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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42 views

Explain how scaling of the inverse square law breaks down at a stars surface

If the radiation pressure at distance $d>R$ from the center of an isotropic black body star is found to be $$P_{rad}=\large{\frac{4\sigma T^4}{3c}}\left[1-\left(1-\frac{R^2}{d^2}\right)^{\frac{3}{2}...
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Scale invariance of lagrangians and transformation properties of fields under dilations

Consider a field theory, and a rescaling transformation of the coordinates \begin{equation} T_\epsilon[\phi(x)]=\phi((1+\epsilon)x). \end{equation} From what I understand, one usually requires that, ...
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1answer
50 views

If space expands, why does a liter of water stay a liter? [duplicate]

From observing the universe, we know that space expands. I see what that means on cosmic scales. But what does it mean on smaller scales? If I have a graduated beaker of 2 liter, and 1 liter of ...
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1answer
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Why traditional turbulence theory concerns so much about statistics such as correlations?

I have been wondering why the traditional turbulence theory, e.g., Kolmogorov's 1941 theory, concerns so much about things like two-point correlations, structure functions, their scalings, and so ...
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How do the similarity transformation connects between characteristic length and time scales?

I'm currently taking a course in analytical mechanics, and we we're studying about similarity transformation. when I read the lecturer's notes, he gave as an example the harmonic oscillator $$ L = (1/...
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22 views

Rules on combining dimensionless (Buckingham) $\pi$ terms?

The best way I know how to ask my question is to provide two examples described in two textbooks, and ask why the first example was able to perform a particular operation and if the same operation ...
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1answer
42 views

Scaling transformations, definitions and all that's not mentioned

If we transform the massless scalar field Lagrangian $$\mathcal{L}=\frac{1}{2}(\partial_\mu\varphi)^2-\frac{\alpha}{4!}\varphi^4$$ with the simultaneous transformations $$x\mapsto x^\prime= \lambda x,\...
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Scaling analysis of the Nernst Planck equation for a battery

The Nernst Planck equation states $$ \frac{\partial c}{\partial t} = - \nabla \cdot J \quad | \quad J = -\left[ D \nabla c - u c + \frac{Dze}{k_\mathrm{B} T}c\left(\nabla \phi+\frac{\partial \mathbf ...
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1answer
79 views

Anomalous dimension for 1D quantum Ising model

I am reading Chapter 10.2, Quantum Phase Transition--Subir Sachdev(P144), it said All previous scaling dimensions of the d = 1 Ising model coincided with their so-called engineering dimension; the ...
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Why/When would one study Renormalization Group flow of a system?

It is not that I am looking for a cheap way out of reading a book about RG flow, but I would like to know few key insights that RG flow study provides, backed with some specific examples. I know a ...
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1answer
67 views

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
58 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
25 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
42 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
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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
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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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4answers
390 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
106 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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458 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
23 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
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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
86 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
370 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
152 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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74 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
117 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
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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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1answer
460 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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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
320 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
553 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
163 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
54 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
212 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
1k 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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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
164 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
309 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
534 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
195 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
365 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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183 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
801 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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1answer
331 views

How to scale variables in a classical Hamiltonian?

So I looked at some research articles where one has a classical Hamiltonian $H(p,q,t) = p^{2}/2 + V(q,t)$. If one introduces the scaling transformation $$t \mapsto t/\sqrt{s}, \quad H \mapsto Hs, \...
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61 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
189 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
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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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1answer
58 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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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
2k 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 ...