Self-organized criticality and stochastic resonance in the human brain

The human brain spontaneously generates neuronal network oscillations at around 10 and 20 Hz with a large variability in amplitude, duration, and recurrence. Despite more than 70 years of research, the complex dynamics and functional significance of these oscillations have remained poorly understood. This Thesis concerns the dynamic character and functional significance of noninvasively recorded 10- and 20-Hz oscillations in the human brain. The hypotheses, experimental paradigms, data analyses, and interpretations of the results are inspired by recent insights from physics - most notable the theory of self-organized criticality and the phenomenon of stochastic resonance whose applicability to large-scale neuronal networks is explained. We show that amplitude fluctuations of 10- and 20-Hz oscillations during wakeful rest are correlated over thousands of oscillation cycles and that the decay of temporal correlations exhibits power-law scaling behavior. However, when these ongoing oscillations are perturbed with sensory stimuli, the amplitude attenuates quickly, reliably, and transiently, and the long-range temporal dynamics is affected as evidenced by changes in scaling exponents compared to rest. In addition to the rich temporal dynamics in local areas of the cortex, ongoing oscillations tend to synchronize their phases and exhibit correlated amplitude fluctuations across the two hemispheres, as shown for oscillations in homologous areas of the sensorimotor cortices. Finally, it is revealed that intermediate amplitude levels of ongoing oscillations provide the optimal oscillatory state of the sensorimotor cortex for reliable and quick conscious detection of weak somatosensory stimuli. We propose that the long-range temporal correlations, the power-law scaling behavior, the high susceptibility to stimulus perturbations, and the large amplitude variability of ongoing oscillations may find a unifying explanation within the theory of self-organized criticality. This theory offers a general mechanism for the ubiquitous emergence of complex dynamics with power-law decay of spatiotemporal correlations in non-linear self-organizing stochastic systems consisting of many units. The optimal ability to detect consciously and respond behaviorally to weak somatosensory stimuli at intermediate levels of ongoing sensorimotor oscillations is attributed to stochastic resonance - the intuitively paradoxical phenomenon that the signal-to-noise ratio of detecting or transmitting a signal in a non-linear system can be enhanced by noise. Based on the above results, we conjecture that a mechanism of intrinsic stochastic resonance between self-organized critical and stimulus-induced activities may be a general organizing principle of great importance for central nervous system function and account for some of the variability in the way we perceive and react to the outside world.reviewe

Kinetic Energy Transport in Rayleigh--B\'enard Convection

The kinetic energy balance in Rayleigh--B\'{e}nard convection is investigated for the Prandtl number range $0.01\le Pr \le 150$ and for fixed Rayleigh number $Ra=5\cdot10^{6}$. The kinetic energy balance is divided into a dissipation, a production and a flux term. We discuss profiles of all terms and find that the different contributions to the energy balance can be spatially separated into regions where kinetic energy is produced and where kinetic energy is dissipated. Analysing the Prandtl number dependence of the kinetic energy balance, we show that the height-dependence of the mean viscous dissipation is closely related to the flux of kinetic energy. We show that the flux of kinetic energy can be divided into four additive contributions, each representing a different elementary physical process (advection, buoyancy, normal viscous stresses and viscous shear stresses). The behaviour of these individual flux contributions is found to be surprisingly rich and exhibits a pronounced Prandtl number dependence. Different flux contributions dominate the kinetic energy transport at different depth, such that a comprehensive discussion requires a decomposition of the domain into a considerable number of sub-layers. On a less detailed level, our results reveal that advective kinetic energy fluxes play a key role in balancing the near-wall dissipation at low Prandtl number, whereas normal viscous stresses are particularly important at high Prandtl number. Finally, our work reveals that classical velocity boundary layers are deeply connected to the kinetic energy transport, but fail to correctly represent regions of enhanced viscous dissipation