Ionization in atmospheres of brown dwarfs and extrasolar planets III. Breakdown conditions for mineral clouds

Electric discharges were detected directly in the cloudy atmospheres of Earth, Jupiter, and Saturn, are debatable for Venus, and indirectly inferred for Neptune and Uranus in our solar system. Sprites (and other types of transient luminous events) have been detected only on Earth, and are theoretically predicted for Jupiter, Saturn, and Venus. Cloud formation is a common phenomenon in ultra-cool atmospheres such as in brown dwarf and extrasolar planetary atmospheres. Cloud particles can be expected to carry considerable charges which may trigger discharge events via small-scale processes between individual cloud particles (intra-cloud discharges) or large-scale processes between clouds (inter-cloud discharges). We investigate electrostatic breakdown characteristics, like critical field strengths and critical charge densities per surface, to demonstrate under which conditions mineral clouds undergo electric discharge events which may trigger or be responsible for sporadic X-ray emission. We apply results from our kinetic dust cloud formation model that is part of the Drift-Phoenix model atmosphere simulations. We present a first investigation of the dependence of the breakdown conditions in brown dwarf and giant gas exoplanets on the local gas-phase chemistry, the effective temperature, and primordial gas-phase metallicity. Our results suggest that different intra-cloud discharge processes dominate at different heights inside mineral clouds: local coronal (point discharges) and small-scale sparks at the bottom region of the cloud where the gas density is high, and flow discharges and large-scale sparks near, and maybe above, the cloud top. The comparison of the thermal degree of ionization and the number density of cloud particles allows us to suggest the efficiency with which discharges will occur in planetary atmospheres.Publisher PDFPeer reviewe

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

Modelling general anaesthesia as a first-order phase transition in the cortex

Since 1997 we have been developing a theoretical foundation for general anaesthesia. We have been able to demonstrate that the abrupt change in brain state broughton by anaesthetic drugs can be characterized as a first-order phase transition in the population-average membrane voltage of the cortical neurons. The theory predicts that, as the critical point of phase-change into unconsciousness is approached, the electrical fluctuations in cortical activity will grow strongly in amplitude while slowing in frequency, becoming more correlated both in time and in space. Thus the bio-electrical change of brain-state has deep similarities with thermodynamic phase changes of classical physics. The theory further predicts the existence of a second critical point, hysteretically separated from the first, corresponding to the return path from comatose unconsciousness back to normal responsiveness. There is a steadily accumulating body of clinical evidence in support of all of the phasetransition predictions: low-frequency power surge in EEG activity; increased correlation time and correlation length in EEG fluctuations; hysteresis separation, with respect to drug concentration, between the point of induction and the point of emergence

Wicked Problems, Foolish Decisions: Promoting Sustainability through Urban Governance in a Complex World Symposium: Governing Wicked Problems

Why do wicked problems often give birth to bad policy choices? Put another way, why do people—in the face of complex social challenges—make misdiagnoses, ineffective decisions, or no decisions at all? Typical answers point to a plethora of suspects: impatience, myopia, political stalemate, narrow-mindedness, fear and risk aversion, hubris, greed, rational self-interest, ignorance, reliance on emotionally appealing but misleading anecdotal stories, misuse of evidence, and misunderstanding of uncertainty. Amid these divergent explanations, two classes emerge: one lies in the shortcomings and mistakes of the problem solvers, and the other lies in the nature of the problem itself. One stance is to fault the ostensible problem solvers: people are not always rational, fair, patient, thoughtful, or deliberative, but instead are myopic, selfish, greedy, power hungry, or out for revenge (among other motivations). The second stance is to point to the nature of the problem. This is the focus of this Article. In particular, we examine how the dynamics of wicked problems undermine traditional problem-solving efforts. This is not to absolve the problem solvers of responsibility for poor policy choices. It is the responsibility of policymakers to diagnose the distinctive challenges and needs of wicked problems and act accordingly. As urban planning scholars, we focus on entrenched urban problems. This focus is not accidental. Horst Rittel (an architect) and Melvin Webber (a planning theorist and transportation planner) developed the idea of “wicked problems” at the University of California, Berkeley’s College of Environmental Design in the early 1970s—an era when the optimism of solving complex social issues through technical, scientific solutions was colliding hard with the failure of such efforts to conclusively resolve urban poverty, inequality, deindustrialization, racism, white flight, and the violence of the “Urban Crisis.” In this Article, we build on previous research to demonstrate how complexity thinking can engage urban challenges at three levels: (1) describing “complexity” as a symptom of urban systems; (2) analyzing the dynamics of complex urban systems; and ultimately (3) intervening through appropriate planning strategies that account for complexity. We employ this thinking to engage the politics of sustainability at the same three levels, illustrating this at two geographic scales: the neighborhood (specifically, the challenge of ecogentrification) and the megaregion (and the resulting regional externalities and trade-offs). These scales involve actors, conflicts, and specializations within planning. Yet both represent new, hybrid patterns of urbanization that produce intractable problems of environmental unsustainability and social-spatial inequality—two core planning priorities that too often collide. Both situations also generate novel social policy challenges that conventional planning, thinking, and governance tools are ill-equipped to address. These challenges instead call for interdepartmental or intergovernmental cooperation

Phase transitions in single neurons and neural populations: Critical slowing, anesthesia, and sleep cycles

The firing of an action potential by a biological neuron represents a dramatic transition from small-scale linear stochastics (subthreshold voltage fluctuations) to gross-scale nonlinear dynamics (birth of a 1-ms voltage spike). In populations of neurons we see similar, but slower, switch-like there-and-back transitions between low-firing background states and high-firing activated states. These state transitions are controlled by varying levels of input current (single neuron), varying amounts of GABAergic drug (anesthesia), or varying concentrations of neuromodulators and neurotransmitters (natural sleep), and all occur within a milieu of unrelenting biological noise. By tracking the altering responsiveness of the excitable membrane to noisy stimulus, we can infer how close the neuronal system (single unit or entire population) is to switching threshold. We can quantify this “nearness to switching” in terms of the altering eigenvalue structure: the dominant eigenvalue approaches zero, leading to a growth in correlated, low-frequency power, with exaggerated responsiveness to small perturbations, the responses becoming larger and slower as the neural population approaches its critical point–-this is critical slowing. In this chapter we discuss phase-transition predictions for both single-neuron and neural-population models, comparing theory with laboratory and clinical measurement

Cortical patterns and gamma genesis are modulated by reversal potentials and gap-junction diffusion

In this chapter we describe a continuum model for the cortex that includes both axon-to-dendrite chemical synapses and direct neuron-to-neuron gap-junction diffusive synapses. The effectiveness of chemical synapses is determined by the voltage of the receiving dendrite V relative to its Nernst reversal potential Vrev. Here we explore two alternative strategies for incorporating dendritic reversal potentials, and uncover surprising differences in their stability properties and model dynamics. In the “slow-soma” variant, the (Vrev - V) weighting is applied after the input flux has been integrated at the dendrite, while for “fast-soma”, the weighting is applied directly to the input flux, prior to dendritic integration. For the slow-soma case, we find that–-provided the inhibitory diffusion (via gap-junctions) is sufficiently strong–-the cortex generates stationary Turing patterns of cortical activity. In contrast, the fast-soma destabilizes in favor of standing-wave spatial structures that oscillate at low-gamma frequency ( 30-Hz); these spatial patterns broaden and weaken as diffusive coupling increases, and disappear altogether at moderate levels of diffusion. We speculate that the slow- and fast-soma models might correspond respectively to the idling and active modes of the cortex, with slow-soma patterns providing the default background state, and emergence of gamma oscillations in the fast-soma case signaling the transition into the cognitive state

Instabilities of the cortex during natural sleep

The electrical signals generated by the human cortex during sleep have been widely studied over the last 50 years. The electroencephalogram (EEG) observed during natural sleep exhibits structures with frequencies from 0.5 Hz to over 50 Hz and complicated waveforms such as spindles and K-complexes. Understanding has been enhanced by comprehensive intra-cellular measurements from the cortex and thalamus such as those performed by Steriade et al [1] and Sanchez-Vives and McCormick [2]. Models of the cerebal cortex have been developed in order to explain many of the features observed. These can be classified in terms of individual neuron models or collective models. Since we wish to compare predictions with gross features of the human EEG, we choose a collective model, where we average over a population of neurons in macrocolumns. A number of models of this form have been developed recently; that developed at Waikato draws from a number of different sources to describe the temporal and spatial dynamics of the system

X-ray Emission From Nearby M-dwarfs: the Super-saturation Phenomenon

A rotation rate and X-ray luminosity analysis is presented for rapidly rotating single and binary M-dwarf systems. X-ray luminosities for the majority of both single & binary M-dwarf systems with periods below $\simeq 5-6$ days (equatorial velocities, V$_{eq}>$ 6 km~s$^{-1}$) are consistent with the current rotation-activity paradigm, and appear to saturate at about $10^{-3}$ of the stellar bolometric luminosity. The single M-dwarf data show tentative evidence for the super-saturation phenomenon observed in some ultra-fast rotating ($>$ 100 km~s$^{-1}$) G & K-dwarfs in the IC 2391, IC 2602 and Alpha Persei clusters. The IC 2391 M star VXR60b is the least X-ray active and most rapidly rotating of the short period (P$_{rot}<$ 2 days) stars considered herein, with a period of 0.212 days and an X-ray activity level about 1.5 sigma below the mean X-ray emission level for most of the single M-dwarf sample. For this star, and possibly one other, we cautiously believe that we have identified the first evidence of super-saturation in M-dwarfs. If we are wrong, we demonstrate that only M-dwarfs rotating close to their break up velocities are likely to exhibit the super-saturation effect at X-ray wavelengths.Comment: 12 pages, 4 figures, accepted by MNRA

A continuum model for the dynamics of the phase transition from slow-wave sleep to REM sleep

Previous studies have shown that activated cortical states (awake and rapid eye-movement (REM) sleep), are associated with increased cholinergic input into the cerebral cortex. However, the mechanisms that underlie the detailed dynamics of the cortical transition from slow-wave to REM sleep have not been quantitatively modeled. How does the sequence of abrupt changes in the cortical dynamics (as detected in the electrocorticogram) result from the more gradual change in subcortical cholinergic input? We compare the output from a continuum model of cortical neuronal dynamics with experimentally-derived rat electrocorticogram data. The output from the computer model was consistent with experimental observations. In slow-wave sleep, 0.5–2-Hz oscillations arise from the cortex jumping between “up” and “down” states on the stationary-state manifold. As cholinergic input increases, the upper state undergoes a bifurcation to an 8-Hz oscillation. The coexistence of both oscillations is similar to that found in the intermediate stage of sleep of the rat. Further cholinergic input moves the trajectory to a point where the lower part of the manifold in not available, and thus the slow oscillation abruptly ceases (REM sleep). The model provides a natural basis to explain neuromodulator-induced changes in cortical activity, and indicates that a cortical phase change, rather than a brainstem “flip-flop”, may describe the transition from slow-wave sleep to REM

What can a mean-field model tell us about the dynamics of the cortex?

In this chapter we examine the dynamical behavior of a spatially homogeneous two-dimensional model of the cortex that incorporates membrane potential, synaptic flux rates and long- and short-range synaptic input, in two spatial dimensions, using parameter sets broadly realistic of humans and rats. When synaptic dynamics are included, the steady states may not be stable. The bifurcation structure for the spatially symmetric case is explored, identifying the positions of saddle–node and sub- and supercritical Hopf instabilities. We go beyond consideration of small-amplitude perturbations to look at nonlinear dynamics. Spatially-symmetric (breathing mode) limit cycles are described, as well as the response to spatially-localized impulses. When close to Hopf and saddle–node bifurcations, such impulses can cause traveling waves with similarities to the slow oscillation of slow-wave sleep. Spiral waves can also be induced. We compare model dynamics with the known behavior of the cortex during natural and anesthetic-induced sleep, commenting on the physiological significance of the limit cycles and impulse responses