Theoretical Scaling Research Articles

Large internal variability dominates over global warming signal in observed lower stratospheric QBO amplitude

AbstractGlobal warming projections of dynamics are less robust than projections of thermodynamics. However, robust aspects of the thermodynamics can be used to constrain some dynamical aspects. This paper argues that tropospheric expansion under global warming (a thermodynamical process) explains changes in the amplitude of the Quasi-Biennial Oscillation (QBO) in the lower and middle stratosphere (a dynamical process). A theoretical scaling for tropospheric expansion of approximately 6 hPa K−1 is derived, which agrees well with global climate model (GCM) experiments. Using this theoretical scaling, the response of QBO amplitude to global warming is predicted by shifting the climatological QBO amplitude profile upwards by 6 hPa per Kelvin of global warming. In global warming simulations, QBO amplitude in the lower- to mid-stratosphere shifts upwards as predicted by tropospheric expansion. Applied to observations, the tropospheric expansion framework suggests a historical weakening of QBO amplitude at 70 hPa of 3% decade−1 from 1953-2020. This expected weakening trend is half of the 6% decade−1 from 1953-2012 detected and attributed to global warming in a recent study. The previously reported trend was reinforced by record low QBO amplitudes during the mid-2000s, from which the QBO has since recovered. Given the modest weakening expected on physical grounds, past decadal modulations of QBO amplitude are reinterpreted as a hitherto unrecognized source of internal variability. This large internal variability dominates over the global warming signal, such that despite 65 years of observations, there is not yet a statistically significant weakening trend.

Rotating Horizontal Convection

Global differences of temperature and buoyancy flux at the ocean surface are responsible for small-scale convection at high latitudes, global overturning, and the top-to-bottom density difference in the oceans. With planetary rotation the convection also contributes to the large-scale horizontal, geostrophic circulation, and it crucially involves a 3D linkage between the geostrophic circulation and vertical overturning. The governing dynamics of such a surface-forced convective flow are fundamentally different from Rayleigh–Bénard convection, and the role of buoyancy forcing in the oceans is poorly understood. Geostrophic balance adds to the constraints on transport in horizontal convection, as illustrated by experiments, theoretical scaling, and turbulence-resolving simulations for closed (mid-latitude) basins and an annulus or reentrant zonal (circumpolar) channel. In these geometries, buoyancy drives either horizontal mid-latitude gyre recirculations or a strong Antarctic Circumpolar Current, respectively, in addition to overturning. At large Rayleigh numbers the release of available potential energy by convection leads to turbulent mixing with a mixing efficiency approaching unity. Turbulence-resolving models are also revealing the relative roles of wind stress and buoyancy when there is mixed forcing, and in future work they need to include the effects of turbulent mixing due to energy input from tides.

Air film contact modes of drop impact on lubricated surfaces under reduced pressures

Air film evolution underneath a drop impacting on a surface can cause the drop to either bounce off or make contact. Water drops impacting on a dry surface exhibited a transition from bouncing to the kink and film modes of contact. Additionally, a dimple mode of contact was observed on a lubricated, smooth surface. Here, we report experimental findings of drops impacting on a lubricated, smooth surface under both reduced and atmospheric pressures using liquids of two different viscosities. The kink mode observed on a dry surface only occurs at low impact velocities under reduced pressures but is completely absent at the atmospheric pressure on a lubricated surface. The horizontal extent of the dimple agrees well with the incompressible and compressible scaling within the inertial regime. The experimentally measured horizontal extent of the kink shows good agreement with the existing theoretical scaling. Slight deviations in the contact mode transition were observed between experiments and previously reported simulations, presumably due to the velocity slip at the air–lubricant interface in the present study.

Dynamo constraints on the long-term evolution of Earth’s magnetic field strength

SUMMARY Elucidating the processes in the liquid core that have produced observed palaeointensity changes over the last 3.5 Gyr is crucial for understanding the dynamics and long-term evolution of Earth’s deep interior. We combine numerical geodynamo simulations with theoretical scaling laws to investigate the variation of Earth’s magnetic field strength over geological time. Our approach follows the study of Aubert et al., adapted to include recent advances in numerical simulations, mineral physics and palaeomagnetism. We first compare the field strength within the dynamo region and on the core–mantle boundary (CMB) between a suite of 314 dynamo simulations and two power-based theoretical scaling laws. The scaling laws are both based on a Quasi-Geostropic (QG) force balance at leading order and a Magnetic, Archimedian, and Coriolis (MAC) balance at first order and differ in treating the characteristic length scale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the data set is filtered to retain only simulations with magnetic to kinetic energy ratios greater than at least two we find that the internal field together with the root-mean-square and dipole CMB fields exhibit power-law behaviour that is compatible with both scalings within uncertainties arising from different heating modes and boundary conditions. However, while the extrapolated intensity based on the QG-MAC-free scaling matches Earth’s modern CMB field, the QG-MAC-fixed prediction shoots too high and also significantly overestimates palaeointensities over the last 3.5 Gyr. We combine the QG-MAC-free scaling with outputs from 275 realizations of core–mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyr. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation (ICN) within observational uncertainties, but PINT does not contain the predicted strong increase and subsequent high TDMs during the early stages of inner core growth. The best-fitting models are obtained for a present-day CMB heat flow of 11–16 TW, increasing to 17–22 TW at 4 Ga, and predict a minimum TDM at ICN.

Effects of a velocity shear on double current sheet systems: Explosive reconnection and particle acceleration

The effect of a parallel velocity shear on the explosive phase of a double current sheet system is investigated within the 2D resistive magnetohydrodynamic framework. We further explore the effect of this shear on acceleration of test particles. The general evolution pattern of the double current sheets is similar for all sub-Alfvénic shears with respect to the initial transient phase, the onset of the plasmoid instability, and the final relaxation phase. We find that the theoretical scaling of the reconnection rate with shear holds if the rate is measured when the islands have a similar size. The larger island widths for lower shears greatly enhance the reconnection rate during the explosive phase. We have further examined the modification of the energy spectrum of the accelerated particles in the presence of a shear. Our results also show that the flow only modifies the high energy tail of the particle spectrum and has negligible effect on the power-law index. Individual particle trajectories help to explore the various mechanisms associated with the acceleration. Based on the location of the particles, the acceleration mechanisms are found to vary. We highlight the importance of the convective electric field in the inflow as well as the outflow region inside large magnetic islands in the acceleration of particles. The interaction and reflection of the particles with the reconnection exhausts inside the large scale primary magnetic islands is found to have a significant effect on the energization of the particles.

Polyelectrolyte Complex Coacervation across a Broad Range of Charge Densities

Polyelectrolyte complex coacervates of homologous (co)polyelectrolytes with a near-ideally random distribution of a charged and neutral ethylene oxide comonomer were synthesized. The unique platform provided by these building blocks enabled an investigation of the phase behavior across charge fractions 0.10 ≤ f ≤ 1.0. Experimental phase diagrams for f = 0.30–1.0 were obtained from thermogravimetric analysis of complex and supernatant phases and contrasted with molecular dynamics simulations and theoretical scaling laws. At intermediate to high f, a dependence of polymer weight fraction in the salt-free coacervate phase (wP,c) of wP,c ∼ f0.37±0.01 was extracted; this trend was in good agreement with accompanying simulation predictions. Below f = 0.50, wP,c was found to decrease more dramatically, qualitatively in line with theory and simulations predicting an exponent of 2/3 at f ≤ 0.25. Preferential salt partitioning to either coacervate or supernatant was found to be dictated by the chemistry of the constituent (co)polyelectrolytes.

Parallel tridiagonal matrix inversion with a hybrid multigrid-Thomas algorithm method

Tridiagonal matrix inversion is an important operation with many applications. It arises frequently in solving discretized one-dimensional elliptic partial differential equations, and forms the basis for many algorithms for block tridiagonal matrix inversion for discretized PDEs in higher-dimensions. In such systems, this operation is often the scaling bottleneck in parallel computation. In this paper, we derive a hybrid multigrid-Thomas algorithm designed to efficiently invert tridiagonal matrix equations in a highly-scalable fashion in the context of time evolving partial differential equation systems. We decompose the domain between processors, using multigrid to solve on a grid consisting of the boundary points of each processor’s local domain. We then reconstruct the solution on each processor using a direct solve with the Thomas algorithm. This algorithm has the same theoretical optimal scaling as cyclic reduction and recursive doubling. We use our algorithm to solve Poisson’s equation as part of the spatial discretization of a time-evolving PDE system. Our algorithm is faster than cyclic reduction per inversion and retains good scaling efficiency to twice as many cores.

Parametric dependencies of locked mode thresholds in KSTAR L-mode plasmas

Resonant error fields with toroidal harmonics n = 1 and n = 2 in otherwise axisymmetric tokamak plasmas can drive disruptive locked modes when their strength exceeds a threshold value. This paper presents the sensitivity of error field threshold in global parameters such as line-averaged density and toroidal magnetic field as well as toroidal harmonics dependence in KSTAR L-mode plasmas. The error field threshold for mode-locking increases along with density up to a roll-over density, which coincides well with the linear ohmic confinement (LOC) to saturated ohmic confinement (SOC) density for the studied KSTAR plasmas. This non-monotonic density correlation of the error field threshold in LOC–SOC can be explained by a modification of existing theoretical scaling in SOC, while plasma rotation can also play an important role in setting the resonant error field threshold.

Investigation of theoretical scaling laws using large eddy simulations for airborne spreading of viral contagion from sneezing and coughing.

Using a set of large eddy point-particle simulations, we explore the fluid dynamics of an ejected puff resulting from a cough/sneeze. The ejection contains over 61 000 potentially virus-laden droplets at an injection Reynolds number of about 46 000, comparable to an actual cough/sneeze. We observe that global puff properties, such as centroid, puff volume, momentum, and buoyancy vary little across realizations. Other properties, such as maximum extent, shape, and edge velocity of the puff, may exhibit substantial variation. In many realizations, a portion of the puff splits off and advances along a random direction, while keeping airborne droplet nuclei afloat. This peeled-off portion provides a mechanism for virus-laden droplets to travel over large distances in a short amount of time. We also observe that the vast majority of droplets remain suspended within the puff after all liquid has evaporated. The main objectives of the study are to (i) evaluate assumptions of Balachandar's et al. theory [Int. J. Multiphase Flow 132, 103439 (2020)], which include buoyancy effects, shape of the puff, and droplet evaporation rate, (ii) obtain values of closure parameters, which include location and time of the virtual origin, and puff entrainment and drag coefficients, and (iii) evaluate the accuracy of the theory in predicting the shape, size, and location of the puff, as well as droplet number density long after ejection. The theory adequately predicts global puff properties including size, velocity, and distance traveled, the largest size of droplets that exit the puff due to settling, and the droplet size distribution within the puff long after ejection.

Theory-based scaling laws of near and far scrape-off layer widths in single-null L-mode discharges

Theory-based scaling laws of the near and far scrape-off layer (SOL) widths are analytically derived for L-mode diverted tokamak discharges by using a two-fluid model. The near SOL pressure and density decay lengths are obtained by leveraging a balance among the power source, perpendicular turbulent transport across the separatrix, and parallel losses at the vessel wall, while the far SOL pressure and density decay lengths are derived by using a model of intermittent transport mediated by filaments. The analytical estimates of the pressure decay length in the near SOL is then compared to the results of three-dimensional, flux-driven, global, two-fluid turbulence simulations of L-mode diverted tokamak plasmas, and validated against experimental measurements taken from an experimental multi-machine database of divertor heat flux profiles, showing in both cases a very good agreement. Analogously, the theoretical scaling law for the pressure decay length in the far SOL is compared to simulation results and to experimental measurements in TCV L-mode discharges, pointing out the need of a large multi-machine database for the far SOL decay lengths.

Aerobic and anaerobic metabolic scaling in the burrowing freshwater crayfish Parastacus pugnax.

Metabolic scaling is a well-known biological pattern. Theoretical scaling exponents near 0.67 and 0.75 are the most widely accepted for aerobic metabolism, but little is known about the scaling of anaerobic metabolism. Furthermore, metabolic scaling has been mainly evaluated in organisms primarily relying on aerobic pathways. Here we evaluate both aerobic and anaerobic metabolic scaling in Parastacus pugnax, a burrowing freshwater crayfish endemic to Chile, which inhabits waters with low pO2 (~ 1mg O2 L-1, measured in this study). We determined the metabolic rate, total oxidative capacity (Electron Transport System: ETS), critical oxygen tension (Pcrit) and muscular Lactate dehydrogenase (LHD) and Malate dehydrogenase (MDH) enzymatic activities (proxies of anaerobic metabolism) over a wide range of P. pugnax sizes (0.24-42.93g wet mass). Aerobic metabolism scaled with crayfish size with an exponent of 0.78, remarkably similar to the 0.73 which scaled the ETS, the enzymatic complex behind respiration. Critical partial pressure of oxygen (Pcrit) was calculated as 15.6 ± 2.9mmHg, showing that aerobic metabolism was efficiently maintained until ~ 10% air saturation. Below this threshold, P. pugnax switched to anaerobic metabolism, evidenced by a reduction in aerobic metabolism and ETS activity under chronic low oxygen conditions. None of the activities of MDH, LDH, their ratio (MDH/LDH), nor Pcrit scaled with crayfish size, indicating that these animals are equally adapted to hypoxic environments throughout their whole ontogeny. Given the particularities of its habitat, the information presented here is valuable for a proper management and successful conservation.

Influence of density change during melting inside a cavity: Theoretical scaling laws and numerical analysis

An exact prediction of melting processes is important for the design of latent heat thermal energy storages. However, in phase change models based on continuum theory, the effect of density change during melting is often not considered, although there is no clear estimate of the error caused by this assumption. To overcome this problem, we use scaling analysis to predict the difference between two macroscopic models that handle the density change during melting differently. As a test case, we choose the melting in a two-dimensional cavity heated from one side. Numerical simulations are used to confirm the scaling analysis. Hence, two different models are built and implemented into OpenFoam. In the first model, the density is constant and equal in both phases and the natural convection is taken into account by the Boussinesq approximation. In the second model, the density is different for both phases and varies with the temperature in the liquid phase. The scaling analysis reveals that for small Stefan numbers, the theoretical maximum deviation in the average phase front position at the same time between these two models is solely controlled by the liquid/solid density ratio. Furthermore, this maximum deviation is different for the different regimes of the melting process. The results of the numerical simulations confirm these results and show that the maximum deviation occurs at the end of the convection dominated regime. Our analysis further reveals that while the results strongly differ in time (≈11% for Octadecane), the flow field and the shape of the phase front is nearly the same if the time is shifted or the latent heat is scaled accordingly. Taking into account the uncertainty prevailing in the literature regarding the latent heat of fusion and other material properties of PCM, this may explain why many researchers found excellent agreement between experiments and their simulations despite neglecting the density change.

Multithreaded two-pass connected components labelling and particle analysis in ImageJ.

Sequential region labelling, also known as connected components labelling, is a standard image segmentation problem that joins contiguous foreground pixels into blobs. Despite its long development history and widespread use across diverse domains such as bone biology, materials science and geology, connected components labelling can still form a bottleneck in image processing pipelines. Here, I describe a multithreaded implementation of classical two-pass sequential region labelling and introduce an efficient collision resolution step, ‘bucket fountain’. Code was validated on test images and against commercial software (Avizo). It was performance tested on images from 2 MB (161 particles) to 6.5 GB (437 508 particles) to determine whether theoretical linear scaling (O(n)) had been achieved, and on 1–40 CPU threads to measure speed improvements due to multithreading. The new implementation achieves linear scaling (b = 0.905–1.052, time ∝ pixelsb; R2 = 0.985–0.996), which improves with increasing thread number up to 8–16 threads, suggesting that it is memory bandwidth limited. This new implementation of sequential region labelling reduces the time required from hours to a few tens of seconds for images of several GB, and is limited only by hardware scale. It is available open source and free of charge in BoneJ.

Classical hydraulic ram pump performance in comparison with modern hydro-turbine pumps for low drive heads

We present a unique comparison of two types of renewable hydro pumping devices, namely the ram and turbine pump having different working principles. This comparison is based on experiments with these pumping devices at a field station in a village in central-east India. Our work identifies the major gaps in the study of large ram pumps, covering the hydraulic scaling conformance to creation of a unified platform for the investigation of such pumping devices with respect to operating parameters like head, flow, efficiency and, most importantly, size. The field tests of ram revealed that its non-dimensional performance parameters fit perfectly on the theoretical scaling curves. The investigations further showed that while rams had more efficiency (53–62%), they could not handle more than 40–50 l/s of discharge. In comparison, the turbine pumps, tested in laboratory conditions, were more compact for flows beyond 100 l/s, but they settled for overall efficiencies between 49% and 55%. The study recommends a limiting design flow line for rams to be 50 l/s because of the size-factor. It further finds that for absolute flows between 50 and 100 l/s within the low-head range of 3–5 meters, the design of geometrical shapes for turbine pumps could be a challenge for optimized efficiencies. The head-discharge-diameter (H-Q-D) chart developed here is a useful way of interpreting the technology with respect to boundary conditions and it creates a roadmap for future inventions in such renewable hydro-pumping devices. The paper makes a case for axial flow pumps as turbines. It concludes with a call for the propagation of research on such nature-friendly pumping technologies, where most (90–95%) of the water is returned to the stream, paving the way for a new era of sustainability.

Power allocation and scaling law analysis for secured and energy efficient URLLC IoT networks

This paper investigates the security and energy efficiency of ultra-high reliability and low latency (URLLC) internet of things (IoT) networks. We first formulate an optimization problem to maximize the secured energy efficiency of the network based on a new capacity formula. We then seek an approximation to the original intractable cost function, and apply convex optimization methods to solve the approximated problem. Moreover, the statistical throughput of secured IoT networks is theoretically analyzed for the varying number of users by presenting a scaling law. The scaling factor is derived in analytical expression and proved to be of a concise form in the high transmit power regime. Numerical simulations are undertaken to demonstrate the near-optimal power allocation performance and the derived theoretical scaling law of the secured throughput of the whole URLLC IoT network.

Scaling analysis and evaluation for the design of integral test facility of HPR1000 containment (PANGU)

This paper summarized the key aspects of the scaling analysis method adopted in the design of the integral test facility for the containment of HPR1000 -an advanced pressurized water reactor featuring both active and passive safety systems in reactor coolant (RCS) and containment. Based on the existing scaling analysis methods for complicated thermal-hydraulic systems, i.e. Hierarchical Two-Tiered Scaling (H2TS) method and Three-Level Scaling method, the present study developed a specific scaling analysis method which did not only provide theoretical derivation of scaling parameters and ratios, but also implemented the scaling criteria in the engineering design of the HPR1000 containment integral test facility (PANGU), with an evaluation of distortions in the final design. This approach allowed the theoretical scaling parameters can be reasonably adjusted to meet the boundary limits/conditions of the facility design. The scaling analysis and evaluation of so-designed test facility ensured the experimental results are applicable to verify the safety functions of the HPR1000 containment coping with representative accident scenarios.

Scaling Performance Analysis and Optimization Based on the Node Spatial Distribution in Mobile Content‐Centric Networks

Content‐centric networks (CCNs) have become a promising technology for relieving the increasing wireless traffic demands. In this paper, we explore the scaling performance of mobile content‐centric networks based on the nonuniform spatial distribution of nodes, where each node moves around its own home point and requests the desired content according to a Zipf distribution. We assume each mobile node is equipped with a finite local cache, which is applied to cache contents following a static cache allocation scheme. According to the nonuniform spatial distribution of cache‐enabled nodes, we introduce two kinds of clustered models, i.e., the clustered grid model and the clustered random model. In each clustered model, we analyze throughput and delay performance when the number of nodes goes infinity by means of the proposed cell‐partition scheduling scheme and the distributed multihop routing scheme. We show that the node mobility degree and the clustering behavior play the fundamental roles in the aforementioned asymptotic performance. Finally, we study the optimal cache allocation problem in the two kinds of clustered models. Our findings provide a guidance for developing the optimal caching scheme. We further perform the numerical simulations to validate the theoretical scaling laws.

Blob interactions in 2D scrape-off layer simulations

Interaction of coherent structures known as blobs in the scrape-off layer of magnetically confined plasmas is investigated. Isolated and interacting seeded blobs, as well as full plasma turbulence, are studied by two-dimensional numerical simulations. The features of the blobs (position, size, amplitude) are determined with a blob tracking algorithm, which identifies them as coherent structures with amplitudes above a chosen particle density threshold, and their velocities are compared to a conventional center of mass approach. We find that the theoretical velocity-size scaling dependence for isolated blobs is correctly resolved by the blob tracking method. The benchmarked approach is then extended to a population of interacting plasma blobs with statistically distributed amplitudes, sizes, and initial positions for different levels of blob interaction. We observe a correlation between the level of blob interaction and the number of blobs deviating from size–velocity scaling laws of perfectly isolated blobs. This is found to be caused by the interaction of blobs with the electrostatic potential of one another, leading to higher average blob velocities. We introduce a model specific intermittency parameter, quantifying the degree of blob interaction. For interacting blobs, we estimate the deviation from the picture of perfectly isolated blobs as a function of the intermittency parameter. For full plasma turbulence simulations, we observe a strong correlation between the blob amplitudes, sizes, and velocities estimated by the blob tracking algorithm.

DiCoDiLe: Distributed Convolutional Dictionary Learning.

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to represent signals or images. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. Contrarily to standard patch-based dictionary learning, patterns estimated by CDL can be positioned anywhere in signals or images. Optimization techniques consequently face the difficulty of working with extremely large inputs with millions of pixels or time samples. To address this optimization problem, we propose a distributed and asynchronous algorithm, employing locally greedy coordinate descent and a soft-locking mechanism that does not require a central server. Computation can be distributed on a number of workers which scales linearly with the size of the data. The parallel computation accelerates the parameter estimation and the distributed setting allows our algorithm to be used with data that do not fit into a single computer's RAM. Experiments confirm the theoretical scaling properties of the algorithm. This allows to demonstrate an improved pattern recovery as images grow in size, and to learn patterns on images from the Hubble Space Telescope containing tens of millions of pixels.

Global Energetics of Solar Flares. XII. Energy Scaling Laws

Abstract In this study we test 18 versions of five fundamental energy scaling laws that operate in large solar flares. We express scaling laws in terms of the magnetic potential field energy E p , the mean potential field strength B p , the free energy E free, the dissipated magnetic flare energy E diss, the magnetic length scale L, the thermal length scale L th, the mean helically twisted flux tube radius R, the sunspot radius r, the emission-measure-weighted flare temperature T e , the electron density n e , and the total emission measure EM, measured from a data set of 173 GOES M- and X-class flare events. The five categories of physical scaling laws include (i) a scaling law of the potential field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner–Tucker–Vaiana scaling law, and (v) the Shibata–Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two criteria: a cross-correlation coefficient of CCC > 0.5 between the theoretically predicted scaling laws and observed values, and a linear regression fit with a slope of α ≈ 1 within one standard deviation σ. These two criteria enable us (i) to corroborate some existing (or modified) scaling laws, (ii) to reject other scaling laws that are not consistent with the observations, (iii) to probe the dimensionality of flare geometries, and (iv) to predict various energy parameters based on tested scaling laws.