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8
votes
1answer
165 views

Deviation from power law distribution of earthquakes

One of the most accepted frameworks for the relationship between the magnitude and frequency of an earthquake is that of the critical phenomena. In this framework, the magnitude of events must be ...
3
votes
1answer
114 views

SOC and the butterfly effect

We knows that in a critical system and self organized criticality we have long range interaction due power law decay in correlation. Is this fact equivalent to the butterfly effect?
2
votes
1answer
151 views

Lacking of scale and distribution moments

Given a physical random variable x, $E(x)$ and $E((x-<x>)^2)$ defines mean and variance. From a statistical point of view variance represents the statistic error (isn't it?). If variance is not ...
1
vote
1answer
101 views

Rainfalls and critical phenomena

By definition, rainfalls are transitions from vapor state to liquid state of water. I can say that "by definition" rainfalls must viewed as critical phenomenon?
2
votes
1answer
229 views

Examples of piecewise smooth dynamical systems [closed]

I have recently been studying continuous dynamical systems whose phase space can be divided into a number of regions. Inside each of these the flow is smooth, but there is a discrete jump in the flow ...
0
votes
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
votes
1answer
230 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
votes
1answer
361 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
votes
1answer
95 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
vote
5answers
238 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
vote
1answer
407 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
vote
1answer
139 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
votes
2answers
180 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 ...
1
vote
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 ...
2
votes
2answers
2k 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
votes
1answer
693 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
votes
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 ...