The scaling tag has no wiki summary.
14
votes
3answers
793 views
Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
11
votes
5answers
444 views
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 ...
8
votes
2answers
572 views
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\ ...
7
votes
2answers
661 views
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 ...
6
votes
2answers
376 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, ...
5
votes
2answers
225 views
Are we big or small?
How does the size of humans compare to the size of other objects in the universe? Are we among the relatively large or the relatively small things?
My very preliminary research suggests that the ...
4
votes
2answers
1k views
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 ...
4
votes
2answers
58 views
How does the correlation length of weather emerge?
The question is pretty simple: If I know the weather where I stand, I can estimate the weather 5 meters or 1 km away away pretty well, but I'll have a hard time guessing what the weather is, say, 50 ...
4
votes
0answers
67 views
Design of experiments to determine proportionality
A common result of theoretical analysis in physics is some sort of relation derived from physical parameters and typically expressed in the form of a non-dimensional parameter. These scale relations ...
4
votes
1answer
210 views
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 ...
3
votes
2answers
182 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 ...
3
votes
1answer
156 views
How can you tell a model explosion from the real thing?
Movies and TV shows frequently show buildings being bombed, cars blowing up, etc. Frequently these are really explosions of miniatures filmed up close.
Aside from the speed that the explosion ...
2
votes
2answers
212 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 ...
2
votes
6answers
589 views
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 ...
2
votes
1answer
95 views
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 ...
2
votes
1answer
166 views
how to solve this scaling equation
I am confronted with the following scaling equation (in Laplace domain if that matters):
$\tilde\psi(s) = a \tilde\psi(s/b)$
I know the answer is such that $\tilde\psi(s) \sim s^{\beta} K(s)$ where ...
2
votes
0answers
47 views
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 ...
2
votes
2answers
482 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 ...
1
vote
1answer
168 views
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 ...
1
vote
1answer
80 views
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 ...
1
vote
1answer
115 views
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?
...
1
vote
0answers
48 views
How to express energy-momentum tensor of conformal fluid in terms of temperature?
I heard that conformal fluid has only one scaling governed by temperature, by how exactly the relation is derived between energy-momentum tensor and temperature? I will really appreciate if some ...
1
vote
0answers
67 views
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 ...
1
vote
2answers
91 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 ...
-2
votes
1answer
139 views
Understanding pregnancy length and life time based on dimension analysis and order of magnitude estimation [closed]
Based on dimensional analysis and order of magnitude estimation one can understand why for example no warm blooded animal of small size such as rats can live in the north pole, only big animals like ...
