Statistical properties of aggregation with injection

We study a generalized aggregation process in which charged particles diffuse and coalesce randomly on a lattice. For one-dimensional and mean-field models, we show that there exists a statistically-invariant steady state when randomly charged particles are continuously injected. The steady-state charge distribution obeys a power law with the exponent depending both on the type of the injection and on the spatial dimension. The response of the system to a perturbation (i.e., relaxation) is characterized by either a power law decay (t ^– ,1) or a compressed exponential decay [exp(–t ),>1].     

Dissipative oscillations in spatially restricted ecosystems due to long range migration

An ecosystem containing three interacting species is studied using both Mean Field approach and Kinetic Monte Carlo simulations on a lattice substrate. The so called 3rd order LLV model involves birth, death and reaction processes with 3rd order nonlinearities and feedbacks. At the mean field level this system exhibits conservative oscillations; the analytic form of the constant of motion is presented. The stochastic simulations show that the density oscillations disappear for sufficiently large lattices, while they are present locally, on small lattice windows. Introduction of mixing via long range migration in the two reacting species changes this picture. For small migration rates p, the behavior remains as with p = 0 and the system is divided into local asynchronous oscillators. As p increases the system passes through a phase transition and exhibits a weak disorder limit cycle through a supercritical Hopf-like bifurcation. The amplitude of the limit cycle depends on the rate p, on the range of migration r and on the system kinetic rates k₁, k₂ and k₃.     

A microscopic aggregation model of droplet dynamics in warm clouds

A microscopic model of warm clouds involving input of water droplets, dropletdroplet aggregation, droplet breakup, and precipitation is presented. Numerical simulations and analytical arguments indicate that after the stage of growth and just before precipitation sets in, a warm cloud is characterized by a droplet-size distribution which follows from an inverse power law as a function of the droplet size. When precipitation is taken into account, the above distribution is transformed into a distribution decaying exponentially with the droplet size, in agreement with field observations. It is suggested that the initiation of rainfall in a precipitating warm cloud can be viewed as an instability triggered by the presence of a power-law distribution.     

Nonextensive statistical approach to non-coding human DNA

We use q-exponential distributions, which maximize the nonextensive entropy S_q (defined as ), to study the size distributions of non-coding DNA (including introns and intergenic regions) in all human chromosomes. We show that the value of the exponent q describing the non-coding size distributions is similar for all chromosomes and varies between 2≤q≤2.3 with the exception of chromosomes X and Y.     

Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity

The effects of nonlocal and fractal connectivity are investigated in a network of Leaky Integrate-and-Fire (LIF) elements. The idea of fractal coupling originates from the hierarchical topology of networks formed by neuronal axons, which transmit the electrical signals in the brain. If a number of LIF elements with finite refractory period are nonlocally coupled, multi-chimera states emerge whose multiplicity depends both on the coupling strength and on the refractory period. We provide evidence that the introduction of a hierarchical topology in the coupling induces novel complex spatial and temporal structures, such as nested chimera states and transitions between multi-chimera states with different multiplicities. These results demonstrate new complex patterns, as well as transitions between different multi-chimera states arising from the combination of nonlinear dynamics with the hierarchical coupling.     

Fractality in the neuron axonal topography of the human brain based on 3-D diffusion MRI

We report our results on the effect of incorporation of inorganic fullerene like nanoparticles (IF) and inorganic nanotubes (INT) of WS₂ into hybrid LED device structures. To disperse into a uniform fashion, the semiconducting INT/IF WS₂ NTs were functionalized with SDS (sodium dodecylsulphate). The IF/INT WS₂ nanotubes were used in combination with PEDOT:PSS and P3HT to realize the following LED device structures: ITO/(PEDOT:PSS):(WS₂:SDS)/P3HT/LiF-Al; ITO/PEDOT:PSS/P3HT/WS₂:SDS/LiF-Al. Morphological, optical and electrochemical analysis were performed to obtain the HOMO and the LUMO energy levels to hypothesize the most efficient device structure. The spectral positions of the electroluminescent bands were found out to be device-dependent and exhibits blue shift when the proposed nanostructure is dip coated on top of P3HT. Electro-optical analysis indicate that the WS₂:SDS based P3HT/semiconductor film can improve the charge recombination probability owing to its dual functionality as hole blocking layer and electron injection moiety.     

Fractal formations in the Lattice Limit Cycle model

We examine the fractal patterns arising in the Lattice Limit Cycle model, when it is restricted on square and fractal lattices. We show that, for processes taking place on regular 2d substrates, the fractal dimensions depend on the kinetic constants and we have observed a sharp phase-transition from uniform 2d spatial distributions (d_f=2) when the kinetic parameters are near the Hopf bifurcation point, to a inside the limit cycle region. For processes taking place on substrates which contain inactive sites, we observe nucleation of homologous species around inactive regions leading to poisoning, when the active sites are distributed in a fractal manner on the substrate. This is less frequent in cases where the active sites are distributed uniformly and randomly on the lattice leading, normally, to non-trivial steady states.     

Dynamics of chaotic maps for modelling the multifractal spectrum of human brain Diffusion Tensor Images

The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.     

Editorial: Ecological complex systems

Main aim of this topical issue is to report recent advances in noisy nonequilibrium processes useful to describe the dynamics of ecological systems and to address the mechanisms of spatio-temporal pattern formation in ecology both from the experimental and theoretical points of view. This is in order to understand the dynamical behaviour of ecological complex systems through the interplay between nonlinearity, noise, random and periodic environmental interactions. Discovering the microscopic rules and the local interactions which lead to the emergence of specific global patterns or global dynamical behaviour and the noise’s role in the nonlinear dynamics is an important, key aspect to understand and then to model ecological complex systems.