Multifractality in spin glasses.

We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Collective phase transitions in confined fish schools.

The collective patterns that emerge in schooling fish are often analyzed using models of self-propelled particles in unbounded domains. However, while schooling fish in both field and laboratory settings interact with domain boundaries, these effects are typically ignored. Here, we propose a model that incorporates geometric confinement, by accounting for both flow and wall interactions, into existing data-driven behavioral rules. We show that new collective phases emerge where the school of fish "follows the tank wall" or "double mills." Importantly, confinement induces repeated switching between two collective states, schooling and milling. We describe the group dynamics probabilistically, uncovering bistable collective states along with unintuitive bifurcations driving phase transitions. Our findings support the hypothesis that collective transitions in fish schools could occur spontaneously, with no adjustment at the individual level, and opens venues to control and engineer emergent collective patterns in biological and synthetic systems that operate far from equilibrium.

Forecasting small-scale dynamics of fluid turbulence using deep neural networks.

Turbulence in fluid flows is characterized by a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small-scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small-scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and explicitly incorporate Reynolds number dependence to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small-scale features of turbulence.

Hydrodynamic coupling melts acoustically levitated crystalline rafts.

Going beyond the manipulation of individual particles, first steps have recently been undertaken with acoustic levitation in air to investigate the collective dynamical properties of many-body systems self-assembled within the levitation plane. However, these assemblies have been limited to two-dimensional, close-packed rafts where forces due to scattered sound pull particles into direct frictional contact. Here, we overcome this restriction using particles small enough that the viscosity of air establishes a repulsive streaming flow at close range. By tuning the particle size relative to the characteristic length scale for viscous streaming, we control the interplay between attractive and repulsive forces and show how particles can be assembled into monolayer lattices with tunable spacing. While the strength of the levitating sound field does not affect the particles' steady-state separation, it controls the emergence of spontaneous excitations that can drive particle rearrangements in an effectively dissipationless, underdamped environment. Under the action of these excitations, a quiescent particle lattice transitions from a predominantly crystalline structure to a two-dimensional liquid-like state. We find that this transition is characterized by dynamic heterogeneity and intermittency, involving cooperative particle movements that remove the timescale associated with caging for the crystalline lattice. These results shed light on the nature of athermal excitations and instabilities that can arise from strong hydrodynamic coupling among interacting particles.

Temporal Variation and Persistence of Methane Emissions from Shallow Water Oil and Gas Production in the Gulf of Mexico.

Methane emissions from the oil and gas supply chain can be intermittent, posing challenges for monitoring and mitigation efforts. This study examines shallow water facilities in the US Gulf of Mexico with repeat atmospheric observations to evaluate temporal variation in site-specific methane emissions. We combine new and previous observations to develop a longitudinal study, spanning from days to months to almost five years, evaluating the emissions behavior of sites over time. We also define and determine the chance of subsequent detection (CSD): the likelihood that an emitting site will be observed emitting again. The average emitting central hub in the Gulf has a 74% CSD at any time interval. Eight facilities contribute 50% of total emissions and are over 80% persistent with a 96% CSD above 100 kg/h and 46% persistent with a 42% CSD above 1000 kg/h, indicating that large emissions are persistent at certain sites. Forward-looking infrared (FLIR) footage shows many of these sites exhibiting cold venting. This suggests that for offshore, a low sampling frequency over large spatial coverage can capture typical site emissions behavior and identify targets for mitigation. We further demonstrate the preliminary use of space-based observations to monitor offshore emissions over time.

Bistability in oxidative stress response determines the migration behavior of phytoplankton in turbulence.

Turbulence is an important determinant of phytoplankton physiology, often leading to cell stress and damage. Turbulence affects phytoplankton migration both by transporting cells and by triggering switches in migratory behavior, whereby vertically migrating cells can actively invert their direction of migration upon exposure to turbulent cues. However, a mechanistic link between single-cell physiology and vertical migration of phytoplankton in turbulence is currently missing. Here, by combining physiological and behavioral experiments with a mathematical model of stress accumulation and dissipation, we show that the mechanism responsible for the switch in the direction of migration in the marine raphidophyte Heterosigma akashiwo is the integration of reactive oxygen species (ROS) signaling generated by turbulent cues. Within timescales as short as tens of seconds, the emergent downward-migrating subpopulation exhibited a twofold increase in ROS, an indicator of stress, 15% lower photosynthetic efficiency, and 35% lower growth rate over multiple generations compared to the upward-migrating subpopulation. The origin of the behavioral split as a result of a bistable oxidative stress response is corroborated by the observation that exposure of cells to exogenous stressors (H2O2, UV-A radiation, or high irradiance), in lieu of turbulence, caused comparable ROS accumulation and an equivalent split into the two subpopulations. By providing a mechanistic link between the single-cell mechanics of swimming and physiology on the one side and the emergent population-scale migratory response and impact on fitness on the other, the ROS-mediated early warning response we discovered contributes to our understanding of phytoplankton community composition in future ocean conditions.

The microstructure of intra- and interpersonal coordination.

Movements are naturally composed of submovements, i.e. recurrent speed pulses (2-3 Hz), possibly reflecting intermittent feedback-based motor adjustments. In visuomotor (unimanual) synchronization tasks, partners alternate submovements over time, indicating mutual coregulation. However, it is unclear whether submovement coordination is organized differently between and within individuals. Indeed, different types of information may be variably exploited for intrapersonal and interpersonal coordination. Participants performed a series of bimanual tasks alone or in pairs, with or without visual feedback (solo task only). We analysed the relative timing of submovements between their own hands or between their own hands and those of their partner. Distinct coordinative structures emerged at the submovement level depending on the relevance of visual feedback. Specifically, the relative timing of submovements (between partners/effectors) shifts from alternation to simultaneity and a mixture of both when coordination is achieved using vision (interpersonal), proprioception/efference-copy only (intrapersonal, without vision) or all information sources (intrapersonal, with vision), respectively. These results suggest that submovement coordination represents a behavioural proxy for the adaptive weighting of different sources of information within action-perception loops. In sum, the microstructure of movement reveals common principles governing the dynamics of sensorimotor control to achieve both intra- and interpersonal coordination.

Mean structure of the supercritical turbulent spiral in Taylor-Couette flow.

The large-scale laminar/turbulent spiral patterns that appear in the linearly unstable regime of counter-rotating Taylor-Couette flow are investigated from a statistical perspective by means of direct numerical simulation. Unlike the vast majority of previous numerical studies, we analyse the flow in periodic parallelogram-annular domains, following a coordinate change that aligns one of the parallelogram sides with the spiral pattern. The domain size, shape and spatial resolution have been varied and the results compared with those in a sufficiently large computational orthogonal domain with natural axial and azimuthal periodicity. We find that a minimal parallelogram of the right tilt significantly reduces the computational cost without notably compromising the statistical properties of the supercritical turbulent spiral. Its mean structure, obtained from extremely long time integrations in a co-rotating reference frame using the method of slices, bears remarkable similarity with the turbulent stripes observed in plane Couette flow, the centrifugal instability playing only a secondary role. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical transactions paper (Part 2)'.

Parabolic Potential Surfaces Localize Charge Carriers in Nonblinking Long-Lifetime "Giant" Colloidal Quantum Dots.

Materials for studying biological interactions and for alternative energy applications are continuously under development. Semiconductor quantum dots are a major part of this landscape due to their tunable optoelectronic properties. Size-dependent quantum confinement effects have been utilized to create materials with tunable bandgaps and Auger recombination rates. Other mechanisms of electronic structural control are under investigation as not all of a material's characteristics are affected by quantum confinement. Demonstrated here is a new structure-property concept that imparts the ability to spatially localize electrons or holes within a core/shell heterostructure by tuning the charge carrier's kinetic energy on a parabolic potential energy surface. This charge carrier separation results in extended radiative lifetimes and in continuous emission at the single-nanoparticle level. These properties enable new applications for optics, facilitate novel approaches such as time-gated single-particle imaging, and create inroads for the development of other new advanced materials.

Wavelet-Based Multiscale Intermittency Analysis: The Effect of Deformation.

Intermittency represents a certain form of heterogeneous behavior that has interest in diverse fields of application, particularly regarding the characterization of system dynamics and for risk assessment. Given its intrinsic location-scale-dependent nature, wavelets constitute a useful functional tool for technical analysis of intermittency. Deformation of the support may induce complex structural changes in a signal. In this paper, we study the effect of deformation on intermittency. Specifically, we analyze the interscale transfer of energy and its implications on different wavelet-based intermittency indicators, depending on whether the signal corresponds to a 'level'- or a 'flow'-type physical magnitude. Further, we evaluate the effect of deformation on the interscale distribution of energy in terms of generalized entropy and complexity measures. For illustration, various contrasting scenarios are considered based on simulation, as well as two segments corresponding to different regimes in a real seismic series before and after a significant earthquake.

Fractal Geometric Model for Statistical Intermittency Phenomenon.

The phenomenon of intermittency has remained a theoretical concept without any attempts to approach it geometrically with the use of a simple visualization. In this paper, a particular geometric model of point clustering approaching the Cantor shape in 2D, with a symmetry scale θ being an intermittency parameter, is proposed. To verify its ability to describe intermittency, to this model, we applied the entropic skin theory concept. This allowed us to obtain a conceptual validation. We observed that the intermittency phenomenon in our model was adequately described with the multiscale dynamics proposed by the entropic skin theory, coupling the fluctuation levels that extended between two extremes: the bulk and the crest. We calculated the reversibility efficiency γ with two different methods: statistical and geometrical analyses. Both efficiency values, γstat and γgeo, showed equality with a low relative error margin, which actually validated our suggested fractal model for intermittency. In addition, we applied the extended self-similarity (E.S.S.) to the model. This highlighted the intermittency phenomenon as a deviation from the homogeneity assumed by Kolmogorov in turbulence.

On-off intermittency and irruptions in host-parasitoid dynamics.

Environmental stochasticity affects population dynamics in a variety of ways, including the possibility of drastic modifications in the stability properties of the ecosystem. In this work, we investigate a case of coupled host-parasitoid dynamics adopting Beddington's conceptual two-dimensional map. We stochastically perturb some of the parameters controlling either the host dynamics or the host-parasitoid interaction, observing a dramatic change in the system dynamics with the emergence of on-off intermittency, a behavior characterized by the irregular alternation between quiescent phases and sudden population bursts. This phenomenon is herein offered as a qualitative, environmental-based description of population outbreaks.

High clutch failure rate due to unpredictable rainfall for an ephemeral pool-breeding frog.

Animals that reproduce in temporary aquatic systems expose their offspring to a heightened risk of desiccation, as they must race to complete development and escape before water levels recede. Adults must therefore synchronise reproduction with the changing availability of water, yet the conditions they experience to trigger such an event may not relate to those offspring face throughout development, potentially leading to clutch failure. The sandpaper frog (Lechriodus fletcheri) breeds in ephemeral pools that dry within days to weeks after rainfall has ceased. We examined whether spawning frequency and offspring survival differed across two consecutive breeding seasons based on (1) rainfall at the moment of oviposition and throughout offspring development, and (2) pool volume, given their combined effect on hydroperiod. Reproduction was triggered by rainfall, with more spawn laid during periods of greater rainfall and in larger pools. While pool size was a predictor of offspring survival, rainfall during oviposition was not. Rather, follow-up rain events were required to prevent pools drying prior to metamorphosis, with rainfall evenness during development the strongest predictor of reproductive success. High clutch failure rates recorded in both seasons suggest that adults do not have the capability to predict rainfall frequency post-oviposition. We thus conclude that unpredictable rainfall leading to premature desiccation of spawning sites is the primary source of pre-metamorphic mortality for this species. Understanding the influence of rainfall predictability on offspring survival could be critical in predicting the effects of altered hydroperiod regimes due to climate change for species that exploit temporary waters.

Self-similar properties of avalanche statistics in a simple turbulent model.

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time [Formula: see text] followed by abrupt avalanche-like energy drops of sizes [Formula: see text] due to strong intermittent fluctuations of energy dissipation. We study the probability distribution [Formula: see text] and [Formula: see text] which both exhibit a quite well-defined scaling behaviour. Although [Formula: see text] and [Formula: see text] are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Hidden scale invariance in Navier-Stokes intermittency.

We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centres. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

A correspondence between the multifractal model of turbulence and the Navier-Stokes equations.

The multifractal model of turbulence (MFM) and the three-dimensional Navier-Stokes equations are blended together by applying the probabilistic scaling arguments of the former to a hierarchy of weak solutions of the latter. This process imposes a lower bound on both the multifractal spectrum [Formula: see text], which appears naturally in the Large Deviation formulation of the MFM, and on [Formula: see text] the standard scaling parameter. These bounds respectively take the form: (i) [Formula: see text], which is consistent with Kolmogorov's four-fifths law ; and (ii) [Formula: see text]. The latter is significant as it prevents solutions from approaching the Navier-Stokes singular set of Caffarelli, Kohn and Nirenberg. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.

Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment.

A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon-anomalous dissipation-is sometimes called the 'zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions [Formula: see text] exhibit persistent power-law scaling in the inertial range, namely [Formula: see text] for exponents [Formula: see text] over an ever increasing (with Reynolds) range of scales. This behaviour indicates that the velocity field retains some fractional differentiability uniformly in the Reynolds number. The Kolmogorov 1941 theory of turbulence predicts that [Formula: see text] for all [Formula: see text] and Onsager's 1949 theory establishes the requirement that [Formula: see text] for [Formula: see text] for consistency with the zeroth law. Empirically, [Formula: see text] and [Formula: see text], suggesting that turbulent Navier-Stokes solutions approximate dissipative weak solutions of the Euler equations possessing (nearly) the minimal degree of singularity required to sustain anomalous dissipation. In this note, we adopt an experimentally supported hypothesis on the anti-alignment of velocity increments with their separation vectors and demonstrate that the inertial dissipation provides a regularization mechanism via the Kolmogorov 4/5-law. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

λ-Navier-Stokes turbulence.

We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value [Formula: see text]. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number [Formula: see text]. We show that for a fixed injection rate, as [Formula: see text], the kinetic energy diverges with a scaling law [Formula: see text]. The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as [Formula: see text] is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to [Formula: see text] a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as [Formula: see text] is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Puff turbulence in the limit of strong buoyancy.

We provide a numerical validation of a recently proposed phenomenological theory to characterize the space-time statistical properties of a turbulent puff, both in terms of bulk properties, such as the mean velocity, temperature and size, and scaling laws for velocity and temperature differences both in the viscous and in the inertial range of scales. In particular, apart from the more classical shear-dominated puff turbulence, our main focus is on the recently discovered new regime where turbulent fluctuations are dominated by buoyancy. The theory is based on an adiabaticity hypothesis which assumes that small-scale turbulent fluctuations rapidly relax to the slower large-scale dynamics, leading to a generalization of the classical Kolmogorov and Kolmogorov-Obukhov-Corrsin theories for a turbulent puff hosting a scalar field. We validate our theory by means of massive direct numerical simulations finding excellent agreement. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Editorial: Scaling the Turbulence Edifice.

Turbulence is unique in its appeal across physics, mathematics and engineering. And yet a microscopic theory, starting from the basic equations of hydrodynamics, still eludes us. In the last decade or so, new directions at the interface of physics and mathematics have emerged, which strengthens the hope of 'solving' one of the oldest problems in the natural sciences. This two-part theme issue unites these new directions on a common platform emphasizing the underlying complementarity of the physicists' and the mathematicians' approaches to a remarkably challenging problem. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.