Critical Time Scale Research Articles

Competition of long-range interactions and noise at a ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain

The nonequilibrium dynamics of long-range pairing Kitaev model with noiseless/noisy linear time dependent chemical potential, is investigated in the framework of dynamical quantum phase transitions (DQPTs). We have shown that for the ramp crossing a single quantum critical point, while the short-range pairing Kitaev model displays a single critical time scale, the long-range pairing induces a region with three DQPTs time scales. We have found that the region with three DQPTs time scales shrinks in the presence of the noise. In addition, we have uncovered that for a quench crossing two critical points, the critical sweep velocity above which the DQPTs disappear enhances by the long-range pairing exponent while decreases in the presence of the noise. On the basis of numerical simulations, we have shown that noise diminishes the long-range pairing inductions. Published by the American Physical Society 2024

The time horizon for stochastic homogenization of the one-dimensional wave equation

The wave equation with stochastic rapidly oscillating coefficients can be classically homogenized on bounded time intervals; solutions converge in the homogenization limit to solutions of a wave equation with constant coefficients. This is no longer true on large time scales: Even in the periodic case with periodicity ε, classical homogenization fails for times of the order ε − 2 . We consider the one-dimensional wave equation with random rapidly oscillation coefficients on scale ε and are interested in the critical time scale ε − β from where on classical homogenization fails. In the general setting, we derive upper and lower bounds for β in terms of the growth rate of correctors. In the specific setting of i.i.d. coefficients with matched impedance, we show that the critical time scale is ε − 1 .

Shoulder viscoelasticity in a raptor-inspired model alleviates instability and enhances passive gust rejection

Recent experiments with gliding raptors reveal a perplexing dichotomy: remarkably resilient gust rejection, but, at the same time, an exceptionally high degree of longitudinal instability. To resolve this incompatibility, a multiple degree of freedom model is developed with minimal requisite complexity to examine the hypothesis that the bird shoulder joint may embed essential stabilizing and preflexive mechanisms for rejecting rapid perturbations while simplifying and reducing control effort. Thus, the formulation herein is centrally premised upon distinct wing pitch and body pitch angles coupled via a Kelvin–Voigt viscoelastic shoulder joint. The model accurately exhibits empirical gust response of an unstable gliding raptor, generates biologically plausible equilibrium configurations, and the viscoelastic shoulder coupling is shown to drastically alleviate the high degree of instability predicted by conventional linear flight dynamics models. In fact, stability analysis of the model predicts a critical system timescale (the time to double amplitude of a pitch divergence mode) that is commensurate with in vivo measured latency of barn owls (Tyto alba). Active gust mitigation is studied by presupposing the owl behaves as an optimal controller. The system is under-actuated and the feedback control law is resolved in the controllable subspace using a Kalman decomposition. Importantly, control-theoretic analysis precisely identifies what discrete gust frequencies may be rapidly and passively rejected versus disturbances requiring feedback control intervention.

Predicting resting-state brain functional connectivity from the structural connectome using the heat diffusion model: a multiple-timescale fusion method

Objective. Understanding the intricate relationship between structural connectivity (SC) and functional connectivity (FC) is pivotal for understanding the complexities of the human brain. To explore this relationship, the heat diffusion model (HDM) was utilized to predict FC from SC. However, previous studies using the HDM have typically predicted FC at a critical time scale in the heat kernel equation, overlooking the dynamic nature of the diffusion process and providing an incomplete representation of the predicted FC. Approach. In this study, we propose an alternative approach based on the HDM. First, we introduced a multiple-timescale fusion method to capture the dynamic features of the diffusion process. Additionally, to enhance the smoothness of the predicted FC values, we employed the Wavelet reconstruction method to maintain local consistency and remove noise. Moreover, to provide a more accurate representation of the relationship between SC and FC, we calculated the linear transformation between the smoothed FC and the empirical FC. Main results. We conducted extensive experiments in two independent datasets. By fusing different time scales in the diffusion process for predicting FC, the proposed method demonstrated higher predictive correlation compared with method considering only critical time points (Singlescale). Furthermore, compared with other existing methods, the proposed method achieved the highest predictive correlations of 0.6939 ± 0.0079 and 0.7302 ± 0.0117 on the two datasets respectively. We observed that the visual network at the network level and the parietal lobe at the lobe level exhibited the highest predictive correlations, indicating that the functional activity in these regions may be closely related to the direct diffusion of information between brain regions. Significance. The multiple-timescale fusion method proposed in this study provides insights into the dynamic aspects of the diffusion process, contributing to a deeper understanding of how brain structure gives rise to brain function.

Dimensional analysis of literature formulas to estimate the characteristic flood response time in ungauged basins: A velocity-based approach

When investigating the wide literature dealing with the assessment of the critical time scale for basin hydrological response, several aspects still to be clarified can be acknowledged. Despite the high sensitivity of design flood peaks to the estimated time parameter value, there is still no agreement on the conceptual and operational definitions of the basin response time, resulting in several different approaches and formulations available.In our work, we suggest a conceptual approach to either reject or recommend formulas of the characteristic basin response time for ungauged basins, with the aim of devising some practical steps in the choice of a robust formulation to be used in hydrological modelling and flood hydrograph design. To this end, 29 empirical and semi-empirical formulas, all containing a basin length and slope, have been carefully selected and their structure compared in dimensional terms, using a simple hydraulic reasoning (e.g., the Chezy formula) as indicator of hydraulic consistency. 13 hydraulically consistent formulas have been identified.Starting from wave celerities and using the river network morphology of 135 watersheds in north-western Italy, we have then investigated and compared the variability of the average flow velocities estimated using all formulas whose input data are available within the study area. By comparing the magnitude and basin scale dependence of the inferred velocities with the values observed in the literature, which generally increase with basin size, some formulas are considered not reasonable, while 5 of them are identified as more robust, i.e. consistent with the observations. These are the formulas of Chow (1962), NERC (1975), SCS (1954), McEnroe and Zhao (1999) and Watt and Chow (1985).Our findings lead to identify analytically the relationships between the exponents of each formula and those of the scaling law linking the length and slope of the basin. These relationships, driving the increase or decrease in the velocity values with basin size, allow us to identify the range of length and slope exponents in the characteristic time formulas for which velocity increases with basin area, as literature suggests. Based on the same relationships, one of the 5 formulas above can be adopted in practical applications and a guideline for calibrating new formulations can be followed.

A Novel Energy-Intensity Model Based on Time Scale for Quasi-Continuous Production in Iron and Steel Industry

Energy intensity is an important assessment indicator of energy consumption. Unfortunately, the traditional energy intensity model (TEIM) has obvious limitations when applied to quasi- continuous production process, especially for small time scales (STS). Therefore, a novel energy intensity model (NEIM) has been established in this study. The NEIM includes three main stages. Firstly, the statistical period and time scale have been determined. Secondly, the concept of workpiece valid weight has been proposed for a given time scale. Then the specific calculation method has also been established. Thirdly, a NEIM has been suggested according to the definition of energy intensity. The application results for a reheating furnace show that the NEIM’s effectiveness has been verified via comparison with the TEIM for large time scale (LTS) and critical time scale (CTS), whereas the NEIM still has validity at STS. Additionally, calculation results for the NEIM reflect more trend information at LTS and CTS; whereas, more dynamic information has been reflected at STS. The aim of this research was to expand the NEIM application for different time scales. Meanwhile, NEIM can also be applied to various energy-consuming facilities.

Single-Molecule Sizing through Nanocavity Confinement.

An approach relying on nanocavity confinement is developed in this paper for the sizing of nanoscale particles and single biomolecules in solution. The approach, termed nanocavity diffusional sizing (NDS), measures particle residence times within nanofluidic cavities to determine their hydrodynamic radii. Using theoretical modeling and simulations, we show that the residence time of particles within nanocavities above a critical time scale depends on the diffusion coefficient of the particle, which allows the estimation of the particle's size. We demonstrate this approach experimentally through the measurement of particle residence times within nanofluidic cavities using single-molecule confocal microscopy. Our data show that the residence times scale linearly with the sizes of nanoscale colloids, protein aggregates, and single DNA oligonucleotides. NDS thus constitutes a new single molecule optofluidic approach that allows rapid and quantitative sizing of nanoscale particles for potential applications in nanobiotechnology, biophysics, and clinical diagnostics.

In-river weir effects on the alteration of flow regime and regarding structural stream habitat

In-river hydraulic structures may negatively impact aquatic ecosystems, including changing river flow regimes and the habitat quality of endemic fish habitats. This study integrates the wavelet analysis and the time-series exceedance probability method to quantify the degree of evolution in the river flow regime caused by weirs and determine the critical time scale most affected in the environmental flow. Hydrodynamic and habitat models were conducted to analyze the influence of the variant flow characteristics between the dry and wet seasons on the habitat structure. Four endemic fishes were selected as the indicator species to represent different habitat preferences and reveal the spatiotemporal changes in habitat quality. The flow difference between dry and wet seasons became more extensive after the weir construction, indicating the alternative flow regime downstream. The annual deviation of daily flow dramatically raised, showing the flow rates decline in the dry season and enlarge in the wet season. The findings exhibit that the downstream flow amplitude changes regardless of time scale after constructing the weir. The flow data from the 2-days scale to the 1-week scale were most adjusted, meaning that these periods to meet the environmental flow decline significantly. The critical environmental flow corresponding to lower flow events was apparently influenced in the dry season, in which the Q75 and Q90 displayed the highest degradation in fish habitat quality. In addition, the simulation results of the habitat model found that glide is the primary habitat type. The total water area and the habitat diversity were reduced, while the habitat quality also had a lowered tendency after the weir operation. The habitat run was most degraded, and the riffle was also significantly negatively impacted. Regarding the endemic fish species,F. lacustresuffered the most harmful effects on suitable-habitat quality and quantity from the weir. This study suggests considering natural flow regimes at the planning and design phases of weir construction and rehabilitating these essential habitat patterns to mitigate the downstream ecosystem impacts.

Chaos onset in large rings of Bose-Einstein condensates

We consider large rings of weakly-coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, non-zero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $\pi/2$ and $3\pi/2$ and interparticle interaction in condensates exceeds a critical interaction value $u_c$, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only a part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero is generally offset by a critical time-scale $t_c$, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical time-scale in detail in a broad parameter range.

Life rather than climate influences diversity at scales greater than 40 million years

The diversity of life on Earth is controlled by hierarchical processes that interact over wide ranges of timescales1. Here, we consider the megaclimate regime2 at scales ≥1 million years (Myr). We focus on determining the domains of 'wandering' stochastic Earth system processes ('Court Jester'3) and stabilizing biotic interactions that induce diversity dependence of fluctuations in macroevolutionary rates ('Red Queen'4). Using state-of-the-art multiscale Haar and cross-Haar fluctuation analyses, we analysed the global genus-level Phanerozoic marine animal Paleobiology Database record of extinction rates (E), origination rates (O) and diversity (D) as well as sea water palaeotemperatures (T). Over the entire observed range from several million years to several hundred million years, we found that the fluctuations of T, E and O showed time-scaling behaviour. The megaclimate was characterized by positive scaling exponents-it is therefore apparently unstable. E and O are also scaling but with negative exponents-stable behaviour that is biotically mediated. For D, there were two regimes with a crossover at critical timescale [Formula: see text] ≈ 40 Myr. For shorter timescales, D exhibited nearly the same positive scaling as the megaclimate palaeotemperatures, whereas for longer timescales it tracks the scaling of macroevolutionary rates. At scales of at least [Formula: see text] there is onset of diversity dependence of E and O, probably enabled by mixing and synchronization (globalization) of the biota by geodispersal ('Geo-Red Queen').

Skilful decadal-scale prediction of fish habitat and distribution shifts

Many fish and marine organisms are responding to our planet’s changing climate by shifting their distribution. Such shifts can drive international conflicts and are highly problematic for the communities and businesses that depend on these living marine resources. Advances in climate prediction mean that in some regions the drivers of these shifts can be forecast up to a decade ahead, although forecasts of distribution shifts on this critical time-scale, while highly sought after by stakeholders, have yet to materialise. Here, we demonstrate the application of decadal-scale climate predictions to the habitat and distribution of marine fish species. We show statistically significant forecast skill of individual years that outperform baseline forecasts 3–10 years ahead; forecasts of multi-year averages perform even better, yielding correlation coefficients in excess of 0.90 in some cases. We also demonstrate that the habitat shifts underlying conflicts over Atlantic mackerel fishing rights could have been foreseen. Our results show that climate predictions can provide information of direct relevance to stakeholders on the decadal-scale. This tool will be critical in foreseeing, adapting to and coping with the challenges of a changing future climate, particularly in the most ocean-dependent nations and communities.

Quantum version of Prisoners’ Dilemma under interacting environment

Quantum game theory is a rapidly evolving subject that extends beyond physics. In this research work, a schematic picture of quantum game theory has been provided with the help of the famous game Prisoners’ Dilemma, where both of the prisoners possess an entangled qubit. Increasing the payoffs of the prisoners, quantum theory introduces a new Nash equilibrium. It has been considered that the shared qubits may interact with the environment, which is a bath of simple harmonic oscillators. This interaction introduces decoherence. Calculating the decoherence factor, we have shown that as time increases, the new Nash equilibrium disappears and accordingly the corresponding payoffs reduce. The decoherence factor has been analyzed for different time regions, and a characteristic time scale of decoherence has also been provided. A critical time scale, below which Alice and Bob can use the quantum strategy to achieve a higher payoff, has been described with its connection to the off-diagonal elements of the reduced density matrix of the prisoners. The critical time scale has also been discussed based on whether the decoherence occurred once or twice. A comparative discussion establishes that the process of decoherence is faster when it occurs twice. It needs to be mentioned here that the total time of decoherence is the same in both cases.

Sticky Rouse Time Features the Self-Adhesion of Supramolecular Polymer Networks

Supramolecular polymers are fascinating materials due to their strikingly self-healing capabilities empowered by reversible bonds. However, due to the lack of knowledge about the molecular structure evolution at the fractured interfaces, there is no existing theory to explain and predict the diverse healing times of different supramolecular materials observed in experiments. Here, we systematically study the self-adhesion of both unentangled and entangled supramolecular polymer networks through molecular simulations. We find that the recovery of macroscopic interfacial strength almost linearly depends on the microscopic molecular formations at fractured interfaces of supramolecular polymers, including reversible bonds and entanglements (entangled systems only). More importantly, we place the healing time into the context of intrinsic relaxation timescales of supramolecular polymer networks. It is found that the intrinsic sticky Rouse time features the self-adhesion process of all fractured supramolecular polymers, representing the full recovery of interfacial strength. At this critical timescale, two things happened to guarantee the full recovery of fractured systems: (i) polymer chains have diffused across the fractured interface with a displacement comparable to their sizes; (ii) the crossed stickers and polymer chains have updated their reversible bonds and entanglements (entangled systems only), respectively. The clear molecular description and suggested characteristic self-adhesion time will help the molecular design of supramolecular polymers.

Critical scaling of compression-driven jamming of athermal frictionless spheres in suspension.

We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate ε[over ̇], we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction ϕ and compression rate ε[over ̇], and that the bulk viscosity p/ε[over ̇] diverges upon jamming. A scaling analysis determines the critical exponents associated with the compression-driven jamming transition. Our results suggest that stress-isotropic, compression-driven jamming may be in the same universality class as stress-anisotropic, shear-driven jamming.

Hurst Exponents for Intra- and Intercycle Thermoacoustic Oscillations

The detrended fluctuation analysis, a technique for detecting long-range correlations in fractal time series, is used to characterize thermoacoustic oscillations of impending combustion instabilities. The slope of the linear regime of the structure function with respect to the time scale in a logarithmic plot, referred to as the Hurst exponent, takes a different value across a critical time scale corresponding to one pressure cycle. The slope for pressure oscillations over one pressure cycle, termed as the intercycle Hurst exponent, is a power-law scaling parameter for long-range oscillations; however, the slope for pressure oscillations within one pressure cycle, termed as the “intracycle Hurst exponent,” is no longer a power-law scaling parameter but resultant from the nonstationary, local average of highly nonlinear (as a function of time), seemingly sinusoidal, nearly periodic pressure oscillations. Both parametric studies and analyses of experimental data show that the intracycle Hurst exponent consistently increases with the signal-to-noise ratio and peaks at 1.6, thus having potentials for assessments of the safety margin to the onset of combustion instabilities. Given the same observation window, the measurement error (or uncertainty) of the intracycle Hurst exponent is significantly lower than that of the intercycle Hurst exponent.

Unraveling nucleation pathway in methane clathrate formation

Methane clathrates are widespread on the ocean floor of the Earth. A better understanding of methane clathrate formation has important implications for natural-gas exploitation, storage, and transportation. A key step toward understanding clathrate formation is hydrate nucleation, which has been suggested to involve multiple evolution pathways. Herein, a unique nucleation/growth pathway for methane clathrate formation has been identified by analyzing the trajectories of large-scale molecular dynamics (MD) simulations. In particular, ternary water-ring aggregations (TWRAs) have been identified as fundamental structures for characterizing the nucleation pathway. Based on this nucleation pathway, the critical nucleus size and nucleation timescale can be quantitatively determined. Specifically, a methane hydration layer compression/shedding process is observed to be the critical step in (and driving) the nucleation/growth pathway, which is manifested through overlapping/compression of the surrounding hydration layers of the methane molecules, followed by detachment (shedding) of the hydration layer. As such, an effective way to control methane hydrate nucleation is to alter the hydration layer compression/shedding process during the course of nucleation.

Self-Assembled Monolayers of Copper Sulfide Nanoparticles on Glass as Antibacterial Coatings.

We developed an easy and reproducible synthetic method to graft a monolayer of copper sulfide nanoparticles (CuS NP) on glass and exploited their particular antibacterial features. Samples were fully characterized showing a good stability, a neat photo-thermal effect when irradiated in the Near InfraRed (NIR) region (in the so called “biological window”), and the ability to release controlled quantities of copper in water. The desired antibacterial activity is thus based on two different mechanisms: (i) slow and sustained copper release from CuS NP-glass samples, (ii) local temperature increase caused by a photo-thermal effect under NIR laser irradiation of CuS NP–glass samples. This behavior allows promising in vivo applications to be foreseen, ensuring a “static” antibacterial protection tailored to fight bacterial adhesion in the critical timescale of possible infection and biofilm formation. This can be reinforced, when needed, by a photo-thermal action switchable on demand by an NIR light.

A turbulent-entropic instability and the fragmentation of star-forming clouds

ABSTRACT The kinetic energy of supersonic turbulence within interstellar clouds is subject to cooling by dissipation in shocks and subsequent line radiation. The clouds are therefore susceptible to a condensation process controlled by the specific entropy. In a form analogous to the thermodynamic entropy, the entropy for supersonic turbulence is proportional to the log of the product of the mean turbulent velocity and the size scale. We derive a dispersion relation for the growth of entropic instabilities in a spherical self-gravitating cloud and find that there is a critical maximum dissipation time-scale, about equal to the crossing time, that allows for fragmentation and subsequent star formation. However, the time-scale for the loss of turbulent energy may be shorter or longer, for example, with rapid thermal cooling or the injection of mechanical energy. Differences in the time-scale for energy loss in different star-forming regions may result in differences in the outcome, for example, in the initial mass function.

A general definition of formation time for starting jets and forced plumes at low Richardson number

As an important dimensionless parameter for the vortex formation process, the general form of the formation time defined by Dabiri (Annu. Rev. Fluid Mech., vol. 41, 2009, pp. 17–33) is refined so as to provide better normalization for various vortex generator configurations. Our proposed definition utilizes the total circulation over the entire flow domain rather than that of the forming vortex ring alone. It adopts an integral form by considering the instantaneous infinitesimal increment in the formation time so that the effect of temporally varying properties of the flow configuration can be accounted for properly. By including the effect of buoyancy, the specific form of the general formation time for the starting forced plumes with negative and positive buoyancy is derived. A theoretical prediction based on the Kelvin–Benjamin variational principle shows that the general formation time manifests the invariance of the critical time scale, i.e. the formation number, under the influence of a source–ambient density difference. It demonstrates that the general formation time, based on the circulation production over the entire flow field, could take into account the effect of various vorticity production mechanisms, such as from a flux term or in a baroclinic fluid, on the critical formation number. The proposed definition may, therefore, serve as a guideline for deriving the specific form of the formation time in other types of starting/pulsatile flows.

Selection of a Critical Time Scale of Real-Time Dispatching for Power Systems With High Proportion Renewable Power Sources

The power prediction error of uncertain renewable energy sources (URESs) affects the power balance of a power grid. In the power systems with high proportion renewable power sources (PSHPRPSs), automatic generation control (AGC) cannot accommodate the day-ahead power prediction error. The dispatching control system (DCS) of PSHPRPSs adds real-time dispatching links to modify the day-ahead dispatching plan so that the grid power error is within the range of AGC accommodation. This paper proposes a critical time scale (CTS) selection algorithm based on time aggregation characteristics for real-time dispatching of PSHPRPSs and calculates the annual CTS of real-time dispatching of power grids. The uncertainty function is used to describe the relationship between the prediction error of the URESs and the prediction lead time. The total uncertainty function is calculated based on the time aggregation characteristics and is used to select the annual CTS of real-time dispatching. The proposed algorithm quantitatively describes the relationship between the CTS and the operation proportion of URESs and also AGC accommodation capacity. The calculated annual CTS not only ensures the power balance of the power grid, but also avoids the daily change of the CTS. Using the data of URESs in the Irish power grid, the feasibility of the proposed method was verified. The research results of this paper are helpful to accommodate the day-ahead power prediction error of URESs and maintain the safe operation of power grid.