Formation of ring-like structures in flared α-discs with X-ray/FUV photoevaporation

ABSTRACT Protoplanetary discs are complex dynamical systems where several processes may lead to the formation of ring-like structures and planets. These discs are flared following a profile where the vertical scale height increases with radius. In this work, we investigate the role of this disc flaring geometry on the formation of rings and holes. We combine a flattening law change with X-ray and FUV photoevaporative winds. We have used a semi-analytical 1D viscous α approach, presenting the evolution of the disc mass and mass rate in a grid of representative systems. Our results show that changing the profile of the flared disc may favour the formation of ring-like features resembling those observed in real systems at the proper evolutionary times, with proper disc masses and accretion rate values. However, these features seem to be short-lived and further enhancements are still needed for better matching all the features seen in real systems.

Neural closure models for dynamical systems

Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile and rigorous methodology to learn non-Markovian closure parametrizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new neural closure models augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori–Zwanzig formulation and the inherent delays in complex dynamical systems. We demonstrate that neural closures efficiently account for truncated modes in reduced-order-models, capture the effects of subgrid-scale processes in coarse models and augment the simplification of complex biological and physical–biogeochemical models. We find that using non-Markovian over Markovian closures improves long-term prediction accuracy and requires smaller networks. We derive adjoint equations and network architectures needed to efficiently implement the new discrete and distributed nDDEs, for any time-integration schemes and allowing non-uniformly spaced temporal training data. The performance of discrete over distributed delays in closure models is explained using information theory, and we find an optimal amount of past information for a specified architecture. Finally, we analyse computational complexity and explain the limited additional cost due to neural closure models.

Pseudocritical and Precritical States in Brain Dynamics

Scale-free brain dynamics under external stimuli raises an apparent paradox since the critical point of the brain dynamics locates at the limit of zero external drive. Here, we demonstrate that relaxation of the membrane potential removes the critical point but facilitates scale-free dynamics in the presence of strong external stimuli. These findings feature biological neural networks as systems that have no real critical point but bear critical-like behaviors. Attainment of such pseudocritical states relies on processing neurons into a precritical state where they are made readily activatable. We discuss supportive signatures in existing experimental observations and advise new ones for these intriguing properties. These newly revealed repertoires of neural states call for reexamination of brain's working states and open fresh avenues for the investigation of critical behaviors in complex dynamical systems.

Testing Jump-Diffusion in Epileptic Brain Dynamics: Impact of Daily Rhythms

Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, however, to what extent stochastic qualifiers of brain dynamics are affected by other endogenous and/or exogenous influencing factors. Addressing this issue, we investigate multi-day, multi-channel electroencephalographic recordings from a subject with epilepsy. We apply a recently proposed criterion to differentiate between Langevin-type and jump-diffusion processes and observe the type of process most qualified to describe brain dynamics to change with time. Stochastic qualifiers of brain dynamics are strongly affected by endogenous and exogenous rhythms acting on various time scales—ranging from hours to days. Such influences would need to be taken into account when constructing evolution equations for the epileptic brain or other complex dynamical systems subject to external forcings.

Narrativity in Complex Systems

Humans use narrative for making sense of their environment. In this chapter we ask if, and if so how and to what extent, our narrative mind can help us deal scientifically with complexity. In order to answer this question, and to show what this means for education, we discuss fundamental aspects of narrative understanding of dynamical systems by working on a concrete story. These aspects involve perception of complex systems, experientiality of narrative, decomposition of systems into mechanisms, perception of forces of nature in mechanisms, and the relation of story-worlds to modelling-worlds, particularly in so-called ephemeral mechanisms. In parallel to describing fundamental issues, we develop a practical heuristic strategy for dealing with complex systems in five steps. (1) Systems thinking: Identify phenomena and foreground a system associated with these phenomena. (2) Mechanisms: Find and describe mechanisms responsible for these phenomena. (3) Forces of nature: Learn to perceive forces of nature as agents acting in these mechanisms. (4) Story-worlds and models: Learn how to use stories of forces (of nature) to construct story-worlds; translate the story-worlds into dynamical-model-worlds. (5) Ephemeral mechanisms for one-time, short-lived, unpredictable, and historical (natural) events: Learn how to create and accept ephemeral story-worlds and models. Ephemeral mechanisms and ephemeral story-worlds are a means for dealing with unpredictability inherent in complex dynamical systems. We argue that unpredictability does not fundamentally deny storytelling, modelling, explanation, and understanding of natural complex systems.