Space-time Scales Research Articles

On the Effects of Mixed and Deep Ocean Layers on Climate Change and Variability

The ocean, one of the five major components of the Earth’s climate system, plays a key role in climate-forming processes, affecting its change and variability. The ocean influences climate over a wide range of time–space scales. To explore the climate, its components, interactions between them and, in particular, the effect of the ocean on weather and climate, researchers commonly use extremely complex mathematical models of the climate system that describe the atmospheric and ocean general circulations. However, this class of climate models requires enormous human and computing resources to simulate the climate system itself and to analyze the output results. For simple climate models, such as energy balance and similar models, the computational cost is insignificant, which is why these models represent a test tool to mimic a complex climate system and obtaining preliminary estimates of the influence of various internal and external factors on climate, its change and variability. The global mean surface temperature (GMST) and its fluctuations in time serve as critical indicators of changes in the climate system state. We apply a simple two-box ocean model to explore the effect of mixed and deep ocean layers on climate-forming processes and especially on climate change and variability. The effect of mixed and deep ocean layers on GMST is parameterized via the layers’ effective heat capacities and heat exchange between layers. For the listed parameters, the sensitivity functions were derived numerically and analytically, allowing one to obtain an idea of how the mixed and deep ocean layers affect climate change and variability. To study climate change, a deterministic version of the model was used with radiative forcing parameterized by both stepwise and linear functions. In climate variability experiments, a stochastic version of the model was applied in which the radiative forcing is considered as a delta-correlated random process.

Dynamics on time scales of wave solutions for nonlinear neural networks

A time scale is an arbitrary non-empty closed subset of denoted by . In this work, the traveling wave solutions on time scales for a class of nonlinear delayed dynamical neural networks are investigated. The outcomes of this study are new and have been obtained by inequality technique, Ikehara's theorem, the weighted energy method, Taylor formula, comparison principle and the first integral mean value theorem. This is the first work focused for the wave solution in time space scales for a dynamical delayed neural networks model.

Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate

Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces1 and of interfaces in bacterial colonies2, and spin transport in quantum magnets3-6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space-time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar-Parisi-Zhang (KPZ) equation7. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence8-17. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space-time scaling laws18,19, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantumsystems.

Spatiotemporal Evaluation and Estimation of Precipitation of Multi-Source Precipitation Products in Arid Areas of Northwest China—A Case Study of Tianshan Mountains

In the arid areas of Northwest China, especially in the Tianshan Mountains, the scarcity of meteorological stations has brought some challenges in collecting accurate information to describe the spatial distribution of precipitation. In this study, the applicability of TRMM3B42, GPM IMERG, and MSWEP V2.2 in different regions of Tianshan Mountain is comprehensively evaluated by using ten statistical indicators, three classification indicators, and variation coefficients at different time–space scales, and the mechanism of accuracy difference of precipitation products is discussed. The results show that: (1) On the annual and monthly scales, the correlation between GPM and measured precipitation is the highest, and the ability of three precipitation products to capture precipitation in the wet season is stronger than that in the dry season; (2) On the daily scale, TRMM has the highest ability to estimate the frequency of light rain events, and MSWEP has the highest ability to monitor extreme precipitation events; (3) On the spatial scale, GPM has the highest fitting degree with the spatial distribution of precipitation in Tianshan Mountains, MSWEP is the closest to the precipitation differentiation pattern in Tianshan Mountains; (4) The three satellite products generally perform best in low and middle longitude regions and middle elevation regions. This study provides a reference for the selection of grid precipitation datasets for hydrometeorological simulation in northwest arid areas and also provides a basis for multi-source data assimilation and fusion.

Black strings thermodynamics in noncommutative spacetime

Black holes have been a subject of investigation over years not only because they have interesting physical properties, but also because they seem to be the appropriate tool for studying gravity in quantum scale. A lot of effort has been made to understand the aspects of spacetime on the quantum scale. Among several possibilities, the approach which includes noncommutativity of spacetime proves to be promising. In this paper, we use the Hamilton–Jacobi method to study the thermodynamic properties of cylindrical black holes (black strings) in noncommutative spacetime. The behavior of the black string is also investigated in the presence of back reaction as well as its influence on the system can be understood as an anomaly. This work aims to provide an understanding about black strings thermodynamics in noncommutative spacetime since this scale of spacetime is important for the comprehension of the relation between quantum mechanics and general relativity.

Multilamellar Liposomes as a Model for Biological Membranes: Saturation Recovery EPR Spin-Labeling Studies.

EPR spin labeling has been used extensively to study lipids in model membranes to understand their structures and dynamics in biological membranes. The lipid multilamellar liposomes, which are the most commonly used biological membrane model, were prepared using film deposition methods and investigated with the continuous wave EPR technique (T2-sensitive spin-labeling methods). These investigations provided knowledge about the orientation of lipids, their rotational and lateral diffusion, and their rate of flip-flop between bilayer leaflets, as well as profiles of membrane hydrophobicity, and are reviewed in many papers and book chapters. In the early 1980s, the saturation recovery EPR technique was introduced to membrane studies. Numerous T1-sensitive spin-label methods were developed to obtain detailed information about the three-dimensional dynamic membrane structure. T1-sensitive methods are advantageous over T2-sensitive methods because the T1 of spin labels (1–10 μs) is 10 to 1000 times longer than the T2, which allows for studies of membrane dynamics in a longer time–space scale. These investigations used multilamellar liposomes also prepared using the rapid solvent exchange method. Here, we review works in which saturation recovery EPR spin-labeling methods were applied to investigate the properties of multilamellar lipid liposomes, and we discuss their relationships to the properties of lipids in biological membranes.

Proposing spacetime scale for space tourism economics

This research proposes the spacetime scale to derive a space tourism economic model based on the General Relativity Theory. The space curvature is considered in the economic model analogized to a physic theory to expand the horizons of tourism economics. The deductive reasoning and analogy methods were adopted to propose the spacetime scale for space tourism economics, accommodating the conventional economic models of near-flat space commodities on the earth. Conclusions suggest conquering our perception acceptance from linear time to curvilinear spacetime for space tourism economics.

Kinetic investigations of nonlinear electrostatic excitations in quantum plasmas.

For plasmas in an extremely high-density state, like stellar cores or compressed fuel in inertial fusion facilities, their behavior turns out to be quite different when compared with those plasmas in interstellar space or magnetic confinement devices. To figureout those differences and uncover the kinetic physics in electrostatic excitations, a quantum kinetic code solving Wigner-Poisson equationshas been developed. Basic plasmon decay, Landau damping, and two-stream instability of extremely high-density plasmas are investigated by using our newly developed code. Numerical simulations show that in the linear region, the dispersion relations of intrinsic modes can be significantly affected by quantum effects, and such simulation results can be well described by the existing analytical theory. Especially in the nonlinear region, since the space-time scale of collective modes of plasmas is comparable to the electron de Broglie wavelength, their couplings produce some new physics: the energy exchange between the electron and the collective mode results in an abnormal oscillation that does not exist in classical plasmas.

Uncertain differential equation based accelerated degradation modeling

Due to economic and technical reasons, in accelerated degradation testing (ADT) there are usually limited ADT data, which embody lots of epistemic uncertainties that cannot be depicted well by probability theory. Noting these facts, several uncertain processes based accelerated degradation models (UADMs) are proposed under the framework of uncertainty theory. However, these UADMs described uncertainties from a macro perspective which ignored the characteristic of performance degradation in small time scales and failed to describe the essence of nonlinear degradation. What is more, to estimate unknown parameters, these models used empirical distribution functions, which may have a great impact on the estimation results with limited samples. Motivated by these problems, based on uncertainty theory this paper builds up an uncertain differential equation based accelerated degradation model (UDEADM), which considers the dynamic cumulative change process of performance in small space–time scale, and explains the essence of nonlinear for uncertainties in degradation trend. Unknown parameters are estimated using uncertain generalized moment estimations. Furthermore, reliability and lifetime are analyzed under the normal operating condition based on belief reliability theory. A simulation study and a real data analysis are conducted to illustrate the effectiveness and advantages of the proposed methodology in details.

Model-based characterization of permeability damage control through inhibitor injection under parametric uncertainty

Damage in subsurface formations caused by mineral precipitation decreases the porosity and permeability, eventually reducing the production rate of wells in plants producing oil, gas or geothermal fluids. A possible solution to this problem consists in stopping the production followed by the injection of inhibiting species that slow down the precipitation process. In this work we model inhibitor injection and quantify the impact of a set of model parameters on the outputs of the system. The parameters investigated concern three key factors contributing to the success of the treatment: i) the inhibitor affinity, described by an adsorption Langmuir isotherm, ii) the concentration and time related to the injection and iii) the efficiency of the inhibitor in preventing mineral precipitation. Our simulations are set in a stochastic framework where these inputs are characterized in probabilistic terms. Forward simulations rely on a purpose-built code based on finite differences approximation of the reactive transport setup in radial coordinates. We explore the sensitivity diverse outputs, encompassing the well bottom pressure and space-time scales characterizing the transport of the inhibitor. We find that practically relevant output variables, such as inhibitor lifetime and well bottom pressure, display a diverse response to input uncertainties and display poor mutual dependence. Our results quantify the probability of treatment failure for diverse scenarios of inhibitor-rock affinity. We find that treatment optimization based on single outputs may lead to high failure probability when evaluated in a multi-objective framework. For instance, employing an inhibitor displaying an appropriate lifetime may fail in satisfying criteria set in terms of well-bottom pressure history or injected inhibitor mass.

Superballistic and superdiffusive scaling limits of stochastic harmonic chains with long-range interactions

We consider one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials which have polynomial decay rate |x|−θ , x → ∞, θ > 1 where is the interaction range. The dynamics conserve total momentum, total length and total energy. We prove that the systems evolve macroscopically on superballistic space-time scale when 1 < θ < 3, when θ = 3, and hyperbolic space-time scale (yɛ −1, tɛ −1) when θ > 3. Combining our results and the results in (Suda 2021 Ann. Inst. Henri Poincare B 57 2268–2314), we show the existence of two different space-time scales on which the systems evolve. In addition, we prove the fluctuations of the normal modes of the superballistic wave equation, which are analogues of the Riemann invariants and capture fluctuations along the characteristics. For the normal modes, the space-time scale is superdiffusive when 2 < θ ⩽ 4 and diffusive when θ > 4.

Microclimate, yield, and income of a jujube–cotton agroforestry system in Xinjiang, China

The purpose of this study was to establish a jujube (Zizyphus jujuba Mill.)–cotton (Gossypium hirsutum Linn.) intercropping agroforestry system in the south and north of Xinjiang Uygur Autonomous Region and to determine the impact of intercropping systems on microclimate, yield, and income compared with sole-cropping planting. Therefore, a two-year field experiment was carried out in the Hotan and Shihezi areas to measure photosynthetically active radiation (PAR) on the space-time scale, air temperature on the time scale, wind speed and windproof efficiency on the time scale, and yield and income. Through correlation analysis, the relationship between intercropping microclimate and intercropping yield were revealed. Compared with corresponding sole-cropping cotton, the PAR of intercropping in Hotan and Shihezi was 13.04% and 12.75% lower, respectively, and the closer to the tree alley, the smaller it was. Intercropping changed the daily dynamics of air temperature, especially at high temperatures, under which the decrease range was significant. Intercropping has buffer effect and latent heat release on air temperature and the maximum temperature in Hotan and Shihezi intercropping was 13.57% and 6.49 lower than that in sole-cropping, respectively. Intercropping reduced the wind speed, the greater the wind speed in a certain range, the stronger the windproof efficiency. The maximum windproof efficiency of Hotan intercropping was 50.92%, and that of Shihezi was 48.56%. The intercropping system had advantages in land equivalent ratio (LER), yield, and income. The income of intercropping was 11622.38–12528.55 USD·hm−2, 55.41–61.91% higher than that of sole-cropping cotton and 19.19–20.37% higher than that of sole-cropping jujube. The results showed that the development of jujube-cotton intercropping could protect the growing environment of cotton and increase farmers' economic income by improving the field microclimate.

In.To. COVID-19 socio-epidemiological co-causality

Social media can forecast disease dynamics, but infoveillance remains focused on infection spread, with little consideration of media content reliability and its relationship to behavior-driven epidemiological outcomes. Sentiment-encoded social media indicators have been poorly developed for expressed text to forecast healthcare pressure and infer population risk-perception patterns. Here we introduce Infodemic Tomography (InTo) as the first web-based interactive infoveillance cybertechnology that forecasts and visualizes spatio-temporal sentiments and healthcare pressure as a function of social media positivity (i.e., Twitter here), considering both epidemic information and potential misinformation. Information spread is measured on volume and retweets, and the Value of Misinformation (VoMi) is introduced as the impact on forecast accuracy where misinformation has the highest dissimilarity in information dynamics. We validated InTo for COVID-19 in New Delhi and Mumbai by inferring distinct socio-epidemiological risk-perception patterns. We forecast weekly hospitalization and cases using ARIMA models and interpolate spatial hospitalization using geostatistical kriging on inferred risk perception curves between tweet positivity and epidemiological outcomes. Geospatial tweet positivity tracks accurately sim 60% of hospitalizations and forecasts hospitalization risk hotspots along risk aversion gradients. VoMi is higher for risk-prone areas and time periods, where misinformation has the highest non-linear predictability, with high incidence and positivity manifesting popularity-seeking social dynamics. Hospitalization gradients, VoMi, effective healthcare pressure and spatial model-data gaps can be used to predict hospitalization fluxes, misinformation, healthcare capacity gaps and surveillance uncertainty. Thus, InTo is a participatory instrument to better prepare and respond to public health crises by extracting and combining salient epidemiological and social surveillance at any desired space-time scale.

Hirota-Miwa equations on a time space scale

We derive a general time scale version of the Hirota–Miwa equation as a compatibility condition arising from a new version of a three-dimensional Lax system, construct its 3-soliton solutions, and consider various examples. We prove the invariance of the compatibility condition of the two-dimensional Lax system under a gauge transformation. The 3-soliton solution obtained here may be used in modeling in view of its variable graininess and a large number of free parameters.

AERA5-Asia: A Long-Term Asian Precipitation Dataset (0.1°, 1-hourly, 1951–2015, Asia) Anchoring the ERA5-Land under the Total Volume Control by APHRODITE

Abstract Accurate long-term precipitation information is critical for understanding the mechanisms behind how precipitation couples with Earth’s water fluxes, energy balances, and biogeochemical cycles across space–time scales under the changing climate. This study proposes a novel approach [daily total volume controlled merging and disaggregation algorithm (DTVCMDA)] for generating a new long-term precipitation dataset, AERA5-Asia (0.1°, 1-hourly, 1951–2015, Asia; “AERA5” is a combination of the “A” from APHRODITE and the “ERA5” from ERA5-Land), by comprehensively considering the characteristics of the high spatiotemporal resolutions and continuity of the ERA5-Land dataset and the high quality of the APHRODITE dataset. The main conclusions include, but are not limited to, the following: 1) AERA5-Asia provides time series of precipitation of sufficient resolutions, length, consistency, continuity, and quality over Asia. 2) AERA5-Asia substantially outperforms ERA5-Land and IMERG-Final in terms of both magnitudes and occurrences of precipitation events in Mainland China, especially the systematic biases. For instance, the bias of ERA5-Land, IMERG-Final, and AERA5-Asia against ground gauge-based observations in Mainland China are ∼20%, ∼11%, and ∼5%, respectively. 3) AERA5-Asia performs notably better than ERA5-Land and IMERG-Final against ground gauge-based observations in regional extreme rainfall systems (e.g., two typhoon events, Trami and Usagi). 4) AERA5-Asia should prove to be a useful precipitation dataset for addressing various key climatological and hydrological research questions that require precipitation data with longer spans and finer resolutions (0.1°, 1-hourly).

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.

Innovation for sustainable mining: Integrated planning of underground coal mining and mine reclamation

Coal supplies essential materials for social development. In many cases, however, the separation planning of underground coal mining (UCM) and mine reclamation (MR) and “mining first, reclamation later” lead to the accumulation of land degradation. Thus, the integrated planning of UCM and MR needs to be studied urgently. In this study, concurrent mining and reclamation (CMR) technologies were adopted to divide UCM planning into four key steps from the space-time scale: i) development roadway (macro); ii) preparation roadway (moderate); iii) panel roadway (meso) and iv) working face (micro), and the impacts of mining steps on MR were discussed. In addition, the requirements of four-key links of MR for UCM were discussed: i) reclamation elevation (RE); ii) digging depth (DD); iii) reclamation layout (RL), and iv) reclamation timing (RT). UCM and MR were optimized on macro, moderate, meso, and micro scales. Results show that: (1) RE and DD are moderate and meso scales; (2) RL is macro and moderate scales; (3) RT is meso and micro scales. Integrated planning of UCM and MR can reduce mining damage from the source, which can timely reclaim degraded land, and alleviate the contradictions of the government, colliery and farmer. We hope CMR will be valued to jointly improve application scenarios and guide sustainable mining.

Rogue waves in nonlinear optics

Understanding the phenomenon of rogue wave formation, often called extreme waves, in diverse branches of nonlinear science has become one of the most attractive domains. Given the great richness of the new results and the increasing number of disciplines involved, we are focusing here on two pioneering fields: hydrodynamics and nonlinear optics. This tutorial aims to provide basic background and the recent developments on the formation of rogue waves in various systems in nonlinear optics, including laser physics and fiber optics. For this purpose we first discuss their formation in conservative systems, because most of the theoretical and analytical results have been realized in this context. By using a multiple space–time scale analysis, we review the derivation of the nonlinear Schrödinger equation from Maxwell’s equations supplemented by constitutive equations for Kerr materials. This fundamental equation describes the evolution of a slowly varying envelope of dispersive waves. This approximation has been widely used in the majority of systems, including plasma physics, fluid mechanics, and nonlinear fiber optics. The basic property of this generic model that governs the dynamics of many conservative systems is its integrability. In particular, we concentrate on a nonlinear regime where classical prototypes of rogue wave solutions, such as Akhmediev breathers, Peregrine, and Ma solitons are discussed as well as their experimental evidence in optics and hydrodynamics. The second part focuses on the generation of rogue waves in one- and two-dimensional dissipative optical systems. Specifically, we consider Kerr-based resonators for which we present a detailed derivation of the Lugiato–Lefever equation, assuming that the resonator length is shorter than the space scales of diffraction (or the time scale of the dispersion) and the nonlinearity. In addition, the system possesses a large Fresnel number, i.e., a large aspect ratio so that the resonator boundary conditions do not alter the central part of the beam. Dissipative structures such as solitons and modulational instability and their relation to frequency comb generation are discussed. The formation of rogue waves and the control employing time-delayed feedback are presented for both Kerr and semiconductor-based devices. The last part presents future perspectives on rogue waves to three-dimensional dispersive and diffractive nonlinear resonators.

On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs

This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time stepping for PDEs involving multiple space-time scales. The semi-Lagrangian (SL) approach fully couples the space and time discretization, thus making the use of RK strategies particularly difficult to be combined with. First, a simple scalar advection-diffusion equation is considered as a prototype PDE for the development of a high order formulation of the semi-Lagrangian IMEX algorithms. The advection part of the PDE is discretized explicitly at the aid of a SL technique, while an implicit discretization is employed for the diffusion terms. In this way, an unconditionally stable numerical scheme is obtained, that does not suffer any CFL-type stability restriction on the maximum admissible time step. Second, the SL-IMEX approach is extended to deal with hyperbolic systems with multiple scales, including balance laws, that involve shock waves and other discontinuities. A conservative scheme is then crucial to properly capture the wave propagation speed and thus to locate the discontinuity and the plateau exhibited by the solution. A novel SL technique is proposed, which is based on the integration of the governing equations over the space-time control volume which arises from the motion of each grid point. High order of accuracy is ensured by the usage of IMEX RK schemes combined with a Cauchy–Kowalevskaya procedure that provides a predictor solution within each space-time element. The one-dimensional shallow water equations (SWE) are chosen to validate the new conservative SL-IMEX schemes, where convection and pressure fluxes are treated explicitly and implicitly, respectively. The asymptotic-preserving (AP) property of the novel schemes is also studied considering a relaxation PDE system for the SWE. A large suite of convergence studies for both the non-conservative and the conservative version of the novel class of methods demonstrates that the formal order of accuracy is achieved and numerical evidences about the conservation property are shown. The AP property for the corresponding relaxation system is also investigated.

Scale-dependence of observational and modelling uncertainties in forensic flash flood analysis

The mismatch between the space–time scales of flash flood occurrence and those of the typical hydro-meteorological monitoring networks has stimulated the development of forensic flash flood analysis, which involves post-flood indirect peak discharge estimation in ungauged channels and flood response modelling driven by weather-radar rainfall estimates. However, both approaches are potentially affected by significant uncertainties. Assessment of scale dependence of such uncertainties is important to identify how uncertainty affecting forensic flash flood analysis increases with decreasing basin size. In this work, we apply the forensic methodology to the flash flood of November 18, 2013 in Sardinia (Italy). We introduce the ‘flash flood forensic consistency index’ as a tool to compare the probability distribution of peak discharge uncertainties from observational and model estimates, and to determine the scale effects of the forensic analysis concept. Uncertainties in field-based peak flow estimates are evaluated through a first-order error analysis of the Taylor-series approximation of the slope-conveyance method, whereas uncertainties in flash flood modelling are based on the Generalized Likelihood Uncertainty Estimation methodology using a distributed hydrologic model. Results show no significant relationship between observational and modelling uncertainties, considered independently, and basin area and channel bed slope. Conversely, when considering the interaction between the two uncertainty distributions, a relationship arises between their degree of overlap and basin size. In particular, with decreasing basin area or increasing channel bed slope, the absolute relative bias between the estimated peak flow values increases more than their relative uncertainties, decreasing the consistency index. This calls for more robust approaches for the analysis of flash flood response in small-sized rugged-relief mountain basins, which are of high interest for flood risk management.