Heterogeneous and Self-Organized Pacemakers in Reaction-Diffusion Systems

2003 ◽  
Author(s):  
Michael Stich
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Self Organized ◽  
Diffusion Systems

scholarly journals Control of traveling localized spots

2021 ◽  
Author(s):  
Steffen Martens ◽  
Christopher Ryll ◽  
Jakob Löber ◽  
Fredi Tröltzsch ◽  
Harald Engel
Keyword(s):  
Reaction Diffusion ◽  
Open Loop ◽  
Open Loop Control ◽  
Loop Control ◽  
Reaction Diffusion Systems ◽  
Self Organized ◽  
Nonlinear Reaction ◽  
Diffusion Systems ◽  
Goldstone Modes ◽  
Analytical Expressions

Traveling localized spots represent an important class of self-organized two- dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stable spot along a desired trajectory with desired velocity. Simultaneously, the spot's concentration profile does not change under control. For a given protocol of motion, we first express the control signal analytically in terms of the Goldstone modes and the propagation velocity of the uncontrolled spot. Thus, detailed information about the underlying nonlinear reaction kinetics is unnecessary. Then, we confirm the optimality of this solution by demonstrating numerically its equivalence to the solution of a regularized, optimal control problem. To solve the latter, the analytical expressions for the control are excellent initial guesses speeding-up substantially the otherwise time-consuming calculations.

Self-organization at the frictional interface for green tribology

2010 ◽  
Vol 368 (1929) ◽  
pp. 4755-4774 ◽  
Author(s):  
Michael Nosonovsky
Keyword(s):  
Reaction Diffusion ◽  
Self Organization ◽  
Irreversible Processes ◽  
Protective Film ◽  
Self Healing ◽  
Structure Property ◽  
Reaction Diffusion Systems ◽  
Self Organized ◽  
Diffusion Systems ◽  
Green Tribology

Despite the fact that self-organization during friction has received relatively little attention from tribologists so far, it has the potential for the creation of self-healing and self-lubricating materials, which are important for green or environment-friendly tribology. The principles of the thermodynamics of irreversible processes and of the nonlinear theory of dynamical systems are used to investigate the formation of spatial and temporal structures during friction. The transition to the self-organized state with low friction and wear occurs through destabilization of steady-state (stationary) sliding. The criterion for destabilization is formulated and several examples are discussed: the formation of a protective film, microtopography evolution and slip waves. The pattern formation may involve self-organized criticality and reaction–diffusion systems. A special self-healing mechanism may be embedded into the material by coupling the corresponding required forces. The analysis provides the structure–property relationship, which can be applied for the design optimization of composite self-lubricating and self-healing materials for various ecologically friendly applications and green tribology.

scholarly journals A new mechanism for spatial pattern formation via lateral and protrusion-mediated lateral signalling

2016 ◽  
Vol 13 (124) ◽  
pp. 20160484 ◽  
Author(s):  
Zena Hadjivasiliou ◽  
Ginger L. Hunter ◽  
Buzz Baum
Keyword(s):  
Reaction Diffusion ◽  
Cell Contact ◽  
Receptor Ligand ◽  
Reaction Diffusion Systems ◽  
Single Receptor ◽  
Self Organized ◽  
Tissue Organization ◽  
Diffusion Systems ◽  
Different Types ◽  
Spatial Pattern Formation

Tissue organization and patterning are critical during development when genetically identical cells take on different fates. Lateral signalling plays an important role in this process by helping to generate self-organized spatial patterns in an otherwise uniform collection of cells. Recent data suggest that lateral signalling can be mediated both by junctional contacts between neighbouring cells and via cellular protrusions that allow non-neighbouring cells to interact with one another at a distance. However, it remains unclear precisely how signalling mediated by these distinct types of cell–cell contact can physically contribute to the generation of complex patterns without the assistance of diffusible morphogens or pre-patterns. To explore this question, in this work we develop a model of lateral signalling based on a single receptor/ligand pair as exemplified by Notch and Delta. We show that allowing the signalling kinetics to differ at junctional versus protrusion-mediated contacts, an assumption inspired by recent data which show that the cleavage of Notch in several systems requires both Delta binding and the application of mechanical force, permits individual cells to act to promote both lateral activation and lateral inhibition. Strikingly, under this model, in which Delta can sequester Notch, a variety of patterns resembling those typical of reaction–diffusion systems is observed, together with more unusual patterns that arise when we consider changes in signalling kinetics, and in the length and distribution of protrusions. Importantly, these patterns are self-organizing—so that local interactions drive tissue-scale patterning. Together, these data show that protrusions can, in principle, generate different types of patterns in addition to contributing to long-range signalling and to pattern refinement.

Sign in / Sign up

Export Citation Format

Share Document