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 Self-organization of nanoparticles and molecules in periodic Liesegang-type structures

2021 ◽  
Vol 7 (16) ◽  
pp. eabe3801
Author(s):  
Amanda J. Ackroyd ◽  
Gábor Holló ◽  
Haridas Mundoor ◽  
Honghu Zhang ◽  
Oleg Gang ◽  
...  
Keyword(s):  
Constant Velocity ◽  
Periodic Structures ◽  
Reaction Diffusion ◽  
Self Organization ◽  
Reaction Diffusion Systems ◽  
Structural Hierarchy ◽  
Preparation Conditions ◽  
Diffusion Systems ◽  
Film Preparation ◽  
Self Organizing

Chemical organization in reaction-diffusion systems offers a strategy for the generation of materials with ordered morphologies and structural hierarchy. Periodic structures are formed by either molecules or nanoparticles. On the premise of new directing factors and materials, an emerging frontier is the design of systems in which the precipitation partners are nanoparticles and molecules. We show that solvent evaporation from a suspension of cellulose nanocrystals (CNCs) and l-(+)-tartaric acid [l-(+)-TA] causes phase separation and precipitation, which, being coupled with a reaction/diffusion, results in rhythmic alternation of CNC-rich and l-(+)-TA–rich rings. The CNC-rich regions have a cholesteric structure, while the l-(+)-TA–rich bands are formed by radially aligned elongated bundles. The moving edge of the pattern propagates with a finite constant velocity, which enables control of periodicity by varying film preparation conditions. This work expands knowledge about self-organizing reaction-diffusion systems and offers a strategy for the design of self-organizing materials.

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.

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.

PATTERN FORMATION IN FRACTIONAL REACTION–DIFFUSION SYSTEMS WITH MULTIPLE HOMOGENEOUS STATES

2012 ◽  
Vol 22 (04) ◽  
pp. 1250087 ◽  
Author(s):  
BOHDAN DATSKO ◽  
YURY LUCHKO ◽  
VASYL GAFIYCHUK
Keyword(s):  
Reaction Diffusion ◽  
Self Organization ◽  
Cubic Nonlinearity ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Standard Reaction ◽  
Simulation Results ◽  
Spatio Temporal ◽  
Derivatives Of ◽  
Fractional Reaction

This paper is devoted to the investigation of self-organization phenomena in time-fractional reaction–diffusion systems with multiple homogeneous states. It is shown that the fractional reaction–diffusion systems possess some new properties compared to the systems with derivatives of integer orders. In particular, some complex spatio-temporal solutions that cannot be found in the standard reaction–diffusion systems are identified. The simulation results are presented for the case of a incommensurate time-fractional reaction–diffusion system with a cubic nonlinearity.

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