Kicker rotator (or rotor) problem is one of the classical examples of dynamical chaos in physics. The focus of this problem is a particle which moves in circular motion (e.g., pendulum on a stick). This particle is being acted upon periodically, lets assume that \( T=1 \), by homogeneous field (e.g., gravitational field, which is being turned on periodically for a brief periods of time). When the field is on, it creates a force, acting on the particle, of strength \( K \). As field is on only for a very brief periods of time, the force may be approximated by the Dirac delta function.

This summer T. Piketty published his research in a book called "Capital in the Twenty-first Century". In this book he explains how economic inequality emerges in capitalist economy (mostly from historical perspective). T. Piketty also suggest some measures to stop inequality growth. We invite you to listen to his talk given in TED event (see here).

One of the classical examples of power-law distributions may be found in geology. It is the Gutenberg-Richeter law, which relates the number of earthquakes to their magnitude. Mathematically this relation is expressed as \( \lg N = a - b M \). Here \( N \) is a number of earthquakes of certain magnitude \( M \) or stronger, \( b \) is empirically determined and depends on seismic activity of the region, while \( a = \lg N_0 \).

In this text we will briefly present self-organized criticality model, which reproduces the power-law distribution of earthquakes - Olami-Feder-Christensen model.

q-Gaussian distribution is rather interesting generalization of the well-known Gaussian distribution. This generalization arises from the generalized, non-extensive, statistical mechanics, which was proposed by C. Tsallis two decades ago. Despite the fact twenty years have passed there is no simple physical model reproducing the q-Gaussian distribution. But our colleague Julius Ruseckas recently proposed one [1]. In this text we will briefly discuss his "correlated spin" model and will present two related interactive applets.

Herfindahl-Hirschman index (or HHI) describing how close the market is to monopolistic market. This tool is used by organizations responsible for the supervision of fair competition (e.g., when considering corporate mergers). This index is obtained using known market shares, \( s_i \in (0,1] \), of competitors in the market: