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2
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0answers
50 views

Why is there roughness on every surface?

Why is there roughness on every surface? I think a smooth surface could better minimize the surface energy. Besides, why does the roughness happen to be fractal?
2
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3answers
502 views

Non-linear dynamics vs Chaos

I am confusing between non linear dynamics and chaos. Chaos is also a non-linear dynamics right? then what is the difference between chaos and non-linear dynamics? What I understood about chaos is ...
1
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1answer
57 views

Minimum amount of fluid to experience turbulence?

Turbulence is a challenge to model and simulate: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the ...
1
vote
0answers
61 views

Spin-statistics theorem on spaces with non-integer dimensions

What would be the spin-statistics relation for particles in a space with non-integer dimension, $ 2 \lt D \lt 3 $? In other words (cf. stackexchange questions here and here), what is the first ...
3
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0answers
82 views

Link between anomalous dimensions and fractal dimensions

I just realized that anomalous dimensions in quantum/statistical field theory is not that different from fractal dimensions of objects. They both describe how quantitaive objects transform under a ...
4
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1answer
536 views

“windows of order” in the Bifurcation diagram

When looking at the bifurcation diagram of a chaotic system, one observes "windows of order", namely short intervals where the system briefly leaves its chaotic state and then rapidly returns to ...
9
votes
1answer
533 views

Calculate/Estimate the fractal dimention of the logistic map

This is the logistic map:. It is a fractal, as some might know here. It has a Hausdorff fractal dimension of 0.538. Is it possible to calculate/measure its fractal dimension using the box counting ...
4
votes
1answer
100 views

Are there real life applications for Hausdorff dimensions, specifically crack formations?

I was curios about Hausdorff dimensions. They seem to neatly describe rough surfaces. So I was wondering if there are common applications of Hausdorff dimensions in things like complicated friction ...
2
votes
1answer
788 views

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 ...
2
votes
2answers
237 views

Do we live in an integer dimension?

I have read that there exist non-integer fractal dimensions and the images generated from these dimensions look organic and they seem to provide a new way of describing the world around us, which ...
9
votes
1answer
619 views

How or why is fractional quantum mechanics important?

I read about Fractional Quantum Mechanics and it seemed interesting. But are there any justifications for this concept, such as some connection to reality, or other physical motivations, apart from ...
2
votes
1answer
174 views

Fractal Cosmology and Misner's Chaotic Cosmology

I have a question pertaining to the ideas behind the considered homogeneity and isotropic nature of the universe (at a grand scale) versus the theory of a chaotic and anisotropy structure of the ...
9
votes
1answer
68 views

Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
5
votes
1answer
429 views

Physics-oriented books on fractals

I'm looking for some good books on fractals, with a spin to applications in physics. Specifically, applications of fractal geometry to differential equations and dynamical systems, but with emphasis ...
1
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1answer
134 views

Current Physical Applications of Elastic Fractals

Are there any known uses of modeling with elastic fractals in current physical applications? (Especially uses concerning with self-similarity)