Self-organization In Nonequilibrium Systems Research Articles

Dynamic Destruction as Analogs of Critical Phenomena in Metal Samples with Various Geometries within a Wide Ranges of Amplitude–Time Characteristics of External Action

The quantitative characteristics of the products of dispersion and the cascade of dissipative structures arising in metals under shock-wave loading are determined. The fractal dimension df and the Hurst exponent H (standardized range of dissipative structures) of the cascade of hydrodynamic modes, the roughness of the fracture surface, and the dispersion products are determined. Destructive processes occurring in loaded samples are numerically simulated using the Lagrangian technique TIM 3D [1, 2]. It is shown that a cascade of dissipative structures at different scale–temporal levels (nanolevel, mesolevel I, mesolevel II, and macrolevel) is a fractal cluster, and it is a percolation cluster on the threshold of a macrofracture, when there is connectivity in the system of dissipative structures [1, 2]. The self-similarity of dissipative structures is due to the self-organization in nonequilibrium systems; and the dynamic fracture and dispersion processes are examples of scale invariance. The scale invariance of the dissipative structures indicates the nonequilibrium system has reached a critical state.

Dissipative Structures, Organisms and Evolution.

Self-organization in nonequilibrium systems has been known for over 50 years. Under nonequilibrium conditions, the state of a system can become unstable and a transition to an organized structure can occur. Such structures include oscillating chemical reactions and spatiotemporal patterns in chemical and other systems. Because entropy and free-energy dissipating irreversible processes generate and maintain these structures, these have been called dissipative structures. Our recent research revealed that some of these structures exhibit organism-like behavior, reinforcing the earlier expectation that the study of dissipative structures will provide insights into the nature of organisms and their origin. In this article, we summarize our study of organism-like behavior in electrically and chemically driven systems. The highly complex behavior of these systems shows the time evolution to states of higher entropy production. Using these systems as an example, we present some concepts that give us an understanding of biological organisms and their evolution.

General Thermodynamic Efficiency Loss and Scaling Behavior of Eukaryotic Organisms

A simple and general thermodynamic theory is applied to describe the irreversible aspects of the continuous process of functional efficiency loss, which occurs in dissipative biological structures after they reach maturity. Following Prigogine [G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New York, 1997), pp. 2–3], this theory considers that these dissipative structures perform their functions carrying out cyclic processes per se since they are self-organized far from equilibrium. Starting from the theoretical fact that after biological dissipative systems reach adulthood, the functionality of their organs decreases linearly over time. We show that cumulative damage leads to the exponential law of increasing mortality rate with age for population groups, known as Gompertz’s law. The theory was applied to the determination of functional efficiency loss parameter, [Formula: see text], for 71 living beings as a function of mass covering 18 orders of magnitude. The mathematical adjustment allowed us to conclude that there is a minimum in the value of the [Formula: see text] parameter for a 23.3 kg mass which is close enough to the Homo sapiens one. We obtained useful expressions to describe the [Formula: see text] parameter for smaller masses than those of saccharomyces cerevisiae, so perhaps this theory may contribute to the study of the evolution of some dissipative pre-biological structures.

Hierarchically self-organized filler particles in polymers: cascade evolution of dissipative structures to ordered structures

Self-organization in nonequilibrium systems is an important research topic in the physical sciences for understanding the formation of patterns or orders in various systems, including patterns in nature. In this study, we investigated the self-organization of nanoparticles dispersed in polymer melts under applied mechanical energy imposed to mixtures that are composed of a bulk of the particle powder and a bulk of the polymer melt. Using various scattering methods that enable the exploration of structures that exist over a length scale that spans from ~0.1 nm to ~20 μm, we elucidated that the self-organized particles had hierarchical structures with various hierarchical levels as follows: primary particles (PPs), aggregates of the PPs fused together, clusters of the aggregates, and partially interdigitating mass-fractal structures built up by the clusters. The structures of the cluster and the fractal structures depend on attractive interactions between the polymers and the aggregates in given mixing conditions. We propose that the self-organization is caused by cascade evolutions of various dissipative structures, which are involved in the following energy dissipation processes driven by the deformation and flow of polymers during the mixing process. Dissipation Process I involves the fracture and flow of the particle grains in the powder, within which particles are bonded by interparticle attractive forces in air; the outer surfaces of which are in contact with the polymer matrix via polymer–particle interaction. Dissipation Process II involves the initial formation of the clusters, in which the aggregates are bound by polymers and subsequent formation of the mass-fractal agglomerates of the clusters via the diffusion-limited cluster–cluster association in the polymer matrix. The cascade structure evolutions and applied energy dissipation invoke a cascade reduction of the free energy of systems toward a minimum driven by net attractive interactions between the particles and the polymers throughout Dissipation Processes I and II. Self-organization in nonequilibrium systems composed of a bulk filler powder and a bulk polymer melt as an initial state (i) into a final ordered state (f) in applied mechanical field occurs via cascade evolution of the dissipative structures (a) to (e) accompanied by the cascade energy dissipation processes [Process (I) and Process (II)]. These processes also induce the relevant cascade changes in free energy and stress level.

Self-Organization in Electrospun Polymer Solutions: From Dissipative Structures to Ordered Fiber Structures through Fluctuations

Self-organization in nonequilibrium systems is a research topic in the statistical physics universally important for formation of patterns or orders in various systems, including nature. In this work, we investigated the self-organization processes of ordered structures via cascade evolutions of various dissipative structures through fluctuations in electrospun poly(vinyl alcohol) aqueous solutions in both mesoscopic and macroscopic length scales. The flowing jets were investigated both in situ, macroscopically with a high speed video imaging and ex situ, mesoscopically under optical and electron microscopies as a function of the polymer concentration. In the semidilute unentangled solutions, the main jet evolved a self-similar, cascade network composed of a set of the bulge and the branched subjets issued from the bulge as a building block of the network. In the semidilute entangled solutions, the main jet evolved a series of bulges elongated along the jet axis without formation of the branched subjets. ...

Dissipative structures, machines, and organisms: A perspective.

Self-organization in nonequilibrium systems resulting in the formation of dissipative structures has been studied in a variety of systems, most prominently in chemical systems. We present a study of a voltage-driven dissipative structure consisting of conducting beads immersed in a viscous medium of oil. In this simple system, we observed remarkably complex organism-like behavior. The dissipative structure consists of a tree structure that spontaneously forms and moves like a worm and exhibits many features characteristic of living organisms. The complex motion of the beads driven by the applied field, the dipole-dipole interaction between the beads, and the hydrodynamic flow of the viscous medium result in a time evolution of the tree structure towards states of lower resistance or higher dissipation and thus higher rates of entropy production. The resulting end-directed evolution manifests as the tree moving to locations seeking higher current, the current that sustains its structure and dynamics. The study of end-directed evolution in the dissipative structure gives us a means to distinguish the fundamental difference between machines and organisms and opens a path for the formulation of physics of organisms.

Downward Causation: Polanyi and Prigogine

Downward Causation: Polanyi and Prigogine

Competitive dynamics in the brain: Comment on “Information flow dynamics in the brain” by M.I. Rabinovich et al.

Rabinovich et al. [1] motivate the importance of itinerant and competitive dynamics when considering the brain as an information processing device [2,3]. They treat us to a rich series of insights afforded by a dynamical perspective that emphasizes metastability and winnerless competition. Their review pursues a compelling tradition of trying to understand neuronal activity in terms of attractor dynamics and how the resulting dynamics are coupled to the sensorium [4–11]. The authors start by making a key point — to properly understand neural processing one has to move beyond classical information theoretic approaches and look at the itinerant dynamics that underpin self-organization in nonequilibrium systems, like the brain, that maintain a steady state or homeostasis [6,11,12]. Rabinovich et al. cover many themes. I will focus on the broad implications for understanding brain function from the Helmholtzian perspective on the brain as an inference machine [12–14]. In this view, the brain tries to model its sensory exchanges with the world, where this modelling gives rise to perception and the selection of sensory evidence that we know as behavior. Winnerless competition and metastable dynamics are absolutely central to this notion, given the metastability of the world we are obliged to model. A nice example here is communication among conspecifics that has a deep hierarchical structure and a separation of temporal scales. One perspective, on this remarkable capacity of higher organisms, is that their brains contain the same central pattern generators or stable heteroclinic channels that are coupled through sensory exchanges. Rabinovich et al. look at this in terms of the binding of stable heteroclinic channels [15]. It is interesting to reflect on the nature of this binding in the context of language [16]. To cut a long story short, it is possible for the itinerant pattern generators in a speaker to entrain equivalent dynamics in a listener, if the listener uses his pattern generator to predict the behavior (i.e., speech) of the speaker. This leads naturally to a view of the brain in terms of predictive coding [17], where prediction errors bind metastable orbits in different brains and, indeed, hierarchical levels of a single brain [12]. The key thing here is that winnerless competition and competitive dynamics provide a model or prior beliefs about the unfolding world and therefore provide a basis for predicting our sensory impressions of that world [18]. Exactly the same perspective can be applied to action, where kinaesthetic or proprioceptive predictions produce movements through classical reflex arcs. Rabinovich et al. provide a beautiful example of this in the Mollusc Clione limacina. They consider the competitive dynamics between statocyst receptor neurons and how these provide command signals

Hot Giant Fullerenes Eject and Capture C2 Molecules: QM/MD Simulations with Constant Density

Quantum chemical molecular dynamics (QM/MD) simulations using periodic boundary conditions show that hot giant fullerene (GF) cages can both eject and capture C2 molecules dependent on the concentration of noncage carbons in the simulated system, and that the cage size can therefore both increase and decrease under high temperature conditions. The reaction mechanisms for C2 elimination and incorporation involve sp3 carbon defects and polygonal rings larger than hexagons, and are thus closely related to previously described mechanisms (Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature1993, 366, 665). The atoms constituting the cage are gradually replaced by the two processes, suggesting that a fullerene cage during high-temperature synthesis is a dissipative structure in the sense of Ilya Prigogine’s theory of self-organization in nonequilibrium systems. Explicit inclusion of Lennard-Jones-type helium or argon noble gas atoms is found to increase the GF shrinking rate. Large GFs shrink at a ...

Control of spiral waves in excitable media

The propagation of spiral-shaped excitation waves is a prominent example of self-organization in nonequilibrium systems. The properties of these waves are studied in a chemical model system––the Belousov–Zhabotinsky (BZ) reaction––and in various biological excitable media such as heart or neuronal tissue. An important aspect lies in finding tools for external control of these waves. A light-sensitive variant of the BZ reaction has proven to be a suitable system for investigating local and global control by means of a time-dependent uniform illumination. A local feedback control, in which short light pulses are applied at instants corresponding to the passage of a wave front through a measuring point, results in a drift of the spiral center along a discrete set of stable circular orbits. In a confined-domain control, where the illumination intensity is taken to be proportional to the average wave activity observed in a circular domain of the reaction layer, the stabilization and destabilization of spiral wave trajectories are demonstrated. The presented methods could be useful for the control of biological excitation waves.

The re‐emergence of “emergence”: A venerable concept in search of a theory

Despite its current popularity, “emergence” is a concept with a venerable history and an elusive, ambiguous standing in contemporary evolutionary theory. This paper briefly recounts the history of the term and details some of its current usages. Not only are there radically varying interpretations about what emergence means but “reductionist” and “holistic” theorists have very different views about the issue of causation. However, these two seemingly polar positions are not irreconcilable. Reductionism, or detailed analysis of the parts and their interactions, is essential for answering the “how” question in evolution -how does a complex living system work? But holism is equally necessary for answering the “why” question -why did a particular arrangement of parts evolve? In order to answer the “why” question, a broader, multi-leveled paradigm is required. The reductionist approach to explaining emergent complexity has entailed a search for underlying “laws of emergence.” Another alternative is the “Synergism Hypothesis,” which focuses on the “economics” – the functional effects produced by emergent wholes and their selective consequences. This theory, in a nutshell, proposes that the synergistic (co-operative) effects produced by various combinations of parts have played a major causal role in the evolution of biological complexity. It will also be argued that emergent phenomena represent, in effect, a subset of a much larger universe of combined effects in the natural world; there are many different kinds of synergy, but not all synergies represent emergent phenomena.

Structural effects on the strength of ceramics

The key features of the processes underlying the failure of ceramics are considered for a wide temperature range. The brittleness and high-temperature plasticity of ceramics are correlated with their crystal chemistry. The general issues related to the strength of ceramics are treated in terms of synergetics, which deals with the spatiotemporal ordering and self-organization in nonequilibrium systems. The strength of ceramics is shown to be governed by its structure on different scales—from atomic to macroscopic. The conclusion is drawn that, in the strict sense, strength is not a property of the material; rather it characterizes its quality.

Strength and structure of ceramics

The special features of the processes that occur in ceramic materials fracturing in a wide temperature range are considered. It is shown that the brittleness of these materials is explainable by the special features of their crystalline structure. For the same reasons they exhibit plasticity only in the range of high temperatures. General problems of the strength of ceramics are considered from the standpoint of synergetics, which studies the processes of time-and-space ordering and self-organization in nonequilibrium systems.

鉛直平行二平板の加熱と冷却による安定密度成層水溶液の混合機構に関する研究 光ファイバ濃度センサによる水溶液の二重拡散対流の計測

In this report an experimental study of double diffusive natural convection is performed for a sucrose solution between vertical parallel plates which is heated from one side and cooled from opposite side with an initial condition of a vertically linear concentration gradient. An optical fiber sensor with a thermocouple is used to obtain the vertical distributions of concentration and temperature. The number of multi-layered convection cells changing with the elapsed time from the start of cooling and heating can be counted and the thickness of cells are measured precisely. It is shown that the evolution of layering is a typical example of self-organization in non equilibrium systems. The relationship between the lifetime which is the elapsed time required to become to a vertically uniform concentration and Rayleigh number is obtained. The observation by shadowgraph is also conducted as an auxiliary method.

Dynamic pattern generation in behavioral and neural systems.

In the search for principles of pattern generation in complex biological systems, an operational approach is presented that embraces both theory and experiment. The central mathematical concepts of self-organization in nonequilibrium systems (including order parameter dynamics, stability, fluctuations, and time scales) are used to show how a large number of empirically observed features of temporal patterns can be mapped onto simple low-dimensional (stochastic, nonlinear) dynamical laws that are derivable from lower levels of description. The theoretical framework provides a language and a strategy, accompanied by new observables, that may afford an understanding of dynamic patterns at several scales of analysis (including behavioral patterns, neural networks, and individual neurons) and the linkage among them.

Thermocapillary convection and dynamics of the cathode spot at the liquid cathode

Consideration is given to the influence of the Marangoni convection, which develops in a layer of liquid metal under the cathode spot, on its properties. The structure and parameters of the thermocapillary cell formed have been determined. It is shown that the convective transfer of heat plays a dominant role in the cathode spot and the thermal model, which ignores it, will lead to highly overestimated temperature values. We describe a dynamic model of equilibrium of the liquid-metal surface in the spot which explains the possibility of appearance of high local pressures in the fluid. We discuss the absolute instability of the cathode spot rest state and the hydrodynamic mechanism of motion, which is determined by breakdown of the symmetry of a convective cell. It appears that such different (at first glance) phenomena as the random motion of the cathode spot, the repulsion of the spots during the approach and division, the detention of the spot on the wetting line and the retrograde motion of the spot in a magnetic field can be explained in unified terms with the aid of the above-mentioned hydrodynamic mechanism. The cited effects are characterized by external actions on the spot of different nature, which give rise to an asymmetry of convection with respect to the heating centre and, consequently, the ordered motion of the cathode spot. The behaviour of the cathode spot on a liquid-metal layer of variable thickness is considered and a new method of detention of the spot is proposed. We propose ideas of experiments which would make it possible to determine the size of a thermocapillary cell and to check the hydrodynamic mechanism of the cathode spot motion. We discuss the relationship of the phenomena considered with the processes of ordering and self-organization in nonequilibrium systems.

The simulation of random processes on digital computers: Unavoidable order

Nonrandom features of pseudorandom number generators are usually regarded as defects which may be minimized by improving the algorithms or resorting to larger computers. There are, however, certain elements of order which cannot be avoided even on digital devices of arbitrarily large capacity. For instance, on an N-state machine, pseudorandom number generators will terminate on fixed points or fall into loops after approximately √ N steps. Combinatorial arguments then can be used to show that for any given algorithm and any finite device it is highly improbable that there are more than three or four distinct terminal loops. All pseudorandom sequences merging into these loops can be traced backwards to their initial numbers; and the resulting pattern of ”ancestor numbers“ can be charted in detail for any computer, even for noninvertible algorithms. The conflicting requirements of randomness and finite numerical precision lead to an ordered distribution of the set of initial numbers. In this sense neither the initial nor the final states of a simulation of chaotic behavior can ever be random. The ”few loop“ constraint could generate patterns of self-organization in nonequilibrium systems. Experimental evidence from the hysteresis of Ewing arrays supports this conjecture.

Self-Organization in Nonequilibrium Systems (G. Nicolis and I. Prigogine)

Self-Organization in Nonequilibrium Systems (G. Nicolis and I. Prigogine)

Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order Through Fluctuations.G. Nicolis , I. Prigogine

Previous articleNext article No AccessNew Biological BooksSelf-Organization in Nonequilibrium Systems. From Dissipative Structures to Order Through Fluctuations. G. Nicolis , I. Prigogine Alan S. PerelsonAlan S. Perelson Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Quarterly Review of Biology Volume 53, Number 3Sep., 1978 Published in association with Stony Brook University Article DOIhttps://doi.org/10.1086/410785 Views: 14Total views on this site Citations: 3Citations are reported from Crossref Copyright 1978 The Stony Brook Foundation, Inc.PDF download Crossref reports the following articles citing this article:F. Drubi, A. Mayora-Cebollero, C. Mayora-Cebollero, S. Ibáñez, J.A. Jover-Galtier, Á. Lozano, L. Pérez, R. Barrio Connecting chaotic regions in the Coupled Brusselator System, Chaos, Solitons & Fractals 169 (Apr 2023): 113240.https://doi.org/10.1016/j.chaos.2023.113240Chuanlai Xu, Xiaoling Wu, Changlong Hao Chiral Nanoassemblies, (May 2022): 79–147.https://doi.org/10.1002/9783527833603.ch3Qiang Han, Deren Yang Hierarchical Information Entropy System Model for TWfMS, Entropy 20, no.1010 (Sep 2018): 732.https://doi.org/10.3390/e20100732

Formative Processes: Self-Organization in Nonequilibrium Systems . From Dissipative Structures to Order through Fluctuations. G. Nicolis and I. Prigogine. Wiley-Interscience, New York, 1977. xiv, 492 pp., illus. $27.50.

Formative Processes: <i>Self-Organization in Nonequilibrium Systems</i> . From Dissipative Structures to Order through Fluctuations. G. Nicolis and I. Prigogine. Wiley-Interscience, New York, 1977. xiv, 492 pp., illus. $27.50.