scholarly journals Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback

2021 ◽  
Vol 379 (2213) ◽  
Author(s):  
Frits Veerman ◽  
Moritz Mercker ◽  
Anna Marciniak-Czochra
Keyword(s):  
Evolution Equations ◽  
Active Role ◽  
Theme Issue ◽  
Homogeneous Steady State ◽  
Future Challenges ◽  
Far From Equilibrium ◽  
Abstract Framework ◽  
Inhibitor Interaction ◽  
Activator Inhibitor ◽  
Two Alternatives

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator–inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’.

scholarly journals Beyond Turing: Far-from-equilibrium patterns and mechano-chemical feedback

2021 ◽  
Author(s):  
Frits Veerman ◽  
Moritz Mercker ◽  
Anna Marciniak-Czochra
Keyword(s):  
Evolution Equations ◽  
Active Role ◽  
Homogeneous Steady State ◽  
Future Challenges ◽  
Far From Equilibrium ◽  
Spatially Homogeneous ◽  
Abstract Framework ◽  
Inhibitor Interaction ◽  
Activator Inhibitor ◽  
Two Alternatives

AbstractTuring patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilised by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternative to the ‘classical’ Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the ‘classical’ Turing analysis, and give an overview of recent results and future challenges for both approaches.

scholarly journals Variational principles and nonequilibrium thermodynamics

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190178 ◽  
Author(s):  
P. Ván ◽  
R. Kovács
Keyword(s):  
Symplectic Structure ◽  
Evolution Equations ◽  
Nonequilibrium Thermodynamics ◽  
Variational Principles ◽  
Dissipative Systems ◽  
Second Law ◽  
Theme Issue ◽  
Dissipative Processes ◽  
Variational Techniques ◽  
Lagrange Form

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler–Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and applications to stochastic evolution equations

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190622
Author(s):  
Jan van Neerven ◽  
Mark Veraar
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Theme Issue ◽  
Maximal Inequalities ◽  
Stochastic Convolutions

This paper presents a survey of maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue ‘Semigroup applications everywhere’.

scholarly journals One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics

2019 ◽  
Vol 374 (1775) ◽  
pp. 20180255 ◽  
Author(s):  
Adam Kleczkowski ◽  
Andy Hoyle ◽  
Paul McMenemy
Keyword(s):  
Infectious Disease ◽  
Disease Outbreaks ◽  
Host Population ◽  
Theme Issue ◽  
Influenza Outbreak ◽  
Infectious Disease Outbreaks ◽  
Modelling Framework ◽  
Future Challenges ◽  
1918 Influenza ◽  
Modelling Approaches

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a ‘disease tetrahedron’ (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the ‘OneHealth’ approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.

First-order evolution equations with dynamic boundary conditions

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190615
Author(s):  
Tim Binz ◽  
Klaus-Jochen Engel
Keyword(s):  
Boundary Conditions ◽  
Evolution Equations ◽  
Abstract Cauchy Problem ◽  
Dynamic Boundary Conditions ◽  
Theme Issue ◽  
First Order ◽  
Dynamic Boundary ◽  
Equivalent Systems ◽  
Dirichlet To Neumann Operator ◽  
Boundary Space

In this paper, we introduce a general framework to study linear first-order evolution equations on a Banach space X with dynamic boundary conditions, that is with boundary conditions containing time derivatives. Our method is based on the existence of an abstract Dirichlet operator and yields finally to equivalent systems of two simpler independent equations. In particular, we are led to an abstract Cauchy problem governed by an abstract Dirichlet-to-Neumann operator on the boundary space ∂ X . Our approach is illustrated by several examples and various generalizations are indicated. This article is part of the theme issue ‘Semigroup applications everywhere’.

scholarly journals Nonequilibrium thermodynamics: emergent and fundamental

2020 ◽  
Vol 378 (2170) ◽  
pp. 20200066 ◽  
Author(s):  
P. Ván
Keyword(s):  
Evolution Equations ◽  
Nonequilibrium Thermodynamics ◽  
Dissipative Systems ◽  
Second Law ◽  
Theme Issue ◽  
New Methods

How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics? This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Self-organization across scales: from molecules to organisms

2018 ◽  
Vol 373 (1747) ◽  
pp. 20170113 ◽  
Author(s):  
Tanumoy Saha ◽  
Milos Galic
Keyword(s):  
Cell Biology ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Biological Processes ◽  
Theme Issue ◽  
Ordered Structures ◽  
Biological Features ◽  
The Core ◽  
Open Questions ◽  
Future Challenges

Creating ordered structures from chaotic environments is at the core of biological processes at the subcellular, cellular and organismic level. In this perspective, we explore the physical as well as biological features of two prominent concepts driving self-organization, namely phase transition and reaction–diffusion, before closing with a discussion on open questions and future challenges associated with studying self-organizing systems. This article is part of the theme issue ‘Self-organization in cell biology’.

scholarly journals The rehabilitation of irreversible processes and dissipative structures’ 50th anniversary

2018 ◽  
Vol 376 (2124) ◽  
pp. 20170365 ◽  
Author(s):  
René Lefever
Keyword(s):  
Statistical Physics ◽  
Research Effort ◽  
50Th Anniversary ◽  
Dissipative Structures ◽  
Irreversible Processes ◽  
Theme Issue ◽  
The Road ◽  
Self Organized ◽  
Far From Equilibrium ◽  
First Time

In 2017, Ilya Prigogine would have been 100 years of age. As for any human being, this centenary is a notable event. For him, as a scientist, 2017 was also above all the 50th anniversary of dissipative structures . It was indeed in 1967 that for the first time he used this denomination at the occasion of an important scientific event and in publications. The attribution of this qualification for self-organized behaviours of matter only possible far from equilibrium coincided with the outcome of a research effort of more than 25 years. Centred in thermodynamics and statistical physics on the role played by irreversible processes in the physical evolution of matter, the aim of this research is clear from the outset of his scientific career. With visionary personal intuition and iron-willed determination, it was pursued. The road to success had been long and sinuous, but finally it led to what he called the rehabilitation of irreversible processes . The progresses that stand out as major landmarks of this endeavour that imposed a U-turn with respect to conceptions of classical physics deeply rooted since the nineteenth century will be described. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (Part 1)’.

scholarly journals Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes

2018 ◽  
Vol 376 (2124) ◽  
pp. 20180023 ◽  
Author(s):  
N. Akhmediev ◽  
J. M. Soto-Crespo ◽  
Peter Vouzas ◽  
N. Devine ◽  
Wonkeun Chang
Keyword(s):  
New York ◽  
Landau Equation ◽  
Chem Phys ◽  
Dissipative Structures ◽  
Thermodynamic Theory ◽  
Self Organization ◽  
Theme Issue ◽  
Ginzburg Landau ◽  
Dissipative Solitons ◽  
Far From Equilibrium

Prigogine’s ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 J. Chem. Phys. 48 , 1695–1700 ( doi:10.1063/1.1668896 ); Glansdorff & Prigogine. 1971 Thermodynamic theory of structures, stability and fluctuations . New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered—dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic–quintic Ginzburg–Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.

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