Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast, c=(mu(1)-mu(2))/(mu(1)+mu(2)), in a model porous medium defined as a Hele-Shaw cell with random gap b(0)+delta b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, nonconserved, and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number Ca as l(1) approximately b(0)(cCa)(-1/2) and l(2) approximately b(0)Ca-1. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.     

Transition of a loose medium to the fluid state: A phenomenological theory

In terms of a self-consistent approach, it is shown that taking into account velocity and elastic stress fluctuations allows one to describe the transition of a loose medium to the fluid state in both continuous and stick-slip regimes. In the latter case, elastic stress fluctuations favor the manifestation of self-organized criticality.     

Self-organized critical drainage networks

We introduce time-dependent boundary conditions in a model of drainage network evolution based on local erosion rules. The changing boundary conditions prevent the model from becoming stationary; it approaches a state where fluctuations of all sizes occur. The fluctuations in the sizes of the drainage areas show power law behavior with an exponent that differs significantly from that of the static distribution of the drainage areas. Thus, the model exhibits self-organized criticality and proposes a novel concept for predicting fractal properties of drainage networks.     

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.     

Fluctuations and finite-size effect in the Bak-Sneppen model

The self-organized criticality in the nearest-neighbor version of the Bak-Sneppen model is investigated from the event-by-event fluctuations of the mean fitness. The finite-size effect on the evolution of the critical state is shown, and a scaling solution to the gap equation for an infinite one-dimensional lattice is given numerically for the first time. The mean lifetime of avalanches is presented as a function of the gap from the solution. The critical value of the gap and an exponent are calculated from the solution. Received 10 December 2000 and Received in final form 18 January 2001     

The origins of dragon-kings and their occurrence in society

A society is a medium with a complex structure of one-to-one relations between people. Those could be relations between friends, wife–husband relationships, relations between business partners, and so on. At a certain level of analysis, a society can be regarded as a gigantic maze constituted of one-to-one relationships between people. From a physical standpoint it can be considered as a highly porous medium. Such media are widely known for their outstanding properties and effects like self-organized criticality, percolation, power-law distribution of network cluster sizes, etc. In these media supercritical events, referred to as dragon-kings, may occur in two cases: when increasing stress is applied to a system (self-organized criticality scenario) or when increasing conductivity of a system is observed (percolation scenario). In social applications the first scenario is typical for negative effects: crises, wars, revolutions, financial breakdowns, state collapses, etc. The second scenario is more typical for positive effects like emergence of cities, growth of firms, population blow-ups, economic miracles, technology diffusion, social network formation, etc. If both conditions (increasing stress and increasing conductivity) are observed together, then absolutely miraculous dragon-king effects can occur that involve most human society. Historical examples of this effect are the emergence of the Mongol Empire, world religions, World War II, and the explosive proliferation of global internet services. This article describes these two scenarios in detail beginning with an overview of historical dragon-king events and phenomena starting from the early human history till the last decades and concluding with an analysis of their possible near future consequences on our global society. Thus we demonstrate that in social systems dragon-king is not a random outlier unexplainable by power-law statistics, but a natural effect. It is a very large cluster in a porous percolation medium. It occurs as a result of changes in external conditions, such as supercritical load, increase in system elements’ sensitivity, or system connectivity growth.     

Avalanche dynamics of idealized neuron function in the brain on an uncorrelated random scale-free network

We study a simple model for a neuron function in a collective brain system. The neural network is composed of an uncorrelated configuration model (UCM) for eliminating the degree correlation of dynamical processes. The interaction of neurons is assumed to be isotropic and idealized. These neuron dynamics are similar to biological evolution in extremal dynamics with locally isotropic interaction but has a different time scale. The functioning of neurons takes place as punctuated patterns based on avalanche dynamics. In our model, the avalanche dynamics of neurons exhibit self-organized criticality which shows power-law behavior of the avalanche sizes. For a given network, the avalanche dynamic behavior is not changed with different degree exponents of networks, γ≥2.4 and various refractory periods referred to the memory effect, T_r. Furthermore, the avalanche size distributions exhibit power-law behavior in a single scaling region in contrast to other networks. However, return time distributions displaying spatiotemporal complexity have three characteristic time scaling regimes Thus, we find that UCM may be inefficient for holding a memory.     

Fluctuations in fluid invasion into disordered media

Interfaces moving in a disordered medium exhibit stochastic velocity fluctuations obeying universal scaling relations related to the presence or absence of conservation laws. For fluid invasion of porous media, we show that the fluctuations of the velocity are governed by a geometry-dependent length scale arising from fluid conservation. This result is compared to the statistics resulting from a nonequilibrium (depinning) transition between a moving interface and a stationary, pinned one.     

Number theoretic example of scale-free topology inducing self-organized criticality

In this Letter we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale-free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.     

Self-organization of the critical state in granular superconductors

The critical state in granular superconductors is studied using two mathematical models: systems of differential equations for the gauge-invariant phase difference and a simplified model that is described by a system of coupled mappings and in many cases is equivalent to the standard models used for studying self-organized criticality. It is shown that the critical state of granular superconductors is self-organized in all cases studied. In addition, it is shown that the models employed are essentially equivalent, i.e., they demonstrate not only the same critical behavior, but they also lead to the same noncritical phenomena. The first demonstration of the existence of self-organized criticality in a system of nonlinear differential equations and its equivalence to self-organized criticality in standard models is given in this paper.     

Macroscopic capillarity without a constitutive capillary pressure function

This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions of nonpercolating phases. The resulting equations of motion open the possibility to describe flow processes where drainage and imbibition occur simultaneously. The theory predicts hysteresis and process dependence of capillary phenomena. The traditional theory is recovered as a special case in the residual decoupling approximation. Explicit calculations are presented for quasistatic equilibrium profiles near hydrostatic equilibrium. The results are found to agree with experiment.     

Olami-Feder-Christensen model on different networks

We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cut-off region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.     

Scaling relations in the spherically symmetric Landau—Ginzburg model and a possible connection with self-organized criticality

Solutions of the spherically symmetric Landau—Ginzburg model are analyzed numerically and analytically in the subcritical temperature region. Special attention is paid to their scaling behavior both in time and space domains. We demonstrate through a number of scaling relations that these solutions can be viewed as manifesting self-organized criticality in the system, with a power spectrum consistent with 1/f-noise characteristics.     

Aging kinetics of porous media due to freezing-thawing cycles

The two-dimensional Ausloos et al. model of fluid invasion, freezing and thawing in a porous medium is elaborated upon and investigated in order to take into account the pore volume redistribution and conservation during freezing. The results are qualitatively different from previous work, since the damaged pore sizes are found to be much less than the possible maximum value and is reached after a large number of invasion-freezing-thawing cycles, e.g. the material is “slowly damaged”. The pore size distribution is thus found in better agreement with expected practical findings. The successive invasion percolation clusters are still found to be self-avoiding with aging. The cluster size decreases with a power law as a function of invasion-frost-thaw iterations. The aging kinetics is also discussed through the normalized totally invaded pore volume. Received 24 September 1999 and Received in final form 5 January 2000     

Scaling and universality of self-organized patterns on unstable vicinal surfaces

We propose a unified treatment of the step bunching instability during epitaxial growth. The scaling properties of the self-organized surface pattern are shown to depend on a single parameter, the leading power in the expansion of the biased diffusion current in powers of the local surface slope. We demonstrate the existence of universality classes for the self-organized patterning appearing in models and experiments.     

非均匀毛细多孔层气液渗透传输特性研究

可视化实验研究了不同液/气流速和孔壁面浸润性对非均匀毛细多孔层内稳态饱和度、侵入时间及气、液微观传输特性的影响.结果表明:多孔层内液相饱和度及侵入时间均随液相侵入速率的增大而减小;亲水性多孔介质内液体优先选择小孔侵渗,且孔内侵渗速度变化较大;亲水性多孔层内的稳态气相饱和度随气相驱替速率的增加析增加,憎水性多孔层内的稳态...     

Criticality in a simple model for brain functioning

We introduce a simple model for a set of interacting idealized neurons. The model presents a self-organized state in which avalanches of all sizes are observed and activity is detected in the whole extension of the simulated system without a typical length scale. The basic elements of the model are endowed with the main features of a neuron function. On this basis it is speculated that the collective system that they form, i.e., the brain, could display self-organized criticality in some situations.     

Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional 4-State Potts Model

We analyze the scaling and finite-size-scaling behavior of the two-dimensional 4-state Potts model. We find new multiplicative logarithmic corrections for the susceptibility, in addition to the already known ones for the specific heat. We also find additive logarithmic corrections to scaling, some of which are universal. We have checked the theoretical predictions at criticality and off criticality by means of high-precision Monte Carlo data.     

Prediction of extreme events in the OFC model on a small world network

We investigate the predictability of extreme events in a dissipative Olami-Feder-Christensen model on a small world topology. Due to the mechanism of self-organized criticality, it is impossible to predict the magnitude of the next event knowing previous ones, if the system has an infinite size. However, by exploiting the finite size effects, we show that probabilistic predictions of the occurrence of extreme events in the next time step are possible in a finite system. In particular, the finiteness of the system unavoidably leads to repulsive temporal correlations of extreme events. The predictability of those is higher for larger magnitudes and for larger complex network sizes. Finally, we show that our prediction analysis is also robust by remarkably reducing the accessible number of events used to construct the optimal predictor.