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.
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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 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 ...
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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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Scalable quantum computation vs Uncertainty Principle
tl;dr. : If we want the result of a quantum computation to have scalable more bits, we will need inner measurements to have scalable precision, if we already know the result of the computation (from a ...
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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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Ignore terms in the equation of motion
While working on a problem relative to particles motion, I ended up with the following second order nonlinear differential equation:
$$\tag{1} \ddot{y}(t)+\frac{y(t)}{b^2}\left(a-\frac{\dot{y}(t)^2}{2}...
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Using Wien's Law to show spectral distruibution function of one temperature represents all temperatures
This is a exercise question from Quantum Mechanic textbook by Bransden:
Using Wien's Law to show that if the spectral distribution function of black body radiation, $\rho(\lambda,T)$ is known at ...
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Has a system of natural units been designed for human-like scales?
A long time ago I was thinking about how the Imperial system of measurements is arbitrary and annoying, and I decided to design the best system of units ever (I wasn't very old then). I worked on this ...
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How does the height of a jump change if the body is scaled down?
This is a physics question that appeared in the movie 'The Internship.'
If you are reduced to the size of a coin and put into a blender what would you do?
Apparently the answer was that with a ...
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Is there a general relationship between the conformal weight of a field and its (classical) scaling dimension?
A field $\phi(z)$ has the conformal weight $h$, if it transforms under $z\rightarrow z_1(z)$ as
$$
\phi(z) = \tilde{\phi}(z_1)\left(\frac{dz_1}{dz}\right)^h
$$
The (classical) scaling dimension can ...
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Scaling in Vlasov equations
This question is in reference to the paper,
http://arxiv.org/abs/1301.7182
What exactly is the argument being made on page 6 and 7?
One deduces that the function $\Delta$ has to be such that, $\...
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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 (...
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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 ...
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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 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 ...
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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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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 ...
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Data requirement 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 ...
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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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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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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 ...
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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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Why do we need more power to do a job fast? [closed]
Let's assume we have two identical electric trains. One has a big electric motor (high power) and the other has small motor (low power). Let us assume the electric motors are of the same brand and ...
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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 ...
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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 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 $...
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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 ...
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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, ...
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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 ...
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Characteristic length, characteristic time and complexity of the process
Different physical processes (starting from elementary particles or even below to the universe itself) have different length scales $L$ and different characteristic times $T$. Larger processes 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\ ...
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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 ...
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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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