Buzsáki György
- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195301069
- eISBN:
- 9780199863716
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195301069.003.0005
- Subject:
- Neuroscience, Neuroendocrine and Autonomic, Techniques
Neuronal networks in the mammalian cortex generate several distinct oscillatory bands. These neuronal oscillators are linked to the much slower metabolic oscillators. The mean frequencies of the ...
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Neuronal networks in the mammalian cortex generate several distinct oscillatory bands. These neuronal oscillators are linked to the much slower metabolic oscillators. The mean frequencies of the experimentally observed oscillator categories form a linear progression on a natural logarithmic scale with a constant ratio between neighboring frequencies. Because the ratios of the mean frequencies of the neighboring cortical oscillators are not integers, adjacent bands cannot linearly phase-lock. Oscillators of different bands couple with shifting phases and give rise to a state of perpetual fluctuation between unstable and transient stable phase synchrony. The resulting interference dynamics are a fundamental feature of the global temporal organization of the cerebral cortex. Although brain states are highly labile, neuronal avalanches are prevented by oscillatory dynamics. Scale-free dynamics generate complexity, whereas oscillations allow for temporal predictions. Dynamics in the cerebral cortex constantly alternate between the most complex metastable state and the highly predictable oscillatory state.Less
Neuronal networks in the mammalian cortex generate several distinct oscillatory bands. These neuronal oscillators are linked to the much slower metabolic oscillators. The mean frequencies of the experimentally observed oscillator categories form a linear progression on a natural logarithmic scale with a constant ratio between neighboring frequencies. Because the ratios of the mean frequencies of the neighboring cortical oscillators are not integers, adjacent bands cannot linearly phase-lock. Oscillators of different bands couple with shifting phases and give rise to a state of perpetual fluctuation between unstable and transient stable phase synchrony. The resulting interference dynamics are a fundamental feature of the global temporal organization of the cerebral cortex. Although brain states are highly labile, neuronal avalanches are prevented by oscillatory dynamics. Scale-free dynamics generate complexity, whereas oscillations allow for temporal predictions. Dynamics in the cerebral cortex constantly alternate between the most complex metastable state and the highly predictable oscillatory state.
J. C. Kaimal and J. J. Finnigan
- Published in print:
- 1994
- Published Online:
- November 2020
- ISBN:
- 9780195062397
- eISBN:
- 9780197560167
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195062397.003.0005
- Subject:
- Earth Sciences and Geography, Atmospheric Sciences
Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of ...
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Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.
Less
Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.
