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.
Questions tagged [scaling]
149 questions
55
votes
3 answers
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 fall through the rocks and form a puddle on the…
Mark Eichenlaub
- 53,961
30
votes
6 answers
Why do objects with big size break easily?
Why do objects with big size break easily? For example: if I drop a chalk of length $L$ from height $h$ then there is a greater probability that it might break, when compared it to a chalk of length $\frac{L}{2}$ dropped from that same height $h$.…
Bhavay
- 1,701
27
votes
6 answers
What's wrong with Arnold's scaling argument on jumping height?
The following question was put on hold: Is it possible to prove that an elephant and a human could jump to the same height?
It reminded me of an exercise (24a) on that exact topic in Arnold's "Mathematical Methods of Classical Mechanics". The…
Antoine
- 835
21
votes
6 answers
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.e. you are, say, scaled down by two orders of…
gatsu
- 7,550
16
votes
5 answers
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 easily than larger ones. This can be seen clearly…
Alan Rominger
- 21,318
12
votes
2 answers
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 $0.1 \pm 0.01\ {\rm mm}$ in diameter but keep the hourglass…
Mark Eichenlaub
- 53,961
12
votes
6 answers
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 example, we can ask ourselves, are the description of…
asanlua
- 600
12
votes
1 answer
Why is the ratio of two extensive quantities always intensive?
Is this something that we observe that always happens or is there some fundamental reason for two extensive quantities to give an intensive when divided?
user225529
12
votes
4 answers
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 looking at the behavior of the smaller of the two…
icurays1
- 273
11
votes
3 answers
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 big enough you can achieve self-sustaining nuclear…
Prokop Hapala
- 1,007
10
votes
4 answers
Rigorous Definitions of Intensive and Extensive Quantities in Classical Thermodynamics
Most undergraduate books on Thermodynamics offer intuitive definitions for intensive and extensive thermodynamic variables. Authors assert, for example, that the former is independent of the system's size while the latter is not. Other authors argue…
Andrew
- 845
10
votes
4 answers
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 smallest thing in the physical universe is the…
DQdlM
- 353
10
votes
2 answers
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, I gather this is equivalent to scale invariance,…
John R Ramsden
- 817
10
votes
3 answers
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 physics, but I am not even sure what to search…
Sonny Ordell
- 203
9
votes
1 answer
What does the exponentiated generator of scale transformation do when it acts on a function?
We know that $d/dx$ is the generator of translation in the sense that $$e^{ad/dx}f(x)=f(x+a)\tag{1}$$ which can be easily be proved from the Taylor series of $f(x+a)$.
Studying the very basics of conformal group/transformations suggest that the…
Solidification
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