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A rapid-response Lagrangian model for the use in simulation of the transport of a chemical pollutant in the Arabian/Persian Gulf is described. The model is well suited to the provision of a fast response after an emergency due to an accident or a deliberate spill. It is easy to set up for any situation since only requires the modification of a few input files specifying the pollutant properties and release characteristics. Running times are short, even on a desktop PC, which makes it appropriate for a rapid assessment of a hypothetical accident occurring in the region. Baroclinic circulation was obtained from an HYCOM ocean model, and tides were calculated using a barotropic model. The interactions of pollutants with sediments (uptake/release processes) were described using a dynamic approach based on kinetic transfer coefficients and a stochastic numerical method. Some examples of model applications are shown, showing the influence of the geochemical behaviour of the pollutant in its distribution pattern Ministerio de Ciencia, Innovación y Universidades PGC2018-094546-B-I00 Junta de Andalucía US-1263369

A computationally efficient source inversion algorithm was developed and applied with the Lagrangian atmospheric dispersion model DIPCOT. In the process of source location estimation by minimizing a correlation-based cost function, the algorithm uses only the values of the time-integrated concentrations at the monitoring stations instead of all of the individual measurements in the full concentration-time series, resulting in a significant reduction in the number of integrations of the backward transport equations. Following the source location estimation the release start time, duration and emission rate are assessed. The developed algorithm was verified for the conditions of the ETEX-I (European Tracer Experiment—1st release). Using time-integrated measurements from all available stations, the distance between the estimated and true source location was 108 km. The estimated start time of the release was only about 1 h different from the true value, within the possible accuracy of estimate of this parameter. The estimated release duration was 21 h (the true value was 12 h). The estimated release rate was 4.28 g/s (the true value was 7.95 g/s). The estimated released mass almost perfectly fitted the true released mass (323.6 vs. 343.4 kg). It thus could be concluded that the developed algorithm is suitable for further integration in real-time decision support systems.

Despite the existing myriad of tools and models to assess atmospheric source–receptor relationships, their uncertainties remain largely unexplored and arguably stem from the scarcity of observations available for validation. Yet, Lagrangian models are increasingly used to determine the origin of precipitation and atmospheric heat, scrutinizing the changes in moisture and temperature along air parcel trajectories. Here, we present a holistic framework for the process-based evaluation of atmospheric trajectories to infer source–receptor relationships of both moisture and heat. The framework comprises three steps: (i) the diagnosis of moisture and heat from Lagrangian trajectories using multi-objective criteria to evaluate the accuracy and reliability of the fluxes, (ii) the attribution of sources following mass- and energy-conserving algorithms in order to establish source–receptor relationships, and (iii) the bias correction of diagnosed fluxes and the corresponding source–receptor relationships. Applying this framework to simulations from the Lagrangian model FLEXPART, driven with ERA-Interim reanalysis data, allows us to quantify the errors and uncertainties associated with the resulting source–receptor relationships for three cities in different climates (Beijing, Denver and Windhoek). Our results reveal large uncertainties inherent in the estimation of heat and precipitation origin with Lagrangian models, but they also demonstrate the synergistic impacts of source- and sink bias-corrections. The proposed framework paves the way for a cohesive assessment of the dependencies in source–receptor relationships.

This paper proposes a multilane traffic flow model based on the notions of conservation laws in Lagrangian coordinates. Both the mathematical formulation and the graphical representation are provided. A logit choice model is applied to describe drivers’ lane choice probability. The lane changing rate is estimated by employing the Incremental Transfer (IT) principle and the lane choice probability model. The numerical implementation of the model in the case of two lanes is discussed. The simulation results reveal that the proposed Lagrangian model is able to describe lane changing dynamics of vehicle platoons; while the lane changing equilibrium curve at the macroscopic level is consistent with that from the multilane Eulerian model as well as the observed data on the highway.

Aircraft atmospheric profiling is a valuable technique for determining greenhouse gas fluxes at regional scales (104&ndash, 106 km2). Here, we describe a new, simple method for estimating the surface influence of air samples that uses backward trajectories based on the Lagrangian model Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT). We determined &ldquo, regions of influence&rdquo, on a quarterly basis between 2010 and 2018 for four aircraft vertical profile sites: SAN and ALF in the eastern Amazon, and RBA and TAB or TEF in the western Amazon. We evaluated regions of influence in terms of their relative sensitivity to areas inside and outside the Amazon and their total area inside the Amazon. Regions of influence varied by quarter and less so by year. In the first and fourth quarters, the contribution of the region of influence inside the Amazon was 83&ndash, 93% for all sites, while in the second and third quarters, it was 57&ndash, 75%. The interquarter differences are more evident in the eastern than in the western Amazon. Our analysis indicates that atmospheric profiles from the western sites are sensitive to 42&ndash, 52.2% of the Amazon. In contrast, eastern Amazon sites are sensitive to only 10.9&ndash, 25.3%. These results may help to spatially resolve the response of greenhouse gas emissions to climate variability over Amazon.

Animal group dynamics have often been studied by biologists through the use of mathematical models and statistical analyses. Wildebeest herds (Connochaetes taurinus) occur in large numbers and follow certain migration patterns throughout the year. However, it is not known whether the aggregation patterns of migrating wildebeest herds follow predictable statistical distributions. In this work, we investigated whether social interactions between individual wildebeest can generate the observed distribution patterns of herds based on empirical data of wildebeest in the Serengeti, Tanzania. We quantified the distribution of real herds by analyzing the frequency distribution of wildebeest counts in aerial survey images collected in 2015. We then used a Lagrangian model of animal interactions to simulate individual movement and herd aggregation patterns. We equipped the model with parameter values that matched empirical distributions. Our results from the empirical data analysis reveal that wildebeest herds follow a truncated power law in their aggregation patterns. We claim that this behaviour can be explained by social interactions between individual wildebeest.

In the framework of the Urban Dispersion International Evaluation Exercise (UDINEE) project coordinated by the European Commission’s Joint Research Centre, a case study was conducted of the Joint Urban 2003 (JU2003) experimental campaign in the central area of Oklahoma City, USA. The UDINEE project concerned the cases of puff dispersion of the JU2003 campaign, which are of special interest to scenarios related to security studies, such as explosions of radiological dispersal devices. Starting from the fact that puff-dispersion variability is substantial, especially in complex urban areas, even for puffs released under similar meteorological conditions, a methodology is presented for assessing this variability, which is applied to the dispersion of puffs in two of the intensive operation periods of the JU2003 campaign. Lagrangian and Eulerian dispersion models are applied for the simulations. For the Lagrangian model, variability is assessed by repeating the computations a large number of times. For the Eulerian model, variability is assessed by constructing probability density functions of concentrations on the basis of the dispersion-model results. Peak concentrations, dosages, puff-arrival times and puff durations are considered. Percentiles calculated by the Lagrangian model for all the above quantities and by the Eulerian model for peak concentrations and dosages are compared with the measurements. The results are encouraging since in several cases the measured and computed ranges of values overlap.

We estimate the overall CO2 , CH4 , and CO flux from the South Coast Air Basin using an inversion that couples Total Carbon Column Observing Network (TCCON) and Orbiting Carbon Observatory-2 (OCO-2) observations, with the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the Open-source Data Inventory for Anthropogenic CO2 (ODIAC). Using TCCON data we estimate the direct net CO2 flux from the SoCAB to be 104 ± 26 Tg CO2 yr −1 for the study period of July 2013–August 2016. We obtain a slightly higher estimate of 120 ± 30 Tg CO2 yr −1 using OCO-2 data. These CO2 emission estimates are on the low end of previous work. Our net CH4 (360 ± 90 Gg CH4 yr −1 ) flux estimate is in agreement with central values from previous top-down studies going back to 2010 (342–440 Gg CH4 yr −1 ). CO emissions are estimated at 487 ± 122 Gg CO yr −1 , much lower than previous top-down estimates (1440 Gg CO yr −1 ). Given the decreasing emissions of CO, this finding is not unexpected. We perform sensitivity tests to estimate how much errors in the prior, errors in the covariance, different inversion schemes, or a coarser dynamical model influence the emission estimates. Overall, the uncertainty is estimated to be 25 %, with the largest contribution from the dynamical model. Lessons learned here may help in future inversions of satellite data over urban areas.

The Arctic Ocean has suffered extreme reductions in sea ice in recent decades, and these observed changes suggest implications in terms of moisture transport. The Arctic region is a net sink of moisture in terms of the total hydrological cycle, however, its role as a moisture source for specific regions has not been extensively studied. Our results show that 80% of the moisture supply from the Arctic contributes to precipitation over itself, representing about 8% of the global moisture supply to the Arctic, the remaining 20% is distributed in the surrounding. A reduction in the sea ice extent could make the Arctic Ocean a slightly higher source of moisture to itself or to the surrounding areas. The analysis of the areas affected by Arctic moisture transport is important for establishing those areas vulnerable to change in a framework of a growing sea ice decline. To this end, the Lagrangian model FLEXPART was used in this work to establish the main sinks for the Arctic Ocean, focusing on the moisture transport from this region. The results suggest that most of the moisture loss occurs locally over the Arctic Ocean itself, especially in summer. Some moisture contribution from the Arctic Ocean to continental areas in North America and Eurasia is also noted in autumn and winter especially from Central Arctic, the East Siberian Sea, the Laptev, Kara, Barents, East Greenland and Bering Seas, and the Sea of Okhotsk.

The Moving-Particle Semi-implicit (MPS) method is a type of meshless Lagrangian calculation technique that uses particles to perform calculations instead of meshes. This method is straightforward and has a high computational efficiency. In this paper, a Lagrangian model for the numerical simulation of fluid-structure interaction problems is proposed. In the proposed method, both the fluid and the structure are described by the MPS. The fluid is fully coupled with the solid that can undergo large structural deformations. In practical engineering, many existing fluid problems involve turbulent flows. The large eddy simulation (LES) method is a major means of studying turbulence. The modified MPS method with the LES method is applied in two-dimensional dam-break problems, which validates the use of the MPS method for solving fluid-structure coupled problems with turbulent flows. By taking the meshless advantage of the MPS method, a preliminary simulation of the plate break problem is carried out, and the simulation results are theoretically verified.

he extended plate theory of I.N. Vekua – A.A. Amosov type is constructed on the background of the dimensional reduction approach and the Lagrangian variational formalism of analytical dynamics. The proposed theory allows one to obtain the hierarchy of refined plate models of different orders and to satisfy the boundary conditions on plates’ faces exactly by introducing the corresponding constraint equations into the Lagrangian model of two-dimensional continuum. The normal wave dispersion in an elastic layer is considered, the convergence of the two-dimensional solutions to the exact one is studied for the locking phase frequencies, the dimensionless stress distributions across the thickness of a layer are shown.

European eel can be found at the Bay of Biscay after a long migration across the Atlantic. The duration of migration, which takes place at larval stage, is of primary importance to understand eel ecology and, hence, its survival. This duration is still a controversial matter since it can range from 7 months to > 4 years depending on the method to estimate duration. The minimum migration duration estimated from our lagrangian model is similar to the duration obtained from the microstructure of eel otoliths, which is typically on the order of 7–9 months. The lagrangian model showed to be sensitive to different conditions like spatial and time resolution, release depth, release area and initial distribution. In general, migration showed to be faster when decreasing the depth and increasing the resolution of the model. In average, the fastest migration was obtained when only advective horizontal movement was considered. However, faster migration was even obtained in some cases when locally oriented random migration was taken into account.

The presence of vegetation plays a significant role in the sustainable development of aquatic systems in steams and rivers, and it affects water hydrodynamics and scalar mixing process. This paper developed a three dimensional large eddy simulation model for flows and scalar transport in an open channel with vegetation. An Eulerian and Lagrangian model was applied to simulate the scalar transport in an open channel with vegetation, respectively. A random walk model was used to describe the mechanical dispersion coefficient in the Eulerian and Lagrangian model. The model was validated by three tests, i.e., the flows in an open channel with submerged vegetation, the flows in an open channel with partly submerged vegetation and the scalar transport in a vegetated channel. The simulation results are in good agreement with the measurement data. As a result, the model has a potential application in simulating the flow and/or scalar transport in an open channel with vegetation.

Firebrands are a harbinger of damage to infrastructure; their effects cause a particularly important threat to people living within the wildland-urban-interface. Short-range firebrands travel with the wind with little or no lofting, and cause spotfires. In this work, the design of a novel firebrand generator prototype is discussed to achieve a uniform shower of firebrands. The transport of short-range firebrand is studied to verify the existing Lagrangian particle model of Fire Dynamics Simulator. Uniform, non-combusting cubiform and cylindrical firebrands are projected using the firebrand generator. The experimentally observed distribution of particles on the ground is compared with a simulated distribution using the fire dynamic simulator. The results show that the existing Lagrangian model gives a good agreement with the experimental data.

In this paper, a review of the Lagrangian stochastic models developed in the last decades for the simulation of the concentration–fluctuation dispersion is presented. The main approaches available in the literature are described and their ability in reproducing the higher order moments of the probability density function is discussed. Then, the Lagrangian approaches for evaluating of the odor annoyance are presented. It is worth to notice that, while Lagrangian stochastic models for mean concentrations are well-known and their ability in correctly reproducing the observation is well assessed, concerning concentration fluctuations the approaches are often new and unknown for most of the scientific community.

International audience; The kinematics of scalar gradient in three-dimensional turbulence is revisited using stochastic Lagrangian modelling. The equilibrium direction is computed numerically. It noticeably departs from the compressional direction, and is the attracting -- and preferential -- alignment for the scalar gradient.

The need to develop models to predict the motion of microrobots, or robots of a much smaller scale, moving in fluids in a low Reynolds number regime, and in particular, in non Newtonian fluids, cannot be understated. The article develops a Lagrangian based model for one such mechanism - a two-link mechanism termed a microscallop, moving in a low Reynolds number environment in a non Newtonian fluid. The modelling proceeds through the conventional Lagrangian construction for a two-link mechanism and then goes on to model the external fluid forces using empirically based models for viscosity to complete the dynamic model. The derived model is then simulated for different initial conditions and key parameters of the non Newtonian fluid, and the results are corroborated with a few existing experimental results on a similar mechanism under identical conditions. Lastly, with a view to implementing control algorithms we explore accessibility of the system at certain configurations.

In this paper, a new method for the simulation of evolving multi-domains problems will be presented. The method is inspired by the front-tracking approaches where only the interfaces between domains are discretized. The presented method maintains the discretization of the interior of the domains using an evolving triangular mesh (valid for a Finite Element (FE) study) and treats the topological events such as the disappearance of domains or the creation of interfaces by means of selective local remeshing operations. Geometric properties are only computed on the interfaces using local spline reconstructions and interfaces are moved using a Lagrangian approach ensuring at all times the validity of the mesh. Accuracy and computational cost of this method will be evaluated in the context of microstructural evolutions, specifically for grain growth mechanism (GG) and it will be compared to a more classical front capturing approach based on a Level-Set (LS) description of grain interfaces which have been proved to be a powerful method for this kind of simulations.

We estimate the overall CO 2 , CH 4 , and CO flux from the South Coast Air Basin using an inversion that couples Total Carbon Column Observing Network (TCCON) and Orbiting Carbon Observatory-2 (OCO-2) observations, with the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model, and the Open-source Data Inventory for Anthropogenic CO 2 (ODIAC). Using TCCON data we estimate the direct net CO 2 flux from the SoCAB to be 139 ± 35 Tg CO 2 yr −1 for the study period of July 2013–August 2016. We obtain a slightly lower estimate of 118 ± 29 Tg CO 2 yr −1 using OCO-2 data. These CO 2 emission estimates are in general agreement with previous work. Our net CH 4 (325 ± 81 Gg CH 4 yr −1 ) flux estimate is slightly lower than central values from previous top-down studies going back to 2010 (342–440 Gg CH 4 yr −1 ). CO emissions are estimated at 555 ± 136 Gg CO yr −1 , much lower than previous top-down estimates (1440 Gg CO yr −1 ). Given the decreasing emissions of CO, this finding is not unexpected. We perform sensitivity tests to estimate how much errors in the prior, errors in the covariance, different inversions schemes or a coarser dynamical model influence the emission estimates. Overall, the uncertainty is estimated to be 25 %, with the largest contribution from the dynamical model. The methods described are scalable and can be used to estimate direct net CO 2 fluxes from other urban regions.

Exotic collections include all non-traditional financial assets that investors pursue for investments and psychological satisfaction purposes. This paper proposes a dynamic Lagrangian model to price these assets, which carry special features compared to traditional assets. The model assumes two types of agents: one has a fixed ratio of traditional investment and the other faces the tradeoff between traditional and exotic investment. The model also incorporates risks of various assets in the utility function to best mimic the real world investor decision. This paper develops the dynamic model and derives the conditions that maximize the agent’s utility in infinite lives. This paper also solves the optimization conditions to present a solution to investment decision.

First we present two classical models of Branched Transport: the Lagrangian model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model, for which we give a complete proof of existence of minimizers in a –hopefully– simplified manner. We also treat in detail some σ-finiteness and rectifiability issues to yield rigorously the energy formula connecting the irrigation cost Iα to the Gilbert Energy Eα. Our main purpose is to use this energy formula and exploit a Smirnov decomposition of vector flows, which was proved via the Dacorogna-Moser approach by Santambrogio, to establish the equivalence between the Lagrangian and Eulerian models.

Modeling of dispersion of air pollutants in the atmosphere is one of the most important and challenging scientific problems. There are several natural and anthropogenic events where passive or chemically active compounds are emitted into the atmosphere. The effect of these chemical species can have serious impacts on our environment and human health. Modeling the dispersion of air pollutants can predict this effect. Therefore, development of various model strategies is a key element for the governmental and scientific communities. We provide here a brief review on the mathematical modeling of the dispersion of air pollutants in the atmosphere. We discuss the advantages and drawbacks of several model tools and strategies, namely Gaussian, Lagrangian, Eulerian and CFD models. We especially focus on several recent advances in this multidisciplinary research field, like parallel computing using graphical processing units, or adaptive mesh refinement.

The focus of this paper is on the analysis of the influence of particles' velocity distribution and their concentration on the sediment transport rate in bed-load from the Lagrangian perspective. Such aims are addressed by use of the relevant Lagrangian model of spherical saltating particles in which turbulence plays a significant role. The Monte Carlo approach is employed in the simulations to obtain the velocity and concentration of the saltating particles. Numerical simulations using two saltating particle models: (1) with; and (2) without particle-particle collisions are carried out. Based on the numerical results, we address the hypothesis that instead of averaged characteristics, the distributions of particles' velocity and sediment concentration should be taken into account in the calculation of sediment transport rate. Moreover, our results also show that the interaction between particles during their collisions is the key for better understanding of the physics of sediment transport. All results are compared with well-known experimental formulae i.e. Meyer-Peter and Muller and Fernandez Luque and van Beek.

The Lagrangian tropospheric ozone model ELMO-v2 (Edinburgh Lancaster Model for Ozone) is applied to the intense 2003 ozone episode in SE England. When using model parameters representative of typical episodes, ELMO-v2 was found to underestimate ozone levels substantially during peak ozone days, but, by increasing three parameters (temperature, biogenic and anthropogenic VOC emission rates) to levels close to those observed, good agreement between modelled and observed ozone was achieved. Using attribution techniques possible with a Lagrangian model, the episode was divided into five phases with each exhibiting different geographical origins for ozone precursor emissions. Anthropogenic VOCs, primarily of European (non-UK) origin, made the biggest contribution to modelled ozone levels. European biogenic VOC emissions significantly contributed to ozone levels on some days, whereas the contribution from UK biogenic VOC emissions was comparatively small throughout. The VOC:NO x ratio was also shown to change during the episode, with high ozone days being less VOC-sensitive. The implications of both variable NO x /VOC sensitivity and the possibility of more frequent heatwaves due to climate change need to be taken into account in planning effective future emissions reductions to control ground-level ozone in the UK.

A comprehensive experimental investigation for an inclined (\(60^{\circ }\) to vertical) dense jet in perpendicular crossflow—with a three-dimensional trajectory—is reported. The detailed tracer concentration field in the vertical cross-section of the bent-over jet is measured by the laser-induced fluorescence technique for a wide range of jet densimetric Froude number \(Fr\) and ambient to jet velocity ratios \(U_r\). The jet trajectory and dilution determined from a large number of cross-sectional scalar fields are interpreted by the Lagrangian model over the entire range of jet-dominated to crossflow-dominated regimes. The mixing during the ascent phase of the dense jet resembles that of an advected jet or line puff and changes to a negatively buoyant thermal on descent. It is found that the mixing behavior is governed by a crossflow Froude number \(\mathbf{F} = U_r Fr\). For \(\mathbf{F} < 0.8\), the mixing is jet-dominated and governed by shear entrainment; significant detrainment occurs and the maximum height of rise \(Z_{max}\) is under-predicted as in the case of a dense jet in stagnant fluid. While the jet trajectory in the horizontal momentum plane is well-predicted, the measurements indicate a greater rise and slower descent. For \(\mathbf{F} \ge 0.8\) the dense jet becomes significantly bent-over during its ascent phase; the jet mixing is dominated by vortex entrainment. For \(\mathbf{F} \ge 2\), the detrainment ceases to have any effect on the jet behavior. The jet trajectory in both the horizontal momentum and buoyancy planes are well predicted by the model. Despite the under-prediction of terminal rise, the jet dilution at a large number of cross-sections covering the ascent and descent of the dense jet are well-predicted. Both the terminal rise and the initial dilution for the inclined jet in perpendicular crossflow are smaller than those of a corresponding vertical jet. Both the maximum terminal rise \(Z_{max}\) and horizontal lateral penetration \(Y_{max}\) follow a \(\mathbf{F}^{-1/2}\) dependence in the crossflow-dominated regime. The initial dilution at terminal rise follows a \(S \sim \mathbf{F}^{1/3}\) dependence.

Delpeche-Ellmann, N.C., Soomere, T., 2013. Using Lagrangian models to assist in maritime management of Coastal and Marine Protected Areas Several previous attempts to mitigate current-driven environmental risks to the nearshore via a concealed structure of surface Lagrangian transport have assumed a constant value to the entire nearshore. We extend these attempts towards more realistic accounting for the Coastal and Marine Protected Areas (MPA). We investigate the effects shifting the present fairway would have on the amount of current-driven pollutants the MPA may receive. The Rossby Centre Ocean circulation model, the TRACMASS Lagrangian trajectory model and statistical methods were employed to identify patterns of current-driven transport in the Gulf of Finland, the Baltic Sea, for the period 1987–1991. Pollution point sources were assumed to occur along the fairway. An analysis was made on how much of the pollution travelled to each of the MPA and the time frame involved. The existing fairway...

In 3D printing process, when small length scales are attained, it is more frequent the onset of imperfections. In the present paper it is studied how the performances of pantographic structures (as defined and introduced in dell’Isola et al. (2005) [1] ) are affected by statistically distributed defects. The relevance of the treated problem is more cogent as the technological tools now available allow for the construction of more and more miniaturised fabrics constituted by beam lattices. Our simulations show that in presence of defects following a (truncated) Gaussian distribution the performances of planar pantographic sheets remain qualitatively the same, even if some relevant negative quantitative effects may occur.

International audience; Pantographic sheets are metamaterials showing some interesting mechanical features. The mechanical behavior of planar pantographic sheets has been studied by means of second gradient continuum models, see 0005 and 0010. In 0015 and 0020 an efficient numerical code has been developed by characterizing equilibrium configurations under imposed displacement boundary conditions as those minimizing a discrete Lagrangian deformation energy. Using this model, it is possible to design experimental setups and, qualitatively and quantitatively, predict the elastic behavior of specimens built by means of 3D printing technology. In the present paper we show the first available experimental evidence obtained for sheared pantographic specimens and we show how effective and predictive is the aforementioned code. Subsequently, a simple fiber rupture mechanism is postulated and added to the initially elastic model. By adding further constitutive parameters to the previous four elastic ones, the generalized numerical model is able to predict very well the observed rupture phenomena. The promising results obtained motivate further development of proposed numerical and theoretical models and the conception of more complex experimental setups.

The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the recent fluid deformation approximation. After recasting the model into the path-integral formalism, the probability distribution function (pdf) is computed along with the most probable path in the weak noise limit through the saddle-point approximation. Evaluation of the instanton solution is implemented numerically by means of the iteratively Chernykh–Stepanov method. In the case of the longitudinal velocity gradient statistics, due to symmetry reasons, the number of degrees of freedom can be reduced to one, allowing the pdf to be evaluated analytically as well, thereby enabling a prediction of the scaling of the moments as a function of Reynolds number. It is also shown that the instanton solution lies in the Vieillefosse line concerning the RQ-plane. We illustrate how instantons can be unveiled in the stochastic dynamics performing a conditional statistics.

This paper describes the further development and application of the Edinburgh-Lancaster Model for Ozone (ELMO). We replace straight-line back-trajectories with trajectories and associated meteorology supplied by the US National Oceanic and Atmospheric Administration Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) service to allow more realistic modelling of specific UK ozone episodes. We call this ELMO-2. Model performance is rigorously tested against observed ozone concentrations for two episodes recorded across 14 rural UK monitoring stations during the spring and summer of 1995. For both episodes, the afternoon concentrations (usually coinciding with the daily maxima) are captured well by the model and the diurnal ozone cycle is reproduced, although the amplitude in concentrations is generally smaller than the observed. The summer episode is investigated further through indicator species analysis and source attribution, and found to be mainly VOC-limited. European emissions account for the majority of ozone production. We demonstrate how improved modelling leads to better understanding of regional and local ozone production across the UK under episodic conditions. (C) 2009 Elsevier Ltd. All rights reserved.

The transport and deposition of polydispersed expiratory aerosols in an aircraft cabin were simulated using a Lagrangian-based model validated by experiments conducted in an aircraft cabin mockup. ...

The present work treats the role of ghost fields in the renormalization procedure of the Lagrangian perturbative formalism of the t–J model. We show that by introducing proper ghost field variables, the propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our previous Lagrangian formalism is studied in detail, and it is shown how the thermal softening of the magnon frequency is predicted by the model. The antiferromagnetic case is also analyzed, and the results are confronted with the previous one obtained by means of the spin-polaron theories.

Data sets from street canyons in Stockholm, Berlin and London are used to investigate the performance of the Gaussian model ADMS-Roads 1 and the Lagrangian model LASAT 2 and the impact of different meteorological input, flow schemes and NO– NO 2 conversion schemes. ADMS-Roads tends to under-predict NO x concentrations. Nevertheless, the more complex Lagrangian model is not always in better agreement with the observations. LASAT with a simpler flow scheme leads to higher concentrations of NO x than the more complex DMK scheme in Stockholm and Berlin. Model runs based on time-series of stability classes render in several cases better results than those with constant neutral conditions. Two NO– NO 2 conversion schemes are used. The scheme after Romberg performs better for LASAT in most of the cases while the Derwent approach is more successful for ADMS-Roads. Although point to point correlations between model results and measurements are generally weak, both dispersion models are quite successful in predicting average values, maximum values as well as the occurrence of exceedances of threshold limits within the street canyons.

8th Vienna International Conference on Mathematical Modelling, VIENNE, AUTRICHE, 18-/02/2015 - 20/02/2015; This paper is concerned with the macroscopic modeling and simulation of traffic flowon junctions. More precisely, we deal with a generic class of second order models, known in the literature as the GSOM family. While classical approaches focus on the Eulerian point-of-view, here we recast the model using its Lagrangian coordinates and we treat the junction as a specific discontinuity in Lagrangian framework. We propose a complete numerical methodology based on a finite difference scheme for solving such a model and we provide a numerical example.

This article presents a case study of a comparison of an Eulerian chemical transport model (CTM) and Lagrangian chemical model with measurements taken by aircraft. High-resolution Eulerian integrations produce improved point-by-point comparisons between model results and measurements compared to low resolution. The Lagrangian model requires mixing to be introduced in order to model the measurements. Copyright © 2005 Royal Meteorological Society

The addition of a Gaussian extension to the Lagrangian model developed in AGricultural DISPersion (AGDISP) enables the aerial application model to extend its prediction distance to 20 km downwind, a distance well beyond its validation distance of 800 m, with an approach whose restrictions and approximations are well understood and documented. This paper summarises the Gaussian model implemented here, and presents predictions of both models for the same aerial spray conditions. Transition between the two models, and possible far-field effects, are discussed, as well as potential uses of the extended aerial application model with respect to long-range risk assessment and large-scale aerial spray operations.

In the present work the renormalized field theory for the Lagrangian formalism in terms of Hubbard operators is given. It is shown that starting from our path-integral representation found recently, it is possible to contruct the perturbative formalism and the standard Feynman diagram approach for operators verifying the Hubbard algebra. We show that by means of the introduction of proper ghost variables, propagators and vertices can be renormalized to each order. Our Lagrangian approach is checked using the Heisenberg ferromagnet and the antiferromagnet simpler models. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details, and it is shown how the softening of the magnon frequency is predicted by the model.

Stratosphere–troposphere exchange (STE) is important for the chemical composition of both the stratosphere and troposphere. Modifications of STE in a changing climate may affect stratospheric ozone depletion and the oxidizing capacity of the troposphere significantly. However, STE is still poorly understood and inadequately quantified, due to the involvement of physical and dynamical processes on local to global scales and to conceptual problems. In this study, a presentday global climatology of STE is developed that is based, from a data standpoint, on 15 yr of global meteorological reanalyses, and, from a conceptual standpoint, on a Lagrangian perspective that considers the pathways of exchange air parcels and their residence times in the troposphere and lowermost stratosphere. To this end, two complementary Lagrangian models are used. Particular consideration is given to “deep” exchange events that, through fast ascent of tropospheric or fast descent of stratospheric air masses, bring into contact air from the (potentially polluted) boundary layer and lower stratosphere. It is shown that they have different characteristics (strongly preferred geographical locations and a pronounced seasonal cycle) from that of the full set of exchange events. This result is important for accurately characterizing the effects of STE. In particular, it can be inferred that the well-documented springtime maximum of surface ozone cannot be explained primarily by STE.

High-resolution hydrodynamic models are a common tool to simulate water dynamics in estuaries. Results from these models are, however, difficult to interpret without the aid of additional parameters to integrate the information. In this paper a methodology to understand the transport patterns in the Tagus Estuary is proposed. It is based on the computation of two renewal time scales: residence time and integrated water fraction. This last parameter is used to build a dependency matrix that gives the integrated influence of each region of the estuary at a selected point. The parameters are computed using a Lagrangian transport model coupled to the hydrodynamic model. Results show that Tagus Estuary has two different types of regions: the central part of the estuary, with low renewal efficiency, and three regions with higher renewal efficiency. Renewal mechanisms are, however, different for each region as shown by the dependency matrix. Comparison of renewal time scales with results from a water-quality model revealed that residence time is not a limiting parameter for primary production in the Tagus Estuary.

In the southern Benguela, successful recruitment of Cape anchovy Engraulis capensis is highly variable and seems to be dependent on the spawning biomass only to a small extent. This paper investigates how the variations in the drift patterns of larvae from the spawning areas on the Agulhas Bank to the upwelling-dominated regions on the west and south-west coasts of South Africa can explain these observed variations. Through the coupling of a three-dimensional circulation model, a Lagrangian particle-tracking model and spawning data, the number of particles ending up in different areas are used to investigate observed variability in recruitment. The model was able to explain 95% of the observed variability in recruitment for the period 1987–1993 (excluding 1989) using a simple linear regression formula. The model also suggests that, of the interannual variability in currents and egg distribution, the latter is the most important cause of the changes observed in the recruitment of anchovy.

We have performed new investigations applying our Lagrangian algorithm described by Alessandrini et al. (2013) to simulate the plume rise in a convective boundary layer capped by a strong inversion layer. We tested our model with the results of a water tank experiment (Weil et al., 2002). For each case, we compared the simulated and measured mean height, horizontal and vertical plume standard deviations and the entrapment (the fraction of the plume that remains captured above the temperature inversion layer located at the top of the boundary layer). The results show that the model is able to reproduce the main characteristics of the plume accurately.

In this paper, a novel approach to modelling and dynamic analysis of full vehicle is proposed based on Udwadia-Kalaba theory. Because the vehicle is hierarchically modelled by using this approach, this approach is easily processed when handling the modelling of many-degrees-of-freedom vehicle. Also, the analytical dynamic model based on this approach is free of calculation of Lagrangian multiplier as used in the Lagrangian equation. To verify this approach, a 15 DOF vehicle is modelled in this paper by using Udwadia-Kalaba theory. Four tyres' displacement is exerted and the vertical dynamic behaviour of each subsystem is simulated and analysed in MATLAB. By solving Udwadia-Kalaba equation, the response of each subsystem is acquired. The simulation result is well coincident with that of the Lagrangian model, which verifies the proposed approach.

A Lagrangian model is used to evaluate source regions of particles collected in the sediment traps at the DYFAMED (Dynamique des Flux Atmospheriques en Mediterranee) station by tracking particles backwards from March 1 to August 31, 2001. The analysis suggests that source regions depend on the flow fields, the settling speed of the particles, and the deployment depths of the traps. Monthly variation is observed in the distribution patterns of source regions, which is caused by the currents. The source regions are located around the traps and up to hundreds of kilometers away. As the settling speed increases with the particle diameters, the distance to the source regions decreases. The vertical flux can be approximately estimated in 1D for the particles with diameters larger than 500 μm. Furthermore, traps moored at various depths at the DYFAMED can collect particles that originated from different regions in the Ligurian Sea.

The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To simulate such flows, volume averaging spatial operators are considered to incorporate pressure drag and skin friction experienced by a porous medium. In this work, a streamline-based Lagrangian methodology is extended for an efficient numerical approach to handle dispersion and diffusion of solvent saturation during a miscible flow. Overall pressure drag on the diffusion and dispersion of solvent saturation is investigated. Numerical results show excellent agreement with the results obtained from asymptotic analysis. The present numerical simulations indicate that the nonlinear effects due to skin friction and pressure drag cannot be accurately captured by Darcy's method if the contribution of the skin friction dominates over that of the pressure drag. Moreover, mass conservation law is investigated, which is an important feature for enhanced oil recovery, and the results help to guide a good agreement with theory. This investigation examines how the flow regime may be optimized for enhanced oil recovery methods., Comment: 11 figures, Journal of Computational Multiphase flow, 2017

Consideration is given to a mathematical model of the nonseparating nonstationary motion of an ideal compressible gas in a pipeline with a variable cross section. A method which enables one to calculate changes in the pressure, density, and the velocity at the sites of contraction and expansion of the pipeline without going beyond the scope of a one‐dimensional model is presented.

Lagrangian stochastic models applicable to the prediction of particle deposition onto hydraulically smooth surfaces are extended to account for the effects of surface roughness. Within the modelling approach, roughness elements are treated as mass ‘sinks’ volumetrically distributed within the flows. The extreme sensitivity of the deposition of micron and sub-micron sized particles to the micro-roughness of hydraulically smooth surfaces is shown to be very well predicted. This suggests that the models can be used to predict the deposition of particles onto leaves and other natural surfaces with micro-roughness elements correctly. Model predictions for the deposition velocities of spores and pollens onto completely rough sticky surfaces are shown to be in very close agreement with the experiment.

A simpler, more efficient, and more robust form of cascade interpolation is proposed. It significantly reduces the considerable overhead required to determine the mesh points of the intermediate mesh, without degrading accuracy. A simple improvement of an existing monotonic filter is also proposed to address a deficiency and enhance robustness. These ideas are demonstrated using two standard test-problems.

A Lagrangian receptor-oriented long-range transport model has been applied in order to estimate the relative contribution of domestic, Austrian, Hungarian, Italian and Slovenian emissions to the long-term deposition of airborne sulphur in Croatia. During the November 1, 1991 to April 30, 1992 period 163.31 thousands of tonnes of sulphur were deposited over Croatia., where 90.9% originated from transboundary emission sources. Relative contribution of domestic sources was the biggest (9.1%), while Austrian contribution was the smallest (0.4%).

To assess the impact of dynamical formulation on climate simulations, a semi-Lagrangian and an Eulerian dynamical core have been used for 5-yr climate simulations with the same physical parameterizations. The comparison of the climate simulations is focused on various eddy statistics (the study of time-mean states from the simulations has been published in a previous paper). Significant differences between the two simulations are evident. Generally, the stationary eddy variances are stronger in the semi-Lagrangian simulation while the transient eddy variances are stronger in the Eulerian simulation. Compared to the data assimilated by the Goddard Earth Observing System data assimilation system, the semi-Lagrangian simulation is closer to the assimilation in many aspects than the Eulerian simulation, even though the Eulerian model was used in the data assimilation. The paper shows that rather than corrupting the ability to diagnose model performance with a parallel data assimilation, quantitative ...