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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23 views

How can one compute an effective probability at the critical point of a first order phase transition

In an excerpt from Finite-Size Scaling by John Cardy I found the following development: At a first-order transition, the correlation length ξ remains finite, and the finite-size scaling properties in ...
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Scaling limit, renormalization group and low-energy effective field theories

Given a quantum lattice theory $T_0$, e.g., in one dimension defined on $L$ sites, I know that there is a scaling limit, which introduces a lattice scale $a_0$ and keeps the following two quantities ...
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Dynamic scaling laws derivation

In the book Critical Dynamics by Tauber the following scaling hypotheses are made for the static correlation function and for the characteristic frequency in Fourier space $$ C(\tau, q) = |q|^{-2+\eta}...
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Viewing and capturing real time values of electronic vernier calliper on large screens viz Television set & Computer monitor

https://en.wikipedia.org/wiki/Vernier_scale https://www.google.com/search?q=electronic+vernier+calipers&oq=&aqs=chrome.1.69i176j35i39i362l4...4.-1j0j7&client=ms-android-lava&sourceid=...
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1answer
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Could gravity be much stronger (or weaker) at the atomic scale?

If gravity is mediated by particles and you are at a scale where those particles are relatively much larger does that perhaps imply that gravity can't work exactly the same way at very small scales as ...
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Analytic change of free energy after renormalization

Suppose we have some model in statistical physics with Hamiltonian $H$ and partition function $$Z=\mathrm{Tr}\left(e^{-H}\right) $$ the free energy per site is defined as $$ f =\frac1N\log Z$$ A ...
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2answers
69 views

Relating scaling and critical exponents in the Ising model

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
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1answer
140 views

Identifying the relevant directions in the Ising model renormalization

I'm reading the chapter about the renormalization group in Yeoman's book "Statistical mechanics of phase transitions" and I'm puzzled about how the author relates the scaling of the RG with ...
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1answer
36 views

Conformal primaries in momentum space

Consider the Fourier transform of a conformal primary $O$ $$\tilde{O}(k) = \int d^dx e^{ik\cdot x} O(x)$$ Now consider the transformation of the momenta $k \to \lambda k$, so that the above reads $$\...
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6answers
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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 $\...
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1answer
102 views

One-point function in CFT on an infinite strip through scaling analysis

In Philippe Di Francesco's book on Conformal Field Theory in section 11.2.3 on the Infinite Strip, the one point function of a primary operator (with scaling dimension $\Delta$) is calculated by ...
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1answer
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Does the action remain dimensionless after the renormalization?

After the renormalization procedure, fields will gain an anomalous dimension, $\gamma$, which means that their scaling dimension will be different from what we would guess from the dimensional ...
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67 views

Picture of poor man's scaling for AFM/FM interaction in Kondo problem

Poor man's scaling in Kondo problem For the Kondo model: $$H=-t\sum_{i,j}c_i^\dagger c_j+JS\cdot \sigma(0)$$ which only including itinerant electrons with the band-width $ W \in[-D,D]$, and $S$ is the ...
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2answers
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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
57 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
38 views

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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1answer
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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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1answer
117 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
178 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
60 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
30 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
645 views

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 ...
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1answer
135 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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586 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
86 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
93 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
499 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
196 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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99 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
128 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
73 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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1answer
596 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
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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
322 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
990 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
202 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
69 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
270 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
2k 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
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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
174 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
374 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
652 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
251 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,...