Showing papers by "Peter A. Robinson published in 2002"

Dynamics of large-scale brain activity in normal arousal states and epileptic seizures.

Abstract: Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms---mainly slow wave, delta, theta, alpha, and sleep spindle---with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

Unified neurophysical model of EEG spectra and evoked potentials.

Abstract: Evoked potentials – the brain's transient electrical responses to discrete stimuli – are modeled as impulse responses using a continuum model of brain electrical activity. Previous models of ongoing brain activity are refined by adding an improved model of thalamic connectivity and modulation, and by allowing for two populations of excitatory cortical neurons distinguished by their axonal ranges. Evoked potentials are shown to be modelable as an impulse response that is a sum of component responses. The component occurring about 100 ms poststimulus is attributed to sensory activation, and this, together with positive and negative feedback pathways between the cortex and thalamus, results in subsequent peaks and troughs that semiquantitatively reproduce those of observed evoked potentials. Modulation of the strengths of positive and negative feedback, in ways consistent with psychological theories of attentional focus, results in d istinct responses resembling those seen in experiments involving attentional changes. The modeled impulse responses reproduce key features of typical experimental evoked response potentials: timing, relative amplitude, and number of peaks. The same model, with further modulation of feedback, also reproduces experimental spectra. Together, these results mean that a broad range of ongoing and transient electrocortical activity can be understood within a common framework, which is parameterized by values that are directly related to physiological and anatomical quantities.

Microstructured optical fibers: where's the edge?

Abstract: We establish that Microstructured Optical Fibers (MOFs) have a fundamental mode cutoff, marking the transition between modal confinement and non-confinement, and give insight into the nature of this transition through two asymptotic models that provide a mapping to conventional fibers. A small parameter space region where neither of these asymptotic models holds exists for the fundamental mode but not for the second mode; we show that designs exploiting unique MOF characteristics tend to concentrate in this preferred region.

Multiple electron beam propagation and Langmuir wave generation in plasmas

Abstract: The propagation of multiple electron beams in a plasma and the generation of Langmuir waves via a streaming instability is investigated numerically using quasilinear theory. The generation of waves by two equal copropagating beams injected at different times is studied in detail. The two beams are observed merging into one far from the injection points. Meanwhile, waves are enhanced in the vicinity of the mean beam speed of the leading beam, and are suppressed in a localized region after the injection of the trailing beam. Effects of beam injection parameters on the generation of the waves are studied. In particular, for the injection of two beams, the temperature, initial number density, and location of the injected particles are found to be relevant to fine structures in wave levels. It is also observed that the mechanism of beam merging is via interactions between beam particles and associated waves, i.e., fast particles in a trailing beam lose energy to waves generated initially by the leading beam, while slow particles in the leading beam absorb energy from waves driven by the trailing beam, which eventually leads to the elimination of systematic speed differences between the two beams. This mechanism of energy exchange generalizes the version studied in previous works, in which fast particles in a single beam lose energy that is later reabsorbed by slower particles. The characteristics of wave generation for multiple beam injections are found to be similar to the basic case of two beams. Finally, the applicability of this work to type III solar radio storms and shock associated type III-like bursts is commented upon.

Wave-number spectrum of electroencephalographic signals.

Abstract: A recently developed, physiologically based continuum model of corticothalamic electrodynamics is used to derive the theoretical form of the electroencephalographic wave-number spectrum and its projection onto a one-dimensional recording array. The projected spectrum is found to consist of a plateau followed by regions of power-law decrease with various exponents, which are dependent on both model parameters and temporal frequency. The theoretical spectrum is compared with experimental results obtained in other studies, showing good agreement. The model provides a framework for understanding the nature of the spatial power spectrum by linking the underlying physiology with the large-scale dynamics of the brain.

A quantitative theory for terrestrial foreshock radio emissions

Abstract: [1] We present the first quantitative theoretical results for the spatial distribution and flux levels of fundamental (fp) and second harmonic (2fp) plasma radiation generated in Earth's foreshock by beam-driven Langmuir waves. The theory predicts that both the fp and 2fp source regions typically extend over several hundred Earth radii (RE) along the tangent magnetic field line. In the direction perpendicular to the magnetic tangent, however, the source regions are more localized, with the peak emission confined to ≲10RE for 2fp radiation and ≲1RE for fp radiation. The flux levels predicted by our model are in close agreement with the levels measured in situ by various spacecraft, with typical values ∼10−14W m−2 for 2fp radiation. The fp flux densities are typically 2–3 orders of magnitude lower.

Unified theory of monochromatic and broadband modulational and decay instabilities of Langmuir waves

Abstract: Modulational and decay instabilities driven by pump Langmuir waves are investigated using a nonlinear dispersion equation that incorporates both classes of instability simultaneously, along with the effects of finite bandwidth of the pump. A rational-function approximation of the plasma density response is then introduced to convert this equation into polynomial form. The resulting equation is used to explore the five instability types: decay, modulational, subsonic modulational, supersonic modulational, and modified decay. Growth rates, corresponding wave numbers, stability boundaries, and instability thresholds for the various instabilities are obtained analytically and verified numerically. In the case of a monochromatic pump the results generalize and clarify the limits of validity of many results in the literature. For broadband pumps, existing results for the growth rate of decay instabilities are reproduced, and it is confirmed that broadband modulational and subsonic-modulational interactions are ...

Field statistics of two vectorially superposed wave populations.

Abstract: Field statistics of observed waves and radiation constrain the physics of the emission process and source region. However, data often contain two or more superposed signals or a signal superposed on a noise background, creating difficulties for interpretation. Here, the combined probability distribution of the field formed by vector superposition of two signals, each with specified statistics, is written as a double integral with integrable singularities. The analytic result and its numerical solutions for combinations of Gaussian and lognormally distributed signals show that these predictions differ from those for field or intensity convolution and from the individual wave distributions. At high fields, the combined distribution takes the qualitative form of the dominant individual distribution (which is localized or otherwise extends to larger fields) but develops a significant tail at low fields due to vector superposition of almost antiparallel fields with similar magnitudes. It is shown that very nearly power-law distributions can develop in significant field domains, despite neither component distribution being power law. This is relevant to alternative interpretations in terms of self-organized criticality and certain modulational wave instabilities. The formalism is then applied to observations of the Vela pulsar, resulting in greatly improved fits to data and different interpretations. Specifically, the results are strong evidence that stochastic growth theory (SGT) is relevant and that the approximate power-law statistics found at some phases are not intrinsic but rather due to vector convolution of a Gaussian background with a lognormal; the latter is interpretable in terms of SGT. The field statistics are consistent with the emission mechanism being a direct linear instability or indirect generation via linear mode conversion of nonescaping waves driven by a linear instability. They are inconsistent with nonlinear self-focusing instabilities generating the observed pulsar radiation. This formalism and its results should also be widely applicable to other types of wave growth in inhomogeneous media.

Mean field theory of the coherent to random-phase state transition in three-wave interactions

Abstract: The crossover of three-wave interactions from the coherent monochromatic limit to the wide bandwidth random-phase limit is investigated as the bandwidth of the waves is varied in a system exhibiting nonlinear three-wave oscillations. A recently observed sudden transition between the coherent and incoherent interaction is confirmed. As the bandwidth is increased from the monochromatic limit, it is found that the coherence of the interaction decreases slowly. At the transition point of the interaction the coherence then falls abruptly and nonlinear oscillations cease. An analytic mean-field approach is used to model the transition. Below the transition point, each frequency component of the wave spectra oscillates at its own individual frequency about the aggregate quasicoherent oscillation of the wave as a whole. It is when the frequency component at the spectral edge cannot sustain such oscillations that the system switches to random phase behavior. The analytic model’s estimate of the transition point and other interaction properties agrees semiquantitatively with numerical solutions of the full equations.