Shape Of Diagram Research Articles

Shape diagram determination of a multiphase system in stratified configuration by CFD

Shape diagram determination of a multiphase system in stratified configuration by CFD

The rush to the poles and the role of magnetic buoyancy in the solar dynamo

The butterfly diagram of the solar cycle shows a poleward migration of the diffuse magnetic field resulting from the decay of trailing sunspots. It is one component of what is sometimes referred to as the `rush to the poles' and is responsible for the reversal and buildup of the polar cap fields. We investigated under which conditions the rush to the poles can be reproduced in flux-transport Babcock-Leighton dynamo models. We also considered other observational consequences of the different mechanisms that reproduce the rush to the poles. We identified three main ways to achieve the rush to the poles: a flux emergence probability that decreases rapidly with latitude; a threshold for the sub-surface toroidal field strength below which the toroidal flux emerges only slowly and above which the emergence rate is high; and an emergence rate that depends on the mean magnetic field squared, mimicking magnetic buoyancy. We implemented these three mechanisms in a 2D Babcock-Leighton flux transport dynamo model that incorporates toroidal flux loss and deep downward turbulent pumping. Moreover, we directly compared the observational sunspot zone migration law with what our models predict. We find that all three mechanisms lead to solar-like butterfly diagrams, but with notable differences. The shape of the butterfly diagram is very sensitive to model parameters for the threshold prescription, while most models that incorporate magnetic buoyancy converge to very similar butterfly diagrams, with butterfly wing widths of $ in very good agreement with observations. With turbulent diffusivities above $35 km s $ but below about $40 km s $, buoyancy models are strikingly solar-like. The threshold and magnetic buoyancy prescriptions make the models non-linear and as such they can saturate the dynamo through latitudinal quenching; during this process, emergences at higher latitudes are less efficient at transporting fields across the equator and hence less efficient in reversing the polar fields -- although only the magnetic buoyancy prescription can saturate the dynamo when emergence loss is turned off. The period of the models that involve buoyancy is independent of the source term amplitude, but emergence loss increases it by $ 60<!PCT!>$. The models with the right advection amplitude and turbulent diffusivity match the observational equatorward migration law very well. For the rush to the poles to be visible, a mechanism suppressing (enhancing) emergences at high (low) latitudes must operate. It is not sufficient that the toroidal field be stored at low latitudes for emergences to be limited to low latitudes. Magnetic buoyancy appears to be the most promising non-linearity as models that incorporate it produce the most solar-like butterfly diagrams, with the exact width of the butterfly wings being roughly independent of model parameters. Dynamo saturation is achieved by a competition between latitudinal quenching and a quenching due to the tilt of the mean bipolar magnetic region. From these models we infer that the Sun is not in the advection-dominated regime, but nor is it in the diffusion-dominated regime. The cycle period is set through a balance between advection, diffusion, and flux emergence in accordance with the observational sunspot zone migration law. This accordance seems to imply that the toroidal field is indeed stored in the equatorial region of the lower convection zone.

Characterisation of the stellar wind in Cyg X-1 via modelling of colour-colour diagrams

Context. Cygnus X-1 (Cyg X-1) is a high-mass X-ray binary where accretion onto the black hole (BH) is mediated by the stellar wind from the blue supergiant companion star HDE 226868. Due to its inclination, the system is a perfect laboratory to study the not yet well-understood stellar wind structure. In fact, depending on the position of the BH along the orbit, X-ray observations can probe different layers of the stellar wind. Deeper wind layers can be investigated at superior conjunction (i.e. null orbital phases). Aims. We aim to characterise the stellar wind in the Cyg X-1/HDE 226868 system, analysing one passage at superior conjunction covered by XMM-Newton during the ‘Cyg X-1 Hard state Observations of a Complete Binary Orbit in X-rays’ (CHOCBOX) campaign. Methods. To analyse the properties of the stellar wind, we computed colour-colour diagrams. Since X-ray absorption is energy-dependent, colour indices provide information on the parameters of the stellar wind, such as the column density, NH, w, and the covering factor, fc. We fitted colour-colour diagrams with models that include both a continuum and a stellar wind component. We used the kernel density estimation method to infer the unknown probability distribution of the data points in the colour-colour diagram, and selected the model corresponding to the highest likelihood. In order to study the temporal evolution of the wind around superior conjunction, we extracted and fitted time-resolved colour-colour diagrams. Results. We found that the model that best describes the shape of the colour-colour diagram of Cyg X-1 at superior conjunction requires the wind to be partially ionised. The shape of the colour-colour diagram strongly varies during the analysed observation, due to concurrent changes of the mean NH, w and the fc of the wind. Our results suggest the existence of a linear scaling between the rapid variability amplitude of NH, w (on timescales between 10 s and 11 ks) and its long-term variations (on timescales > 11 ks). Using the inferred best-fit values, we estimated the stellar mass loss rate to be ∼7 × 10−6 M⊙ yr−1 and the clumps to have a characteristic mass of ∼1017 g.

Interior vertices and edges in integer partitions

This paper characterises the shape of the Young diagram associated with integer partitions in terms of two newly invented statistics which are defined in the text: namely interior vertices and horizontal edges. Generating functions and associated asymptotic results are developed for both interior vertices and horizontal edges.

VELOCITY AND EVOLUTION OF SHOCK WAVES IN SAND WITH INCREASING WATER CONTENT

Interest in the problems of shock wave propagation in saturated porous media is associated with studying seismic exploration issues, modeling the hummer effect during hydraulic fracturing, studying the water-gas impact on formations for the purpose of efficient oil production, etc. Experimental work on waves in bulk media is usually carried out in shock tubes. Traditionally, shock tubes are used to study the characteristics of the propagation of shock waves in various media, to analyze the wave properties of these media based on the speed of the shock waves and the change in the shape of the pulse along the passage of the first – main pulse. In a shock tube equipped with a section of bulk media, the wave is repeatedly reflected from the surface of the porous medium under study and the upper end of the tube. Re-reflected waves can be used to study changes in the environment that occurred under the influence of a shock wave, i.e. as probing pulses. In this article, sounding is understood as identifying acoustic properties (changing the shape of shock pulse diagrams and their velocities). This paper presents the results of experimental studies of the propagation of shock waves of small amplitude in sand with a volumetric content of liquid in the pore space from 0 to 40 %, and illustrates the influence of the presence of liquid in the pores on the shape of the main and probing pulses. The research was carried out using the Shock Tube installation, in the Laboratory of Experimental Hydrodynamics of the Mavlyutov Institute of Mechanics of Ufa Branch RAS. An increase in the speed of wave propagation was established with increasing water saturation of sand in the range from 0 to 40 %. An increase in the amplitude of reflected waves when passing through sand, the formation of peaks and stretching of pulses were discovered. The research results can be used in processing geophysical data to interpret seismograms of sandy deposits saturated with gas-liquid systems.

On preradicals, persistence, and the flow of information

We use Category Theory notions to explore the conceptual axiom that, in a general sense, information flows through a neural network following a path of “least resistance”. To this end, we consider particular endofunctors, called preradicals, whereby we describe persistence in small shape diagrams defined in R-Mod. Specifically, we show that the α preradicals naturally describe persistence in commutative G-modules, for G a directed acyclic graph. Then, we use this results to generalize the notion of persistence to any diagram labeled by a quiver Q. These results, in turn, set the theoretical foundation for our formal framework that explores the notion of “paths of least resistance”. Lastly, we provide a notion of entropy for preradicals in R-Mod, and prove that it respects the order and operations between preradicals.

A 16-Gb/s 3-tap adaptive DFE in 12-nm FinFET CMOS technology

This paper introduces a 3-tap half-rate adaptive decision feedback equalizer (DFE) and a 2-D eye-opening monitor (EOM). A newly developed regenerating sampler (RG-sampler) with smaller setup time and ck2q time is integrated into the proposed DFE, enhancing its performance. To ensure greater robustness, the sign-sign least-mean-squares (SSLMS) algorithm with a pattern filter is employed to adapt DFE tap coefficients. The proposed 2-D EOM accurately captures the shape of the eye diagram using adjustment steps of 1.95ps and 7 mV in the horizontal and vertical directions, respectively. Additionally, by reusing analog components within the adaptive DFE and 2-D EOM modules, significant reductions in silicon area and power consumption are achieved. Implemented in 12-nm FinFET CMOS technology, the transceiver integrated with adaptive DFE and 2-D EOM operates at a data rate of 16 Gb/s over a channel with 30 dB loss at 8 GHz frequency. The proposed adaptive DFE and 2-D EOM occupy a total area of 0.00808 mm2. Measurement results demonstrate that following DFE adaptation, the eye height is 77 mV, and the eye width is 29.25ps at 16 Gb/s.

Correlation between Electrocatalytic Activity and Impedance Shape: A Theoretical Analysis

Though electrochemical impedance spectroscopy (EIS) has been widely used in mechanistic investigations of electrocatalytic reactions, the correlation between the shape of an EIS diagram and the electrocatalytic activity is largely unclear; the complexity of electrocatalytic reactions in terms of reaction mechanisms and influencing factors casts an air of pessimism over the existence and, if it exists, the stability of such a correlation. Nevertheless, understanding the correlation can help select reaction mechanisms and electrical circuit models in data analysis, use the EIS shape as a descriptor of electrocatalytic activity, and detect side reactions if the measured shapes deviate from the theoretical prediction based on the main reaction. Herein, the problem is tackled by a systematic mathematical analysis of firstly single-adsorbate reactions and then more complicated reactions involving multiple adsorbates. A complete regime diagram of all possible EIS shapes of single-adsorbate reactions is provided, navigating the subsequent analysis in the multidimensional parametric space. For single-adsorbate reactions involving two steps with identical transfer coefficients of 0.5 in the absence of lateral adsorbate interactions, several rigorous remarks on the EIS shape are made. Unfortunately, many of them require modifications when different transfer coefficients and lateral interactions are considered. Nevertheless, several trends in EIS shapes are robust against complexities of reaction mechanisms and variations in reaction parameters, which also receive experimental evidence collected from the literature. The theoretical analysis presented here may trigger interest in finding a correlation between the impedance shape and the electrocatalytic activity across a wide range of reactions. Published by the American Physical Society 2024

Multi-uncertainty river health assessment in the Loess Plateau based on a novel comprehensive similarity cloud model

With the development of related research on river health assessment, the traditional assessment methods cannot solve the uncertainty problems caused by diversified indicators and ambiguous weights. In order to comprehensively understand the river health status in the Loess Plateau and solve the uncertainty of assessment results, this study takes Wuding River as the research object, and constructs an assessment indicator system incorporating the ecological environment and social functions of the river. The genetic algorithm-BP neural network was used to establish a weight learning mechanism for assessment indicators, and the system weight was calculated by combining various weighting preferences. Based on the cloud model theory, a sample data cloud and a health level cloud were constructed, and a comprehensive similarity model considering the shape and distance of the cloud diagram was developed to identify the health level of Wuding River. The spatial and temporal variability of the river health status and the sources of pressure causing unhealthy problems were analyzed. It is shown that Wuding River is in basic health status, which gradually decreases from the upstream reaches to the downstream reaches. The health status of social service functions is better than that of the ecological environment attributes such as water resources and water quality. The sources of health pressure in the upstream and downstream reaches are different. In the upstream reaches, the pressure mainly comes from natural attributes such as successive declines in water production, slow governance of water and soil erosion, and the poor stability of the river. The health pressure in the midstream and dowmstream reaches comes from the interference of human economic activities, which include deterioration of water quality caused by the discharge of fossil energy industry, destruction of aquatic habitats, and flood safety hazards caused by insufficient standards for flood control project design. In addition, SDSCM provides river managers with accurate and comprehensive health risk information to help them manage rivers more effectively.

The Influences of Agglomeration and Storage on the Thermal Properties and Stability of Fats in Infant Formulas

The Influences of Agglomeration and Storage on the Thermal Properties and Stability of Fats in Infant Formulas

Modeling of flexible bevel gear rotor systems: Modal and dynamic characterization

Bevel gears, a crucial part of aircraft transmission systems, are more susceptible to wheel body vibration issues as lightweight requirements rise. In the past, the gear wheel body was often considered rigid while assessing the dynamic properties of gear systems. Constructing a bevel gear model with a thin-walled structure might not be appropriate for this modeling technique; this research suggests a dynamic model that considers the flexibility of bevel gears. The web and teeth structure of the gear are preserved by realistic modeling using three-dimensional hexahedral components. The component mode synthesis (CMS) approach reduces the model order for increased computational efficiency. To confirm the accuracy of the modeling method, the modal frequencies and vibration shapes of the proposed model single-gear shaft are compared with results from experiments and ABAQUS. By contrasting ABAQUS system-level meshing modal frequencies and vibration shapes, the accuracy of the system model assembly is further confirmed. The model examines the impact of bevel gear flexibility on the modal frequencies, modal vibration shapes, and system dynamic properties. The mode shape diagram at dangerous modal frequencies found using the modal strain energy technique and the vibration displacement cloud maps at resonance speeds computed using the Newmark-β method are mutually verified, and this demonstrates that lightweight bevel gears are more susceptible to excitation due to nodal diameter type vibrations. Proposed and traditional models anticipate substantially different resonance speeds since the traditional model assumes that the gear, being a rigid disk, can only excite the shaft's bending mode of vibration. The proposed model provides a more comprehensive description of the dynamic characteristics of bevel gear systems, providing a theoretical basis and optimization tool for the high-performance design, vibration reduction, and noise control of high-speed lightweight gear transmission systems.

Research of the semiconductor sensors based on anomal photovoltaic effect with highly sensitive parameters of the deformation

Optical parameters of thin polycrystalline semiconductor films during deformation (t, n, 𝜆, R, T 𝑣a, 𝜑 𝜎) changes. An optical elastic effect has been created. Its physical basis is that deformation affects the shape of the zonal diagram by changing the crystal lattice constants. This condition gives rise to various optical and other electronic phenomena in semiconductor thin films .

Bubbles and drops between circular frames: shape, force and stability analysis.

Interactions between bubbles and drops play an important role in many physical phenomena. Whether we consider the interaction between two bubbles (drops) or between many (foams or emulsions), these interactions are complex and still poorly understood. An interesting case arises when two equal- and constant-volume bubbles (drops) interact with each other while being held by two axisymmetrically positioned frames of circular opening - a configuration which is frequently used in characterisation devices. The minimisation of the surface energy of this "double bubble" (or "double drop") configuration, constrained by the fixed volume and the frame boundaries, creates a complex landscape of shape spaces where physically stable shapes are separated by different types of instabilities. Combining experiments, finite element simulations and theory, we provide here for the first time a complete analysis of these shape spaces, considering the adhesive energy between the bubbles and the drops (expressed by the contact angle) as an additional control parameter. We provide the full shape diagrams for different contact angles (0°, 60° and 90°), including a detailed discussion of four types of instabilities. Two of these instabilities break the axisymmetry, while the two others break the connectivity of the ensemble. As far as we are aware, two of these instabilities have never been reported before. We accompany the shape and stability analysis with detailed mechanical characterisation using force and pressure measurements. Experiments, simulations and theory showing excellent agreement. This work will not only be useful in guiding the exploitation of double bubble (double drop) experiments on frames, but it also opens the possibility to exploit these configurations for the characterisation of increasingly complex bubble or drop interactions. Since the contact angle of 90° corresponds to an "imaginary" film separating the two bubbles (drops), our analysis naturally includes the shape and stability of a capillary bridge between two circular frames.

Detection of Closing Cracks in Beams Based on Responses Induced by Harmonic Excitation.

The non-linear contact model was chosen to simulate a closed crack in a cantilever beam. This study examines the shape and characteristics of the phase diagram of a cantilever beam with closed cracks. It investigates how various crack properties influence the geometry of the phase diagram and proposes a method for identifying cracks based on their features. The area of each closed curve in the phase diagram was determined using the pixel method. Based on the results, the contact model proved effective in simulating closed cracks and was sensitive to nonlinear closing cracks. The vibration responses of beams with different damage severities and positions exhibited distinct geometric features. The crack parameter was identified by locating the intersection of contour lines on the maps. According to numerical calculations, the phase diagrams for super-harmonic resonance seem to be more susceptible to changes in closed cracks with varied damage locations and severities. The wavelet transform was also employed to identify closed cracks using RMS signals, and the results were compared with those obtained from the phase diagram.

Fluctuations in auxin levels depend upon synchronicity of cell divisions in a one-dimensional model of auxin transport.

Auxin is a well-studied plant hormone, the spatial distribution of which remains incompletely understood. Here, we investigate the effects of cell growth and divisions on the dynamics of auxin patterning, using a combination of mathematical modelling and experimental observations. In contrast to most prior work, models are not designed or tuned with the aim to produce a specific auxin pattern. Instead, we use well-established techniques from dynamical systems theory to uncover and classify ranges of auxin patterns as exhaustively as possible as parameters are varied. Previous work using these techniques has shown how a multitude of stable auxin patterns may coexist, each attainable from a specific ensemble of initial conditions. When a key parameter spans a range of values, these steady patterns form a geometric curve with successive folds, often nicknamed a snaking diagram. As we introduce growth and cell division into a one-dimensional model of auxin distribution, we observe new behaviour which can be explained in terms of this diagram. Cell growth changes the shape of the snaking diagram, and this corresponds in turn to deformations in the patterns of auxin distribution. As divisions occur this can lead to abrupt creation or annihilation of auxin peaks. We term this phenomenon 'snake-jumping'. Under rhythmic cell divisions, we show how this can lead to stable oscillations of auxin. We also show that this requires a high level of synchronisation between cell divisions. Using 18 hour time-lapse imaging of the auxin reporter DII:Venus in roots of Arabidopsis thaliana, we show auxin fluctuates greatly, both in terms of amplitude and periodicity, consistent with the snake-jumping events observed with non-synchronised cell divisions. Periodic signals downstream of the auxin signalling pathway have previously been recorded in plant roots. The present work shows that auxin alone is unlikely to play the role of a pacemaker in this context.

Skew Howe duality and limit shapes of Young diagrams

AbstractWe consider the skew Howe duality for the action of certain dual pairs of Lie groups on the exterior algebra as a probability measure on Young diagrams by the decomposition into the sum of irreducible representations. We prove a combinatorial version of this skew Howe duality for the pairs , , , and using crystal bases, which allows us to interpret the skew Howe duality as a natural consequence of lattice paths on lozenge tilings of certain partial hexagonal domains. The ‐representation multiplicity is given as a determinant formula using the Lindström–Gessel–Viennot lemma and as a product formula. These admit natural ‐analogs that we show equals the ‐dimension of a ‐representation (up to an overall factor of ), giving a refined version of the combinatorial skew Howe duality. Using these product formulas (at ), we take the infinite rank limit and prove that the diagrams converge uniformly to the limit shape.

Convexification approaches for regional route guidance and demand management with generalized MFDs

Traffic congestion is one of the main concerns in big cities with many adverse socioeconomic effects. A promising solution is to simultaneously regulate the admission of vehicles (i.e., demand management) and redistribute traffic flows within the network (i.e., route guidance). In this work, we integrate demand management with route guidance within a Model Predictive Control framework using regional traffic dynamics with generalized Macroscopic Fundamental Diagram (MFD) shapes. Dealing with generalized MFD shapes is challenging due to the resulting nonlinear and non-convex optimization formulation. To tackle this challenge, we develop two real-time solution approaches: (i) a successive convexification approach that constructs convex bounding sets for all nonlinear terms, and (ii) a linear approximation approach that solves the problem using triangular macroscopic fundamental diagram approximations. The proposed approaches offer a trade-off between execution speed and solution quality, as the linear approximation approach runs faster while the successive convexification approach yields better quality and accuracy solutions. Macroscopic simulation results illustrate the efficiency of the successive convexification and linear approximation approaches yielding an optimality gap of less than 3.5% and 10% in all considered cases, respectively. Furthermore, both approaches outperform a state-of-practice nonlinear solver in terms of solution quality and execution time. Finally, substantial gains are also obtained regarding travel time and traffic flow efficiency in a realistic microsimulation environment.

LWR and shockwave analysis - Failures under a concave fundamental diagram and unexpected induced disturbances

This paper undertakes a detailed empirical study of traffic dynamics on a freeway. The results show the traffic dynamics that systematically determine the shape of the fundamental diagram, FD, can also violate the stationarity assumptions of both shockwave analysis and Lighthill, Whitham and Richard's models, thereby inhibiting the applicability of these classical macroscopic traffic flow theories. The outcome is challenging because there is no way to identify the problem using only the macroscopic detector data. The research examines conditions local to vehicle detector stations to establish the FD while the single vehicle passage method is used to analyze the composition of vehicles underlying the aggregate samples. Then, traffic states are correlated between successive stations to measure the actual signal velocities and show they are inconsistent with the classical theories. This analysis also revealed that conditions in one lane can induce signals in another lane. Rather than exhibiting a single signal passing a given point in time and space, the induced and intrinsic signals are superimposed on one another in the given lane. We suspect the subtle dynamics revealed in this research have gone unnoticed because they are far below the resolution of conventional traffic monitoring. The findings could have implications to other traffic flow models that rely on the FD, so care should be taken to assess if a given model is potentially sensitive to the non-stationary dynamics presented herein.The results have a direct impact on practice. Traffic flow theory is a critical input to many aspects of surface transportation, e.g., traffic management, traffic control, network design, vehicle routing, traveler information, and transportation planning all depend on models or simulation software that are based upon traffic flow theory. If the underlying traffic flow theory is flawed it puts the higher level applications at risk. So, the findings in this paper should lead to caution in accepting the predictions from traffic flow models and simulation software when the traffic exhibits a concave FD.

A Synchronized Two-Dimensional alpha –Omega Model of the Solar Dynamo

We consider a conventional alpha –Omega -dynamo model with meridional circulation that exhibits typical features of the solar dynamo, including a Hale-cycle period of around 20 years and a reasonable shape of the butterfly diagram. With regard to recent ideas of a tidal synchronization of the solar cycle, we complement this model by an additional time-periodic alpha -term that is localized in the tachocline region. It is shown that amplitudes of some decimeters per second are sufficient for this alpha -term to become capable of entraining the underlying dynamo. We argue that such amplitudes of alpha may indeed be realistic, since velocities in the range of m s−1 are reachable, e.g., for tidally excited magneto–Rossby waves.

Nurturing Neuroplasticity as an Enabler for Growth Mindset through Lifelong Learning and Knowledge Dynamics

Abstract In a world where change and uncertainty prevail, one’s ability to take full responsibility for the development of their own brain renders itself as a propensity to increase neuroplasticity by engaging in mentally challenging endeavors to be broader stimulated. Being an in-built human ability, which enables the brain to reorganize pathways and create new synapses at all times in people’s lives by accumulating new information through experiences, neuroplasticity offers people the opportunity to rewire their behaviors by constantly learning to expose to new contexts and be creative in front of challenging and complex situations. Following an empirical analysis of the literature review covering neuroplasticity, growth mindset, lifelong learning and knowledge dynamics, the paper aims to revels the connection between these forces and understand the influence each other plays in stimulating the brain, increasing its capacity and ensuing an enhanced personal and professional development. The results showcase an organic connection between neuroplasticity, growth mindset, lifelong learning and knowledge dynamics which illustrated itself in the shape of a research diagram, emphasizing the interconnections and the prevalent role of knowledge transformations.