Lagrangian Analysis Research Articles

Novel Approach to Forecasting Photospheric Emergence of Active Regions

One key aspect of understanding the solar dynamo mechanism and the evolution of solar magnetism is to properly describe the emergence of solar active regions. In this Letter, we describe the Lagrangian photospheric flows dynamics during a simulated flux emergence that produces an active region formed by pores. We analyze the lower photospheric flow organization prior, during and following the rise of an active region, uncovering the repelling and attracting photospheric structures that act as sources and sinks for magnetic element transport. Our results show that around 10 hr before the simulated emergence, considerable global changes are taking place on mesogranular scales indicated by an increase of the number of regions acting as a source to the multiple and scattered emergences of small-scale magnetic flux. At the location of active region’s appearance, the converging flows become weaker and there is an arising of a diverging region 8 hr before the emergence time. Our study also indicates that the strong concentration of magnetic field affects the flow dynamics beyond the area of the actual simulated pores, leading to complex and strongly diverging flows in the neighboring regions. Our findings suggest that the Lagrangian analysis is a powerful tool to describe the changes in the photospheric flows due to magnetic flux emergence.

Multi-Objective Approach for User Association to Improve Load Balancing and Blockage in Millimeter Wave Cellular Networks

One of the leading enabling technologies of 5G wireless networks is to use the mm-Wave spectrum band. Despite its large and wide frequency bandwidth, the obtained data rate can be diminished due to link blockage in this frequency band. We formulate a bi-objective optimization problem to optimize user association in cellular networks with mm-Wave enabled base stations. The two objectives to minimize are maximum base station utility and blockage score. We simulate three different scalarization methods to turn a bi-objective vector into a scalar. Since the combinatorial bi-objective problem is NP-Hard, we conduct Lagrangian dual analysis on all of the scalarization methods. Solving the dual problem decreases the time complexity of the solver algorithm, but the solution has a distance from the optimal point created by solving the primal. We also solve the primal optimization problem with a single objective optimization tool. Compared to the time complexity of the primal problem of scalarization methods, the time complexities of solutions to the dual problems are lower. The results show that our solution to the bi-objective optimization problem has a better outcome in terms of the number of link blockage and the maximum base station utility compared to optimizing each objective alone.

Implications of Emission Sources and Biosphere Exchange on Temporal Variations of CO2 and δ13C Using Continuous Atmospheric Measurements at Shadnagar (India)

AbstractDiurnal variation of atmospheric CO2 and its driving factors are studied using high‐precision in situ mixing ratio measurements and stable carbon isotopic CO2 (δ13C‐CO2) for the first time over Shadnagar, a suburban site in India, from November 2018 to October 2019. The annual mean mixing ratios of atmospheric CO2 and δ13C‐CO2 are observed to be 414.76 ± 4.26 ppm and −11.19 ‰ ± 1.63 ‰. Maximum diurnal variability of atmospheric CO2 was observed in summer monsoon (17.30 ± 9.29 ppm), and the minimum was noticed in winter (7.19 ± 0.11 ppm), indicating strong seasonality in diurnal variability of amplitude. To characterize the atmospheric CO2 sources, the Miller‐Tans model was implemented separately using the CO2 and its δ13C‐CO2 isotopic data during day and night. However, a strong source signature of δ13C‐CO2 was observed during the night‐time of summer monsoon with a slope of −37.42‰ ± 0.73‰, obtained using a reduced major axis regression. The identified source indicates possible emissions from fossil fuel combustion. Further, a Lagrangian back trajectory analysis was performed to study the influence of transport on the observed CO2 mixing ratios. The model trajectory confirms the influence of the Indian summer monsoon on the variations of atmospheric CO2 mixing ratios. Our study shows that fossil fuel emissions are one of the major contributors of CO2 in the study location (about ∼2 to 4 ppm) with biogenic fluxes adding a clear seasonality ranging from −8 to 4 ppm.

Agency Selling Format-Based Incentive Scheme in Cooperative Hybrid VLC/RF IoT System With SLIPT

Relay cooperation with energy harvesting provides a promising solution to alleviate coverage limitations and energy constraints in hybrid visible light communication (VLC)/radio frequency (RF) Internet of Things (IoT) system with simultaneous lightwave information and power transfer (SLIPT). In the hybrid system, the VLC service provider (VLCSP) seeks the cooperation of relay nodes (RNs) for information delivery to a certain end node (EN). However, considering the autonomous behaviors of the RNs, there are two challenging issues to address in facilitating relay cooperation: 1) selfishness and 2) information asymmetry. Hence, this article proposes a novel incentive scheme for relay cooperation based on an agency selling format. Unlike previous incentive scheme designs, first, the VLCSP charges the cooperating RN for energy harvesting per unit energy price. Second, once the information is successfully transmitted to the EN, the VLCSP pays a portion of future revenue as an agency payment to the RN, in a format seen as agency selling. By giving the VLCSP pricing power, it needs to design a mutually agreeable contract that includes a menu of unit energy prices and agency payments. Here, aiming to maximize the VLCSP’s expected utility, we apply a joint adverse selection and moral hazard model to formulate and optimize the contract design problem in the presence of information asymmetry. Then, the optimal contract solution is derived by using Lagrangian dual analysis. Besides, we present two extreme scenarios where only adverse selection or moral hazard model is applied. Numerical results illustrate that the proposed incentive scheme outperforms the considered benchmarks in terms of the expected utility of VLCSP and RNs, as well as the expected social welfare. We also demonstrate the incentive efficiency of our scheme

Selective Multi-Grade Charging Scheduling and Rebalancing for One-Way Car-Sharing Systems

This paper investigates the rebalancing and charging scheduling problem of one-way car-sharing systems. Vehicles can be charged either at the stations within the system or at the public charging stations. A framework for selective multi-grade charging scheduling and fleet rebalancing is proposed. To this end, vehicles and customers are classified into different grades for scheduling and matching, according to their state of charge and travel distance, respectively. The number of grades is involved as a decision variable in the combinatorial optimization problem, with the objective of minimizing the maximum response time and the operating cost for both rebalancing and charging. A lower bound optimal solution of the problem is given analytically based on the Lagrangian analysis and the Karush-Kuhn-Tucker (KKT) condition, yielding a joint optimization algorithm that can ensure the quality of service and balanced demand-supply in the system. Simulation results show that the method is effective in reducing system response time, improving vehicle utilization and reducing reliance on vehicle charging.

Chaotic advection in a recirculating flow: Effect of a fluid multiple-flexible-solid interaction.

This paper deals with chaotic advection due to a two-way interaction between flexible elliptical-solids and a laminar lid-driven cavity flow in two dimensions. The present Fluid multiple-flexible-Solid Interaction study involves various number N(= 1-120) of equal-sized neutrally buoyant elliptical-solids (aspect ratio β = 0.5) such that they result in the total volume fraction Φ = 10 % as in our recent study on single solid, done for non-dimensional shear modulus G ∗ = 0.2 and Reynolds number R e = 100. Results are presented first for flow-induced motion and deformation of the solids and later for chaotic advection of the fluid. After the initial transients, the fluid as well as solid motion (and deformation) attain periodicity for smaller N ≤ 10 while they attain aperiodic states for larger N > 10. Adaptive material tracking (AMT) and Finite-Time Lyapunov Exponent (FTLE)-based Lagrangian dynamical analysis revealed that the chaotic advection increases up to N = 6 and decreases at larger N(= 6-10) for the periodic state. Similar analysis for the transient state revealed an asymptotic increase in the chaotic advection with increasing N ≤ 120. These findings are demonstrated with the help of two types of chaos signatures: exponential growth of material blob's interface and Lagrangian coherent structures, revealed by the AMT and FTLE, respectively. Our work, which is relevant to several applications, presents a novel technique based on the motion of multiple deformable-solids for enhancement of chaotic advection.

A Spatio-Temporal Dynamic Visualization Method of Time-Varying Wind Fields Based on Particle System

The particle system is widely used in vector field feature visualization due to its dynamics and simulation. However, there are some defects of the vector field visualization method based on the Euler fields, such as unclear feature expression and discontinuous temporal expression, so the method cannot effectively express the characteristics of wind field on the temporal scale. We propose a Lagrangian visualization method based on spatio-temporal interpolation to solve these problems, which realizes the fusion and expression of the particle system and the time-varying wind data based on the WebGL shader. Firstly, the linear interpolation algorithm is used to interpolate to obtain continuous and dense wind field data according to the wind field data at adjacent moments. Then, we introduce the Lagrangian analysis method to study the structure of the wind field and optimize the visualization effect of the particle system based on Runge–Kutta algorithms. Finally, we adopt the nonlinear color mapping method with double standard deviation (2SD) to improve the expression effect of wind field features. The experimental results indicate that the wind visualization achieves a comprehensive visual effect and the rendering frame rate is greater than 45. The methods can render the particles smoothly with stable and outstanding uniformity when expressing continuous spatio-temporal dynamic visualization characteristics of the wind field.

Hawking radiation as tunneling with pressure and volume of the RN-AdS black hole

In consideration of the thermodynamic pressure and volume, we present a short and direct derivation of Hawking radiation as a tunneling process for the charged particles. Using Parikh's Semi-classical tunneling method and Lagrangian analysis on the action, we provide the geodesic equation of the massive particles via tunneling from the Anit-de Sitter (AdS) black hole. Special attention is given to calculating the imaginary part before and after particles via the horizon as the pressure and volume are considered. The result shows that the emission rates are always related to the change of Bekenstein-Hawking entropy and the exact spectrum is not precisely thermal, which are consistent with the case without pressure and volume.

Dynamic installation of torpedo anchors in slightly overconsolidated clay-overlaying-sand deposit

Torpedo anchor installation involves uncertain design and construction parameters, especially in layered soil deposits. Large deformation finite element and coupled Eulerian–Lagrangian (LDFE/CEL) analyses are performed in this study to elucidate the dynamic installation of torpedo anchors in an over consolidated clay-overlaying-sand deposit. The parametric analysis is conducted after model verification to explore the effect of upper clay layer thickness, anchor impact velocity, anchor submerged weight, soil properties and anchor geometric dimensions. The soil failure patterns and dynamic installation behaviour in the clay-overlaying-sand soil deposit are found to differ substantially from those in single-layer clay and sand deposits, which exhibit a squeezing flow pattern at the clay-sand soil layer interface. As the demarcation of the two velocity phases during the anchor penetration process (acceleration and deceleration phases) falls below the interface of two soil layers, the contribution of the internal friction angle of sand to the anchor final penetration depth exceeds that of the clay undrained shear strength. Based on intensive modelling data, an empirical method for predicting the anchor penetration depth in single and layered soil deposits is derived for engineering applications.

Slope Stability and Effectiveness of Treatment Measures during Earthquake

Slopes are prone to instability during earthquakes, which will cause geological disasters such as landslides and pose a great threat to people’s lives and property. Therefore, it is necessary to analyze the stability of slopes and the effectiveness of treatment measures during earthquakes. In this study, an actual slope in the creeping slide stage was selected and located in an area where earthquakes occur frequently. Once the slope experiences instability, it will produce great damage. Therefore, a finite difference program, Fast Lagrangian Analysis of Continua in Two Dimensions (FLAC2D), was employed in the numerical simulation to explore the stability of the slope before and after treatment under earthquake action. Different from previous studies, this study explores the effectiveness of various treatment measures on slope stability during earthquake. The computed results show that the stability of the slope is greatly influenced by earthquakes, and the slope displacement under seismic conditions is far larger than that under natural conditions. Three treatment measures, including excavation, anti-slide piles, and anchor cables, can significantly reduce slope displacement and the internal force on anti-slide piles, and improve the stability of a slope during an earthquake. This will provide a valuable reference for the strengthening strategies of unstable slopes. The analysis technique as well as the derived insights are of significance for slope stability and the effectiveness of treatment measures.

Temporal Variability of the Labrador Current Pathways Around the Tail of the Grand Banks at Intermediate Depths in a High‐Resolution Ocean Circulation Model

AbstractThe Northwest Atlantic Shelf and Slope have warmed dramatically in the past decade, changing marine life and challenging fisheries management. A rapid warming event in 2009/2010, linked to a reduced supply of cold water from the Labrador Sea, pushed this region to a new state of unprecedentedly high temperatures that persists today. However, a mechanistic understanding of how the Labrador Current connectivity is reduced at the Tail of the Grand Banks of Newfoundland has been lacking. Here, we present the results of a 25‐year (1993–2017) Lagrangian analysis using the HYbrid Coordinate Ocean Model. Synthetic particles were released in the vicinity of the Labrador Current upstream of the Grand Banks and tracked in a 2‐D velocity field. We found that the Labrador Current can be completely blocked by Gulf Stream eddies and meanders that impinge on the shelf break along the Grand Banks. This blocking can occur in many different locations at, upstream, or downstream of the Tail of the Grand Banks, since the Labrador Current needs a clear passage over a long distance to continue its path. In the simulation, the Labrador Current has been blocked more often since 2008, which led to the warming of the Northwest Atlantic Shelf and Slope. These results, which are consistent with satellite observations, can provide predictability for the New England and Nova Scotia shelf environments potentially helpful for ecosystem management.

Cell tracking of convective rainfall: sensitivity of climate-change signal to tracking algorithm and cell definition (Cell-TAO v1.0)

Abstract. Lagrangian analysis of convective precipitation involves identifying convective cells (“objects”) and tracking them through space and time. The Lagrangian approach helps to gain insight into the physical properties and impacts of convective cells and, in particular, how these may respond to climate change. Lagrangian analysis requires both a fixed definition of what constitutes a convective object and a reliable tracking algorithm. Whether the climate-change signals of various object properties are sensitive to the choice of tracking algorithm or to how a convective object is defined has received little attention. Here we perform ensemble pseudo-global-warming experiments at a convection-permitting resolution to test this question. Using two conceptually different tracking algorithms, Lagrangian analysis is systematically repeated with different thresholds for defining a convective object, namely minimum values for object area, intensity and lifetime. It is found that the threshold criteria for identifying a convective object can have a strong and statistically significant impact on the magnitude of the climate-change signal, for all analysed object properties. The tracking method, meanwhile, has no impact on the climate-change signal as long as the precipitation data have a sufficiently high temporal resolution: in general, the lower the minimum permitted object size is, the higher the precipitation data's temporal resolution must be. For the case considered in our study, these insights reveal that irrespective of the tracking method, projected changes in the characteristics of convective rainfall vary considerably between cells of differing intensity, area and lifetime.

Influence of Base-Angle Bolt Support Parameters and Different Sections on Overall Stability of a Roadway under a Deeply Buried High Stress Environment Based on Numerical Simulation

Strengthening the base-angle of a roadway can have a beneficial impact on its overall stability, but the specific optimal parameter selection range is still unclear. Fast Lagrangian Analysis of Continua 3D (FLAC3D) software is used to carry out the stability analysis of 5 kinds of roadway models with different section shapes under the conditions of no support and different base-angle bolt support angles, and the simulation verification is carried out under the actual working conditions of the Sanshandao Gold Mine. The conclusion is as follows: without support, the self-stability of a tri-centric arch roadway is the best, and that of a rectangular roadway is the worst. When the base-angle bolt dip angle is between 15° and 45°, a better supporting effect can be obtained under the established 5 kinds of roadway sections. In the straight wall circular arch roadway of the Sanshandao Gold Mine, the roadway stability is the best when the angle of the base-angle bolt is 15°. However, changing the length of the base-angle bolt, even if the length of the base-angle bolt is increased to a certain extent, will decrease the overall supporting effect of the supporting structure. This paper can provide a reference for the selection of tunnel bottom corner bolt support parameters.

Computational study of three-dimensional Lagrangian transport and mixing in a stirred tank reactor

The detection of compartments and dead zones as well as the estimation of the mixing efficiency in stirred tanks are of vital interest for a variety of biochemical and chemical processes. Here, numerically derived time-dependent 3D fluid velocity fields of a stirred tank reactor are computed using the Lattice Boltzmann Method. Mixing in the stirred tank reactor is analysed by means of Lagrangian Coherent Structures which allow to unravel the mixing states of complex flows. This Lagrangian analysis is achieved by computing Finite Time Lyapunov Exponents and applying recent trajectory-based network methods on the three-dimensional flow. The results reveal a zone of low interaction in the upper region of the stirred tank reactor and five additional transient compartments. The trajectory-based network analysis detects low cross-mixing of fluid parcels between different compartments but a very high mixing of fluid parcels inside of each compartment. This high interaction is also found in an analysis of the Finite Time Lyapunov Mixing Intensity. Time-averaging of the fluid velocity field prior to the Lagrangian analysis is considered to extract the most influential Lagrangian Coherent Structures.

A preliminary analysis of the mining-induced rock movement characteristics in the Xinli deposit of the Sanshandao gold mine

Commensurate with economic globalization, the demand for mineral resources is increasing. With increased mining activity, problems related to ground subsidence and rock movement are becoming increasingly prominent, even affecting mining production activities. However, the physical mechanisms behind the ground subsidence phenomenon have been poorly studied, especially for metal mines with a steep dip. This paper applies the Interferometric Synthetic Aperture Radar (InSAR) technique and the numerical simulation method to deduce the characteristics of rock movement in the Xinli deposit of the steeply inclined Sanshandao gold mine. The InSAR results indicate that more subsidence has occurred in the southern part of the Xinli Village coastline area than in the northern part. This is also supported by the numerical simulation results obtained by the fast Lagrangian analysis of continua in three dimensions (FLAC3D). Notably, the range of ground subsidence obtained by numerical simulation shows an obvious asymmetry. The monitoring data of the No. 55 prospecting profile offer a plausible explanation for this, as the surrounding rock of the fault’s hanging wall has a wider range of rock movements. Furthermore, the sublevels of the No. 55 prospecting profile at different depths show different rock movement characteristics, and a logistic function can be well applied to the right part of the settlement curve; the parameter “a” in the function formula is very close to the maximum subsidence value for each sublevel. We defined the ratio “r” to measure the difference between the maximum subsidence value and the corresponding parameter “a” and found this value to be positively correlated with the fractal dimension value of deeper sublevels (−320 m, −400 m, −480 m, and −600 m) and negatively correlated with the fractal dimension value of lower sublevels (−200 m and −240 m).

Approximate streamsurfaces for flow visualization

Instantaneous features of three-dimensional velocity fields are most directly visualized via streamsurfaces. It is generally unclear, however, which streamsurfaces one should pick for this purpose, given that infinitely many such surfaces pass through each point of the flow domain. Exceptions to this rule are vector fields with a non-degenerate first integral whose level surfaces globally define a continuous, one-parameter family of streamsurfaces. While generic vector fields have no first integrals, their vortical regions may admit local first integrals over a discrete set of streamtubes, as Hamiltonian systems are known to do over Cantor sets of invariant tori. Here we introduce a method to construct such first integrals approximately from velocity data, and show that their level sets indeed frame vortical features of the velocity field in examples in which those features are known from Lagrangian analysis. Moreover, we test our method in numerical datasets, including a flow inside a V-junction and a turbulent channel flow. For the latter, we propound an algorithm to pin down the most salient barriers to momentum transport up to a given scale providing a way out of the occlusion conundrum that typically accompanies other vortex visualization methods.

An efficient approach for computing the finite time Lyapunov exponent in complex three-dimensional flow based on the discrete phase model

We propose a method for computing the finite-time Lyapunov exponent (FTLE) based on the discrete phase model (DPM), which is integrated with a CFD solver and has several advantages as follows. Unlike the conventional method that calculates the fine velocity field first and then calculates the particle trajectory based on the velocity field, the particle position and velocity field in the resulting method are solved simultaneously in the CFD solver, which saves memory and improves the computational efficiency. The resulting method can be applied to arbitrarily complex three-dimensional flows, which helps to promote Lagrangian analysis in the complex flows in aerospace. The discrete phase model used in the resulting method is flexible and easy to be extended. For example, it can be extended from massless tracer particles to real particles with mass. The finite-time Lyapunov exponent is also used to evaluate the uniformity of scalar convection mixing, it is found that the larger the finite-time Lyapunov exponent at the mixture contact line, the longer the contact line for the next time period, indicating more uniform convective mixing.

Monopile installation in clay and subsequent response to millions of lateral load cycles

The installation-induced changes in the state of clayey soils caused by pile driving processes are investigated numerically. Hydro-mechanically coupled Coupled-Eulerian–Lagrangian analyses are carried out for this purpose. After installation, the piles are subjected to one million lateral loading cycles using a novel high-cycle accumulation (HCA) model for clay implemented in an in-house code, modelling loading conditions to which piles are subjected in the offshore environment. Consistent with the results of field tests, it is found that higher values of initial overconsolidation ratio result in a greater increase in radial effective stress during the installation process. Compared to simulations neglecting the installation process, jacked piles show less accumulation of deformations when subjected to lateral cyclic loading, especially for a larger number of load cycles and for initially overconsolidated soil. It is concluded that the assumption of wished-in-place conditions is conservative in terms of pile rotation in most cases, while the stiffness of the soil–pile system at small rotations is comparable for jacked and wished-in-place piles.

Evaluation of the distribution of COVID-19 particles in an Isolation room to reduce the possibility of transmission via CFD simulation

The outbreak and prolonged COVID-19 pandemic has caused a population decline as well as a profound impact on the global economy, the COVID virus spreads highly in the air through the process of sneezing, contact leads to many dangers to the health and safety of people around the world. Many simulation studies have been carried out to predict the risk of spread, as well as to find solutions to limit the infection when spreading sneeze droplets in the air. In this study, the motion and distribution of droplets containing coronaviruses emitted by coughing or sneezing in the isolation room at Ho Chi Minh City, Vietnam National University were investigated using ANSYS Fluent software. The airflow in the isolation room was simulated by a 3D turbulence model and energy equation using the finite volume method (FVM) with a domain of isolation room solved for appropriate boundary conditions. The effect of ventilation airflow speed and the size of droplets on the distribution of particles in the air were investigated by the Lagrangian particle trajectory analysis method. The CFD analysis result showed that the velocity distribution, turbulent kinetic energy, and flow dynamics had strongly affected the reducing rate of average droplet concentration in the isolation room. Specifically, the study focused on the dispersion of liquid droplets containing the virus under fixed operating conditions of ventilation systems and exhaust fans, with a flow rate of 840 m3/h. Under these conditions, the retention time of liquid droplets was determined to be 37.5 seconds, corresponding to droplet diameters ranging from 5 to 100 micrometres. The results indicate that the presence of particles in the room gradually becomes diluted over time due to the continuous circulation of air. The ability of air to diffuse within the vicinity of the occupant's position and the limited spread of small particles within the room demonstrate that the operating conditions are suitable.

A data-driven machine learning framework for modeling of turbulent mixing flows

A novel computationally efficient machine learning (ML) framework has been developed for constructing the turbulent flow field of single-phase or two-phase particle-liquid flows in a mechanically agitated vessel by feeding a very short-term experimental Lagrangian trajectory. Using a supervised k-nearest neighbors regressor learning algorithm coupled with a Gaussian process, the framework predicts the mean flow and turbulent fluctuations by sharing the statistical features learned from experimental data. The capability of the ML framework is evaluated by comparing the flow dynamics of predicted trajectories to extensive Lagrangian particle tracking measurements under various flow conditions. Local velocity distributions, Lagrangian statistical analysis, solid concentration distributions, and phase flow numbers show very good agreement between ML-predictions and experiments. Being accurate, efficient, and robust, the ML framework is a powerful tool for analyzing and modeling multiphase flow systems using a minimal amount of driver data input, which can equally be provided from any reliable numerical simulation, thus avoiding costly experimental measurements.