Vertical Scale Research Articles

Gravity-induced phase phenomena in plate-rod colloidal mixtures

Gravity can affect colloidal suspensions since for micrometer-sized particles gravitational and thermal energies can be comparable over vertical length scales of a few millimeters. In mixtures, each species possesses a different buoyant mass, which can make experimental results counter-intuitive and difficult to interpret. Here, we revisit from a theoretical perspective iconic sedimentation-diffusion-equilibrium experiments on colloidal plate-rod mixtures by van der Kooij and Lekkerkerker. We reproduce their findings, including the observation of five different mesophases in a single cuvette. Using sedimentation path theory, we incorporate gravity into a microscopic theory for the bulk of a plate-rod mixture. We also show how to disentangle the effects of gravity from sedimentation experiments to obtain the bulk behavior and make predictions that can be experimentally tested. These include changes in the sequence by altering the sample height. We demonstrate that both buoyant mass ratio and sample height form control parameters to study bulk phase behavior.

Local linear scale factors in map projections in the direction of coordinate axes

ABSTRACT This paper explains that the terms “horizontal and vertical scales” are not appropriate in map projections theory. Instead, the authors suggest using the term “scales in the direction of coordinate axes.” Since it is not possible to read a local linear scale factor in the direction of a coordinate axis immediately from the definition of a local linear scale factor, this paper considers the derivation of new formulae that enable local linear scale factors in the direction of coordinate x and y axes to be calculated. The formula for computing the local linear scale factor in any direction defined by dx and dy is also derived. Furthermore, the position and magnitude of the extreme values of the local linear scale factor are considered and new formulas derived.

Ring Configurations of Point Vortices in Polar Atmospheres

This paper examines the stability and nonlinear evolution of configurations of equal-strength point vortices equally spaced on a ring of constant radius, with or without a central vortex, in the three-dimensional quasi-geostrophic compressible atmosphere model. While the ring lies at constant height, the central vortex can be at a different height and also have a different strength to the vortices on the ring. All such configurations are relative equilibria, in the sense that they steadily rotate about the \(z\) axis. Here, the domains of stability for two or more vortices on a ring with an additional central vortex are determined. For a compressible atmosphere, the problem also depends on the density scale height \(H\), the vertical scale over which the background density varies by a factor \(e\). Decreasing \(H\) while holding other parameters fixed generally stabilises a configuration. Nonlinear simulations of the dynamics verify the linear analysis and reveal potentially chaotic dynamics for configurations having four or more vortices in total. The simulations also reveal the existence of staggered ring configurations, and oscillations between single and double ring configurations. The results are consistent with the observations of ring configurations of polar vortices seen at both of Jupiter’s poles [1].

AI-Based Resource Provisioning of IoE Services in 6G: A Deep Reinforcement Learning Approach

Currently, researchers have motivated a vision of 6G for empowering the new generation of the Internet of Everything (IoE) services that are not supported by 5G. In the context of 6G, more computing resources are required, a problem that is dealt with by Mobile Edge Computing (MEC). However, due to the dynamic change of service demands from various locations, the limitation of available computing resources of MEC, and the increase in the number and complexity of IoE services, intelligent resource provisioning for multiple applications is vital. To address this challenging issue, we propose in this paper IScaler, a novel intelligent and proactive IoE resource scaling and service placement solution. IScaler is tailored for MEC and benefits from the new advancements in Deep Reinforcement Learning (DRL). Multiple requirements are considered in the design of IScaler's Markov Decision Process. These requirements include the prediction of the resource usage of scaled applications, the prediction of available resources by hosting servers, performing combined horizontal and vertical scaling, as well as making service placement decisions. The use of DRL to solve this problem raises several challenges that prevent the realization of IScaler's full potential, including exploration errors and long learning time. These challenges are tackled by proposing an architecture that embeds an Intelligent Scaling and Placement module (ISP). ISP utilizes IScaler and an optimizer based on heuristics as a bootstrapper and backup. Finally, we use the Google Cluster Usage Trace dataset to perform real-life simulations and illustrate the effectiveness of IScaler's multi-application autonomous resource provisioning.

SMOOTHNESS AND FRACTIONAL INTEGRAL OF HIDDEN VARIABLE RECURRENT FRACTAL INTERPOLATION FUNCTION WITH FUNCTION VERTICAL SCALING FACTORS

In this paper, we analyze the smoothness of hidden variable recurrent fractal interpolation function (HVRFIF) with function vertical scaling factors introduced in Yun [Hidden variable recurrent fractal interpolation function with four function contractivity factors, Fractals 27(7) (2019) 950113] and study on fractional integral of bivariable HVRFIF by using its smoothness. To do it, firstly, we analyze the smoothness of one variable HVRFIF and give the result of smoothness of bivariable HVRFIF. Next, we show that partial and mixed Riemann–Liouville fractional integrals of the bivariable HVRFIF are HVRFIFs.

Kinetic energy cascade in stably stratified open-channel flows

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.

On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations

In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier–Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale motions meaning that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier–Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.

Novel approach to estimate vertical scale of fluctuation based on CPT data using convolutional neural networks

The inherent spatial variability of soil properties is the main sauces of uncertainties in the site investigation, and it is commonly characterized using random field theory. In the context of random fields, the scale of fluctuation (SOF) is a significant parameter to reflect the spatial correlation between the two points of soil properties. However, it is challenging to estimate the SOF value accurately, especially when there are only limited project-specific test results, such as cone penetration test (CPT) data. This study aims to develop a convolutional neural network (CNN) approach to estimate the vertical SOF based on limited CPT data. The CNN model was constructed and trained by the simulated 15,000 CPT samples using random fields. The results show that the CNN model has excellent performance for estimating vertical SOF. The approach is validated and illustrated through newly simulated CPT data, eight real CPT data obtained from the literature, and three CPT data collected from the Shanghai site. The proposed scale factor method can solve the mismatch between the actual CPT depth and the required depth for input data of the CNN model, making the CNN model more widely applicable.

Rain Attenuation Scaling in South Korea: Experimental Results and Artificial Neural Network

Scaling rain attenuation parameters will significantly benefit the quick monitoring of rain attenuation in a particular channel with previously known results or in situ setup attenuation measurements. Most of the rain attenuation scaling techniques have been derived for slant links. In this study, we also applied frequency and polarization scaling techniques for terrestrial link applications. We collected real measured datasets from research paper publications and examined those datasets using International Telecommunication Union-Radiocommunication sector (ITU-R) models (P.530-17, P.618-13). Our analyzed results show that existing long-term frequency and polarization scaling rain attenuation models (ITU-R P.618-13 for slant links and ITU-R P.530-17 for terrestrial links) show reduced performance for frequency and polarization scaling measured locations in South Korea. Hence, we proposed a new scaling technique using artificial neural networks from the measured rain attenuation data of slant and terrestrial links in South Korea. The experimental results confirm that the proposed Artificial Neural Network (ANN)-based scaling model shows satisfactory performance to predict attenuation for frequency and vertical polarization scaling.

Estimation of the Radial Scale Length and Vertical Scale Height of the Galactic Thin Disk from Cepheids

Up-to-date data on 2214 classical Cepheids have been used. The model of an exponential matter density distribution in the Galactic thin disk has been applied. New estimates of the radial disk scale length $h_R,$ the distance of the Sun from the symmetry plane $z_\odot$, and the vertical disk scale height $h_z$ have been obtained. Based on samples of 1087 Cepheids younger than 120 Myr and 1127 Cepheids older than 120 Myr, we have found $h_R=2.30\pm0.09$ kpc and $h_R=1.96\pm0.12$ kpc, respectively. It has turned out that an unambiguous estimate of $h_R$ cannot be obtained from their overall radial distribution. However, we have constructed the radial distribution of 806 Cepheids of different ages at the time of their birth from which we have found $h_R=2.36\pm0.24$ kpc. We show that $h_z$ depends strongly on the age of stars. For example, from 705 Cepheids younger than 120 Myr with heliocentric distances $r<6$ kpc we have found $z_\odot=-17\pm4$ pc and $h_z=75\pm5$ pc. From 393 Cepheids older than 120 Myr at $r<6$ kpc, we have found $z_\odot=-39\pm11$ pc and $h_z=131\pm10$ pc.

Mega riverbed-patterns: linear and weakly nonlinear perspectives.

In this paper, we explore the mega riverbed-patterns, whose longitudinal and vertical length dimensions scale with a few channel widths and the flow depth, respectively. We perform the stability analyses from both linear and weakly nonlinear perspectives by considering a steady-uniform flow in an erodible straight channel comprising a uniform sediment size. The mathematical framework stands on the dynamic coupling between the depth-averaged flow model and the particle transport model including both bedload and suspended load via the Exner equation, which drives the pattern formation. From the linear perspective, we employ the standard linearization technique by superimposing the periodic perturbations on the undisturbed system to find the dispersion relationship. From the weakly nonlinear perspective, we apply the centre–manifold-projection technique, where the fast dynamics of stable modes is projected on the slow dynamics of weakly unstable modes to obtain the Stuart–Landau equation for the amplitude dynamics. We examine the marginal stability, growth rate and amplitude of patterns for a given quintet formed by the channel aspect ratio, wavenumber of patterns, shear Reynolds number, Shields number and relative roughness number. This study highlights the sensitivity of pattern formation to the key parameters and shows how the classical results can be reconstructed on the parameter space.

Elevation-related climate trends dominate fungal co-occurrence network structure and the abundance of keystone taxa on Mt. Norikura, Japan

Soil fungi play an important role in promoting nutrient cycling and maintaining ecosystem stability. Yet, there has been little understanding of how fungal co-occurrence networks differ along elevational climate gradients, a topic of interest to both macroecology and climate change studies. Based on high-throughput sequencing technology, we investigated the trend in co-occurrence network structure of soil fungal communities at 11 elevation levels along a 2300 m elevation gradient on Mt. Norikura, Japan, and identified the keystone taxa in the network, hypothesizing a progressive decline in network connectivity with elevation due to decreased plant diversity and enhanced environmental stress caused by changes in climate and soil characteristics. Our results demonstrated that network-level topological features such as network size, average degree, clustering coefficient, and modularity decreased significantly with increasing elevation, indicating that the fungal OTUs at low elevation were more closely associated and the network structure was more compact at low elevations. This conclusion was verified by the negative correlation between positive cohesion, negative cohesion and elevation. Moreover, the negative/positive cohesion ratio reached its peak value in mid-elevations with moderate environmental stress, indicating that the fungal community structure in mid-elevations was more stable than that at other elevations. We also found that the keystone taxa were more abundant at lower elevations. Furthermore, statistical analysis revealed that against a background of uniform geology, climate may play a dominant role in determining the properties and intensity of soil fungal networks, and significantly affect the abundance distribution of keystone taxa. These findings enhance understanding of the pattern and mechanism of the fungal community co-occurrence network along elevation, as well as the responses of microorganisms to climate change on a vertical scale in montane ecosystems. ImportanceExploration of the elevational distribution of microbial networks and their driving factors and mechanisms may provide opportunities for predicting potential impacts of environmental changes, on ecosystem functions and biogeographic patterns at a broad scale. Although many studies have explored patterns of fungal community diversity and composition along various environmental gradients, it is unclear how the topological structure of co-occurrence networks shifts along elevational temperature gradients. In this study, we found that the connectivity of the fungal community decreased with increasing elevation and that climate was the dominant factor regulating co-occurrence patterns, apparently acting indirectly through soil characteristics. Our results also suggest that higher elevations on mountains have fewer keystone taxa than low elevations. These patterns may be related to the decrease of plant diversity and the increase of environmental stress along elevation gradients.

Effects of a Proposed Hydraulic Project on the Hydrodynamics in the Poyang Lake Floodplain System, China.

Knowledge of dam construction in floodplain systems and its hydrodynamic effects plays a critical role in managing various kinds of floodplains. This study uses 3D floodplain hydrodynamic modeling to explore the possible effects of a proposed hydraulic project in Poyang Lake (PLHP) on the hydrodynamics, exemplified by a large floodplain system. Simulations showed that the water levels across most lake regions presented more significant changes than in the floodplain areas during the study period. The increased water levels upstream from the PLHP (~1.0 m) were distinctly higher than that downstream (~0.1 m). The PLHP may decrease the magnitude of the water velocities in the main channels of the lake, whereas velocities may experience mostly minor changes in the floodplains, depending upon the altered flow dynamics and transport. On average, the water temperature may exhibit mostly minor changes (~<1.0 °C) for both the horizontal and vertical scales within the flood-pulse-influenced lake system. Additionally, the model results indicated that the outflow process caused by the PLHP may be altered from the natural discharge into the Yangtze River to frequent backflow events during the storage period, demonstrating the non-negligible effect of the PLHP on the water supply for the downstream Yangtze River in the future.

Situated perspectives on the city: a reflection on scaling participation through design

This article explores the relationship between design methodologies and the scaling of participation in cities. The article recognizes that the scaling of community-led informal settlement upgrading is a central concern in the broader debate on scaling participation, and it interrogates the potential contribution of design methodologies in connecting localized, community-led upgrading initiatives outwards and upwards. We discuss these ideas by drawing on our own experience of devising and facilitating a number of participatory design and planning initiatives titled Change by Design with the non-profit organization Architecture Sans Frontières – UK (ASF-UK). Reflecting on this experience, we argue that the inclusion of a design-based, city-level perspective in localized upgrading initiatives can be a powerful conceptual and practical tool to support horizontal, vertical and deep scaling; and we highlight the importance of constructing this design tool in an embodied and situated manner, so that scaling processes remain firmly grounded in everyday lives and experiences.

Orographically induced spontaneous imbalance within the jet causing a large-scale gravity wave event

Abstract. To better understand the impact of gravity waves (GWs) on the middle atmosphere in the current and future climate, it is essential to understand their excitation mechanisms and to quantify their basic properties. Here a new process for GW excitation by orography–jet interaction is discussed. In a case study, we identify the source of a GW observed over Greenland on 10 March 2016 during the POLSTRACC (POLar STRAtosphere in a Changing Climate) aircraft campaign. Measurements were taken with the Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) instrument deployed on the High Altitude Long Range (HALO) German research aircraft. The measured infrared limb radiances are converted into a 3D observational temperature field through the use of inverse modelling and limited-angle tomography. We observe GWs along a transect through Greenland where the GW packet covers ≈ 1/3 of the Greenland mainland. GLORIA observations indicate GWs between 10 and 13 km of altitude with a horizontal wavelength of 330 km, a vertical wavelength of 2 km and a large temperature amplitude of 4.5 K. Slanted phase fronts indicate intrinsic propagation against the wind, while the ground-based propagation is with the wind. The GWs are arrested below a critical layer above the tropospheric jet. Compared to its intrinsic horizontal group velocity (25–72 m s−1) the GW packet has a slow vertical group velocity of 0.05–0.2 m s−1. This causes the GW packet to propagate long distances while spreading over a large area and remaining constrained to a narrow vertical layer. A plausible source is not only orography, but also out-of-balance winds in a jet exit region and wind shear. To identify the GW source, 3D GLORIA observations are combined with a gravity wave ray tracer, ERA5 reanalysis and high-resolution numerical experiments. In a numerical experiment with a smoothed orography, GW activity is quite weak, indicating that the GWs in the realistic orography experiment are due to orography. However, analysis shows that these GWs are not mountain waves. A favourable area for spontaneous GW emission is identified in the jet by the cross-stream ageostrophic wind, which indicates when the flow is out of geostrophic balance. Backwards ray-tracing experiments trace into the jet and regions where the Coriolis and the pressure gradient forces are out of balance. The difference between the full and a smooth-orography experiment is investigated to reveal the missing connection between orography and the out-of-balance jet. We find that this is flow over a broad area of elevated terrain which causes compression of air above Greenland. The orography modifies the wind flow over large horizontal and vertical scales, resulting in out-of-balance geostrophic components. The out-of-balance jet then excites GWs in order to bring the flow back into balance. This is the first observational evidence of GW generation by such an orography–jet mechanism.

A fine-grained and dynamic scaling method for service function chains

Network function virtualization (NFV) is a promising approach to solve network ossification, which provides network services through virtual network function (VNF). However, the resource demands of service function chains (SFCs) frequently change during their lifecycles. Network operators need to scale the SFCs when resource demands change. The challenge of SFC scaling is that how to solve the conflict between improving the scaling success ratio and reducing the consumption of resources. This paper proposes a hybrid scaling method (HSM) that effectively solves this conflict. First, we formulate the SFC scaling problem as an integer linear programming model. We then present the improved vertical scaling (IVS) and horizontal scaling (IHS). IVS improves the scaling success ratio by combining vertical scaling and traffic splitting. IHS reduces CPU, forwarding and memory resource consumption by providing resources for VNF instances according to resource demands. IHS considers hop constraints when selecting server nodes and substrate links to deploy new instances and virtual links, thereby reducing the bandwidth resource consumption. The HSM further improves the scaling success ratio and reduces the scaling resource consumption by combining the IVS and IHS. Finally, through theoretical analysis and simulation experiments, we demonstrate the effectiveness of the proposed hybrid scaling method.

ОСОБЛИВОСТІ МАСШТАБУВАННЯ КОНТЕЙНЕРНОГО НАВАНТАЖЕННЯ НА БАЗІ СИСТЕМИ KUBERNETES

Today, the field of software development using container technology is becoming widespread in many areas of business, and the problem of scaling is one of the most important to achieve the expansion of the volume of tasks performed over time, so it is important to use the right scaling schemes. Kubernetes requires relatively easy-to-adapt container management mechanisms, but the problem of scaling them remains poorly described and researched, which increases the complexity of the business transition to container technologies and, in particular, the Kubernetes system. Thanks to the separation of infrastructure and payload concepts in Kubernetes, the classic scaling methods – horizontal and vertical – are revealed in each component separately. Although the Kubernetes system is quite flexible, it has only recently been developed, and the features of scaling with concept separation have not yet been described. Actual scientific researches and issues analysis showed that there is a general trend towards cloud migration recently. In this context, the architectural style of microservices and the use of container load has attracted considerable attention, especially based on the Kubernetes system. It can be concluded that Kubernetes has significant advantages in the speed of development and deployment of container-based applications, but the problem of scaling and features of horizontal and vertical scaling in Kubernetes has not received much attention from academia so far. The aim of the work is to study the features of scaling the container load based on the Kubernetes system. To explain the basic operations to achieve horizontal and vertical scaling. To describe the scalability property of the Kubernetes system. This work reveals the main architectural features of Kubernetes, the principles of working with applications in container virtualization. The main methods of regulating the resource capacity of containers are shown. The concepts of horizontal and vertical scaling in the Kubernetes system with an indication of scalability properties are revealed. The main operations for scaling in the Kubernetes system in the context of separation of payload and infrastructure concepts are given. In this article the features of container load scaling based on the Kubernetes system with a separation of the concepts of payload and infrastructure scaling were investigated and described. This article is a review.

Trajectories of social-emotional development across pre-primary and early primary school

Social-emotional (SE) skills grow rapidly during the preschool years and support children's ability to manage stress and form positive relationships. Yet little research exists on how SE skills develop over time, particularly in low- and middle-income countries. We examined the development of prosocial SE skills with four waves of data over three years in a sample of Ghanaian preschoolers (N = 1916; 47.6% female). We used factor analysis and vertical scaling to assess the dimensionality of prosocial SE skills and latent growth mixture modeling to identify subgroups as defined by different trajectories. We found two distinct subgroups—normative, in which children gained SE skills over time, and low-growth, in which children had lower initial skill levels and acquired skills at a slower rate over time. Group membership was associated with demographic characteristics and children's first grade academic outcomes, as well as other important non-academic skills.

The fate of upwelled nitrate off Peru shaped by submesoscale filaments and fronts

Abstract. Filaments and fronts play a crucial role for a net offshore and downward nutrient transport in Eastern Boundary Upwelling Systems (EBUSs) and thereby reduce regional primary production. Most studies on this topic are based on either observations or model simulations, but only seldom are both approaches are combined quantitatively to assess the importance of filaments for primary production and nutrient transport. Here we combine targeted interdisciplinary shipboard observations of a cold filament off Peru with submesoscale-permitting (1/45∘) coupled physical (Coastal and Regional Ocean Community model, CROCO) and biogeochemical (Pelagic Interaction Scheme for Carbon and Ecosystem Studies, PISCES) model simulations to (i) evaluate the model simulations in detail, including the timescales of biogeochemical modification of the newly upwelled water, and (ii) quantify the net effect of submesoscale fronts and filaments on primary production in the Peruvian upwelling system. The observed filament contains relatively cold, fresh, and nutrient-rich waters originating in the coastal upwelling. Enhanced nitrate concentrations and offshore velocities of up to 0.5 m s−1 within the filament suggest an offshore transport of nutrients. Surface chlorophyll in the filament is a factor of 4 lower than at the upwelling front, while surface primary production is a factor of 2 higher. The simulation exhibits filaments that are similar in horizontal and vertical scale compared to the observed filament. Nitrate concentrations and primary production within filaments in the model are comparable to observations as well, justifying further analysis of nitrate uptake and subduction using the model. Virtual Lagrangian floats were released in the subsurface waters along the shelf and biogeochemical variables tracked along the trajectories of floats upwelled near the coast. In the submesoscale-permitting (1/45∘) simulation, 43 % of upwelled floats and 40 % of upwelled nitrate are subducted within 20 d after upwelling, which corresponds to an increase in nitrate subduction compared to a mesoscale-resolving (1/9∘) simulation by 14 %. Taking model biases into account, we give a best estimate for subduction of upwelled nitrate off Peru between 30 %– 40 %. Our results suggest that submesoscale processes further reduce primary production by amplifying the downward and offshore export of nutrients found in previous mesoscale studies, which are thus likely to underestimate the reduction in primary production due to eddy fluxes. Moreover, this downward and offshore transport could also enhance the export of fresh organic matter below the euphotic zone and thereby potentially stimulate microbial activity in regions of the upper offshore oxygen minimum zone.

Graph-directed random fractal interpolation function

"Barnsley introduced in [1] the notion of fractal interpolation function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties. It has the advantage that it can be also combined with the classical methods or real data interpolation. Hutchinson and Ruschendorf [7] gave the stochastic version of fractal interpolation function. In order to obtain fractal interpolation functions with more exibility, Wang and Yu [9] used instead of a constant scaling parameter a variable vertical scaling factor. Also the notion of fractal interpolation can be generalized to the graph-directed case introduced by Deniz and  Ozdemir in [5]. In this paper we study the case of a stochastic fractal interpolation function with graph-directed fractal function."