Prelude. Cycle 1. Introduction. Cycle 2. Structure defines function. Cycle 3. Diversity of cortical functions is provided by inhibition. Cycle 4. Windows on the brain. Cycle 5. A system of rhythms: from simple to complex dynamics. Cycle 6. Synchronization by oscillation. Cycle 7. The brain's default state: self-organized oscillations in rest and sleep. Cycle 8. Perturbation of the default patterns by experience. Cycle 9. The gamma buzz: gluing by oscillations in the waking brain. Cycle 10. Perceptions and actions are brain state-dependent. Cycle 11. Oscillations in the "other cortex:" navigation in real and memory space. Cycle 12. Coupling of systems by oscillations. Cycle 13. The tough problem. References.

Rhythms of the brain

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

Neuronal activity in the brain gives rise to transmembrane currents that can be measured in the extracellular medium. Although the major contributor of the extracellular signal is the synaptic transmembrane current, other sources — including Na+ and Ca2+ spikes, ionic fluxes through voltage- and ligand-gated channels, and intrinsic membrane oscillations — can substantially shape the extracellular field. High-density recordings of field activity in animals and subdural grid recordings in humans, combined with recently developed data processing tools and computational modelling, can provide insight into the cooperative behaviour of neurons, their average synaptic input and their spiking output, and can increase our understanding of how these processes contribute to the extracellular signal.

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The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes

Interneurons of the hippocampus

EEG alpha oscillations: The inhibition–timing hypothesis

Shock wave propagation through glow discharge plasmas - Evidence of thermal mechanism of shock dispersion

Structure of a mach 8 turbulent boundary layer

Two-color time-ordered dyads of short laser pulses induce a spatially periodic modulation of the refractive index of the atmosphere through resonance-enhanced multiphoton ionization (REMPI), enhancing the back reflection of radio waves The carrier frequencies and the timing of laser pulses in a dyad provide a unique code for selectively accessing the manifold of energy levels of impurity molecules, inducing REMPI gratings of the refractive index only in the presence of impurity molecules, thus suggesting an attractive strategy for the radar-based stand-off detection of trace impurities in the atmosphere

Radar return enhanced by a grating of species-selective multiphoton ionization as a probe for trace impurities in the atmosphere

Megawatt-scale MHD power generation on board of air-breathing hypersonic vehicles is made possible by the high flow enthalpy and velocity, and by the high static temperature (2,300 - 3,500 K) in the combustor and just downstream of it. In this paper, a 1D model of MHD power generation downstream of scramjet combustor is developed, and power generation performance is predicted for a variety of generic hydrogen- fueled engine regimes. A modest amount of potassium seed is shown to yield good performance at magnetic fields on the order of 1 Tesla. One possible use of the MHD-generated power would be to add energy to the flow upstream of the inlet in order to optimize the inlet performance. In particular, MHD generated power can be used to create a virtual cowl that would increase mass capture and thrust of the engine. The paper also demonstrates that the megawatt-scale power, when added to the flow upstream of the inlet throat, can reduce the Mach number, leading to the possibility of substantially shortening or even eliminating the isolator.

MHD Power Generation in Scramjet Engines in Conjunction with Inlet Control

A novel concept of hypersonic cold-air MHD power generators is reviewed. Ionization of the cold air is shown to be a critical issue, determining overall design, geometry, operating conditions, and performance envelope. Electron beams and high-voltage repetitive pulses are shown to represent most efficient methods of ionization. The requirement that the energy cost of ionization be lower than the extracted electric power restricts conductivity and calls for very strong magnetic fields and high Hall parameters, making ion slip and near-anode processes first-order issues. Calculations of hypersonic power generators for flight Mach numbers between 4 and 10 and altitudes of 15-40 km are quite promising: several megawatts of electric power could be generated, while spending only a few hundred kilowatts of that power on sustaining ionization. External MHD devices with ionization by electron beams are shown to be promising for scramjet inlet control at off-design Mach numbers. The self-powered MHD system can bring compression shocks to the cowl lip at Mach numbers higher than the design one, while generating large amounts of electric power on board. High values of Hall electric field are discussed as an important issue, potentially resulting in arcing between electrode segments. Ionization enhancement by change of recombination mechanism with addition of metallic vapor to the flow is discussed, and the minimum seed concentration is estimated.

Richard B. Miles

Papers

Shock wave propagation through glow discharge plasmas - Evidence of thermal mechanism of shock dispersion

Structure of a mach 8 turbulent boundary layer

Radar return enhanced by a grating of species-selective multiphoton ionization as a probe for trace impurities in the atmosphere

MHD Power Generation in Scramjet Engines in Conjunction with Inlet Control

Energy-efficient generation of nonequilibrium plasmas and their applications to hypersonic mhd systems