# Questions tagged [scaling]

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.

83 questions
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### Scale diagram confusion

I’m familiar with scale diagrams where three forces act upon an object and trigonometry is used to find the resultant force, but I’ve come across questions that use units of velocity instead of force. ...
1answer
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### Why does the universe manifest scale?

I'll try outline my question in clear terms, articulating specific aspects that are its primary motivators. I'm just beginning in my exploration of physics as a student, but a persistent question that ...
1answer
18 views

### Scaling of nuclear and electromagnetic force

The Wikipedia article on alpha decay stated: The strength of the attractive nuclear force keeping a nucleus together is thus proportional to the number of nucleons, but the total disruptive ...
0answers
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1answer
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### Why does finite size scaling shift the critical temperature downward?

The question is in the title. Say we have a system where: $$\xi \propto |T-T_c|^{-\nu}$$ In a finite system, $\xi$ cannot diverge and is limited by the size of the system. Thus:  L =|T_\text{...
0answers
150 views

### 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 ...
2answers
620 views

### 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 ...
0answers
59 views

### 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 ...
1answer
174 views

### 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 ...
1answer
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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 ...
1answer
56 views

### 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 ...
0answers
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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 ...
1answer
1k views

### 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 ...
3answers
736 views

### Nuclear fusion scaling with reactor size

Thinking about the physics of thermonuclear fusion, I have always had an intuitive sense that making fusion feasible is matter of reactor size. In other words I feel like: If the fusion reactor is ...
0answers
758 views

### 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 ...
3answers
228 views

### 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 ...
3answers
5k views

### 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 ...
1answer
215 views

### 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 ...
1answer
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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 ...
4answers
2k views

### 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 ...
1answer
359 views

### 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 ...
3answers
580 views

### 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, $\frac{m_e}{m_p}$ ...