Related papers: Order parameter fluctuations in natural time and b…
Self-similarity indicates that large and small earthquakes share the same physics, where all variables scale with rupture length $L$. Here I show that rupture tip acceleration during the start of dynamic rupture (break-out phase) is also…
We show that there is a common mode of origin for the power laws observed in two different models: (i) the Pareto law for the distribution of money among the agents with random saving propensities in an ideal gas-like market model and (ii)…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult…
Quantum critical points (QCPs) are widely accepted as a source of a diverse set of collective quantum phases of matter. A central question is how the order parameters of phases near a QCP interact and determine the fundamental character of…
Upon employing the analysis in a new time domain, termed natural time, it has been recently demonstrated that a remarkable change of seismicity emerges before major mainshocks in California. What constitutes this change is that the…
We proved when random-variable fluctuations obey the central limit theorem the equality of the uncertainty relation corresponds to the thermodynamic equilibrium state. The inequality corresponds to the thermodynamic non-equilibrium state.…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
We develop a technique to estimate spatially varying seismicity patterns. It is based on a Gaussian approximation of the underlying Poisson Process. A link function is used to estimate local moments of the seismicity from observed…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and…
We analyze regional earthquake energy statistics from the Southern California and Japan seismic catalogs and find scale-invariant energy distributions characterized by an exponent $\tau \simeq 1.67$. To quantify how closely scale-invariant…
We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…
The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural,…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…