Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

learn more… | top users | synonyms

0
votes
2answers
30 views

Dimensional equation for measuring logarithm of volume

I have a measure that uses radiation dose (M.U. $Gray$) and $\log(Volume)$. The measure is $[\frac{Dose}{\log(Volume)}]$ that is $[\frac{D}{\log(l^3)}]$ with $D$ as radiation dose (M.U. unit is Gray) ...
2
votes
1answer
108 views

Deriving (dimensionless) physical constants from theory

The Wikipedia entry on Physical Constants says: With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants ...
2
votes
1answer
264 views

Drag - Dimensional Analysis / Buckingham Pi

Dimensional Analysis / Buckingham Pi Theorem I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on for practice. I'm suppose to consider a small ...
1
vote
1answer
59 views

Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I ...
1
vote
1answer
65 views

Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$

I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT. Cosmology: The cosmological constant enters the Einstein equations. In the special case of the ...
0
votes
1answer
41 views

Dimensional consistency of an equation

We know that if an equation has to be physically correct then it must be dimensionally consistent i.e. If an equation is not dimensionally correct then it can never be physically correct. Now in the ...
0
votes
1answer
44 views

Books or other sources for natural units, Planck units, dimensional analysis etc. for someone with only high-school physics knowledge

I'd like to know more about natural units, Planck units, dimensional analysis, etc., and things like how units are "created" by man or by the universe, universal constants and where they come from. ...
0
votes
1answer
139 views

Is the dimension “number of particles” a fundamental, or derived dimension (based on mass), or does it depend on the context, or is it dimensionless?

I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on. "Derived quantities" have dimensions that can be written in terms of ...
0
votes
1answer
82 views

Dimensionless numbers in relativistic theory

Dimensionless numbers allow physicists and engineers to extend the physical modeling landscape by reducing otherwise complex mathematics to a simple proportional relationship. For example by assuming ...
0
votes
1answer
257 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
4
votes
0answers
66 views

Dimensional inconsistency in first law of black hole thermodynamics

The first law of black hole mechanics (let's simplify by considering a uncharged and non-rotating black hole) can be written as $$\delta M = T \delta S$$ If I use the definition of Hawking ...
3
votes
0answers
20 views

Pressure inside a typical white dwarf

Does any one know the order of magnitude of pressure inside a typical white dwarf (better with reference)? Thanks! I think it should be $m_e^4c^5/h^3$ (may be multiplied by $\pi$), which is $10^{22} ...
3
votes
0answers
218 views

When can two quantities be added together?

Whenever two things are to be added together, one typically needs to check whether this actually makes sense, and an addition is said to make sense, in principle, when the units match up. Yet, ...
3
votes
0answers
173 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
2
votes
0answers
29 views

Do the non-dimensionalizing equations that result from the Buckingham-$\pi$ algorithm necessarily have a unique solution?

Consider the Buckingham-$\pi$ algorithm: Let us say that we have $n+1$ relevant variables: $\{Q_0, ..., Q_n\}$. Let us say that we can define their dimensions in terms of $k$ basic dimensions. So, ...
2
votes
0answers
33 views

Quantum Efficiency Estimation

Might there be a way to do a rough estimate of the quantum efficiency of a photo-detector like a CCD or CMOS sensor based only on a picture taken with it? I've read papers and guides (like this one: ...
2
votes
0answers
454 views

What prediction led to the vacuum catastrophe?

The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science. According to this book the predicted energy density was obtained as ...
2
votes
0answers
352 views

Dimensional analysis to estimate order of magnitude of quantities

In the Coursera course From the Big Bang to Dark Energy on several occasions dimensional analysis was used to estimate the scale of quantities. This almost seems like a contradiction in terms to me, ...
2
votes
0answers
48 views

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, ...
1
vote
0answers
96 views

Newton's Second Law of Motion

Newton originally wrote his second law as: "The rate of change of momentum of a body is directly proportional to the resultant force applied to the body, and is in the same direction as the force." ...
1
vote
0answers
57 views

What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
1
vote
0answers
74 views

Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
1
vote
0answers
43 views

Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...
1
vote
0answers
193 views

Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is ...
1
vote
0answers
55 views

How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
0
votes
0answers
43 views

Why is one Telsa equal one weber per square meter instead of one weber per cube meter?

Lines of magnetic flux exist in three-dimensions, so how can they be measured per area unit?
0
votes
0answers
26 views

Dimensional analysis of explosive energy, no temporal element

I have a question about dimensional analysis, using the calculation of the explosive energy of the Bomb by Taylor in the 1940s as example. I am neither physicist nor mathematician so will have ...
0
votes
0answers
34 views

Equations of above three variables cannot be solved with dimensional analysis. What does that mean?

I came across this statement while Googling about dimensional analysis. At first I thought that I understood what the statement meant, but now I realize that I really have no idea. What does the ...
0
votes
0answers
25 views

Effective Medium

Please consider the following problem : A plane wave of wavenumber k is incident on an infinite slab which is inhomogeneous in the z direction. Also assume harmonic time dependence and that the ...
0
votes
0answers
23 views

Dimensional Analysis of tunnelling current expression

I have been racking my head trying to get the units to work on an expression for 1D tunnel current through a potential barrier. This expression is straight from S. Sze's "Physics of Semiconductor ...
0
votes
0answers
153 views

Exercises with solutions in dimensional analysis - reference request

I am currently trying to brush up on my skills in dimensional analysis, and computing with units. Is there a good source of worked examples, and exercises with solutions? I'd prefer to have solutions ...
0
votes
0answers
303 views

How can q=mcp(deltaT) be made dimensionless?

Specifically, how can I make $m C_p$ dimensionless? I've tried using the Reynolds number and Peclet number definitions to plug into there but the closest I've gotten to was: $q=\pi D Re Pe ...
0
votes
0answers
95 views

Choice of units when truncating Taylor series for physical quantities

It is common practice in physics to truncate Taylor series of (possibly) very complicated functions to obtain a good approximation of the relevant physical behaviour; for example, the Coulomb ...