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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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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. ...
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1answer
54 views

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 ...
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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 ...
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0answers
38 views

Apparent similarity paradox

Consider a (p)rototype consisting in an incompressible and newtonian fluid flowing in a pipe of diameter $D_P$, studied by similarity in a (m)odel of the same fluid in another pipe of diameter $D_m<...
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1answer
1k views

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?
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4answers
86 views

Do smaller aircraft have lower take-off speeds?

Assuming there are two aircraft, each of the same density and each the same shape, am I correct in understanding that the smaller aircraft would have a lower take-off speed? I have explained how I ...
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0answers
16 views

Scaling law or order estimation for turbulent viscosity in a rectangular cavity

Is there any recognized scaling law for the eddy viscosity inside a rectangular cavity? Indeed, that should mean some sort of homogenized value, since the quantity is spatially dependent. I have made ...
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4answers
108 views

Rigorous definition of intensive and extensive quantities in thermodynamics

Most books on Thermodynamics give intuitive definitions for intensive and extensive thermodynamic variables. The say, for example that the former is independent of the system's size while the latter ...
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1answer
54 views

What is the magnitude of a super-nova on the Richter scale?

What is the richter scale of a super-nova? If one could measure compare it to standard earthquakes measured in logarithmic richter scale, what would be the value for a super-nova?
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126 views

What is finite size scaling theory?

The question is in the title. I read some articles about it but I could not understand it completely. What does it mean when we say scaling of any system? Can you please give a brief introduction ...
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1answer
16 views

UV Preconditioning test [closed]

I wanna build a solar panel with a new material and I wanna to test the endurance of the material against UV light. I've found in internet a Standard for UV tests. It says it has to be irradiated with ...
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3answers
52 views

Scaling of force between cubes? [closed]

I found an interesting problem online which has been confusing me for quite a while. Basically, two solid cubes of side length $a$ touch each other along one of their faces, and I am to find how many ...
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1answer
76 views

confusion about what Wikipedia says about Renormalization

On the wikipedia page, on renormalization, it says the following: "Renormalization replaces the initially postulated mass and charge with new numbers such that the observed mass and charge matches ...
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1answer
231 views

Why we can't multiply two extensive quantities together?

I have read that regarding the equation of state $PV=nRT$, since $V$ is an extensive quantity $P$ should be an intensive one because the product of extensive quantities is inherently non-linear. ...
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1answer
91 views

Buckingham pi theorem: alternative pi terms and orthogonality

A question on the buckingham pi theorem: It provides one with the socalled pi terms forming linearly independent quantities based on the relevant dimensions occuring in the problem. They are a ...
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0answers
53 views

How do you properly derive atomic units from SI units?

I'm learning atomic units and I'm having trouble figuring out how to derive the atomic units version of energy, time, electric field, magnetic field, etc. For example the Wikipedia page has a list of ...
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0answers
78 views

Restoring Scale Symmetry

To comprehend more about Scale Symmetry.. I need to know what it would take to restore Scale Symmetry that would make mass and length vanish. For example.. to restore Electroweak symmetry breaking.. ...
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1answer
53 views

Scales in Logarithmic CFTs

Logarithmic CFTs have OPEs (and operators) with logarithms. But to have logarithms one needs to have some scale to make the argument of the log a dimensionless quantity. But if the theory has a scale ...
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0answers
69 views

What is the meaning of doing dimensional analysis in Condensed Matter physics?

In QFT, we do dimensional analysis because the superficial degree of divergence is related to the dimension of the dimension of coupling constant, but in Condensed Matter physics, the aim of ...
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1answer
345 views

Does Square Cube Law always hold? [closed]

There is a video that has been doing the round for a few years of an MIT lecture that has become a topic of debate in another forum I am a member of. The lecture by Prof Walter HG Lewin discusses ...
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5answers
5k views

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 "...
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0answers
316 views

Is it possible to prove that an elephant and a human could jump to the same height? [duplicate]

Is there a physics argument, based on scaling, that leads to the conclusion that an elephant and a human could jump about same height? Could this be extended to any two creatures with different ...
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1answer
141 views

Interpretation of the time scale $L^2/\nu$

During the scaling of the Navier-Stokes equations it is often made use the viscous time scale $L^2/\nu$, where $L$ is the characteristic length and $\nu$ the kinematic viscosity. What is the physical ...
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1answer
102 views

Strouhal number motivation

I am looking for a nice way to motivate the Strouhal number definition. Let me illustrate what I mean on the Reynolds number. (As ususal, $\mathbf{u}$, $p$, $\rho$, $\nu$ denote the flow velocity, ...
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1answer
44 views

Scaling arguments for the flow around a cylinder OUTSIDE the Boundary Layer

For a two-dimensional, laminar, incompressible, and steady flow around a non-rotating cylinder with $Re_x\gg1$ how would I determine the scaling arguments for $x$, $y$, $u_x$, and $u_y$ outside of the ...
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1answer
147 views

What is the relation of the mass of vector field in bulk and the scaling dimension of current operator in CFT?

In AdS/CFT correspondence, we know that, $$m^2=\Delta(\Delta-d)$$ where m is the mass of a scalar field and $\Delta$ is the scaling dimension of the dual operator in CFT. What about the relation of ...
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2answers
545 views

What does it mean when someone says “…it scales with…”?

I frequently hear people say something scales with the mass m, or the length l, etc. What does that mean? Let's take a concrete example, the force equation F = ma. Does this mean that F scales ...
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0answers
41 views

In what sense can a “manned model” boat handle identically to a much larger boat?

A YouTube video(relevant part is 1:24 - 1:46) suggests that if you take an oil tanker, scale it down 25 times, and give it an engine with 0.4 horsepower, "they behave exactly like a [larger] ship". ...
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1answer
125 views

Are all correlation functions in a CFT non-zero?

I am particulary interested in the Ising CFT. Is it clear/true that for any field $\phi$ and a large enough number $r \in \mathbb R^+$, we have that $\langle \phi(x) \phi(y) \rangle \neq 0$ if $|x-y| &...
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2answers
229 views

Does the Newton's law break scale invariance?

Under a scale transformation $$t\rightarrow \bar{t}=\mu t\hspace{0.3cm}\text{and}\hspace{0.3cm}\textbf{r}\to\bar{\textbf{r}}=\lambda\textbf{r},\tag{1}$$ Newton's law take the form $$m\frac{d^2\textbf{...
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1answer
399 views

Scaling the Time Independent Schrodinger Equation

What seems like a rather simple question is causing me a lot of difficulty as my base in mathematics is weak. I want to know how I would scale the Schrodinger equation to find dependence on mass, $m$,...
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1answer
142 views

Power and radiance scaling in Coherent Beam Combination

Generally, it's said that for incoherent laser beam combining, the intensity scales with N (where N = # of lasers), whereas the intensity scales with $N^2$ for coherent combining. $$I_{array,...
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1answer
323 views

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{...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
94 views

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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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 ...
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0answers
35 views

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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
442 views

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