the frequency and Q factor both increase. But how exactly do they scale? Linearly? With the square of reduction in size? Or maybe ...
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### Why are log scales so common?

I am currently reading a very nice book on scales in physics. There is a discussion on the different physical scales which are based on the effect of the corresponding phenomena, the given examples ...
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### How small does sand have to be to get wet?

I think of sand as a lot of very small rocks. Suppose I have a pile of rocks, each about 1cm in size, and the pile is a meter tall. If I pour a bucket of water on the rocks, most of the water will ...
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### Operator Dimension and Field Transformation under Rescaling

In conformal field theory the operator dimension $\Delta$ determines how fields and thus correlation functions behave under rescaling. I am having trouble seeing how this number arises from a scale ...
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### Why do flat sheets of paper twist more than paper cones as they fall?

If I cut a 10cm circle out of a piece of paper and drop it, it will twist as it falls, even if it's rigid. If I then cut out a one-quarter wedge of the circle and tape the remaining three-quarters ...
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### How to measure the size of a laser dot?

I'm not a physicist, that's why I'm asking you if there is maybe an easy way (e.g. a mathematical law) to measure the size of a laser dot, or its diameter. The setup It contains a laser, a high ...
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### Would a six-inch person face certain death when falling from a great height?

In Mary Norton's The Borrowers Aloft, the borrowers are like humans in every way except size - normal adult height is six inches. One family of three is captured by a human couple and housed in an ...
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### How to distinguish between the spectrum of an atom in motion and the one of a scaled atom?

Galaxies are moving dragged by the space expansion. When atoms are in motion the doppler effect will shift the spectra of the emitted photons. The proton-to-electron mass ratio, $\frac{m_e}{m_p}$ ...
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### Scaling: Gravity and Friction

I understand how doubling the length of a shape quadrupes it's area and the analog in 3 dimensions. My question however relates to other physical quantities, for example gravitational field strength. ...
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### How are the finite speed of light and the atomic nature of mater related to the end of Moore's law?

In this article from 2007, Moore talks about the end of his Law. Can someone throw more light as to how the finite speed of light and the atomic nature of mater are related to the end of Moore's law?
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### How can an an ant lift 50 times its own weight and pull 30 times its weight?

According to many sites like this one, an ant can apparently lift 50 times its own weight and pull 30 times its weight. Is it true? Can it be proved using physics? Though most sites agree that an ...
666 views

### Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
225 views

### Amount of material required for a pressure tank

I read the answer for the question Why is a hot air balloon “stiff”? and thought something sounded ridiculous. My engineering requirement is that the walls be strong enough. Here $T$ will be the ...
2k views

### Characteristic length, characteristic time and complexity of the process

Different physical processed (starting from elementary particles or even below to the universe itself) have different length scales $L$ and different characteristic times $T$. Larger processed tend to ...
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### How does the period of a temperature fluctuation affect the depth to which the ground freezes?

On account of the annual fluctuation of temperature the ground at the town of Ν freezes to a depth of 2 metres. To what depth would it freeze on account of a daily fluctuation of the same amplitude? ...
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### Why are smaller animals stronger than larger ones, when considered relative to their body weight?

I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat. It has been suggested to me that this is due to ...
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### Which person can handle falls from big heights better: lighter or heavier?

This probably includes a little of biology, but I believe it's mainly physics, so I hope it's ok to ask here: Imagine 2 persons: Person A weights 120 pounds and person B weights 180 pounds. Imagine ...
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### How does the period of an hourglass depend on the grain size?

Suppose I have an hourglass that takes 1 full hour on average to drain. The grains of sand are, say, $1 \pm 0.1\ {\rm mm}$ in diameter. If I replace this with very finely-grained sand \$0.1 \pm 0.01\ ...