Self-organized Critical Process Research Articles

The Relationship between Cyclic Multi-Scale Self-Organized Processes and Wear-Induced Surface Phenomena under Severe Tribological Conditions Associated with Buildup Edge Formation

This paper presents experimental investigations of various interrelated multi-scale cyclic and temporal processes that occur on the frictional surface under severe tribological conditions during cutting with buildup edge formation. The results of the finite element modeling of the stress/temperature profiles on the friction surface are laid out. This study was performed on a multilayer coating with the top alumina ceramic layer deposited by CVD (chemical vapor deposition) on a WC/Co carbide substrate. A detailed analysis of the wear process was conducted by 3D wear evaluation, scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDS) and electron backscattered diffraction (EBSD), as well as X-ray photoelectron spectroscopy (XPS) methods. The following cyclic phenomena were observed on the surface of the tribo-system during the experiments: a repetitive formation and breakage of buildups (a self-organized critical process) and a periodical increase and decrease in the amount of thermal barrier tribo-films with a sapphire structure (which is a self-organization process). These two processes are interrelated with the accompanying progression of cratering, eventually resulting in the catastrophic failure of the entire tribo-system.

Effect of the Adaptive Response on the Wear Behavior of PVD and CVD Coated Cutting Tools during Machining with Built Up Edge Formation.

The relationship between the wear process and the adaptive response of the coated cutting tool to external stimuli is demonstrated in this review paper. The goal of the featured case studies is to achieve control over the behavior of the tool/workpiece tribo-system, using an example of severe tribological conditions present under machining with intensive built-up edge (BUE) formation. The built-ups developed during the machining process are dynamic structures with a dual role. On one hand they exhibit protective functions but, on the other hand, the process of built-up edge formation is similar to an avalanche. Periodical growth and breakage of BUE eventually leads to tooltip failure and catastrophe of the entire tribo-system. The process of BUE formation is governed by the stick–slip phenomenon occurring at the chip/tool interface which is associated with the self-organized critical process (SOC). This process could be potentially brought under control through the engineered adaptive response of the tribo-system, with the goal of reducing the scale and frequency of the occurring avalanches (built-ups). A number of multiscale frictional processes could be used to achieve this task. Such processes are associated with the strongly non-equilibrium process of self-organization during friction (nano-scale tribo-films formation) as well as physical–chemical and mechanical processes that develop on a microscopic scale inside the coating layer and the carbide substrate. Various strategies for achieving control over wear behavior are presented in this paper using specific machining case studies of several hard-to-cut materials such as stainless steels, titanium alloy (TiAl6V4), compacted graphitic iron (CGI), each of which typically undergoes strong built-up edge formation. Various categories of hard coatings deposited by different physical vapor deposition (PVD) and chemical vapor deposition (CVD) methods are applied on cutting tools and the results of their tribological and wear performance studies are presented. Future research trends are outlined as well.

Scaling Laws in the Dynamics of Collapse of Single Bubbles and 2D Foams.

Avalanches of rupturing bubbles play an important role in the dynamics of collapse of macroscopic liquid foams. We hypothesized that the occurrence of cascades of rupturing bubbles in foams depends, at least in part, on the power released during the rupture of a bubble. In this paper, we present results on the dynamics of single bubble bursting obtained by analyzing the pressure wave (sound) emitted by the bubble when collapsing. We found that the released energy varies linearly with bubble size, the frequency of the emitted sound follows a power law with exponent 3/2 (compatible with the Helmholtz resonator model) and the duration of a rupturing event seems to be independent of bubble size. To correlate the dynamics of individual bubbles with the dynamics of foams, we studied the occurrence of avalanches on bubble rafts and found that the phenomenon appears to be a self-organized criticality (SOC) process. The distribution functions for the size of the avalanches are a power law with exponents between 2 and 3, depending on the surfactant concentration. The distribution of times between ruptures also follows a power law with exponents close to 1, independently of the surfactant concentration.

A fractal model of granitic intrusion and variability based on cellular automata

Among the various mechanisms for magma ascent and emplacement, rock fracturing is a highly significant factor. In this study, a cellular automaton based on the Olami-Feder-Christensen model was used to generate a self-organized network in which magma can ascend and be arrested to form granitic intrusions under the influence of their buoyancy. The model embodies the ascent of discrete magma batches in a stepwise style by opening the fractures and then closing them after passage of the magma. In the model, magma ascends towards the subsurface via self-organized networks of rock fractures as long as the density of the surrounding rocks is greater than that of the magma. If magma rises to a zone with negative buoyancy, it stops and starts to solidify; thus forming granitic intrusions. Two fractal dimensional measures, perimeter-area (P-A) and number-area (N-A), were used to quantify the irregularity and spatial distribution of the modeled intrusions. The fractal dimension DAP of P-A, as well as the fractal dimension DP of the perimeter, show that the irregularity of the intrusions increases as the thickness of the negative buoyancy region increases. The N-A exponent D reflects the irregular size and spatial scale-invariance of the intrusions, and an abrupt inflection point occurs at an area of 100 cells, owing to the coalescence of small batches of intrusions into a larger intrusion. The scale-invariance exhibited by this system indicates that magma ascent and the formation process of granitic intrusions is a self-organized critical process and we demonstrate that a cellular automaton and fractal model is suitable for capturing, quantifying and modeling the spatial and temporal evolution of complex granitic intrusions.

Singularity analysis of global zircon U-Pb age series and implication of continental crust evolution

Recently compiled global databases of igneous and detrital zircon U-Pb ages have been integrated with other types of isotope data (e.g., neodymium, hafnium, and oxygen) to characterize the episodic growth of the continental crust and the development of supercontinents. However, to what extent do the age peaks reflect the rate of continent crust growth or the differential preservation due to supercontinent settings is a long-standing question. Instead of analyzing amplitudes and periodicity of the age series, here, the analysis focuses on shapes of the individual age peaks described by a power law model for measuring the scale invariant fractality and singularity of time-series records. The results indicate that zircon age distributions around peaks follow power law distribution, regardless of the bin-size used to measure the age distribution. Based on the commonly accepted mechanisms (phase transition, self-organized criticality and multiplicative cascade processes) for generation of power law distributions one can relate the nonlinearity of the age peaks to short spurts of accelerated magmatic activities due to “avalanches” (superplumes, slab breakoff etc.) occurred during episodic convection of the mantle. The exponents of the power law age distributions estimated from the age peaks can be used as an index to quantify the intensity of a singularity. The values of exponents calculated at all major age peaks from five global databases exhibit an episodic nature, with a mean duration of approximately 600–800Myr. Both intensity of the zircon episodes and their duration for the interval from 3Ga to 0.5Ga depict a descending trend, which may signify mantle cooling.

OUP accepted manuscript

Type I X-ray bursts in a low-mass X-ray binary (LMXB) are caused by unstable nuclear burning of accreted materials. Semi-analytical and numerical studies of unstable nuclear burning have successfully reproduced partial properties of this kind of burst. However, some other properties (e.g. the waiting time) are not well explained. In this paper, we find that the probability distributions of fluence, peak count, rise time, duration and waiting time can be described as power-law-like distributions. This indicates that type I X-ray bursts may be governed by a self-organized criticality (SOC) process. The power-law index of waiting time distribution (WTD) is around $-1$, which is not predicted by any current waiting time model. We propose a physical burst rate model, in which the mean occurrence rate is inversely proportional to time $\lambda\propto t^{-1}$. In this case, the WTD is well explained by a non-stationary Poisson process within the SOC theory. In this theory, the burst size is also predicted to follow a power-law distribution, which requires that the emission area possesses only part of the neutron star surface. Furthermore, we find that the WTDs of some astrophysical phenomena can also be described by similar occurrence rate models.

On prognostication ability of active geosystems: metastability and steady transitions instead of attractors

Some details and special features are under considerations of undertaken experimental and theoretical studies related to prognosticated ability and forecast of geo-systems dynamics which were paid not enough attention but, possibly, might have crucial importance for definition of future studies in this area. According to the ideas of nonlinear dynamics of spatial-temporal processes and systems new capabilities and new approaches to their solutions are being discussed. Crucial dynamic objects of such an approach are meta-stability and steady transitions, and, in addition, to metastable images in phase spaces of the system do not respond the attractors but transitional sets of paths. Active role of geo-medium and its specific dynamic conditions generated by cooperative behavior of its elements and subsystems is underlined. More appropriate definition is formed of seismic process and possible mechanisms of generation of spontaneous emissions of different character, associated with transitional dissipation, more justified from both their physical interpretation and simulation. On this base and taking into account overall criteria, which guarantee the emergence of critical dynamics and discovered lately new nonlinear dynamic regimes in spread active (excited) systems actual problems are discussed of diagnostics and prognostication capability of geosystems, special role and the influence of noises of different character on the active structured geosystems admitting self-organized critical behavior and processes of formation exponential spectra of capacity is noticed. In addition, standing apart of widely declared theses of 70-80 th of last century, and unlike the strange-attractor approach, the basic attention is paid to effects of noises and fluctuations upon large-scale dynamics of geosystems. As a result the problem of local forecast in up-to-date definition may be considered as a study of a response of active (excitable) structured geomedium on multifrequency spontaneous fluctuations and external actions. Attention is paid to some special features and essential factors of formation of focal zones and evolution processes, known from observations and solutions of basal equations of nonlinear dynamics. Strong relation of spontaneous emissions of lithosphere with dynamics of auto-structures and their complexes is underlined. In addition, blocky-hierarchic heterogeneous structure of lithosphere determines not only spatial characteristics of the fields of spontaneous emissions but also, to significant extent, their temporal and energetic characteristics.

Scenario SOC abnormally slow relaxation of the system clusters the fluid in disordered nanoporous confinement environment

The relaxation of the system of the nanoporous medium with the nonwetting liquid is a self-organized criticality process characterized by waiting for fluctuation necessary for overcoming a barrier of local metastable state with the subsequent avalanche decay of local metastable configurations of pores. The dependence of the interaction between local configurations on the number of filled pores belonging to the infinite percolation cluster of filled pores serves as an internal feedback initiating the SOC process.

Control of Self-Organized Criticality through Adaptive Behavior of Nano-Structured Thin Film Coatings

In this paper, we will develop a strategy for controlling the self-organized critical process using the example of extreme tribological conditions caused by intensive build-up edge (BUE) formation that take place during machining of hard-to-cut austentic superduplex stainless steel SDSS UNS32750. From a tribological viewpoint, machining of this material involves intensive seizure and build-up edge formation at the tool/chip interface, which can result in catastrophic tool failure. Built-up edge is considered to be a very damaging process in the system. The periodical breakage of the build-ups may eventually result in tool tip breakage and, thereby, lead to a catastrophe (complete loss of workability) in the system. The dynamic process of build-up edge formation is similar to an avalanche. It is governed by stick-slip phenomenon during friction and associated with the self-organized critical process. Investigation of wear patterns on the frictional surfaces of cutting tools using Scanning Electron Microscope (SEM), combined with chip undersurface characterization and frictional (cutting) force analyses, confirms this hypothesis. The control of self-organized criticality is accomplished through application of a nano-multilayer TiAl60CrSiYN/TiAlCrN thin film Physical Vapor Deposition (PVD) coating containing elevated aluminum content on a cemented carbide tool. The suggested coating enhanced the formation of protective nano-scale tribo-films on the friction surface under operation. Moreover, machining process optimization contributed to further enhancement of this beneficial process, as evidenced by X-ray Photoelectron Spectroscopy (XPS) studies of tribo-films. This resulted in a reduction of the scale of the build ups leading to overall wear performance improvement. A new thermodynamic analysis is proposed concerning entropy production during friction in machining with buildup edge formation. This model is able to predict various phenomena and shows a good agreement with experimental results. In the presented research we demonstrated a novel experimental approach for controlling self-organized criticality using an example of the machining with buildup edge formation, which is similar to avalanches. This was done through enhanced adaptive performance of the surface engineered tribo-system, in the aim of reducing the scale and frequency of the avalanches.

Understanding scaling through history-dependent processes with collapsing sample space

History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample space, or their set of possible outcomes, reduces as they age. We demonstrate that these sample-space-reducing (SSR) processes necessarily lead to Zipf's law in the rank distributions of their outcomes. We show that by adding noise to SSR processes the corresponding rank distributions remain exact power laws, p(x) ~ x(-λ), where the exponent directly corresponds to the mixing ratio of the SSR process and noise. This allows us to give a precise meaning to the scaling exponent in terms of the degree to which a given process reduces its sample space as it unfolds. Noisy SSR processes further allow us to explain a wide range of scaling exponents in frequency distributions ranging from α = 2 to ∞. We discuss several applications showing how SSR processes can be used to understand Zipf's law in word frequencies, and how they are related to diffusion processes in directed networks, or aging processes such as in fragmentation processes. SSR processes provide a new alternative to understand the origin of scaling in complex systems without the recourse to multiplicative, preferential, or self-organized critical processes.

Branching with Local Probability as a Paradigm of Self-Organized Criticality

A self-organized critical branching process based on a local interaction rule is presented. In accordance with the self-organized branching process model introduced by Zapperi, Lauritsen, and Stanley, its event-size distribution follows a power law with scaling exponent τ=3/2, but the new model does not require a global variable to self-organize to a critical point. The self-organized critical behavior of the model seems to be extremely robust. The model may be seen as a new paradigm for progressive mechanical failure (e.g., earthquakes or landslides) or other avalanching phenomena, and perhaps even for self-organized criticality in general.

MONOFRACTAL AND MULTIFRACTAL SCALING ANALYSIS OF pH TIME SERIES FROM DONGTING LAKE INLET AND OUTLET

The water pH series from Dongting Lake Inlet and Outlet in China are analyzed by detrended fluctuation analysis (DFA), spectral analysis and multifractal methods. The results show that these pH series are characterized by long-term memory, 1/f noise and multifractal scaling, and these characteristics have obvious difference between the Lake Inlet and Outlet. The comparison results show that monofractal (DFA exponent) and multifractal (Δα, Δf, B) parameters can be quantitative dynamical indexes reflecting the capability of anti-acidification of Dongting Lake. Furthermore, we investigate the frequency-size distribution of pH series from Dongting Lake Inlet and Outlet. Our findings suggest that water pH is an example of a self-organized criticality (SOC) process. Based on concept of self-organized ctiticality, we analysis the cause that different scale-free power-law behavior between pH series from Dongting Lake Inlet and Outlet. This work can be helpful to improvement of modeling of lake water quality.

Self-organized criticality in quantum gravity

We study a simple model of spin network evolution motivated by the hypothesis that the emergence of classical spacetime from a discrete microscopic dynamics may be a self-organized critical process. Self-organized critical systems are statistical systems that naturally evolve without fine tuning to critical states in which correlation functions are scale invariant. We study several rules for evolution of frozen spin networks in which the spins labeling the edges evolve on a fixed graph. We find evidence for a set of rules which behaves analogously to sand pile models in which a critical state emerges without fine tuning, in which some correlation functions become scale invariant.

Optimization with extremal dynamics for the traveling salesman problem

By mapping the optimization problems to physical systems, the paper presents a general-purpose stochastic optimization method with extremal dynamics. It is built up with the traveling salesman problem (TSP) being a typical NP-complete problem. As self-organized critical processes of extremal dynamics, the optimization dynamics successively updates the states of those cities with high energy. Consequently, a near-optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations (ergodic walk near the phase transition). The computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics, such as simulated annealing (SA). Since the proposed fundamental solution is based on the principles and micromechanisms of computational systems, it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems.

Lifetime of Bubble Rafts: Cooperativity and Avalanches

We have studied the collapse of pseudo-bi-dimensional foams. These foams are made of uniformly sized soap bubbles packed in an hexagonal lattice sitting at the top of a liquid surface. The collapse process follows the sequence: (1) rupture of a first bubble, driven by thermal fluctuations and (2) a cascade of bursting bubbles. We present a simple numerical model which captures the main characteristics of the dynamics of foam collapse. We show that in a certain range of viscosities of the foaming solutions, the size distribution of the avalanches follows power laws as in self-organized criticality processes.

Self-Organized Criticality Processes in HL-1M Tokamak Plasma

We study the dynamics of laminar time between successive bursts inanomalous particle flux measured at the HL-1M tokamak plasma edge. Theresults reveal that the flux fluctuations are self-similar in a narrowrange of time scales and that their probability distribution functionis not Gaussian. These properties are not consistent with thosepredicted by self-organized criticality (SOC) models as well as therunning sand-pile SOC model developed by Hwa and Kardar.

Self-organized criticality in layered, lacustrine sediments formed by landsliding

Research Article| June 01, 2002 Self-organized criticality in layered, lacustrine sediments formed by landsliding Basil Gomez; Basil Gomez 1Geomorphology Laboratory, Indiana State University, Terre Haute, Indiana 47809, USA Search for other works by this author on: GSW Google Scholar Mike Page; Mike Page 2Landcare Research, Private Bag 11 052, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar Per Bak; Per Bak 3Department of Mathematics, Imperial College, London SW7 2BZ, UK Search for other works by this author on: GSW Google Scholar Noel Trustrum Noel Trustrum 4Landcare Research, Private Bag 11 052, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar Geology (2002) 30 (6): 519–522. https://doi.org/10.1130/0091-7613(2002)030<0519:SOCILL>2.0.CO;2 Article history received: 15 Nov 2001 rev-recd: 31 Jan 2002 accepted: 12 Feb 2002 first online: 02 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Basil Gomez, Mike Page, Per Bak, Noel Trustrum; Self-organized criticality in layered, lacustrine sediments formed by landsliding. Geology 2002;; 30 (6): 519–522. doi: https://doi.org/10.1130/0091-7613(2002)030<0519:SOCILL>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Landsliding is the dominant mass-wasting process in humid-temperate uplands and an important regulator of sediment yield from steep-land drainage basins. Information about the magnitude and frequency distribution of landslides has been derived from aerial photography, but it has proved difficult to set limits on the long-term scaling behavior of landsliding because the requirements of spatial and temporal coherence and the large number of observations necessary to undertake magnitude versus frequency analyses are not easy to fulfill. We use a 2250-yr-long record of hillslope erosion associated with extreme hydrologic events preserved in sediments from Lake Tutira, New Zealand, to investigate scaling in landslide deposits. Both the magnitude versus frequency distribution of sediment layers attributed to landsliding and the distribution of time intervals between landsliding events take the form of power laws, the former with an exponent b = 2.06 and the latter with an exponent b = 1.4. These results suggest that the erosional events originate from a self-organized critical process, and are in agreement with observations of scaling in turbidite deposits and grain flows in controlled laboratory experiments. The implications are that the aggregate behavior of landsliding at the catchment scale is orderly and that the stratigraphic record preserves a unique, long-term perspective on a fundamental geomorphic process and the extreme hydrologic events that trigger it. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

A complexity view of rainfall.

We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.

Search of self-organized criticality processes in magnetically confined plasmas: hints from the reversed field pinch configuration.

In order to test the self-organized criticality (SOC) paradigm in transport processes, a novel technique has been applied for the first time to plasmas confined in reversed field pinch configuration. This technique consists of an analysis of the probability distribution function of the times between bursts in density fluctuations measured by microwave reflectometry and electrostatic probes. The same analysis has also been applied to intermittent events sorted out from the Gaussian background. In both cases, the experimental results disagree with the predictions for a SOC system.

A multiplicative multifractal model for originations and extinctions

Recent works have suggested that the fossil record exhibits a fractal structure; i.e., that processes, such as extinction, follow a power-law size distribution and their time series show a 1/f power spectrum. This structure has been used as evidence that evolutionary dynamics are an example of a self-organized critical (SOC) process. We have reexamined this claim by analyzing a detailed record of marine genus-level extinctions and originations. Our results indicate that neither extinctions nor origination metrics show the power-law size distribution or a 1/f power spectrum characteristic of SOC and related models. We also believe that the underlying assumptions of SOC are incompatible with our understanding of the processes controlling macroevolutionary patterns.Statistical analyses of the data sets are compatible, however, with the presence of multifractal self-similarity in both records, consistent with a hierarchical and multiplicative generating process. This model assumes that multiple causal mechanisms, acting over many spatial and temporal scales, interact to promote or inhibit originations and extinctions. In this view, the same event can have quite different impacts depending on the state of the biotic or physical system at the time that it occurs. This may at least partially explain such phenomena as the imperfect correlation between eustatic sea-level changes and macroevolutionary processes and the apparent nonlinear response of biotic systems to bolide impacts.