Inflation Its Factors, Its Mechanism, and a Strategy to Overcome It

Belousov, Roman; Belousov, A.; Белоусов, Д. Р.

doi:10.2753/pet1061-1991390679

Cited by 14 publications

(16 citation statements)

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“…This soup comprises an ensemble of dynamical subsystems, each with its own structural and functional states, that are coupled through short-range interactions. These simulations are similar to (hundreds of) simulations used to characterize pattern formation in dissipative systems; for example, Turing instabilities [62] and reaction-diffusion systems such as the Belousov-Zhabotinsky reaction [63]. The simulations considered here are solutions to stochastic differential equations for coupled structural and functional states.…”

Section: Active Inference and Self-organizationmentioning

confidence: 93%

Cognitive Dynamics: From Attractors to Active Inference

2014

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This paper combines recent formulations of selforganization and neuronal processing to provide an account of cognitive dynamics from basic principles. We start by showing that inference (and autopoiesis) are emergent features of any (weakly mixing) ergodic random dynamical system. We then apply the emergent dynamics to action and perception in a way that casts action as the fulfillment of (Bayesian) beliefs about the causes of sensations. More formally, we formulate ergodic flows on global random attractors as a generalized descent on a free energy functional of the internal states of a system. This formulation rests on a partition of states based on a Markov blanket that separates internal states from hidden states in the external milieu. This separation means that the internal states effectively represent external states probabilistically. The generalized descent is then related to classical Bayesian (e.g., Kalman-Bucy) filtering and predictive codingVof the sort that might be implemented in the brain. Finally, we present two simulations. The first simulates a primordial soup to illustrate the emergence of a Markov blanket and (active) inference about hidden states. The second uses the same emergent dynamics to simulate action and action observation.

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Section: Active Inference and Self-organizationmentioning

confidence: 93%

Cognitive Dynamics: From Attractors to Active Inference

2014

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“…One form of these structures are waves and spots of reactants that are stationary (e.g. Turing patterns) or travelling (Belousov, 1959;Zaikin & Zhabotinsky, 1970). As discussed by Lester et al (2012), an additional form of enhanced mixing in ore deposits can be induced by geometrical structures.…”

Section: A Stationary and Travelling Waves In Fault Networkmentioning

confidence: 99%

“…In accordance with nomenclature from chemistry and physics for chemical waves, and because these zones represent waves geometrically, we use the term 'travelling waves' for zones of maximum instantaneous saturation index that move in space and time, and 'stationary waves' for zones of high saturation index that do not move (Faraday, 1828;Belousov, 1959;Zaikin & Zhabotinsky, 1970) (Fig. 6a-c).…”

Section: A Stationary and Travelling Waves In Fault Networkmentioning

confidence: 99%

Outcrop scale mixing enhanced by permeability variations: the role of stationary and travelling waves of high saturation indices

et al. 2022

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To study the ore mineralization at the outcrop scale we merge an advection–diffusion simulation with the geochemical software iphreeqc to model the mixing of two realistic fluids. We simulate the infiltration of a metal-rich fluid into a rock that is saturated with pore fluid. We test the feedback effects with a number of scenarios based on an outcrop-scale 5 × 5 m model consisting of two high-permeable vertical faults within a low-permeable host rock that lead into a permeable layer. The hot metal-rich fluid enters the model through the faults from below. We solve the advection–diffusion equation for 12 chemical species and temperature, and use iphreeqc to determine the resulting properties of local fluid domains as well as related saturation indices for minerals. The faults in the model act as pathways for the metal-rich fluid, with the infiltrating fluid displacing the pore fluid. Mixing in the model takes place as a function of advection along permeable faults coupled with diffusion of chemical species at the interface between two fluids, while heat diffusion is fast enough (103 times faster) to equilibrate temperature. Simulations show a high saturation index of mixing-derived minerals such as barite at the interface between the two fluids as a result of fluid mixing. Fast fluid pathways (i.e. faults) show travelling waves of high saturation indices of barite, while low-permeability zones such as fault walls and areas below less permeable layers experience stationary waves of high saturation indices. Our results show that, depending on the dominant transport process (advection or diffusion), mineralization will localize next to permeability contrasts in zones where local diffusion dominates.

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“…In general, it has been argued that oscillations and spatio-temporal pattern formation may lead to potentially dangerous operating regimes in industrial reactors, but when properly managed and effectively controlled they could lead to enhancements in the conversion [33], thereby motivating fundamental studies to better understand such phenomena. Moreover, patterns such as spiral waves have been observed in extended chemical media, a well-known case being the Belousov-Zhabotinsky reaction [34]. Applications of such spatio-temporal complexity that might be of practical interest encompass the development of chemical systems that can perform computations [35] or the control of biological systems [36].…”

Section: Introductionmentioning

confidence: 99%

“…The key feature of this method is that it reproduces exactly the dynamics of the underlying stochastic model, without introducing numerical approximations (being only subject to the precision errors of the computing architecture used). This is particularly attractive when simulating complex systems in chemistry and catalysis, such as those that exhibit spatiotemporal inhomogeneities, with examples encompassing chemical oscillators in extended media (Belousov-Zhabotinsky reaction [34]) or pattern formation due to surface reconstruction in catalysis. For such simulations, the absence of artefacts due to numerical approximations is key to confidently ascertain the relationship between the underpinning reaction mechanisms and the observed behaviour.…”

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confidence: 99%

Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks

Savva

Benson

Christidi

et al. 2023

Phil. Trans. R. Soc. A.

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Kinetic Monte Carlo (KMC) simulations have been instrumental in multiscale catalysis studies, enabling the elucidation of the complex dynamics of heterogeneous catalysts and the prediction of macroscopic performance metrics, such as activity and selectivity. However, the accessible length- and time-scales have been a limiting factor in such simulations. For instance, handling lattices containing millions of sites with ‘traditional’ sequential KMC implementations is prohibitive owing to large memory requirements and long simulation times. We have recently established an approach for exact, distributed, lattice-based simulations of catalytic kinetics which couples the Time-Warp algorithm with the Graph-Theoretical KMC framework, enabling the handling of complex adsorbate lateral interactions and reaction events within large lattices. In this work, we develop a lattice-based variant of the Brusselator system, a prototype chemical oscillator pioneered by Prigogine and Lefever in the late 60s, to benchmark and demonstrate our approach. This system can form spiral wave patterns, which would be computationally intractable with sequential KMC, while our distributed KMC approach can simulate such patterns 15 and 36 times faster with 625 and 1600 processors, respectively. The medium- and large-scale benchmarks thus conducted, demonstrate the robustness of the approach, and reveal computational bottlenecks that could be targeted in further development efforts. This article is part of a discussion meeting issue ‘Supercomputing simulations of advanced materials’.

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Inflation Its Factors, Its Mechanism, and a Strategy to Overcome It

Cited by 14 publications

References 0 publications

Cognitive Dynamics: From Attractors to Active Inference

Cognitive Dynamics: From Attractors to Active Inference

Outcrop scale mixing enhanced by permeability variations: the role of stationary and travelling waves of high saturation indices

Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks

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