Self-organized Critical Behavior Research Articles

From Cell States to Cell Fates: Control of Cell State Transitions.

We examine the coordinated behavior of thousands of genes in cell fate transitions through genome expression as an integrated dynamical system using theconcepts of self-organized criticality and coherent stochastic behavior. To quantify theeffects of thecollective behavior of genes, we adopted the flux balance approach and developed it in a new tool termed expression flux analysis (EFA). Here we describe this tool and demonstrate how its application to specific experimental genome-wide expression data provides new insights into the dynamics of the cell-fate transitions. Particularly, we show that in cell fate change, specific stochastic perturbations can spread over the entire system to guide distinct cell fate transitions through switching cyclic flux flow in the genome engine. Utilization of EFA enables us to elucidate a unified genomic mechanism for when and how cell-fate change occurs through critical transitions.

Roots seeking of multiple shear-bands in amorphous alloys at the atomic scale

The propagation of shear-bands is of utmost importance in understanding the macro and microscopic deformations of bulk metallic glasses (BMGs). In this study, using molecular dynamics simulations to elucidate the intricate atomic-scale mechanisms governing dynamic continuum shear-bands and microstructural evolution during deformation. This work provides compelling evidence of self-organized critical behavior, as evidenced by the observation of serrated flow patterns and distributions of elastic energy density. Moreover, we unveil the influence of notch length on the principal shear-band based on the steep stress drop (i.e., Δτ =τy-τs, distinct from serrated flows), strength-normalized difference (i.e., Δτ/τy), and probability distribution of shear-strain. The effective blocking of shear bands by nanocrystal second phase can be attributed to the synergistic reinforcement effect of dislocations and nano-stacking faults. Finally, the analysis of the serrated flow behavior and stress-increment distribution during nanoindentation establishes the connection between micromechanical behavior, shear-band evolution, and macroscopic mechanical properties.

Spiking ruby revisited: self-induced periodic spiking oscillations leading to chaotic state in a Cr:Al2O3 laser with cw 532-nm pumping

This paper reexamines a 60-year-old mystery of spiking behavior in ruby lasers with a cw 532-nm pump, paying special attention to mode matching between the pump and lasing beam within a ruby crystal placed in a semi-confocal laser cavity. Periodic spiking oscillations were observed in a limited pump power regime, where spikes obeying the generic asymmetric hyperbolic function appeared at a repetition rate around 50 kHz and with a 130-150 ns width and 0.1-0.6 µJ energy depending on the pump power. The physics of the spiking behavior based on Kleinman’s mechanical approach and a plausible interpretation for the periodic spiking oscillation in terms of self-induced mode matching between the pump and laser beams through the self-induced Kerr-lens effect are addressed. The statistical nature inherent to spiking and the associated self-organized critical behavior in the quasi-periodic spiking oscillations as well as chaotic states occurring outside the periodic spiking regime are clarified from a nonlinear dynamics point of view and intriguing statistical properties inherent to chaotic oscillations in usual solid-state lasers subjected to external modulations are shown to be present in the self-induced instabilities of the ruby laser

Formation of multiple anodic fire spots inside an electrostatic cavity

AbstractCharged particles exhibit self‐organized behaviour during the discharge state transitions inside an electrostatic cavity, along with the energy redistribution in different coherent modes with progressive anode potential. Multiple sheath formations around the spherical metallic ball anode placed inside the cavity transit to intensely glowing multiple anode spot formations (fireballs) on the anode surface with progressive anode potential. The intensely glowing anode spots reorganize over the anode surface and multiply quickly on increasing the anode potential. The nonlinear analysis of the fluctuating discharge current reveals the presence of self‐organized criticality (SOC) during different states of discharge along with a strong memory effect within (10–104) time lags in every state of discharge. The multiple anode spots exhibit long‐range correlation in the absence of a magnetic field, indicating SOC behaviour. The present study investigates energy distribution among the coherent modes of discharge through the application of the Empirical Mode Decomposition technique. The analysis indicates that the introduction of a magnetic field results in the interchange of coherent modes carrying most of the energy during multiple spot formations. The present experimental configuration produces stable multiple coherent modes along with the evolution of anodic sheath layers in the absence and then in the presence of the magnetic field. Relating SOC with such discharge transitions may help to understand the relation between complex structure formations in plasma with nonlinear aspects of glow discharge, which is of vital importance in the investigation of complexities in space plasma.

Preventing Instabilities and Inducing Controlled, Slow-Slip in Frictionally Unstable Systems.

We propose a theory for preventing instabilities and inducing controlled, slow‐slip in frictionally unstable systems, such as the Generalized‐Burridge‐Knopoff (GBK) model and seismic fault models. We exploit the dependence of friction on pressure and use it as a backdoor for altering the dynamics of the underlying dynamical system. We use the mathematical Theory of Control and, for the first time, we manage to (a) stabilize and restrict chaos in this kind of systems, (b) guarantee slow frictional dissipation and (c) tune the system toward desirable global asymptotic equilibria of lower energy. Our control approach is robust and does not require exact knowledge of the frictional or elastic behavior of the system. Numerical examples of control are given for a Burridge‐Knopoff system and a strike‐slip fault model obeying rate‐and‐state friction. GBK models are known to present Self‐Organized Critical (SOC) behavior. Therefore, the presented methodology shows an additional example of SOC Control. Even though further developments are necessary before any practical application, we expect our methodology to inspire earthquake mitigation strategies regarding anthropogenic and/or natural seismicity.

Scale-free behavioral cascades and effective leadership in schooling fish

Behavioral contagion and the presence of behavioral cascades are natural features in groups of animals showing collective motion, such as schooling fish or grazing herbivores. Here we study empirical behavioral cascades observed in fish schools defined as avalanches of consecutive large changes in the heading direction of the trajectory of fish. In terms of a minimum turning angle introduced to define a large change, avalanches are characterized by distributions of size and duration showing scale-free signatures, reminiscent of self-organized critical behavior. We observe that avalanches are generally triggered by a small number of fish, which act as effective leaders that induce large rearrangements of the group’s trajectory. This observation motivates the proposal of a simple model, based in the classical Vicsek model of collective motion, in which a given individual acts as a leader subject to random heading reorientations. The model reproduces qualitatively the empirical avalanche behavior observed in real schools, and hints towards a connection between effective leadership, long range interactions and avalanche behavior in collective movement.

Shear banding and serrated flow behaviors of high toughness Zr61Ti2Cu25Al12 bulk metallic glass under bending

By interrupted three-point bending experiments, the detailed evolutions of shear-banding and serrated flow as well as their correlation of high toughness Z61Ti2Cu25Al12 bulk metallic glass (BMG) under bending were systematically studied. Three stages can be classified during plastic bending of Z61Ti2Cu25Al12 BMG based on the different characteristics of shear-banding and serrated flow behaviors. Moreover, there has a strong correlation between shear-banding and serrated flow at different stages of plastic bending. It is noteworthy that the driving force for shear bands propagation of BMG beam under bending depends on the bending moment, instead of the applied load. Thus, remarkable positive correlations among bending moment, shear band zone height and average load drop of serrations were found during plastic bending. During the progressive propagation of multiple shear bands, intense interactions and competitions among these shear bands have occurred, which manifested by the self-organized criticality behavior from serrated flow dynamics, as well as the very finer irregular striation patterns and uneven fluctuant morphologies which presented on the shear offset surface. The sizeable plastic zone of Z61Ti2Cu25Al12 BMG is very favorable to achieve the greater macroscopic plasticity and lower the risk of fast catastrophic fracture. Thus, Z61Ti2Cu25Al12 BMG is a promising engineering material for structure elements which are naturally subjected to bending load, such as compliant mechanisms and microelectromechanical systems.

Self-Organized Space Charge Structure Formations in DC Glow Discharge

Experimental investigations of a hollow cathode discharge through the controlled variation of anode potential inside a hollow cylindrical cavity, in the absence and presence of the magnetic field, reveal the self-organization of uniform complex space charge structure formation around the spherical anode into concentrated localized anode spots. The discharge current&#x2013;voltage (<inline-formula> <tex-math notation="LaTeX">$I$ </tex-math></inline-formula>&#x2013;<inline-formula> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula>) characteristic along with the electrostatic floating potential and discharge current fluctuations measured during the glow discharge regime suggest that the initial stable multiple sheath formation around the anode dissociates into intermittent multiple localized anode spot formations while passing through transient states during anode potential variation. On introducing a magnetic field, the localized concentrated anode spot formations on the anode surface undergo random distribution through self-organized criticality (SOC) and pronounced low-frequency oscillations (&#x007E;52.4 kHz). These oscillations gradually develop into harmonics of 100 kHz on further increasing the anode potential in the presence of the external magnetic field. Various discharge regimes are investigated through the time-resolved floating potential variation measurements using a cylindrical Langmuir probe (LP). We report on the relation between the discharge variations with the nonlinear time series analysis of the discharge current and floating potential fluctuations through the reconstructed phase space in different time domains to analyze the dynamics of complex structure formations and the existence of SOC behavior during the present hollow cathode discharge regime. The study of self-organized pattern formations and SOC behavior is vital for understanding the complex behavior of plasmas in the field of strongly coupled plasmas, plasma-based surface treatments, and thrusters for further development.

Nonlinear dynamics of a self-mixing thin-slice solid-state laser subjected to Doppler-shifted optical feedback.

Chaotic oscillations of a linearly polarized single longitudinal-mode thin-slice Nd:GdVO_{4} laser placed in a self-mixing laser Doppler velocity scheme were dynamically characterized in terms of the intensity probability distribution, joint time-frequency analysis, and short-term Fourier transformation of temporal evolutions, and the degree of disorder in the amplitude and phase of the long-term temporal evolutions. The transition from chaotic relaxation oscillations (ROs) to chaotic spiking oscillations (SOs) was explored via the chaotic itinerancy (CI) regime by increasing the feedback ratio toward the laser from a rotating scattering object. The intensity probability distribution was found to change from an exponential decay in the RO regime to an inverse power law in the SO regime, which manifests itself in self-organized critical behavior, while stochastic subharmonic frequency locking among the two periodicities of RO and SO takes place in the CI regime featuring quantum-noise (spontaneous-emission)-induced order in the amplitude and phase of the spiking oscillations. All of the experimental results were reproduced by numerical simulations of a model equation of a single-mode self-mixing solid-state laser subjected to Doppler-shifted optical feedback from a rotating scattering object.

Expanding and self-organizing 2D universe models emerging from frozen trivalent spin networks

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum gravity. We performed a large set of simulations based on extensions of the frozen trivalent spin network (TSN) model explored previously by Ansari and Smolin. Their model mimicked the sandpile dynamics by the application of random vertex propagation rules in the TSN, leading to an SOC behavior in the distribution of the avalanche sizes, as well as a slowly expanding, two-dimensional dual (triangulated) space. Here we show that a growth scheme for the stochastic, slow external driving force, differing from the classical sandpile model, also resulted in power-law distributed avalanche sizes. Our simulations also produced expanding dual spaces, with two basic classes of evolution: one with power-law correlations in ‘space’ and ‘time’, and the other with ‘loitering’ and exponential phases. Our work expands the range of models in which critical states in the TSN may lead to expansion effects in the dual space, without fine-tuning.

Effects of turbulent environment and random noise on self-organized critical behavior: Universality versus nonuniversality.

Self-organized criticality in the Hwa-Kardar model of a "running sandpile" [Phys. Rev. Lett. 62, 1813 (1989)10.1103/PhysRevLett.62.1813; Phys. Rev. A 45, 7002 (1992)10.1103/PhysRevA.45.7002] with a turbulent motion of the environment taken into account is studied with the field theoretic renormalization group (RG). The turbulent flow is modeled by the synthetic d-dimensional generalization of the anisotropic Gaussian velocity ensemble with finite correlation time, introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990)10.1007/BF02161420; Commun. Math. Phys. 146, 139 (1992)10.1007/BF02099212]. The Hwa-Kardar model with time-independent (spatially quenched) random noise is considered alongside the original model with white noise. The aim of the present paper is to explore fixed points of the RG equations which determine the possible types of universality classes (regimes of critical behavior of the system) and critical dimensions of the measurable quantities. Our calculations demonstrate that influence of the type of random noise is extremely large: in contrast to the case of white noise where the system possesses three fixed points, the case of spatially quenched noise involves four fixed points with overlapping stability regions. This means that in the latter case the critical behavior of the system depends not only on the global parameters of the system, which is the usual case, but also on the initial values of the charges (coupling constants) of the system. These initial conditions determine the specific fixed point which will be reached by the RG flow. Since now the critical properties of the system are not defined strictly by its parameters, the situation may be interpreted as a universality violation. Such systems are not forbidden, but they are rather rare. It is especially interesting that the same model without turbulent motion of the environment does not predict this nonuniversal behavior and demonstrates the usual one with prescribed universality classes instead [J. Stat. Phys. 178, 392 (2020)10.1007/s10955-019-02436-8].

Effects of Turbulent Environment on Self-Organized Critical Behavior: Isotropy vs. Anisotropy

We study a self-organized critical system under the influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [Phys. Rev. Lett.62: 1813 (1989)]. The motion of the environment is modelled by the isotropic Kazantsev–Kraichnan “rapid-change” ensemble for an incompressible fluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form ∝δ(t−t′)/kd+ξ, where k is the wave number and ξ is an arbitrary exponent with the most realistic values ξ=4/3 (Kolmogorov turbulence) and ξ→2 (Batchelor’s limit). Using the field-theoretic renormalization group, we find infrared attractive fixed points of the renormalization group equation associated with universality classes, i.e., with regimes of critical behavior. The most realistic values of the spatial dimension d=2 and the exponent ξ=4/3 correspond to the universality class of pure turbulent advection where the nonlinearity of the Hwa–Kardar (HK) equation is irrelevant. Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equation and the (isotropic) advecting velocity field are relevant also exists for some values of the parameters ε=4−d and ξ. Depending on what terms (anisotropic, isotropic, or both) are relevant in specific universality class, different types of scaling behavior (ordinary one or generalized) are established.

Self-organization of multiple anodic double layers in magnetized plasma

We report on the self-organization of multiple double layers (MDLs) and self-organized criticality (SOC) behavior through subsequent layer reduction process around the anode during DC glow discharge in a linear cylindrical vacuum vessel. The present study provides an insight into the characteristic features of self-organized MDLs around the anode itself and the effect of an external magnetic field during its evolution. The MDL formations around the anode initiate through an abrupt jump in the floating potential, ion saturation, and discharge current signals, which suggests an associated sheath—plasma instability of the system. The frequency spectrum of the floating potential exhibits mixed mode oscillations, which later disappears on applying an external magnetic field. The comparative results reveal the complex nature of a simple glow discharge through repeated coupling and decoupling of MDL dynamics during layer reduction process in the presence of an external magnetic field in cusp configuration, while the discharge turns largely oscillatory in the presence of an external magnetic field in mirror configuration. Existence of the SOC behavior in the system is further investigated through nonlinear dynamical analysis of the floating potential fluctuations. The present study on self-organization phenomena in a glow discharge plasma is important for applications regarding utilization or mitigation of self-organization. Self-organized patterns are often formed during plasma interaction with the liquid surface, which play a vital role in diverse applications of plasmas in nanomaterial synthesis and medicine.

Vitreous 2D silica under tension: From brittle to ductile behaviour

Based on measured ring size distributions of real 2D silica, we numerically prepare sample sets of vitreous 2D silica with varying network topology. We use a Monte Carlo bond-switching method to apply a sequence of topological flip transformations to initially hexagonal 2D silica. In doing so, we are able to control the network heterogeneity by means of the ring size distribution. This method also enables physically meaningful ring neighbourhood statistics according to the empirical Aboav-Weaire law. The obtained vitreous 2D silica sample sets undergo athermal quasistatic tensile deformation in order to investigate the changes of the mechanical behaviour as a function of the underlying network heterogeneity. The molecular statics simulations reveal that the ductility and tensile strength of 2D silica can significantly be tuned varying the network ring statistics. Furthermore, the stress-drop statistics of the respective sample sets are evaluated and shown to display a self-organised critical behaviour.

The System Identification and Prediction of the Social Earthquakes Burst in Human Society

The internal mechanism of the social “earthquakes”- the wars burst in human society, is investigated by nonlinear theory. We explore the scaling behavior in the human activity and the historical evolution of ancient China. Based on the war chronology and history chronology from B.C.2000 to A.D.1840, using statistical analysis together with the detrended fluctuation analysis, we find that the social evolution system shows self-organized critical behavior and there exists self-similar scaling behavior during the evolution system. Based on time-delay reconstructed phase space, a modified radial basis function neural network (modified RBF-NN) is used to predict the number of wars and the transformation of the historical stage. It shows that the prediction result matches quite well with the real value for the following two historical stages. Furthermore, by singular value decomposition and the sparse identification algorithm in time-delay coordinates, the coefficients of the candidate functions in identified system can be solved from a sparse regression problem. We extracted the governing equations of big events burst in social system. The identified system fits well with the real data, and it can capture the same topology with the original system of wars. In this paper, we investigated the wars burst in social system by statistic analysis, neural network as well as sparse identification. It sheds light on the study of wars or conflicts from perspective of data science and dynamical theory.

Modeling active fault systems and seismic events by using a fiber bundle model – example case: the Northridge aftershock sequence

Abstract. Earthquake aftershocks display spatiotemporal correlations arising from their self-organized critical behavior. Dynamic deterministic modeling of aftershock series is challenging to carry out due to both the physical complexity and uncertainties related to the different parameters which govern the system. Nevertheless, numerical simulations with the help of stochastic models such as the fiber bundle model (FBM) allow the use of an analog of the physical model that produces a statistical behavior with many similarities to real series. FBMs are simple discrete element models that can be characterized by using few parameters. In this work, the aim is to present a new model based on FBM that includes geometrical characteristics of fault systems. In our model, the faults are not described with typical geometric measures such as dip, strike, and slip, but they are incorporated as weak regions in the model domain that could increase the likelihood to generate earthquakes. In order to analyze the sensitivity of the model to input parameters, a parametric study is carried out. Our analysis focuses on aftershock statistics in space, time, and magnitude domains. Moreover, we analyzed the synthetic aftershock sequences properties assuming initial load configurations and suitable conditions to propagate the rupture. As an example case, we have modeled a set of real active faults related to the Northridge, California, earthquake sequence. We compare the simulation results to statistical characteristics from the Northridge sequence determining which range of parameters in our FBM version reproduces the main features observed in real aftershock series. From the results obtained, we observe that two parameters related to the initial load configuration are determinant in obtaining realistic seismicity characteristics: (1) parameter P, which represents the initial probability order, and (2) parameter π, which is the percentage of load distributed to the neighboring cells. The results show that in order to reproduce statistical characteristics of the real sequence, larger πfrac values (0.85&lt;πfrac&lt;0.95) and very low values of P (0.0&lt;P≤0.08) are needed. This implies the important corollary that a very small departure from an initial random load configuration (computed by P), and also a large difference between the load transfer from on-fault segments than by off-faults (computed by πfrac), is required to initiate a rupture sequence which conforms to observed statistical properties such as the Gutenberg–Richter law, Omori law, and fractal dimension.

Detection of self-organized criticality behavior in an electronic circuit designed to solve a third order non-linear ODE (NL-ODE) for a damped KdV equation.

In this work, we present an electronic implementation of a damped Korteweg-de Vries equation modeled as a third order nonlinear autonomous ordinary differential equation (jerk equation). The circuit has been realized using operational amplifiers, multipliers, and passive electronic components which provides the time series solution of the equation in agreement with the numerical simulation results. Using nonlinear time series analysis on the acquired waveform data, we have obtained different types of phase space portraits and further analysis reflected long range correlation in the chaotic time series. Important findings include hysteresis induced bifurcation and self-organized criticality behavior in the system which is mentioned in this work.

Tsallis non-extensive statistics and multifractal analysis of the dynamics of a fully-depleted MOSFET nano-device

In this study Tsallis non-extensive statistics and multifractal analysis for the physical description and understanding of the Random Telegraph Noise (RTN), observed in UTBB FD-SOI MOSFET current timeseries is presented. Specifically, we estimate the Tsallis q-triplet and q-entropy production, the Hurst exponent, the multifractal singular spectrum and other topological and dynamical characteristics of this MOSFET-current dynamics as a function of the drain voltage. The analysis shows the existence of microscopic intermittent turbulence and anomalous diffusion processes, underlying the noisy timeseries. The relevant results indicate the existence of a self-organized critical behavior manifested by a percolation mechanism and a fractional transport process. The multifractal character of the dynamics was demonstrated and explained by the maximization of the Tsallis q-entropy function. Final, our analysis revealed the existence of a non-equilibrium topological transition process, taking place when the drain voltage increases and satisfies the basic principles of Tsallis non-extensive statistical theory.

Rate-dependent plastic deformation of TiZrHfCuNiBe high entropy bulk metallic glass

Rate-dependent plastic deformation behavior of TiZrHfCuNiBe high entropy bulk metallic glass (HE-BMG) is investigated by the nanoindentation and quasi-static compression tests. The experimental results reveal that the pop-in sizes during nanoindentation and the serrations sizes under compression will reduce when the loading/strain increases. The strain rate sensitivity during nanoindentation creep is enhanced as loading rate increases, which represents more homogeneously deformation of TiZrHfCuNiBe HE-BMG at higher loading/strain rate. The average serrations sizes of TiZrHfCuNiBe HE-BMG are significantly smaller than that of traditional bulk metallic glasses. The plastic deformation behavior of the TiZrHfCuNiBe HE-BMG is discussed with respect to the self-organized critical (SOC) state behavior. The results demonstrated that the shear-band interactions of multiple shear bands could affect the SOC behavior and inhomogeneous deformation. Research suggests the shear transformation zone (STZ) sizes become smaller as the loading rate increases based on the statistical analysis. It is ascribed to have a larger shear band density at lower loading/strain rate. The current research is in coincidence with the shear-band patterns shown in microscopic micrographs of specimen surfaces. More shear-banding distributions at the lower loading/strain rate will result in more inhomogeneous deformation.

Effects of Ni and Si additions on mechanical properties and serrated flow behavior in FeMoPCB bulk metallic glasses

A novel ductile Fe56Ni20Mo4P11C4B4Si1 bulk metallic glass (BMG) with saturation magnetic flux density of 0.93 T, coercivity of 1.9 A/m and plastic strain of 7% was successfully synthesized in this work. Effects of Ni and Si additions on mechanical properties and serrated flow behavior of Fe-Mo-P-C-B BMGs were systematically investigated. It was found that the simultaneous additions of Ni and Si are effective to improve the plasticity of Fe76Mo4P12C4B4 BMG as indicated by the increase in the plastic strain from 1.7% to 7%. Serrated flow behavior is not observed in Fe76Mo4P12C4B4 BMG. However, the chaos state occurs in Fe56Ni20Mo4P12C4B4 BMG, and eventually the self-organized critical (SOC) behavior appears in Fe56Ni20Mo4P11C4B4Si1 BMG. The stable shear-band dynamics leads to the formation of multiple shear bands, resulting in a complex deformation process follow the SOC dynamics. The improved plasticity might result from an increased number of potential shear transition zone sites, and a stronger tendency of forming shear band interactions. This work provides a perspective from serrated flow behavior to understand plastic deformation mechanism in Fe-based BMGs with different plasticity.