Intermittent Dynamics Research Articles

Switch of tonal noise generation mechanisms in airfoil transitional flows

Large eddy simulations are performed to study tonal noise generation by a NACA0012 airfoil at an angle of attack ${\alpha = 3}$ deg. and freestream Mach number of ${M_{\infty} = 0.3}$. Different Reynolds numbers are analyzed spanning ${0.5 \times 10^5 \le Re \le 4 \times 10^5}$. Results show that the flow patterns responsible for noise generation appear from different laminar separation bubbles, including one observed over the airfoil suction side and another near the trailing edge, on the pressure side. For lower Reynolds numbers, intermittent vortex dynamics on the suction side results in either coherent structures or turbulent packets advected towards the trailing edge. Such flow dynamics also affects the separation bubbles on the pressure side, which become intermittent. Despite the irregular occurrence of laminar-turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. Increasing the Reynolds number leads to a permanent turbulent regime on the suction side that reduces the coherence level causing only small scale turbulent eddies to be observed. Furthermore, the laminar separation bubble on the suction side almost vanishes while that on the pressure side becomes more pronounced and permanent. As a consequence, the dominant noise generation mechanism becomes the vortex shedding along the wake.

Chordwise flexible aft-tail suppresses jet-switching by reinstating wake periodicity in a flapping foil

The effect of a chordwise flexible aft-tail of a rigid heaving aerofoil on the dynamical transitions of the trailing-wake is studied here. The two-way coupled fluid–solid dynamics is simulated using an in-house fluid–structure interaction (FSI) platform, comprising a discrete forcing immersed boundary method based incompressible Navier–Stokes solver, weakly coupled with a finite difference method based structural solver. The FSI dynamics is studied in comparison to the corresponding rigid tail configuration. For the latter, mild jet-switching due to quasi-periodic movement of the wake vortices gives way to vigorous jet-switching as the dynamics transitions to a state of intermittency, where the quasi-periodic behaviour gets interspersed with chaotic windows. Introduction of a moderately flexible tail regularises this intermittent dynamics, eliminating jet-switching. The wake exhibits a deflected reverse Kármán pattern with fluctuating angles, governed by quasi-periodicity. With a highly flexible tail (very low rigidity), the wake shows almost a symmetric reverse Kármán street as periodicity is restored. Flexibility of the aft-tail is next controlled by changing its length, and flow is regularised and periodicity retained for moderate rigidity for increased length. Different dynamical states are established through robust nonlinear dynamical tools. The underlying flow-field behaviour, instrumental in suppressing the jet-switching phenomenon, is identified through a detailed investigation of the near-field vortex interactions dictated by the dynamics. A suite of measures has also been derived from the unsteady flow field to quantify the interactions of the key near-field vortices with a view to understanding the mechanism of switching and its subsequent suppression through flexibility.

Disordered Collective Motion in Dense Assemblies of Persistent Particles.

We explore the emergence of nonequilibrium collective motion in disordered nonthermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field.

Intermittent chimera-like and bi-stable synchronization states in network of distinct Izhikevich neurons

Phase synchronization phenomena of neuronal networks are one of many features depicted by real networks that can be studied using computational models. Here, we proceed with numerical simulations of a globally connected network composed of non-identical (distinct) Izhikevich neuron model to study clustered phase synchronization. We investigate the case in which, once coupled, there exist two main neuron clusters in the network: one of them is bi-stable, depicting phase-synchronized or unsynchronized states, depending on the initial conditions; and the second one shows just an unsynchronized state. For the set of initial conditions that lead the first cluster to the synchronized regime, we observe a chimera-like pattern of the network. For small networks, the dynamics can also present intermittent chimera-like scenarios. In this context, the mechanism for intermittent chimera states is based on two features: the coexistence of a synchronized cluster with an unsynchronized one; and the capability of one cluster to display bi-stability depending on the signal trait by which it is forced. We conclude with an understanding of intermittent chimera-like dynamics as the limit case where bi-stability is not maintained, which occurs due to the loss of uniformity in the neuron input synaptic currents.

Cell motility as an energy minimization process.

The dynamics of active matter driven by interacting molecular motors has a nonpotential structure at the local scale. However, we show that there exists a quasipotential effectively describing the collective self-organization of the motors propelling a cell at a continuum active gel level. Such a model allows us to understand cell motility as an active phase transition problem between the static and motile steady-state configurations that minimize the quasipotential. In particular, both configurations can coexist in a metastable fashion and a small stochastic disorder in the gel is sufficient to trigger an intermittent cell dynamics where either static or motile phases are more probable, depending on which state is the global minimum of the quasipotential.

Early detection of lean blowout using recurrence network for varying degrees of premixedness.

Lean premixed combustors are highly susceptible to lean blowout flame instability, which can cause a fatal accident in aircrafts or expensive shutdown in stationary combustors. However, the lean blowout limit of a combustor may vary significantly depending on a number of variables that cannot be controlled in practical situations. Although a large literature exists on the lean blowout phenomena, a robust strategy for early lean blowout detection is still not available. To address this gap, we study a relatively unexplored route to lean blowout using a nonlinear dynamical tool, the recurrence network. Three recurrence network parameters: global efficiency, average degree centrality, and global clustering coefficient are chosen as metrics for an early prediction of the lean blowout. We observe that the characteristics of the time series near the lean blowout limit are highly dependent on the degree of premixedness in the combustor. Still, for different degrees of premixedness, each of the three recurrence network metrics increases during transition to lean blowout, indicating a shift toward periodicity. Thus, qualitatively, the recurrence network metrics show similar trends for different degrees of premixing showing their robustness. However, the sensitivities and absolute trends of the recurrence network metrics are found to be significantly different for highly premixed and partially premixed configurations. Thus, the results indicate that prior knowledge about (i) the degree of premixedness and (ii) the route to lean blowout may be required for accurate early prediction of the lean blowout. We show that the visible structural changes in the recurrence network can be linked to the changes in the recurrence network metrics, helping to better understand the dynamical transition to lean blowout. We observe the power law degree distribution of the recurrence network to break down close to the lean blowout limit due to the intermittent dynamics in the near-LBO regime.

A scale-wise analysis of intermittent momentum transport in dense canopy flows

We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ( $t_p$ ) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$ , with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$ . By separating the flux events based on $t_p$ , we discover that around 80 % of the momentum is transported through the long-lived events ( $t_{p} \geq \varGamma _{w}$ ) at heights immediately above the canopy, while the short-lived ones ( $t_{p} < \varGamma _{w}$ ) only contribute marginally ( $\approx 20\,\%$ ). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.

Critical Intermittency in Random Interval Maps

Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function systems of interval maps and demonstrate the existence of a phase transition when varying probabilities, where the absolutely continuous stationary measure changes between finite and infinite. We discuss further properties of this stationary measure and show that its density is not in L^q for any q>1. This provides a theory of critical intermittency alongside the theory for the well studied Manneville–Pomeau maps, where the intermittency is caused by a neutral fixed point.

Motile Topological Defects Hinder Dynamical Arrest in Dense Liquids of Active Ellipsoids.

Recent numerical studies have identified the persistence time of active motion as a critical parameter governing glassy dynamics in dense active matter. Here we studied dynamics in liquids of granular active ellipsoids with tunable persistence and velocity. We show that increasing the persistence time at moderate supercooling is equivalent to increasing the strength of attraction in equilibrium liquids and results in reentrant dynamics not just in the translational degrees of freedom, as anticipated, but also in the orientational ones. However, at high densities, motile topological defects, unique to active liquids of elongated particles, hindered dynamical arrest. Most remarkably, for the highest activity, we observed intermittent dynamics due to the jamming-unjamming of these defects for the first time.

Direct data-driven forecast of local turbulent heat flux in Rayleigh–Bénard convection

A combined convolutional autoencoder–recurrent neural network machine learning model is presented to directly analyze and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh–Bénard convection flow at Prandtl number Pr=7 and Rayleigh number Ra=107. Two recurrent neural networks are applied for the temporal advancement of turbulent heat transfer data in the reduced latent data space, an echo state network, and a recurrent gated unit. Thereby, our work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework. This suggests that the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to coarse grids of larger-scale computational models, such as global circulation models for atmosphere and ocean.

Shell model intermittency is the hidden self-similarity

We show that the intermittent dynamics observed in the inertial interval of Sabra shell model of turbulence can be rigorously related to the property of scaling self-similarity. In this connection, the space-time scaling symmetries (like in the K41 theory) are replaced by the new hidden scaling symmetry, which is an exact symmetry of inviscid dynamics represented in special rescaled coordinates and times. We derive the formulas expressing anomalous scaling exponents in terms of Perron-Frobenius eigenvalues of linear operators based on the self-similar statistics. Theoretical conclusions are verified by extensive numerical simulations.

Quantifying the capacity for contemporary trait changes to drive intermittent predator–prey cycles

AbstractA large and growing body of theory has demonstrated how the presence of trait variation in prey or predator populations may affect the amplitude and phase of predator–prey cycles. Less attention has been given to so‐called intermittent cycles, in which predator–prey oscillations recurrently disappear and re‐appear, despite such dynamics being observed in empirical systems and modeling studies. A comprehensive understanding of the conditions under which trait changes may drive intermittent predator–prey dynamics, as well as their potential ecological implications, is therefore missing. Here we provide a first systematic analysis of the eco‐evolutionary conditions that may give rise to intermittent predator–prey cycles, investigating 16 models that incorporate different types of trait variation within prey, predators, or both. Our results show that intermittent dynamics often arise through predator–prey coevolution, but only very rarely when only one trophic level can adapt. Additionally, the frequency of intermittent cycles depends on the source of trait variation (genetic variation or phenotypic plasticity) and the genetic architecture (Mendelian or quantitative traits), with intermittency occurring most commonly through Mendelian evolution, and very rarely through phenotypic plasticity. Further analysis identified three necessary conditions for when trait variation can drive intermittent cycles. First, the intrinsic stability of the predator–prey system must depend on the traits of prey, predators, or both. Second, there must be a mechanism causing the recurrent alternation between stable and unstable states, leading to a “trait” cycle superimposed on the population dynamics. Finally, these trait dynamics must be significantly slower than the predator–prey cycles. We show how these conditions explain all the abovementioned patterns. We further show an important unexpected consequence of these necessary conditions: they are most easily met when intraspecific trait variation is at high risk of being lost. As trait diversity is positively associated with ecosystem functioning, this can have potentially severe negative consequences. This novel result highlights the importance of identifying and understanding intermittent cycles in theoretical studies and natural systems. The new approach for detecting and quantifying intermittency we develop here will be instrumental in enabling future study.

Sheared granular matter and the empirical relations of seismicity.

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Intermittent Hormone Therapy Models Analysis and Bayesian Model Comparison for Prostate Cancer

The prostate is an exocrine gland of the male reproductive system dependent on androgens (testosterone and dihydrotestosterone) for development and maintenance. First-line therapy for prostate cancer includes androgen deprivation therapy (ADT), depriving both the normal and malignant prostate cells of androgens required for proliferation and survival. A significant problem with continuous ADT at the maximum tolerable dose is the insurgence of cancer cell resistance. In recent years, intermittent ADT has been proposed as an alternative to continuous ADT, limiting toxicities and delaying time-to-progression. Several mathematical models with different biological resistance mechanisms have been considered to simulate intermittent ADT response dynamics. We present a comparison between 13 of these intermittent dynamical models and assess their ability to describe prostate-specific antigen (PSA) dynamics. The models are calibrated to longitudinal PSA data from the Canadian Prospective Phase II Trial of intermittent ADT for locally advanced prostate cancer. We perform Bayesian inference and model analysis over the models’ space of parameters on- and off-treatment to determine each model’s strength and weakness in describing the patient-specific PSA dynamics. Additionally, we carry out a classical Bayesian model comparison on the models’ evidence to determine the models with the highest likelihood to simulate the clinically observed dynamics. Our analysis identifies several models with critical abilities to disentangle between relapsing and not relapsing patients, together with parameter intervals where the critical points’ basin of attraction might be exploited for clinical purposes. Finally, within the Bayesian model comparison framework, we identify the most compelling models in the description of the clinical data.

Fatigue crack growth in an aluminum alloy: Avalanches and coarse graining to growth laws

This paper presents the results of optical tracking of a crack tip in a fatigue test. The crack tip exhibits intermittent avalanche dynamics and the authors show how these relate to the crack growth law parameters.

Towards Glasses with Permanent Stability.

Unlike crystals, glasses age or devitrify over time, reflecting their nonequilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that the devitrification of quasi-hard-sphere glasses is prevented by suppressing volume-fraction inhomogeneities. A monodisperse glass known to devitrify with "avalanchelike" intermittent dynamics is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this entirely prevents structural relaxation and devitrification over aging time scales, even in the presence of crystallites. There is a dramatic homogenization in the number of load-bearing nearest neighbors each particle has, indicating that ultrastable glasses may be formed via "mechanical homogenization." Our finding provides a physical principle for glass stabilization and opens a novel route to the formation of mechanically stabilized glasses.

Spatial Patterns and Sensitivity of Intermittent Stream Drying to Climate Variability

AbstractIntermittent streams comprise much of the global river network, and are expected to become more prevalent with climate change. Characterizing the expansion and contraction of intermittency in stream networks, and understanding how sensitive these dynamics are to climatic variability, is critical for predicting the trajectory of hydrologic regimes in a changing climate. Here, we consider the spatial patterns of stream intermittency, focusing on wetted channel conditions at the end of the dry season, and identify land cover, physiographic, and climate variables that influence surface water presence and variability across years. We trained statistical models with wetted channel mapping data from 25 streams over 7 years to predict both the spatial and interannual variability of the wetted channel network. We then used the models to assess intermittent stream dynamics across the Russian River watershed in northern California, USA. We found that an average of 3.7% of the stream network was reliably dry, while 16.1% was reliably wet at the end of the dry season, with the remainder of the network exhibiting variability in wetted conditions in response to antecedent precipitation. Both climatic and landscape characteristics controlled the extent of the wetted network, particularly antecedent precipitation at seasonal and annual time scales, highlighting the role of hydrologic memory in this system. Given predictions of increased climate volatility, an improved understanding of the spatial patterns and stability of dry season conditions in intermittent streams can inform climate risk assessments and strategies for protecting biodiversity and the ecosystem services that intermittent streams support.

The nexus of gendered practices, energy, and space use: A comparative study of middleclass housing in Pakistan and Jordan

The nexus of gendered domestic practices, energy and space use remains under-researched in energy studies, particularly in the Global South. This paper takes a gendered practice-theoretical approach to investigate women’s differential energy and space use in domestic practices. Qualitative analysis of semi-structured interviews with middleclass homeowners in Lahore, Pakistan and Amman, Jordan show that energy and space use are implicated in the gendering of domestic practices in three ways: 1) contingency of women’s energy consumption on spatial affordances of housing developments in the gendered division of private/public spheres, 2) women as primary performers of domestic energy flexibility and demand management practices and 3) women’s varied and differential agency in their roles as wives, mothers, caregivers, mothers- and daughters-in-law, income-generators, and housemaids. In Lahore, women as household managers negotiate domestic practices under an intermittent electricity supply and power dynamics of extended families and domestic service. In Amman, nuclear family structures and declining servant culture result in women’s greater reliance on energy-intensive technologies, especially for working women. In both contexts, modernist spatial regulations that determine building density and setbacks, height restrictions, spatial layouts and window placement etc. exhibit gender oversights and conflict with socio-cultural norms of privacy and segregation. This has implications for domestic energy demand, with different women having to negotiate between comfort, convenience, and consumption. The study highlights limitations of current gender-neutral and gender-binary approaches in housing and energy and calls for greater socio-cultural understanding of gender relations and intersectional agencies in domestic energy practices for improved equity and sustainability.

Thermally activated intermittent dynamics of creeping crack fronts along disordered interfaces

We present a subcritical fracture growth model, coupled with the elastic redistribution of the acting mechanical stress along rugous rupture fronts. We show the ability of this model to quantitatively reproduce the intermittent dynamics of cracks propagating along weak disordered interfaces. To this end, we assume that the fracture energy of such interfaces (in the sense of a critical energy release rate) follows a spatially correlated normal distribution. We compare various statistical features from the obtained fracture dynamics to that from cracks propagating in sintered polymethylmethacrylate (PMMA) interfaces. In previous works, it has been demonstrated that such an approach could reproduce the mean advance of fractures and their local front velocity distribution. Here, we go further by showing that the proposed model also quantitatively accounts for the complex self-affine scaling morphology of crack fronts and their temporal evolution, for the spatial and temporal correlations of the local velocity fields and for the avalanches size distribution of the intermittent growth dynamics. We thus provide new evidence that an Arrhenius-like subcritical growth is particularly suitable for the description of creeping cracks.

Excitable networks for finite state computation with continuous time recurrent neural networks

Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints. We describe a direct constructive method of realising finite state input-dependent computations on an arbitrary directed graph. The constructed system has an excitable network attractor whose dynamics we illustrate with a number of examples. The resulting CTRNN has intermittent dynamics: trajectories spend long periods of time close to steady-state, with rapid transitions between states. Depending on parameters, transitions between states can either be excitable (inputs or noise needs to exceed a threshold to induce the transition), or spontaneous (transitions occur without input or noise). In the excitable case, we show the threshold for excitability can be made arbitrarily sensitive.