# 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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### Will Anderson's Poor Man's Scaling loose its effect when band width is small?

The s-d interaction Hamiltonian is as fellows $H_I=Js.S$, J is the coupling strength. We focus on the antiferromagnetic case, where $J>0$. According Anderson's poor man's scaling, the ...
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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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### 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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### Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
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### Calculating Reynolds number for a viscous droplet

I'm trying to develop a very basic scaling law/unit analysis for viscous droplet formation, and I'd like to get some rough numerical values of the Reynolds number to play with. To be specific, I'm ...
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### Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin (i....
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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 ...
191 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 ...
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### What is the $\mu$ problem in SUSY?

I need a little bit of help in understanding the mu problem in SUSY. As I understand it, the gist of the problem is that $\mu$ must be on the same order of magnitude as the electroweak scale (246 GeV)....
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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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### 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 ...
277 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 ...
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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 ...
744 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 ...
903 views

### Anomalous dimension for bare actions with a standard kinetic term

In this paper on p42, it is explained that when starting with a bare action that contains a standard kinetic term, this kinetic term attains a correction in the course of the RG flow which can be ...
257 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 ...
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### Why do fractal systems show power-law behavior?

I'm not sure I quite understand why systems with fractal systems show power-law behavior. My "gut" understanding is that the power-law index indicates the correct scaling factor for the system so that ...
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### How do I correctly scale down a space capsule for testing its physical behaviour on splashdown?

Kristian von Bengtson (on twitter, on Wikipedia) of Copenhagen Suborbitals is building a downscaled test item to test the design for their space capsule. He notes that as volume and area scale down ...
570 views

### What is the exact relationship between scale invariance and renormalizability of a theory?

I have often read that renormalizability and scale invariance are somehow related. For example in this tutorial on page 12 in the first sentence of point (7), self similarity (= scale invariance ?) is ...
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### Is flying really easier on smaller scales?

In the book Playing with Planets, the author makes the following argument, pertinent to flying robots of the future: As it is, an important law of physics says that smaller organisms fly much more ...
348 views

### Scale invariance symmetry as a simple argument in an electrostatics problem

In the comments to this post, it was hinted that proving that the force acting on a charge at a vertical distance from a uniformly charged plane is independent of that distance can be done by ...
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### scaling laws for density and temperature of high-energy explosions

I'm wondering if there are heuristic ways to derive how the peak density and temperature of nuclear explosions scale with the amount of fissile/fusible material. Does it matter what the explosion ...
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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 ...