scholarly journals Self-organized criticality and pattern emergence through the lens of tropical geometry

2018 ◽  
Vol 115 (35) ◽  
pp. E8135-E8142 ◽  
Author(s):  
N. Kalinin ◽  
A. Guzmán-Sáenz ◽  
Y. Prieto ◽  
M. Shkolnikov ◽  
V. Kalinina ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Tropical Geometry ◽  
Scaling Limit ◽  
Reaction Diffusion ◽  
Auction Theory ◽  
Discrete Models ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Pure Mathematics ◽  
Self Organized Criticality

Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.

scholarly journals The role of order and disorder in thermal and material sciences part 2: Scientific world and new insights

2003 ◽  
Vol 39 (3-4) ◽  
pp. 407-425
Author(s):  
Jaroslav Sesták
Keyword(s):  
Open Systems ◽  
Thermal Environment ◽  
Reaction Diffusion ◽  
Big Bang ◽  
Alternative Theory ◽  
Order And Disorder ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Basic Ideas ◽  
The Impact

The notion of heat is thoroughly analyzed and its historical links are search particularly with relation to both the Greek philosophy (Mile in print sians Pythagoreans, atomists, etc) and the in the present day thermal physics. Fluctuation, spontaneity and chaos is discussed. Thermodynamics is reviewed in the relation to both the traditional development and the modern description of disequilibria (open systems). Effect of dissipation is shown often to provide new, self-organized structures. Exploitation of fire and its conscious use as a manufacturing power are analyzed in terms of generalized engines to act in the sense of as the information transducers. The part 2 reveals the impact of mathematics as explained on some simple cases showing development of basic ideas (vibration, topology, bifurcations etc). Earth thermal environment is discussed in relation to the existence of life (antropy principles). Alternative theory of reaction-diffusion model of the space-time is put in contrast with big bang hypothesis and related to the herewith-discussed specialty of self-catalyzed chemical reactions. The text gives a consistent view to various historical and modern concepts that emerged during the gradual understanding of order and disorder.

scholarly journals Self-organized tissue mechanics underlie embryonic regulation

2021 ◽  
Author(s):  
Paolo Caldarelli ◽  
Alexander Chamolly ◽  
Olinda Alegria-Prevot ◽  
Jerome Gros ◽  
Francis Corson
Keyword(s):  
Gene Expression ◽  
Reaction Diffusion ◽  
Tissue Mechanics ◽  
Mechanical Forces ◽  
Avian Embryos ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Persistent Pattern ◽  
Molecular Reaction ◽  
Embryonic Regulation

Early amniote development is a highly regulative and self-organized process, capable to adapt to interference through cell-cell interactions, which are widely believed to be mediated by molecules. Analyzing intact and mechanically perturbed avian embryos, we show that the mechanical forces that drive embryogenesis self-organize in an analog of Turing's molecular reaction-diffusion model, with contractility locally self-activating and the ensuing tension acting as a long-range inhibitor. This mechanical feedback governs the persistent pattern of tissue flows that shape the embryo and steers the concomitant emergence of embryonic territories by modulating gene expression, ensuring the formation of a single embryo under normal conditions, yet allowing the emergence of multiple, well-proportioned embryos upon perturbations. Thus, mechanical forces are a central signal in embryonic self-organization, feeding back onto gene expression to canalize both patterning and morphogenesis.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

Self-Organized Criticality in the Autowave Model of Speciation

2020 ◽  
Vol 75 (5) ◽  
pp. 398-408
Author(s):  
A. Y. Garaeva ◽  
A. E. Sidorova ◽  
N. T. Levashova ◽  
V. A. Tverdislov
Keyword(s):  
Self Organized ◽  
Self Organized Criticality

Modeling Extinction

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Evolutionary Biology ◽  
Large Scale ◽  
Competitive Exclusion ◽  
Applied Mathematics ◽  
Santa Fe ◽  
New Approach ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Extinction Events ◽  
Mass Extinction Events

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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