Adaptation Noise And Self Organizing Systems

We propose a non-equilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly non-trivial, and different from the equilibrium model, for d< d c =4 ; nonetheless, we are able to determine its scaling exponents {\it exactly} in d=2 , and show that, unlike equilibrium systems, our model exhibits a broken continuous symmetry even in d=2 . Our model describes a large universality class of microscopic rules, including those recently simulated by Viscek et. al.

A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton, thus allowing a clear comparison between simulation results and analytic calculations. This framework is then applied to simulations of hypercycle-systems in up to three dimensions. Furthermore, a new measurement quantity is introduced and applied to the hypercycle-systems in two and three dimensions. It can be shown that this quantity can be interpreted as a measure for the macroscopic order of the hypercycle systems.

We present a hydrodynamic model that captures the essence of granular dynamics in a vibrating bed. We carry out the linear stability analysis and uncover the instability mechanism that leads to the appearance of the convective rolls via a supercritical bifurcation of a bouncing solution. We also explicitly determine the onset of convection as a function of control parameters and confirm our picture by numerical simulations of the continuum equations.

Granular flows in a narrow pipe are studied numerically by the model taking account of hydrodynamic effects of fluid surrounding particles. In the simulations density waves are observed over the wide range of the Stokes number, which represents the inertial effect of particles. The mechanisms of formation of the density waves are considered and two types of density waves, which are observed in the systems with zero and finite Stokes numbers, are presented. Power spectra of density waves obtained from the simulations with non-zero Stokes number show 1/ f α power law which is similar to that in experiments.

Mutual imitation games among artificial birds are studied. By employing a variety of mappings and game rules, the evolution to the edge between chaos and windows is universally confirmed. Some other general features are observed, including punctuated equilibria, and successive alternations of dominant species with temporal complexity. Diversity of species aided by the symbolization of artificial birds' song are also shown.

Traffic simulations are made more realistic by giving individual drivers intentions, i.e. an idea of where they want to go. One possible implementation of this idea is to give each driver an exact pre-computed path, that is, a sequence of roads this driver wants to follow. This paper shows, in a realistic road network, how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this.

We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is suggested that in the BS model there is only one independent critical exponent.

We develop the principle of dynamic invariance to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials.

Isologous diversification theory for cell differentiation is proposed, based on simulations of interacting cells with biochemical networks and cell division process following consumption of some chemicals. According to the simulations of the interaction-based dynamical systems model, the following scenario of the cell differentiation is proposed. (1) Up to some threshold number, divisions bring about almost identical cells with synchronized biochemical oscillations. (2)As the number is increased the oscillations lose the synchrony, leading to groups of cells with different phases of oscillations. (3)Amplitudes of oscillation and averaged chemical compositions start to differ by groups of cells. The differentiated behavior of states is transmitted to daughter cells. (4)Recursivity is formed so that the daughter cells keep the identical chemical character. This ``memory" is made possible through the transfer of initial conditions. (5) Successive differentiation proceeds. Mechanism of tumor cell formation, origin of stem cells, anomalous differentiation by transplantations, apoptosis and other features of cell differentiation process are also discussed, with some novel predictions. (Keywords: differentiation, chemical network, cell division, clustering, open chaos)

The plasma turbulence as is well known plays crucial role in the processes of plasma dynamics and transport phenomena. It affects both macroscopic plasma behaviour and distribution of particles, and besides suprathermal component of particle ensemble is even more sensitive to turbulent processes. We have performed investigation of behaviour of fast particles in turbulent inhomogeneous magnetized plasma. The general kinetic equation describing evolution of fast particle distribution at the presence of MHD plasma turbulence has been derived and analyzed. We constructed semi-analytical solution of the kinetic equation into suprathermal energy region. Several factors have been examined among them like turbulence else are nonuniform external electric and magnetic field, and inhomogeneity of the plasma. It was shown that last one is essential and may lead to some unexpected effects.