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3answers
2k views

The meaning of scale invariance in power law distribution

A function $f(ax)$ that satisfies $$ f(ax)=a^\Delta f(x)\,\,\, (\Delta \in R) $$ is said to be scale invariant. The most general function $f(x)$ that satisfies the previous condition is of the form ...
4
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1answer
227 views

Scale invariance in sandpile model and forest fire model

I asked a similar question but the wrong way here. Because my intention was to ask about non thermodynamic system, i will be more specific: What is the relation between critical behaviour and the ...
2
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1answer
347 views

Scale invariance and self organized criticality

On wikipedia i have found this statement: In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their ...
4
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1answer
94 views

Can a system that holds information about it's past ever be Markovian?

To my (basic) understanding a Markov process is a process wherein the future state of a system only depends on the current state, and not on the past states of the system. I was wondering on what ...
1
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5answers
235 views

Normal distribution of x, xdot [closed]

I have some real measurements from a process and I happened to look at the mutual distribution of (x(t), xdot(t)). I found that they seem to follow 2d normal distribution around (mu, 0). See image, ...
1
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1answer
395 views

How to find the value of the parameter a in this transfer function? [duplicate]

Possible Duplicate: How to find the value of the parameter $a$ in this transfer function? I am given a transfer function of a second-order system as: $$G(s)=\frac{a}{s^{2}+4s+a}$$ and I ...
1
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1answer
137 views

How to find the value of the parameter $a$ in this transfer function?

I am given a transfer function of a second-order system as: $$G(s)=\frac{a}{s^{2}+4s+a}$$ and I need to find the value of the parameter $a$ that will make the damping coefficient $\zeta=.7$. I am not ...
3
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2answers
178 views

Infinitesimal input, macroscopic output

I must admit that I never got well how physicists handle infinitesimal quantities, mainly because of my education as a mathematician. So the following lines (taken from the preface of Berezin and ...
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1answer
113 views

What are the patterns appear after kernel averaging?

Having a 2D map filled uniformly by random values (Figure:top-left) to demonstrate a disordered phenomena, the next maps are ...
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2answers
1k views

Characteristic length, characteristic time and complexity of the process

Different physical processed (starting from elementary particles or even below to the universe itself) have different length scales $L$ and different characteristic times $T$. Larger processed tend to ...
5
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1answer
654 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 ...
11
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1answer
1k views

Which areas in physics overlap with those of social network theory for the analysis of the graphs?

I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...