A 3D copepod trajectory is recorded in the laboratory, using two digital cameras. The copepod undergoes a very structured type of trajectory, with successive moves displaying intermittent amplitudes. We perform a statistical analysis of this 3D trajectory using statistical tools developed in the...

We obtain new exact classes of solutions for the nonlinear fractional Fokker–Planck-like equation ∂tρ=∂x{D(x)∂μ−1xρν−F(x)ρ} by considering a diffusion coefficient D=D|x|−θ(θ∈R and D0) and a drift force F=−k1x+k̄γx|x|γ−1(k1,k̄γ,γ∈R). Connection with nonextensive...

Generalized transport equations covering both normal transport processes (such as neutron transport) and anomalous ones including Lévy walk and trapping are derived. The behaviours of the spatial distribution and mean-square displacement are investigated for fractal space–time processes....

An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state x as x and |x|α. An exactly soluble model of a system is constructed due to consideration of a specific relation between noises. Exact expressions...

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks)...

In this work we extend the recently considered toy model of Weierstrass or Lévy walks with varying velocity of the walker (Quantitative Finance 3 (2003) 201; Chem. Phys. 284 (2002) 481; Comp. Phys. Comm. 147 (2002) 565; Phys. A 264 (1999) 84; Phys. A 264 (1999) 107) by introducing a more realistic...

We consider the conservative web map xn+1=yn, yn+1=−xn−Ksinyn+Γ where Γ is the external constant force. For a range of values of K with Γ=0 the diffusion is found to be anomalous (Zaslavsky et al., Chaos 7 (1997) 159) due to the presence of accelerator mode islands. We investigate the...

In order to perform quantum Hamiltonian dynamics minimizing localization effects, we introduce a quasi-one-dimensional tight-binding model whose mean free path is smaller than the size of the sample. This size, in turn, is smaller than the localization length. We study the return probability to...

In this paper we present a method used in quantitative description of weakly predictable hydrological, extreme events at inland sea. Investigations for correlations between variations of individual measuring points, employing combined statistical methods, were carried out. As a main tool for...

The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A...