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Can we elaborate a traffic-sensitive eco-driving or GLOSA (Green Light Optimal Speed Advice) strategy with a frugal amount of data when approaching an intersection? Here is the purpose of this work, which aims to adapt a traffic-theory-based estimation of the expected queue-length within mixed traffic (Connected and non-Connected Vehicles) in the vicinity of a signalized intersection. While the expected queue-length methodology was developed recently and fits natively with Eulerian traffic indicators resulting from loop sensors or cameras, this paper adapts such a methodology to Lagrangian indicators as the traces produced by any Connected Vehicle, including Floating Car or Probe Data. The main interest of the methodology lies in the frugal amount of data and expenses required to perform the traffic-sensitive speed-advisory at any connected road intersection. The full methodology is developed to extend the SPAT messages broadcast to end-users and take advantage of the Cooperative Awareness Messages (CAM) acting as GPS traces for Connected Vehicles. Contrary to Eulerian-based indicators, no supplementary and costly investment is required to collect the input data and compute the queue-length estimation. However, applying strategies based on Lagrangian indicators will affect the direct traffic observation through these indicators. Therefore, it requires to develop an assessment and predictive framework to estimate the traffic conditions. The performance of the introduced methodology is compared to alternative methods, among other Eulerian-based methods. It results from the analysis that the introduced approach performs almost as well as the ones based on exhaustive, but costly data collections. [ABSTRACT FROM AUTHOR]

This paper makes significant contributions to the study of a generalized form of the Duffing-type equation. We derive the generating operators of the optimal system associated with this equation, enabling us to characterize an implicit solution. Additionally, we present a complete classification of group symmetries and obtain the Lagrangian for the equation. Our results include the classification of the Lie algebra and the optimal system, providing a thorough understanding of the equation's underlying structure. These contributions serve to enhance the current body of knowledge on the Duffing-type equation and provide useful insights for future research in this area. [ABSTRACT FROM AUTHOR]

Ocean currents are a crucial means of dispersing natural and human-made materials on the ocean surface. Macroalgae are among the most conspicuous natural dispersers, often called the 'tumbleweeds of the ocean.' Despite numerous studies on the subject, the relative influence of wind and surface currents on the trajectory of macroalgal dispersal remains uncertain. Previous studies have focused on kelp rafts of varying sizes, making it challenging to determine the impact of wind versus currents. These studies have also disregarded the macroalgae's drag characteristics and surface area, which have been shown to impact the trajectory and accumulation of floating flotsam. This numerical study aims to shed light on the relative influence of wind and currents and the role of drag in determining the course and accumulation of macroalgae. By comparing simulations of virtual kelp 'particles' that incorporate drag and those without, this study focused on solitary kelp plants and considered the impact of morphological characteristics, flow-field combinations, and the presence of Stokes drift. Our results show that virtual kelp particles generally followed ocean currents, but the inclusion of drag caused deviations from purely Lagrangian particles' trajectories and sheds light on the complex interplay of factors affecting macroalgal dispersal in the ocean. [ABSTRACT FROM AUTHOR]

The objective was to construct and test an economical, accurate, and open‐source Lagrangian drifter design suitable for lakes <200 km2. Lagrangian drifters are used to trace water currents in marine and freshwater settings and comprise of a low‐friction surface float containing instrumentation for location and environmental measurement, tethered to a high‐friction drogue at the depth of interest. Oceanic drifters are robust but expensive, and this design tailored to inland lake waterbodies fills a durability and cost gap for lake environments. Water‐following characteristics were tested using theoretical drag coefficient calculations, practical drag measurements, and comparison of wind and drifter vectors while deployed on two deep inland lakes (maximum area 175 km2) in the Finger Lakes region of New York, USA. The ratio of drag between float and drogue met or exceeded the minimum value of 40 recommended in the literature, and the vectors of wind and drifter during deployment were independent of one another, meaning the device accurately traced the movement of water currents at depth without undue influence of wind and waves. Each device cost USD $265 in 2021 and was built from materials readily available at hardware and sporting goods stores, allowing their use by research institutions and communities with smaller budgets. This design reliably measured lake currents at sampling depths that ranged from 2 to 30 m. We anticipate that this design will have application to a wide range of hydrodynamic and ecological research where empirical insights to physical processes like lake currents are sought by scientists and managers. Plain Language Summary: Lake currents are complex, yet often lack data for scientists to analyze them. We built and tested a low‐cost, accurate device that can follow water currents in lakes, made from easily available parts. Unlike similar devices for oceans which can be bulky and costly, this device is well‐suited for lakes. It works by floating on the water's surface and has a part that hangs below it in the water to track water movement at different depths. Tests in two New York lakes showed it does a great job of tracking water without being thrown off by wind or waves. Making each device costs USD $265, using parts found in regular stores, so it's affordable for smaller research teams or local communities. It's good for studying water movements from near the surface down to 30 m or even deeper, helping scientists and local managers learn more about how water moves in lakes. Key Points: An economical, open‐source Lagrangian drifter designed to collect current data on lakes <200 km2 was evaluated against existing designsThe new design was tested in deep inland lakes in the Finger Lakes region of New York, USA and is effective at tracking deep currentsThe ease and low‐cost of fabrication and launch/recovery should facilitate use of this design by less‐advantaged communities & researchers [ABSTRACT FROM AUTHOR]

A computationally time-efficient method is introduced to implement pressure load to a Finite element model. Hexahedron elements of the Lagrangian family with Gauss–Lobatto nodes and integration quadrature are utilized, where the integration points follow the same sequence as the nodes. This method calculates the equivalent nodal force due to pressure load using a single Hadamard multiplication. The arithmetic operations of this method are determined, which affirms its computational efficiency. Finally, the method is tested with finite element implementation and observed to increase the runtime ratio compared to the conventional method by over 20 times. This method can benefit the implementation of finite element models in fields where computational time is crucial, such as real-time and cyber–physical testbed implementation. [ABSTRACT FROM AUTHOR]

In a Wilberforce pendulum, two mechanical oscillators are coupled: one pertains to the longitudinal (tension) motion and the other to the rotational (twisting) motion. It is shown that the longitudinal magnetic moment of circular currents, and similarly the magnetic moment of a spin-chain, can exhibit a Wilberforce-like vibration. The longitudinal oscillation is related to the Langevin diamagnetism, while the twisting motion is superimposed on the magnetic moment and spin precession. The calculations show that the coupling term is nonlinear in this (longitudinal) vibrating and (magnetic moment) precession system. By increasing the strength of the coupling we arrive at a spectrum, where further vibrational modes can be associated with the rotation of the precession. This means that the extent of the change in coherence can be demonstrated. Since the coupling strength can be different due to local effects, this can be an important factor from the point of view of signal propagation and in preserving signal shapes. The amount specifying the dissipation is introduced to express the degree of deviation. A relationship exists between the parameter characteristic of the coupling strength and how its quantity influences decoherence and dissipation. [ABSTRACT FROM AUTHOR]

Accurate mechanical system models are crucial for safe and stable control. Unlike linear systems, Lagrangian systems are highly nonlinear and difficult to optimize because of their unknown system model. Recent research thus used deep neural networks to generate linear models of original systems by mapping nonlinear dynamic systems into a linear space with a Koopman observable function encoder. The controller then relies on the Koopman linear model. However, without physical information constraints, ensuring control consistency between the original nonlinear system and the Koopman system is tough, as the learning process of the Koopman observation function is unsupervised. This paper thus proposes a two-stage learning algorithm that uses structural subnetworks to build a physics-informed network topology to simultaneously learn the Koopman observable functions and the system energy representation. In the Koopman matrix learning session, a quadratic-constrained optimization problem is solved to ensure that the Koopman representation satisfies the energy difference matching hard constraint. The proposed energy-preserving deep Lagrangian Koopman (EPDLK) framework effectively represents the dynamics of the Lagrangian system while ensuring control consistency. The effectiveness of EPDLK is compared with those of various Koopman observable function construction methods in multistep prediction and trajectory tracking tasks. EPDLK achieves better control consistency by guaranteeing energy difference matching, which facilitates the application of the control law generated on the Koopman system directly to the original nonlinear Lagrangian system. [ABSTRACT FROM AUTHOR]

A computationally time-efficient method is introduced to implement pressure load to a Finite element model. Hexahedron elements of the Lagrangian family with Gauss–Lobatto nodes and integration quadrature are utilized, where the integration points follow the same sequence as the nodes. This method calculates the equivalent nodal force due to pressure load using a single Hadamard multiplication. The arithmetic operations of this method are determined, which affirms its computational efficiency. Finally, the method is tested with finite element implementation and observed to increase the runtime ratio compared to the conventional method by over 20 times. This method can benefit the implementation of finite element models in fields where computational time is crucial, such as real-time and cyber–physical testbed implementation.

This paper presents an overlay-based one-way coupled Eulerian–Lagrangian computational approach designed to investigate the dynamics of particulate phases in extreme high-speed, high-altitude flight conditions characterized by very low particulate mass loading. Utilizing the Direct Simulation Monte Carlo method to generate accurate gas flow fields, this study explores two canonical hypersonic flow systems. First we focus on the hypersonic flow over a sphere-cone, revealing the formation of dust-free zones for small particulate diameters and describing the particulate interaction with gas shocks. As particulate diameter and flight speed increase, the characteristics of the particulate phase evolve, leading to the emergence of distinctive features such as high particulate concentration bands or regions void of particulates. Subsequently, the investigation considers flow over a double-cone, emphasizing the behavior of particulate phases in separated vortex-dominated systems where particulate-inertia-driven interactions with vortices result in unique particulate-free zones in the vicinity of the primary and secondary vortices. Additionally, the paper addresses the importance of using realistic fractal-like particulate shapes and demonstrates that the shape effect tends to decelerate the fractal aggregates and trap them along the boundaries of the primary vortex. This research contributes to a deeper understanding of particulate phase dynamics in extreme flight conditions, offering insights relevant to aerospace and aerodynamic applications. [ABSTRACT FROM AUTHOR]

The goal of this article is to compute conservation law, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation using the homotopy operator, the $\mu$-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the $\mu$-conservation law of these three equation.

The paper defines a class of Hamiltonian systems whose phase flows are exact solutions of the two-dimensional hydrodynamics of an incompressible fluid. The properties of this class are considered. An example of a Lagrangian one-dimensional system is given, which after the transition to the Hamiltonian formalism leads to an unsteady flow, that is, to an exact solution of two-dimensional hydrodynamics. The connection between these formalisms is discussed and the Lagrangians that give rise to Lagrangian hydrodynamics are introduced. The obtained results make it possible to obtain accurate solutions, such as phase flows of special Hamiltonian systems.

For gas turbine combustors, injecting liquid fuel in crossflow can achieve superior mixing characteristics to improve performance and reduce emissions. Robust numerical design tools are needed to accelerate the development of low-emissions technologies. Atomization modeling is often facilitated by using the Lagrangian approach rather than the more complex and computationally expensive Volume-of-Fluid (VOF) approach. However, most Lagrangian breakup models rely on empirical constants that must be fully calibrated for jets in crossflow and representative conditions. A hybrid approach could deliver a better compromise between accuracy and computational cost. This study proposes and validates a novel numerical methodology for coupling the VOF and Lagrangian approaches using a stochastic breakup model with Adaptive Mesh Refinements for turbulent liquid fuel jets in crossflow under more representative gas turbine conditions. The predictions were validated in the near and far-field regions using datasets at high pressures (1-8 bar), Weber numbers (720-1172), and momentum flux ratios (6-33). The predictive capabilities and computational cost were also compared to the Lagrangian approach coupled with large eddy simulations (LES) and with the unsteady Reynolds-Averaged Navier-Stokes (RANS) methodology previously developed and validated by the authors. The effect of different VOF-Lagrangian transition criteria on the computational cost was also assessed and recommendations were provided for further improvements. The overall LES predictions were significantly improved by the proposed hybrid methodology. Although it tends to underpredict the spray trajectory and Sauter Mean Diameter compared to the URANS methodology, it better captures the diameter in the wake region and the droplet velocities. [ABSTRACT FROM AUTHOR]

This paper describes several different variational formulations of the so-called 'cellular problem'' which is a system of partial differential equations arising in the theory of homogenization, subject to periodicity boundary conditions. These variational formulations of the cellular problem, all of them equivalent, have as main unknown the displacement, the stress or the strain, respectively. For each of these three cases, an equivalent minimization problem is introduced. The variational formulation in stress proves to have a distinguished role and it gives rise to two dual formulations, one in displacement-stress and another one in strain-stress. The corresponding Lagrangians may be used in numerical optimization for developing algorithms based on alternated directions, of Uzawa type. [ABSTRACT FROM AUTHOR]

Thermal spray coating is a procedure that deposits many particles on the coating layer. This paper reviews thermal spray process numerical models. These models have both benefits and drawbacks. The future in the thermal coating process numerical simulation trends have been addressed in this article. The research closes with a numerical model analysis and development possibilities. FGCs solve traditional coatings' problems. It involves mathematical and computer simulations of FGC behaviour. To verify model accuracy, experimental data is compared to numerical model output. The numerical model shows stress distribution, thermal behaviour, and diffusion processes, allowing design optimisation. It also simplifies physics. FGC and numerical modelling can improve advanced engineering coating performance, durability, and functionality. Coatings can improve energy conversion, storage, and other applications. Future work includes using advanced numerical methods to increase model accuracy and creating new models for specialised purposes. [ABSTRACT FROM AUTHOR]

The goal of this article is to compute conservation law, Lagrangian and μ-conservation law of the generalized Rosenau-type equation using the homotopy operator, the μ-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the μ-conservation law of these three equation. [ABSTRACT FROM AUTHOR]

North Atlantic subtropical mode water (NASTMW) serves as a major conduit for dissolved carbon to penetrate into the ocean interior by its wintertime outcropping events. Prior research on NASTMW has concentrated on its physical formation and destruction, as well as Lagrangian pathways and timescales of water into and out of NASTMW. In this study, we examine how dissolved inorganic carbon (DIC) concentrations are modified along Lagrangian pathways of NASTMW on subannual timescales. We introduce Lagrangian parcels into a physical‐biogeochemical model and release these parcels annually over two decades. For different pathways into, out of, and within NASTMW, we calculate changes in DIC concentrations along the path (ΔDIC), distinguishing contributions from vertical mixing and biogeochemical processes. The strongest ΔDIC is during subduction of water parcels (+101 μmol L−1 in 1 year), followed by transport out of NASTMW due to increases in density in water parcels (+10 μmol L−1). While the mean ΔDIC for parcels that persist within NASTMW in 1 year is relatively small at +6 μmol L−1, this masks underlying dynamics: individual parcels undergo interspersed DIC depletion and enrichment, spanning several timescales and magnitudes. Most DIC enrichment and depletion regimes span timescales of weeks, related to phytoplankton blooms. However, mixing and biogeochemical processes often oppose one another at short timescales, so the largest net DIC changes occur at timescales of more than 30 days. Our new Lagrangian approach complements bulk Eulerian approaches, which average out this underlying complexity, and is relevant to other biogeochemical studies, for example, on marine carbon dioxide removal. Plain Language Summary: Mode waters are relatively thick water masses with homogeneous properties, such as temperature and salinity. The North Atlantic subtropical mode water (NASTMW), found in the Sargasso Sea, is one such water mass. Lying underneath the ocean surface, it comes into contact with the atmosphere during winter, when the surface layer is vigorously mixed due to strong winds, causing the mixed layer to connect with NASTMW. This way, NASTMW can buffer atmospheric temperature and carbon anomalies during the summer, when there is no surface connection. It is also a conduit for carbon to penetrate beneath the ocean's upper mixed layer, with the potential to sequester it. We study NASTMW from the viewpoint of a water parcel that moves with the currents and see how carbon concentrations in the water parcels change along different NASTMW pathways. For each pathway, the carbon concentration changes due to an interplay of vertical mixing and biogeochemical processes, for example, related to plankton growth and decay. These processes can unfold over different timescales and may counteract or enhance themselves or one another. The largest change in carbon concentration is found when a parcel moves from the upper ocean mixed layer into NASTMW, mostly due to vertical mixing. Key Points: Carbon transformations along pathways of North Atlantic Subtropical Mode Water are split into mixing and biogeochemical contributionsAlong paths into, within, and out of this mode water, mixing and biogeochemistry alter carbon in water parcels over a range of timescalesEnrichment is highest during mixed layer subduction, which few parcels undergo annually; persistence in mode water is the dominant pathway [ABSTRACT FROM AUTHOR]

This paper develops a theoretical basis and a systematic process for resolving all inertia forces along generalized coordinates from the overall energy equation of a dynamical system. The theory is developed for natural systems with scleronomic constraints, where the potential energy is independent of generalized velocities. The process involves expansion of the energy equation, and specifically a special expansion of the kinetic energy term, from which the inertia forces emerge. The expansion uses fundamental kinematic identities of the phase space. It is also guided by insights drawn from the structure of the Hamiltonian function. The resulting equation has the structure of the D'Alembert's equation but involving generalized coordinates, from which the Lagrange's equations of motion are obtained. The expansion process elucidates how certain inertia forces manifest in the energy equation as composite terms that must be accurately resolved along different generalized coordinates. The process uses only the system energy equation, and neither the Hamiltonian nor the Lagrangian function are required. Extension of this theory to non-autonomous and non-holonomic systems is an area of future research. [ABSTRACT FROM AUTHOR]

We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show a relationship between an appropriate formulation of Colding-Minicozzi entropy and a quantity we call the CR-volume that is computed from the asymptotic geometry of such submanifolds. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop a numerical tool for computing the weak periodic solution for a class of parabolic equations with nonlinear boundary conditions. We formulate our problem as a minimization problem by introducing a least-squares cost function. With the help of the Lagrangian method, we calculate the gradient of the cost function. We build an iterative algorithm to simulate numerically the weak periodic solution to the considered problem. To illustrate our approach, we present some numerical examples. [ABSTRACT FROM AUTHOR]

Variational Integrator (VI) is a numerical technique, in which the Lagrangian of the system is used as the action integral. It is a special type of numerical solution that preserves the energy and momentum of the system. In this paper, we retrieve numerical solutions for heat and wave equation with the help of all possible combinations of finite difference scheme like forward–forward, forward–backward, forward–centered, backward–forward, backward–backward, backward–centered, centered–forward, centered–backward, centered–centered. We also use Lagrangian approach along with the projection technique to obtain approximate solutions of these linear models. This approach provides the best approximate solutions as well as preserves the energy of the system while the finite difference scheme gives only the numerical solutions. We also draw a comparison of existing exact solution with all approximate solutions for both models and provide graphical representation of these solutions. [ABSTRACT FROM AUTHOR]

Convergence zones (CZs) are known drivers of precipitation regimes from regional to planetary scales. However, there is a scarcity of accounts of the contribution of CZs to the global precipitation. In this study, we build upon a recently developed Lagrangian diagnostic to attribute precipitation to CZ events in observations and simulations submitted to the Coupled Model Intercomparison Project 6 (CMIP6). Observed CZs are identified using ERA5 reanalysis wind and attributed precipitation from observational products based on satellite estimates and rain gauges. We estimate that approximately 54% (51%–59%, depending on the precipitation product) of global precipitation falls over CZs; in some regions, such as the Intertropical Convergence Zone (ITCZ) and subtropical monsoon regions, this proportion is greater than 60%. All CMIP6 simulations analyzed here attribute about 10% more precipitation to CZ events than what the observations suggest. To investigate this overestimation, we decompose the precipitation error in terms of frequency and intensity of CZ precipitation and find that all models present a substantial positive bias in the frequency of CZ precipitation, suggesting that climate models trigger precipitation too easily in regions of airmass confluence; such positive frequency biases in CZ precipitation help explaining well‐known biases in climate models, such as the double‐ITCZ in the Pacific. We also find that models with better mass conservation present an apportionment of CZ precipitation closest to the observational estimates, demonstrating the relevance of mass conservation in advection schemes. Plain Language Summary: Rain is crucial for human and animal livelihoods. In the Earth's atmosphere, rain often occurs in organized cloud bands of hundreds or thousands of kilometers lengthwise. This type of organized rain is usually denominated as occurring within a convergence zone (CZ). In this study, we use a recently developed method to identify these CZs and apply it to observational data to find out how much of Earth's rain falls in regions under the influence of CZs (approximately 54%). We repeat this exercise in climate model data and find that all models overestimate rain in regions under the influence of CZs by about 10%. Our results point to the importance of CZs for the global hydrological cycle and ways in which climate models need improvement to better simulate CZ rainfall. Key Points: Approximately 54% of global precipitation falls over convergence zonesClimate models overestimate this ratio by approx. 10%Conservative moisture advection schemes seem to alleviate this overestimation [ABSTRACT FROM AUTHOR]

In this paper, we study Lagrangian submanifolds of the pseudo‐nearly Kähler SL(2,R)×SL(2,R)$\mathrm{SL}(2,\mathbb {R})\times \mathrm{SL}(2,\mathbb {R})$. First, we show that they split into four different classes depending on their behavior with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space. [ABSTRACT FROM AUTHOR]

The Raychaudhuri equation (RE) for a congruence of curves in a general non-Riemannian geometry is derived. A formal connection is established between the expansion scalar and the cross-sectional volume of the congruence. It is found that the expansion scalar is equal to the fractional rate of change of volume, weighted by a scalar factor that depends on the non-Riemannian features of the geometry. Treating the congruence of curves as a dynamical system, an appropriate Lagrangian is derived such that the corresponding Euler–Lagrange equation is the RE. A Hamiltonian formulation and Poisson brackets are also presented. [ABSTRACT FROM AUTHOR]

Mesoscale convective systems (MCSs) are clusters of thunderstorms that are important in Earth's water and energy cycle. Additionally, they are responsible for extreme events such as large hail, strong winds, and extreme precipitation. Automated object‐based analyses that track MCSs have become popular since they allow us to identify and follow MCSs over their entire life cycle in a Lagrangian framework. This rise in popularity was accompanied by an increasing number of MCS tracking algorithms, however, little is known about how sensitive analyses are concerning the MCS tracker formulation. Here, we assess differences between six MCS tracking algorithms on South American MCS characteristics and evaluate MCSs in kilometer‐scale simulations with observational‐based MCSs over 3 years. All trackers are run with a common set of MCS classification criteria to isolate tracker formulation differences. The tracker formulation substantially impacts MCS characteristics such as frequency, size, duration, and contribution to total precipitation. The evaluation of simulated MCS characteristics is less sensitive to the tracker formulation and all trackers agree that the model can capture MCS characteristics well across different South American climate zones. Dominant sources of uncertainty are the segmentation of cloud systems in space and time and the treatment of how MCSs are linked in time. Our results highlight that comparing MCS analyses that use different tracking algorithms is challenging. We provide general guidelines on how MCS characteristics compare between trackers to facilitate a more robust assessment of MCS statistics in future studies. Plain Language Summary: Large clusters of thunderstorms, called mesoscale convective systems (MCSs), are important in Earth's water and energy cycle including extreme weather events like large hail, strong winds, and heavy rainfall. To better understand MCSs, researchers have developed computer programs called MCS trackers that can identify and track MCSs throughout their lifespan. Different MCS tracking algorithms have been created and used for various purposes, but little is known about how sensitive the results are to the specific algorithm used. This study aims to address this knowledge gap by comparing six different MCS tracking algorithms and assessing their impact on the characteristics of MCSs in South America. We also analyze how sensitive high‐resolution climate simulation evaluations are to the used tracking algorithm. The results show that the choice of tracking algorithm has a large influence on various characteristics of MCSs, such as their frequency, size, duration, and importance to the regional water cycle. However, when it comes to evaluating simulated MCS characteristics, the choice of tracker has less impact. Importantly, all trackers agree that the high‐resolution climate model accurately represents MCS characteristics across different climate zones in South America. Key Points: Mesoscale convective system (MCS) tracker formulation has a profound impact on MCS characteristics such as their frequencies, size, duration, and precipitation volumeTracker formulation uncertainties are smaller for evaluating modeled MCS characteristics but larger for MCS frequency statisticsMCS tracking studies have to be compared cautiously, particularly when different tracking algorithms and MCS classifications are used [ABSTRACT FROM AUTHOR]

The paper defines a class of Hamiltonian systems whose phase flows are exact solutions of the two-dimensional hydrodynamics of an incompressible fluid. The properties of this class are considered. An example of a Lagrangian one-dimensional system is given, which after the transition to the Hamiltonian formalism leads to an unsteady flow, that is, to an exact solution of two-dimensional hydrodynamics. The connection between these formalisms is discussed and the Lagrangians that give rise to Lagrangian hydrodynamics are introduced. The obtained results make it possible to obtain accurate solutions, such as phase flows of special Hamiltonian systems. [ABSTRACT FROM AUTHOR]

The Bertotti–Robinson (BR) spacetime is an important class of spherically symmetric spacetime. It is a conformally flat and static solution of the Einstein–Maxwell equations. In this article a complete list of the BR spacetime is obtained according to the Noether symmetries. This classification not only classifies the said spacetime but also provides Noether symmetries and conservation laws along with each class. [ABSTRACT FROM AUTHOR]

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Introduction: Patterns of larval dispersal in the marine environment have many implications for population dynamics, biodiversity, fisheries, ecosystem function, and the effectiveness of marine protected areas. There is tremendous variation in factors that influence the direction and success of marine larval dispersal, making accurate prediction exceedingly difficult. The key physical factor is the pattern of water movement, while two key biological factors are the amount of time larvae spend drifting in the ocean (pelagic larval duration - PLD) and the time of the year at which adult populations release larvae. Here, we assess the role of these factors in the variation of predicted larval dispersal and settlement patterns from 15 locations around Aotearoa New Zealand. Methods: The Moana Project Backbone circulation model paired with OpenDrift was used to simulate Lagrangian larval dispersal in the ocean with basic vertical control across four differing PLD groups (7, 14, 30, and 70 days) for each of twelve months. Results: Considerable variation was observed in the pattern of particle dispersal for each major variable: release location, PLD group, and the month of release. As expected, dispersal distances increased with PLD length, but the size of this effect differed across both release location and month. Increased and directional particle dispersal matched some expectations from well-known currents, but surprisingly high self-recruitment levels were recorded in some locations. Discussion: These predictions of larval dispersal provide, for the first time, an empirical overview of coastal larval dispersal around Aoteaora New Zealand's main islands and highlight potential locations of "barriers" to dispersal. This dataset should prove valuable in helping predict larval connectivity across a broad range of species in this environment for diverse purposes. [ABSTRACT FROM AUTHOR]

Through the discussion of three physical processes, we show that the Klein–Gordon equations with a negative mass term describe special dynamics. In the case of two classical disciplines—mechanics and thermodynamics—the Lagrangian-based mathematical description is the same, even though the nature of the investigated processes seems completely different. The unique feature of this type of equation is that it contains wave propagation and dissipative behavior in one framework. The dissipative behavior appears through a repulsive potential. The transition between the two types of dynamics can be specified precisely, and its physical meaning is clear. The success of the two descriptions inspires extension to the case of electrodynamics. We reverse the suggestion here. We create a Klein–Gordon equation with a negative mass term, but first, we modify Maxwell's equations. The repulsive interaction that appears here results in a charge spike. However, the Coulomb interaction limits this. The charge separation is also associated with the high-speed movement of the charged particle localized in a small space domain. As a result, we arrive at a picture of a fast vibrating phenomenon with an electromagnetism-related Klein–Gordon equation with a negative mass term. The calculated maximal frequency value ω = 1.74 × 10 21 1/s. [ABSTRACT FROM AUTHOR]

We consider a method for obtaining equations of the Hamiltonian dynamics for system of interacting massive charged particles using the general relativistic Einstein–Hilbert action. In the general relativistic case, Vlasov-type equations are derived in the nonrelativistic and weakly relativistic limits. Expressions are proposed for corrections to the Poisson equation, which can contribute to the effective action of dark matter and dark energy. In this case, an efficient approach to synchronizing the proper times of different particles of a many-particle system is proposed. Based on the obtained expressions for the action, we analyze the possibility of a composite structure of the cosmological term in the Einstein equations. Reduced Euler equations leading to the Milne–McCrea cosmological model are derived using a hydrodynamic substitution and are solved in the self-similar class. [ABSTRACT FROM AUTHOR]

The evolution of ice‐phase particles within precipitating clouds depends on the environmental properties of the cloud and on physical characteristics of the particles themselves, which can be modified by airflow over steep terrain. Through employing a unique Lagrangian particle‐based precipitation model, this study investigates the sensitivities in ice‐phase particle growth and transport due to variabilities in riming processes over an orographic barrier. This analysis is applied to two wintertime stratiform cyclones sampled by in situ aircraft over windward slopes during the Olympic Mountains Experiment. For both events, we simulate the ice‐phase particle evolution and trajectory within a two‐dimensional prescribed state representative of median observed cloud properties. Sensitivity simulations were constructed based on observed variabilities in supercooled liquid water (SLW) properties and its vertical extent above the melting level. Perturbations of SLW concentration equivalent to the 85th and 15th percentiles of observed values, which typically amounted to a change of less than 0.05 g m−3, resulted in respective increases or decreases in the ice‐phase contribution to surface precipitation mass by as much as 50% and horizontal particle trajectories differences exceeding 10 km. Similar sensitivities were found in response to varying the vertical extent of SLW above the melting level and to adjustments in mean SLW droplet size. The significant precipitation response to small variations in cloud properties principally arises from changing rates of rime mass accumulation and correspondingly, increases in particle fall speed. Considerations for the numerical representation of the riming process and its complex effects on precipitation are discussed. Plain Language Summary: Precipitating clouds produce rain and snow at varying rates depending on the properties of the cloud. At below freezing temperatures in clouds, it is common to have a mixed‐phase layer where ice crystals and liquid droplets, in a supercooled state, coexist. Collection of the supercooled liquid droplets on the ice crystals greatly affects the mass and fall speed of the ice crystals, thereby affecting where, and how much, precipitation reaches the surface. In this study, we use a numerical model to simulate the evolution of individual precipitating ice crystals and evaluate sensitivities to the concentration and distribution of supercooled liquid droplets in the cloud. Based on variabilities measured in clouds upstream of the Olympic Mountains, small changes in the concentration of supercooled liquid droplets, the size of the liquid droplets, or the depth of the mixed‐phase layer produces changes in rain rates of up to 50% and increases or decreases in the distance a particle travels by as much as 10 km. We discuss the implications of these significant sensitivities to the precipitation rate and fall characteristics. Key Points: Particle‐based models provide frameworks for simulating the evolution and trajectory of precipitating particles in stratiform winter stormsFor sufficiently deep mixed‐phase clouds, small variations in supercooled liquid water mass may alter precipitation rates by as much as 50%Particle trajectory is significantly modulated by mixed‐phase layer depth through cumulative adjustments in fall velocity during riming [ABSTRACT FROM AUTHOR]

Wave propagation or acoustic emission waves caused by impact load can be simulated using the finite element (FE) method with a refined high-fidelity mesh near the impact location. This paper presents a method to refine a 3D finite element mesh by increasing the polynomial order near the impact location. Transition elements are required for such a refinement operation. Three protocols are defined to implement the transition elements within the low-order FE mesh. Due to the difficulty of formulating shape functions and verification, there are no transition elements beyond order two in the current literature for 3D elements. This paper develops a complete set of transition elements that facilitate the transition from first- to fourth-order Lagrangian elements, which facilitates mesh refinement following the protocols. The shape functions are computed and verified, and the interelement compatibility conditions are checked for each element case. The integration quadratures and shape function derivative matrices are also computed and made readily available for FE users. Finally, two examples are presented to illustrate the applicability of this method. [ABSTRACT FROM AUTHOR]

Recent advancements in particle dispersion modeling have significantly enhanced our understanding and capabilities in predicting and analyzing the behavior of particulate matter in various environments. However, this field still confronts several research gaps and challenges that span across scientific inquiry and technological applications. This paper reviews the current state of particle dispersion modeling, focusing on various models such as Lagrangian, Eulerian, Gaussian, and Box models, each with unique strengths and limitations. It highlights the importance of accurately simulating multi-phase interactions, addressing computational intensity for practical applications, and considering environmental and public health implications. Furthermore, the integration of emerging technologies like machine learning (ML) and artificial intelligence (AI) presents promising avenues for future advancements. These technologies could potentially enhance model accuracy, reduce computational demands, and enable handling complex, multi-variable scenarios. The paper also emphasizes the need for real-time monitoring and predictive capabilities in particle dispersion models, which are crucial for environmental monitoring, industrial safety, and public health preparedness. [ABSTRACT FROM AUTHOR]

The concept of video motion magnification has become increasingly relevant due to its ability to detect small and invisible motions that can be of great value in a variety of applications. A variety of approaches have been developed to magnify these motions and variations. While both Eulerian and Lagrangian processing methods are widely used for motion magnification, Eulerian approaches are more commonly employed due to their lower computational cost. This paper provides an overview of the powerful Eulerian motion magnification techniques. We begin with a brief introduction to technical concepts associated with Eulerian motion techniques such as pyramids and filters in image processing. Additionally, we provide a comparison between the Lagrangian and Eulerian perspectives, followed by a comprehensive overview of the various Eulerian motion magnification (EVM) techniques available. Finally, we present implementation results and a comparative analysis of some of the Eulerian motion techniques. [Display omitted] • Detecting Imperceptible Motions: Explore motion magnification's role in revealing subtle movements. • Demystifying Eulerian Processing: Simplify complex concepts, mathematical foundations. • Real-World Applications: Illustrate motion magnification's utility in healthcare, construction, etc. • Eulerian Advantages: Compare and emphasize the strength of Eulerian over Lagrangian methods. • Comprehensive Survey: Cover a range of Eulerian motion magnification techniques. [ABSTRACT FROM AUTHOR]

ABSTRACT The Madeira River is characterized by large amount of woody material transported, especially during floods, which interferes with the operation of the Jirau Hydroelectric Power Plant. There are many logs and the log boom structures inserted to retain them do not always present the desired efficiency. This work involves the hydrodynamic simulation of the Madeira River and the three-dimensional simulation of these woody materials to analyze their trajectories along the river and to obtain knowledge of their transport and position according to the flow, different plant operations ways and the influence of log booms. The logs are simulated as particles by the PART module of Delft3d, using the Lagrangian particle tracking model. The hydrodynamic model was validated and it was possible to represent the main variations of three-dimensional velocities and water levels. The particle tracking simulation was consistent with the flow distribution and thus it was possible to identify the most attractive destination for the logs, according to power plant operations.

Abstract The evolution of ice‐phase particles within precipitating clouds depends on the environmental properties of the cloud and on physical characteristics of the particles themselves, which can be modified by airflow over steep terrain. Through employing a unique Lagrangian particle‐based precipitation model, this study investigates the sensitivities in ice‐phase particle growth and transport due to variabilities in riming processes over an orographic barrier. This analysis is applied to two wintertime stratiform cyclones sampled by in situ aircraft over windward slopes during the Olympic Mountains Experiment. For both events, we simulate the ice‐phase particle evolution and trajectory within a two‐dimensional prescribed state representative of median observed cloud properties. Sensitivity simulations were constructed based on observed variabilities in supercooled liquid water (SLW) properties and its vertical extent above the melting level. Perturbations of SLW concentration equivalent to the 85th and 15th percentiles of observed values, which typically amounted to a change of less than 0.05 g m−3, resulted in respective increases or decreases in the ice‐phase contribution to surface precipitation mass by as much as 50% and horizontal particle trajectories differences exceeding 10 km. Similar sensitivities were found in response to varying the vertical extent of SLW above the melting level and to adjustments in mean SLW droplet size. The significant precipitation response to small variations in cloud properties principally arises from changing rates of rime mass accumulation and correspondingly, increases in particle fall speed. Considerations for the numerical representation of the riming process and its complex effects on precipitation are discussed.

Purpose: Worldwide, cardiovascular disease is the leading cause of hospitalization and death. Recently, the use of magnetizable nanoparticles for medical drug delivery has received much attention for potential treatment of both cancer and cardiovascular disease. However, proper understanding of the interacting magnetic field forces and the hydrodynamics of blood flow is needed for effective implementation. This paper presents the computational results of simulated implant assisted medical drug targeting (IA-MDT) via induced magnetism intended for administering patient specific doses of therapeutic agents to specific sites in the cardiovascular system. The drug delivery scheme presented in this paper functions via placement of a faintly magnetizable stent at a diseased location in the carotid artery, followed by delivery of magnetically susceptible drug carriers guided by the local magnetic field. Using this method, the magnetic stent can apply high localized magnetic field gradients within the diseased artery, while only exposing the neighboring tissues, arteries, and organs to a modest magnetic field. The localized field gradients also produce the forces needed to attract and hold drug-containing magnetic nanoparticles at the implant site for delivering therapeutic agents to treat in-stent restenosis. Methods: The multi-physics computational model used in this work is from our previous work and has been slightly modified for the case scenario presented in this paper. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetic stented region using the magnetic properties of magnetite (Fe3O4) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. The electromagnetic coil produces a uniform magnetic field in the computational arterial flow model domain, while both the particles and the implanted stent are paramagnetic. A Eulerian-Lagrangian technique is adopted to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (Br = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10 nm–4 µm in diameter were evaluated. Two dimensionless numbers were evaluated in this work to characterize relative effects of Brownian motion (BM), magnetic force induced particle motion, and convective blood flow on particle motion. Results: The computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range of 0.7–4 µm, specifically in regions where flow separation and vortices are at a minimum. Similar to our previous work (which did not involve the use of a magnetic stent), it was also observed that the capture efficiency of particles decreases substantially with particle diameter, especially in the superparamagnetic regime. Contrary to our previous work, using a magnetic stent tripled the capture efficiency of superparamagnetic particles. The highest capture efficiency observed for superparamagnetic particles was 78% with an 8 T magnetic field strength and 65% with a 2 T magnetic field strength when analyzing 100 nm particles. For 10 nm particles and an 8 T magnetic field strength, the particle capture efficiency was 55% and for a 2 T magnetic field strength the particle capture efficiency was observed to be 43%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1 µm and above), and slower blood flow velocity improves the particle capture efficiency. The distribution of captured particles on the vessel wall along the axial and azimuthal directions is also discussed. Results for captured particles on the vessel wall along the axial flow direction showed that the particle density decreased along the axial direction, especially after the stented region. For the entrance section of the stented region, the captured particle density distribution along the axial direction is large, corresponding to the center-symmetrical distribution of the magnetic force in that section. Conclusion: The simulation results presented in this work have shown to yield favorable capture efficiencies for micron range particles and superparamagnetic particles using magnetized implants such as the stent discussed in this work. The results presented in this work justify further investigation of MDT as a treatment technique for cardiovascular disease. [ABSTRACT FROM AUTHOR]

Some exact solutions of boundary or initial conditions formulated for Bogomolny equations (derived by using the strong necessary conditions and associated with some ordinary equation and some partial differential equations) have been found. The solution obtained for the restricted baby Skyrme model, as well the density of energy for this solution, are localized. Moreover, it turns out that the densities of the ungauged Hamiltonian and the gauged Hamiltonian are correspondingly, non-zero and zero for the found solution of the Cauchy problem associated with the Bogomolny equation of the restricted baby Skyrme model. Hence, a degeneracy of the Hamiltonian for this model has been established. As such, one can see the breaking of some symmetry. [ABSTRACT FROM AUTHOR]

We study closed-form interference-exploitation precoding for multi-level modulations in the downlink of multi-user multiple-input single-output (MU-MISO) systems. We consider two distinct cases: first, when the number of served users is not larger than the number of transmit antennas at the base station (BS), we mathematically derive the optimal precoding structure based on the Karush-Kuhn-Tucker (KKT) conditions. By formulating the dual problem, the precoding problem is transformed into a pre-scaling operation using quadratic programming (QP) optimization. We further consider the case where the number of served users is larger than the number of transmit antennas at the BS. By employing the pseudo inverse, we show that the optimal solution of the pre-scaling vector is equivalent to a linear combination of the right singular vectors corresponding to zero singular values, and derive the equivalent QP formulation. We also present the condition under which multiplexing more streams than the number of transmit antennas is achievable. For both considered scenarios, we propose a modified iterative algorithm to obtain the optimal precoding matrix, as well as a sub-optimal closed-form precoder. Numerical results validate our derivations on the optimal precoding structures for multi-level modulations, and demonstrate the superiority of interference-exploitation precoding for both scenarios.

One might think that a Lagrangian function of any form is suitable for a complete description of a process. Indeed, it does not matter in terms of the equations of motion, but it seems that this is not enough. Expressions with Poisson brackets are displayed as required fulfillment filters. In the case of the Schrödinger equation for a free particle, we show what we have to be careful about. [ABSTRACT FROM AUTHOR]

Spray drift is a major contributor to pesticide losses in the atmosphere leading to nontargeted ecosystem exposure. An overview of currently used ground-application spray drift models highlighted gaps in the description of the processes occurring during and after spraying. The ADDI-Spraydrift model was developed to bridge some of these gaps and provide a comprehensive, yet concise description of spray drift processes. The model is based on a random walk approach that describes droplet emission, dispersion and evaporation, ground deposition and canopy interception, and accounts for atmospheric stability regimes, and in-canopy turbulence. It predicts airborne concentration, canopy interception and deposition to the ground downwind from the sprayer. The sensitivity analysis to wind speed, active matter content, leaf angle, canopy height, leaf area index, ejection angle and velocity demonstrated the consistency of the model behaviour. The model was calibrated and evaluated against the Ganzelmeier et al. (1995) sedimentary spray drift data in vineyards. The model satisfactorily predicted droplets deposition to the ground downwind from the field boundary with a mean deviation between modelled and measured deposition of 1.3%. A discrepancy was observed at 3 and 5 m downwind from the field boundary attributed to the sensitivity to spraying conditions for which several hypotheses are discussed. Bearing in mind the need to explicitly describe the emitted droplet size and velocity, the overall predictive performance of the model appeared to be sufficient for assessing and comparing application techniques efficiency, quantifying pesticide loss and bystanders or resident exposure and evaluating the efficiency of mitigation measures. [Display omitted] • Model estimates spray drift and crop interception for ground sprayers. • Model is based on a random walk approach integrating spray drift key processes. • Model predictions are highly sensitive to droplet ejection characteristics. • Model predictions well represent Ganzelmeier drift experiments on vineyards. • Model is expected to be valuable for impact studies of spray drift. [ABSTRACT FROM AUTHOR]