A Lagrangian effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

2015-09-02

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

Time-resolved large-scale volumetric pressure fields of an impinging jet from dense Lagrangian particle tracking

NASA Astrophysics Data System (ADS)

Huhn, F.; Schanz, D.; Manovski, P.; Gesemann, S.; Schröder, A.

2018-05-01

Time-resolved volumetric pressure fields are reconstructed from Lagrangian particle tracking with high seeding concentration using the Shake-The-Box algorithm in a perpendicular impinging jet flow with exit velocity U=4 m/s (Re˜ 36,000) and nozzle-plate spacing H/D=5. Helium-filled soap bubbles are used as tracer particles which are illuminated with pulsed LED arrays. A large measurement volume has been covered (cloud of tracked particles in a volume of 54 L, ˜ 180,000 particles). The reconstructed pressure field has been validated against microphone recordings at the wall with high correlation coefficients up to 0.88. In a reduced measurement volume (13 L), dense Lagrangian particle tracking is shown to be feasable up to the maximal possible jet velocity of U=16 m/s.

Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

NASA Technical Reports Server (NTRS)

Squires, Kyle D.; Eaton, John K.

1991-01-01

Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

Time-variant Lagrangian transport formulation reduces aggregation bias of water and solute mean travel time in heterogeneous catchments

NASA Astrophysics Data System (ADS)

Danesh-Yazdi, Mohammad; Botter, Gianluca; Foufoula-Georgiou, Efi

2017-05-01

Lack of hydro-bio-chemical data at subcatchment scales necessitates adopting an aggregated system approach for estimating water and solute transport properties, such as residence and travel time distributions, at the catchment scale. In this work, we show that within-catchment spatial heterogeneity, as expressed in spatially variable discharge-storage relationships, can be appropriately encapsulated within a lumped time-varying stochastic Lagrangian formulation of transport. This time (variability) for space (heterogeneity) substitution yields mean travel times (MTTs) that are not significantly biased to the aggregation of spatial heterogeneity. Despite the significant variability of MTT at small spatial scales, there exists a characteristic scale above which the MTT is not impacted by the aggregation of spatial heterogeneity. Extensive simulations of randomly generated river networks reveal that the ratio between the characteristic scale and the mean incremental area is on average independent of river network topology and the spatial arrangement of incremental areas.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Acoustic streaming: an arbitrary Lagrangian-Eulerian perspective.

PubMed

Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco

2017-08-25

We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

Subgrid-scale stresses and scalar fluxes constructed by the multi-scale turnover Lagrangian map

NASA Astrophysics Data System (ADS)

AL-Bairmani, Sukaina; Li, Yi; Rosales, Carlos; Xie, Zheng-tong

2017-04-01

The multi-scale turnover Lagrangian map (MTLM) [C. Rosales and C. Meneveau, "Anomalous scaling and intermittency in three-dimensional synthetic turbulence," Phys. Rev. E 78, 016313 (2008)] uses nested multi-scale Lagrangian advection of fluid particles to distort a Gaussian velocity field and, as a result, generate non-Gaussian synthetic velocity fields. Passive scalar fields can be generated with the procedure when the fluid particles carry a scalar property [C. Rosales, "Synthetic three-dimensional turbulent passive scalar fields via the minimal Lagrangian map," Phys. Fluids 23, 075106 (2011)]. The synthetic fields have been shown to possess highly realistic statistics characterizing small scale intermittency, geometrical structures, and vortex dynamics. In this paper, we present a study of the synthetic fields using the filtering approach. This approach, which has not been pursued so far, provides insights on the potential applications of the synthetic fields in large eddy simulations and subgrid-scale (SGS) modelling. The MTLM method is first generalized to model scalar fields produced by an imposed linear mean profile. We then calculate the subgrid-scale stress, SGS scalar flux, SGS scalar variance, as well as related quantities from the synthetic fields. Comparison with direct numerical simulations (DNSs) shows that the synthetic fields reproduce the probability distributions of the SGS energy and scalar dissipation rather well. Related geometrical statistics also display close agreement with DNS results. The synthetic fields slightly under-estimate the mean SGS energy dissipation and slightly over-predict the mean SGS scalar variance dissipation. In general, the synthetic fields tend to slightly under-estimate the probability of large fluctuations for most quantities we have examined. Small scale anisotropy in the scalar field originated from the imposed mean gradient is captured. The sensitivity of the synthetic fields on the input spectra is assessed by

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

Lagrangian acceleration statistics in a turbulent channel flow

NASA Astrophysics Data System (ADS)

Stelzenmuller, Nickolas; Polanco, Juan Ignacio; Vignal, Laure; Vinkovic, Ivana; Mordant, Nicolas

2017-05-01

Lagrangian acceleration statistics in a fully developed turbulent channel flow at Reτ=1440 are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced Lagrangian stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.

Lagrangian Perturbation Approach to the Formation of Large-scale Structure

NASA Astrophysics Data System (ADS)

Buchert, Thomas

The present lecture notes address three columns on which the Lagrangian perturbation approach to cosmological dynamics is based: 1. the formulation of a Lagrangian theory of self-gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of Eulerian fields from the Lagrangian picture, and 3. a precise definition of a Newtonian cosmology framework in which Lagrangian perturbation solutions can be studied. While the first is a discussion of the basic equations obtained by transforming the Eulerian evolution and field equations to the Lagrangian picture, the second exemplifies how the Lagrangian theory determines the evolution of Eulerian fields including kinematical variables like expansion, vorticity, as well as the shear and tidal tensors. The third column is based on a specification of initial and boundary conditions, and in particular on the identification of the average flow of an inhomogeneous cosmology with a `Hubble-flow'. Here, we also look at the limits of the Lagrangian perturbation approach as inferred from comparisons with N-body simulations and illustrate some striking properties of the solutions.

Altimetric lagrangian advection to reconstruct Pacific Ocean fine scale surface tracer fields

NASA Astrophysics Data System (ADS)

Rogé, Marine; Morrow, Rosemary; Dencausse, Guillaume

2015-04-01

In past studies, lagrangian stirring of surface tracer fields by altimetric surface geostrophic currents has been performed in different mid to high-latitude regions, showing good results in reconstructing finer-scale tracer patterns. Here we apply the technique to three different regions in the eastern and western tropical Pacific, and in the subtropical southwest Pacific. Initial conditions are derived from weekly gridded temperature and salinity fields, based on hydrographic data and Argo. Validation of the improved fine-scale surface tracer fields is performed using satellite AMSRE SST data, and high-resolution ship thermosalinograph data. We test two kinds of lagrangian advection. The standard one-way advection is shown to introduce an increased tracer bias as the advection time increases. Indeed, since we only use passive stirring, a bias is introduced from the missing physics, such as air-sea fluxes or mixing. A second "backward-forward" advection technique is shown to reduce the seasonal bias, but more data is lost around coasts and islands, a strong handicap in the tropical Pacific with many small islands. In the subtropical Pacific Ocean, the mesoscale temperature and salinity fronts are well represented by the one-way advection over a 10-day advection time, including westward propagating features not apparent in the initial fields. In the tropics, the results are less clear. The validation is hampered by the complex vertical stratification, and the technique is limited by the lack of accurate surface currents for the stirring - the gridded altimetric fields poorly represent the meridional currents, and are not detecting the fast tropical instability waves, nor the wind-driven circulation. We suggest that the passive lateral stirring technique is efficient in regions with moderate the high mesoscale energy and correlated mesoscale surface temperature and surface height. In other regions, more complex dynamical processes may need to be included.

Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Machicoane, Nathanaël; Volk, Romain

We investigate the response of large inertial particle to turbulent fluctuations in an inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding particle dynamics and may permit stochastic process modelization using two-time models (for instance, Sawford’s). As particles are tracked over long timesmore » in the quasi-totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.« less

Computing eddy-driven effective diffusivity using Lagrangian particles

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-08-14

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is comparedmore » against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less

Computing eddy-driven effective diffusivity using Lagrangian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolfram, Phillip J.; Ringler, Todd D.

A novel method to derive effective diffusivity from Lagrangian particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from Lagrangian particles. We compute the effective diffusivity by first performing scalar transport on Lagrangian control areas using stored trajectories computed from online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the Lagrangian scalar transport scheme is comparedmore » against an Eulerian scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian and Lagrangian effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The Eulerian and Lagrangian effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less

Lagrangian Statistics and Intermittency in Gulf of Mexico.

PubMed

Lin, Liru; Zhuang, Wei; Huang, Yongxiang

2017-12-12

Due to the nonlinear interaction between different flow patterns, for instance, ocean current, meso-scale eddies, waves, etc, the movement of ocean is extremely complex, where a multiscale statistics is then relevant. In this work, a high time-resolution velocity with a time step 15 minutes obtained by the Lagrangian drifter deployed in the Gulf of Mexico (GoM) from July 2012 to October 2012 is considered. The measured Lagrangian velocity correlation function shows a strong daily cycle due to the diurnal tidal cycle. The estimated Fourier power spectrum E(f) implies a dual-power-law behavior which is separated by the daily cycle. The corresponding scaling exponents are close to -1.75 and -2.75 respectively for the time scale larger (resp. 0.1 ≤ f ≤ 0.4 day -1 ) and smaller (resp. 2 ≤ f ≤ 8 day -1 ) than 1 day. A Hilbert-based approach is then applied to this data set to identify the possible multifractal property of the cascade process. The results show an intermittent dynamics for the time scale larger than 1 day, while a less intermittent dynamics for the time scale smaller than 1 day. It is speculated that the energy is partially injected via the diurnal tidal movement and then transferred to larger and small scales through a complex cascade process, which needs more studies in the near future.

Next Generation Extended Lagrangian Quantum-based Molecular Dynamics

NASA Astrophysics Data System (ADS)

Negre, Christian

2017-06-01

A new framework for extended Lagrangian first-principles molecular dynamics simulations is presented, which overcomes shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while maintaining important advantages of the unified extended Lagrangian formulation of density functional theory pioneered by Car and Parrinello three decades ago. The new framework allows, for the first time, energy conserving, linear-scaling Born-Oppenheimer molecular dynamics simulations, which is necessary to study larger and more realistic systems over longer simulation times than previously possible. Expensive, self-consinstent-field optimizations are avoided and normal integration time steps of regular, direct Born-Oppenheimer molecular dynamics can be used. Linear scaling electronic structure theory is presented using a graph-based approach that is ideal for parallel calculations on hybrid computer platforms. For the first time, quantum based Born-Oppenheimer molecular dynamics simulation is becoming a practically feasible approach in simulations of +100,000 atoms-representing a competitive alternative to classical polarizable force field methods. In collaboration with: Anders Niklasson, Los Alamos National Laboratory.

Effective Lagrangian in de Sitter spacetime

NASA Astrophysics Data System (ADS)

Kitamoto, Hiroyuki; Kitazawa, Yoshihisa

2017-01-01

Scale invariant fluctuations of metric are a universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating superhorizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.

COLAcode: COmoving Lagrangian Acceleration code

NASA Astrophysics Data System (ADS)

Tassev, Svetlin V.

2016-02-01

COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving Lagrangian Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian Perturbation Theory (LPT). It differs from standard N-body code by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.

Chaotic Lagrangian models for turbulent relative dispersion.

PubMed

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Chaotic Lagrangian models for turbulent relative dispersion

NASA Astrophysics Data System (ADS)

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Lagrangian ocean analysis: Fundamentals and practices

DOE PAGES

van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; ...

2017-11-24

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.« less

Lagrangian ocean analysis: Fundamentals and practices

NASA Astrophysics Data System (ADS)

van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H. A. M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.

2018-01-01

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.

Lagrangian ocean analysis: Fundamentals and practices

DOE Office of Scientific and Technical Information (OSTI.GOV)

van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.« less

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics

DOE PAGES

Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...

2017-10-28

Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of Lagrangian methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible Lagrangian methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less

Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Wiggins, Stephen; Curbelo, Jezabel; Mendoza, Carolina

2013-11-01

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a ``heuristic argument'' that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (``time averages''). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We thank CESGA for computing facilities. This research was supported by MINECO grants: MTM2011-26696, I-Math C3-0104, ICMAT Severo Ochoa project SEV-2011-0087, and CSIC grant OCEANTECH. SW acknowledges the support of the ONR (Grant No. N00014-01-1-0769).

Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

PubMed

Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie

2016-01-01

The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.

Estimation of local scale dispersion from local breakthrough curves during a tracer test in a heterogeneous aquifer: the Lagrangian approach.

PubMed

Vanderborght, Jan; Vereecken, Harry

2002-01-01

The local scale dispersion tensor, Dd, is a controlling parameter for the dilution of concentrations in a solute plume that is displaced by groundwater flow in a heterogeneous aquifer. In this paper, we estimate the local scale dispersion from time series or breakthrough curves, BTCs, of Br concentrations that were measured at several points in a fluvial aquifer during a natural gradient tracer test at Krauthausen. Locally measured BTCs were characterized by equivalent convection dispersion parameters: equivalent velocity, v(eq)(x) and expected equivalent dispersivity, [lambda(eq)(x)]. A Lagrangian framework was used to approximately predict these equivalent parameters in terms of the spatial covariance of log(e) transformed conductivity and the local scale dispersion coefficient. The approximate Lagrangian theory illustrates that [lambda(eq)(x)] increases with increasing travel distance and is much larger than the local scale dispersivity, lambda(d). A sensitivity analysis indicates that [lambda(eq)(x)] is predominantly determined by the transverse component of the local scale dispersion and by the correlation scale of the hydraulic conductivity in the transverse to flow direction whereas it is relatively insensitive to the longitudinal component of the local scale dispersion. By comparing predicted [lambda(eq)(x)] for a range of Dd values with [lambda(eq)(x)] obtained from locally measured BTCs, the transverse component of Dd, DdT, was estimated. The estimated transverse local scale dispersivity, lambda(dT) = DdT/U1 (U1 = mean advection velocity) is in the order of 10(1)-10(2) mm, which is relatively large but realistic for the fluvial gravel sediments at Krauthausen.

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication

NASA Astrophysics Data System (ADS)

Jakovetic, Dusan; Xavier, João; Moura, José M. F.

2011-08-01

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.

Lagrangian single-particle turbulent statistics through the Hilbert-Huang transform.

PubMed

Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico

2013-04-01

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

Effective pore-scale dispersion upscaling with a correlated continuous time random walk approach

NASA Astrophysics Data System (ADS)

Le Borgne, T.; Bolster, D.; Dentz, M.; de Anna, P.; Tartakovsky, A.

2011-12-01

We investigate the upscaling of dispersion from a pore-scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore-scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time random walk (CTRW) characterized by a correlated random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore-scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.

Lagrangian Visualization and Real-Time Identification of the Vortex Shedding Time in the Wake of a Circular Cylinder

NASA Astrophysics Data System (ADS)

Rockwood, Matthew P.

The flow around a circular cylinder, a canonical bluff body, has been extensively studied in the literature to determine the mechanisms that cause the formation of vortices in the cylinder wake. Understanding of these mechanisms has led to myriad attempts to control the vortices either to mitigate the oscillating forces they cause, or to augment them in order to enhance mixing in the near-wake. While these flow control techniques have been effective at low Reynolds numbers, they generally lose effectiveness or require excessive power at Reynolds numbers commonly experienced in practical applications. For this reason, new methods for identifying the locations of vortices and their shedding time could increase the effectiveness of the control techniques. In the current work, two-dimensional, two-component velocity data was collected in the wake of a circular cylinder using a planar digital particle image velocimetry (DPIV) measurement system at Reynolds numbers of 9,000 and 19,000. This experimental data, as well as two-dimensional simulation data at a Reynolds number of 150, and three-dimensional simulation data at a Reynolds number of 400, is used to calculate the finite-time Lyapunov exponent (FTLE) field. The locations of Lagrangian saddles, identified as non-parallel intersections of positive and negative time FTLE ridges, are shown to indicate the timing of von Karman vortex shedding in the wake of a circular cylinder. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex is shown to clearly accelerate away from the cylinder surface as the vortex begins to shed. This provides a novel, objective method to determine the timing of vortex shedding. The saddles are impossible to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the Lagrangian saddle acceleration without direct access to the FTLE, the saddle dynamics are connected to measurable surface quantities

Predictability of the Lagrangian Motion in the Upper Ocean

NASA Astrophysics Data System (ADS)

Piterbarg, L. I.; Griffa, A.; Griffa, A.; Mariano, A. J.; Ozgokmen, T. M.; Ryan, E. H.

2001-12-01

The complex non-linear dynamics of the upper ocean leads to chaotic behavior of drifter trajectories in the ocean. Our study is focused on estimating the predictability limit for the position of an individual Lagrangian particle or a particle cluster based on the knowledge of mean currents and observations of nearby particles (predictors). The Lagrangian prediction problem, besides being a fundamental scientific problem, is also of great importance for practical applications such as search and rescue operations and for modeling the spread of fish larvae. A stochastic multi-particle model for the Lagrangian motion has been rigorously formulated and is a generalization of the well known "random flight" model for a single particle. Our model is mathematically consistent and includes a few easily interpreted parameters, such as the Lagrangian velocity decorrelation time scale, the turbulent velocity variance, and the velocity decorrelation radius, that can be estimated from data. The top Lyapunov exponent for an isotropic version of the model is explicitly expressed as a function of these parameters enabling us to approximate the predictability limit to first order. Lagrangian prediction errors for two new prediction algorithms are evaluated against simple algorithms and each other and are used to test the predictability limits of the stochastic model for isotropic turbulence. The first algorithm is based on a Kalman filter and uses the developed stochastic model. Its implementation for drifter clusters in both the Tropical Pacific and Adriatic Sea, showed good prediction skill over a period of 1-2 weeks. The prediction error is primarily a function of the data density, defined as the number of predictors within a velocity decorrelation spatial scale from the particle to be predicted. The second algorithm is model independent and is based on spatial regression considerations. Preliminary results, based on simulated, as well as, real data, indicate that it performs

A Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann

2003-01-01

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Implementation Strategies for Large-Scale Transport Simulations Using Time Domain Particle Tracking

NASA Astrophysics Data System (ADS)

Painter, S.; Cvetkovic, V.; Mancillas, J.; Selroos, J.

2008-12-01

Time domain particle tracking is an emerging alternative to the conventional random walk particle tracking algorithm. With time domain particle tracking, particles are moved from node to node on one-dimensional pathways defined by streamlines of the groundwater flow field or by discrete subsurface features. The time to complete each deterministic segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, a variety of kinetically controlled retention (sorption) processes, linear transformation, and temporal changes in groundwater velocities and sorption parameters. The simulation results in a set of arrival times at a monitoring location that can be post-processed with a kernel method to construct mass discharge (breakthrough) versus time. Implementation strategies differ for discrete flow (fractured media) systems and continuous porous media systems. The implementation strategy also depends on the scale at which hydraulic property heterogeneity is represented in the supporting flow model. For flow models that explicitly represent discrete features (e.g., discrete fracture networks), the sampling of residence times along segments is conceptually straightforward. For continuous porous media, such sampling needs to be related to the Lagrangian velocity field. Analytical or semi-analytical methods may be used to approximate the Lagrangian segment velocity distributions in aquifers with low-to-moderate variability, thereby capturing transport effects of subgrid velocity variability. If variability in hydraulic properties is large, however, Lagrangian velocity distributions are difficult to characterize and numerical simulations are required; in particular, numerical simulations are likely to be required for estimating the velocity integral scale as a basis for advective segment distributions. Aquifers with evolving heterogeneity scales present additional challenges. Large-scale simulations of radionuclide

Adaptive switching of interaction potentials in the time domain: an extended Lagrangian approach tailored to transmute force field to QM/MM simulations and back.

PubMed

Böckmann, Marcus; Doltsinis, Nikos L; Marx, Dominik

2015-06-09

An extended Lagrangian formalism that allows for a smooth transition between two different descriptions of interactions during a molecular dynamics simulation is presented. This time-adaptive method is particularly useful in the context of multiscale simulation as it provides a sound recipe to switch on demand between different hierarchical levels of theory, for instance between ab initio ("QM") and force field ("MM") descriptions of a given (sub)system in the course of a molecular dynamics simulation. The equations of motion can be integrated straightforwardly using the usual propagators, such as the Verlet algorithm. First test cases include a bath of harmonic oscillators, of which a subset is switched to a different force constant and/or equilibrium position, as well as an all-MM to QM/MM transition in a hydrogen-bonded water dimer. The method is then applied to a smectic 8AB8 liquid crystal and is shown to be able to switch dynamically a preselected 8AB8 molecule from an all-MM to a QM/MM description which involves partition boundaries through covalent bonds. These examples show that the extended Lagrangian approach is not only easy to implement into existing code but that it is also efficient and robust. The technique moreover provides easy access to a conserved energy quantity, also in cases when Nosé-Hoover chain thermostatting is used throughout dynamical switching. A simple quadratic driving potential proves to be sufficient to guarantee a smooth transition whose time scale can be easily tuned by varying the fictitious mass parameter associated with the auxiliary variable used to extend the Lagrangian. The method is general and can be applied to time-adaptive switching on demand between two different levels of theory within the framework of hybrid scale-bridging simulations.

Option volatility and the acceleration Lagrangian

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Cao, Yang

2014-01-01

This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.

A Lagrangian stochastic model for aerial spray transport above an oak forest

USGS Publications Warehouse

Wang, Yansen; Miller, David R.; Anderson, Dean E.; McManus, Michael L.

1995-01-01

An aerial spray droplets' transport model has been developed by applying recent advances in Lagrangian stochastic simulation of heavy particles. A two-dimensional Lagrangian stochastic model was adopted to simulate the spray droplet dispersion in atmospheric turbulence by adjusting the Lagrangian integral time scale along the drop trajectory. The other major physical processes affecting the transport of spray droplets above a forest canopy, the aircraft wingtip vortices and the droplet evaporation, were also included in each time step of the droplets' transport.The model was evaluated using data from an aerial spray field experiment. In generally neutral stability conditions, the accuracy of the model predictions varied from run-to-run as expected. The average root-mean-square error was 24.61 IU cm−2, and the average relative error was 15%. The model prediction was adequate in two-dimensional steady wind conditions, but was less accurate in variable wind condition. The results indicated that the model can simulate successfully the ensemble; average transport of aerial spray droplets under neutral, steady atmospheric wind conditions.

Identifying finite-time coherent sets from limited quantities of Lagrangian data.

PubMed

Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W

2015-08-01

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.

Identifying finite-time coherent sets from limited quantities of Lagrangian data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.

A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods basedmore » on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.« less

Lagrangian postprocessing of computational hemodynamics.

PubMed

Shadden, Shawn C; Arzani, Amirhossein

2015-01-01

Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.

Lagrangian postprocessing of computational hemodynamics

PubMed Central

Shadden, Shawn C.; Arzani, Amirhossein

2014-01-01

Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889

Some Lagrangians for systems without a Lagrangian

NASA Astrophysics Data System (ADS)

Nucci, M. C.; Leach, P. G. L.

2011-03-01

We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.

Lagrangian statistics in weakly forced two-dimensional turbulence.

PubMed

Rivera, Michael K; Ecke, Robert E

2016-01-01

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.

Lagrangian statistics in weakly forced two-dimensional turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivera, Michael K.; Ecke, Robert E.

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less

Lagrangian statistics in weakly forced two-dimensional turbulence

DOE PAGES

Rivera, Michael K.; Ecke, Robert E.

2016-01-14

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less

Variational Lagrangian data assimilation in open channel networks

NASA Astrophysics Data System (ADS)

Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.

2015-04-01

This article presents a data assimilation method in a tidal system, where data from both Lagrangian drifters and Eulerian flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of Lagrangian data, a time series of positions as the sensors moved through the water. Measurements were also taken from Eulerian sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate Lagrangian and Eulerian measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.

Lagrangian methods of cosmic web classification

NASA Astrophysics Data System (ADS)

Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.

2016-05-01

The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.

An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization

DOE PAGES

Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.

2017-04-17

We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less

An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.

We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1992-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Applying Boundary Conditions Using a Time-Dependent Lagrangian for Modeling Laser-Plasma Interactions

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.

An online-coupled NWP/ACT model with conserved Lagrangian levels

NASA Astrophysics Data System (ADS)

Sørensen, B.; Kaas, E.; Lauritzen, P. H.

2012-04-01

Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.

Parallel computing using a Lagrangian formulation

NASA Technical Reports Server (NTRS)

Liou, May-Fun; Loh, Ching Yuen

1991-01-01

A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.

Parallel computing using a Lagrangian formulation

NASA Technical Reports Server (NTRS)

Liou, May-Fun; Loh, Ching-Yuen

1992-01-01

This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian formulation represents the inherent parallelism of the flow field better than the common Eulerian formulation and offers a competitive alternative on parallel computers. The implementation of the Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.

Lagrangian descriptors in dissipative systems.

PubMed

Junginger, Andrej; Hernandez, Rigoberto

2016-11-09

The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of Lagrangian descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the Lagrangian descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the Lagrangian descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.

High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin code

NASA Astrophysics Data System (ADS)

Einkemmer, Lukas

2016-05-01

The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes (which are usually based on polynomial or spline interpolation). In this paper, we consider a parallel implementation of a semi-Lagrangian discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov-Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant-Friedrichs-Lewy) number increases linearly with the problem size. The framework introduced in this paper facilitates a dimension independent implementation of scientific codes (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation.

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.

PubMed

Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N

2015-04-21

Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.

The Ship Tethered Aerostat Remote Sensing System (STARRS): Observations of Small-Scale Surface Lateral Transport During the LAgrangian Submesoscale ExpeRiment (LASER)

NASA Astrophysics Data System (ADS)

Carlson, D. F.; Novelli, G.; Guigand, C.; Özgökmen, T.; Fox-Kemper, B.; Molemaker, M. J.

2016-02-01

The Consortium for Advanced Research on the Transport of Hydrocarbon in the Environment (CARTHE) will carry out the LAgrangian Submesoscale ExpeRiment (LASER) to study the role of small-scale processes in the transport and dispersion of oil and passive tracers. The Ship-Tethered Aerostat Remote Sensing System (STARRS) will observe small-scale surface dispersion in the open ocean. STARRS is built around a high-lift-capacity (30 kg) helium-filled aerostat. STARRS is equipped with a high resolution digital camera. An integrated GNSS receiver and inertial navigation system permit direct geo-rectification of the imagery. Consortium for Advanced Research on the Transport of Hydrocarbon in the Environment (CARTHE) will carry out the LAgrangian Submesoscale ExpeRiment (LASER) to study the role of small-scale processes in the transport and dispersion of oil and passive tracers. The Ship-Tethered Aerostat Remote Sensing System (STARRS) was developed to produce observational estimates of small-scale surface dispersion in the open ocean. STARRS is built around a high-lift-capacity (30 kg) helium-filled aerostat. STARRS is equipped with a high resolution digital camera. An integrated GNSS receiver and inertial navigation system permit direct geo-rectification of the imagery. Thousands of drift cards deployed in the field of view of STARRS and tracked over time provide the first observational estimates of small-scale (1-500 m) surface dispersion in the open ocean. The STARRS imagery will be combined with GPS-tracked surface drifter trajectories, shipboard observations, and aerial surveys of sea surface temperature in the DeSoto Canyon. In addition to obvious applications to oil spill modelling, the STARRS observations will provide essential benchmarks for high resolution numerical modelsDrift cards deployed in the field of view of STARRS and tracked over time provide the first observational estimates of small-scale (1-100 m) surface dispersion in the open ocean. The STARRS

Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.

PubMed

Holm, Darryl D.

2002-06-01

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.

Quantification of errors induced by temporal resolution on Lagrangian particles in an eddy-resolving model

NASA Astrophysics Data System (ADS)

Qin, Xuerong; van Sebille, Erik; Sen Gupta, Alexander

2014-04-01

Lagrangian particle tracking within ocean models is an important tool for the examination of ocean circulation, ventilation timescales and connectivity and is increasingly being used to understand ocean biogeochemistry. Lagrangian trajectories are obtained by advecting particles within velocity fields derived from hydrodynamic ocean models. For studies of ocean flows on scales ranging from mesoscale up to basin scales, the temporal resolution of the velocity fields should ideally not be more than a few days to capture the high frequency variability that is inherent in mesoscale features. However, in reality, the model output is often archived at much lower temporal resolutions. Here, we quantify the differences in the Lagrangian particle trajectories embedded in velocity fields of varying temporal resolution. Particles are advected from 3-day to 30-day averaged fields in a high-resolution global ocean circulation model. We also investigate whether adding lateral diffusion to the particle movement can compensate for the reduced temporal resolution. Trajectory errors reveal the expected degradation of accuracy in the trajectory positions when decreasing the temporal resolution of the velocity field. Divergence timescales associated with averaging velocity fields up to 30 days are faster than the intrinsic dispersion of the velocity fields but slower than the dispersion caused by the interannual variability of the velocity fields. In experiments focusing on the connectivity along major currents, including western boundary currents, the volume transport carried between two strategically placed sections tends to increase with increased temporal averaging. Simultaneously, the average travel times tend to decrease. Based on these two bulk measured diagnostics, Lagrangian experiments that use temporal averaging of up to nine days show no significant degradation in the flow characteristics for a set of six currents investigated in more detail. The addition of random

Lagrangian continuum dynamics in ALEGRA.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Michael K. W.; Love, Edward

Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

NASA Astrophysics Data System (ADS)

Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi

2017-11-01

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.

Here, Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics

DOE PAGES

Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.; ...

2015-04-21

Here, Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less

Lagrangian statistics of mesoscale turbulence in a natural environment: The Agulhas return current.

PubMed

Carbone, Francesco; Gencarelli, Christian N; Hedgecock, Ian M

2016-12-01

The properties of mesoscale geophysical turbulence in an oceanic environment have been investigated through the Lagrangian statistics of sea surface temperature measured by a drifting buoy within the Agulhas return current, where strong temperature mixing produces locally sharp temperature gradients. By disentangling the large-scale forcing which affects the small-scale statistics, we found that the statistical properties of intermittency are identical to those obtained from the multifractal prediction in the Lagrangian frame for the velocity trajectory. The results suggest a possible universality of turbulence scaling.

Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.

PubMed

Cheng, Ching-An; Huang, Han-Pang

2016-12-01

We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.

Lagrangian description of warm plasmas

NASA Technical Reports Server (NTRS)

Kim, H.

1970-01-01

Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.

Lagrangian coherent structures separate dynamically distinct regions in fluid flows.

PubMed

Kelley, Douglas H; Allshouse, Michael R; Ouellette, Nicholas T

2013-07-01

Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this Lagrangian-averaged flux is nearly unchanged from its Eulerian counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of Lagrangian coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.

Shear and shearless Lagrangian structures in compound channels

NASA Astrophysics Data System (ADS)

Enrile, F.; Besio, G.; Stocchino, A.

2018-03-01

Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a Lagrangian analysis based on nonlinear dynamical system theory. Two-dimensional free surface Eulerian experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called Lagrangian Coherent Structures. Lagrangian structures are recognized as the key features that govern particle trajectories. We seek for two particular class of Lagrangian structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear Lagrangian Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless Lagrangian Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these Lagrangian Structures tends to fade in deep flow conditions.

Two-dimensional Lagrangian simulation of suspended sediment

USGS Publications Warehouse

Schoellhamer, David H.

1988-01-01

A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the Lagrangian reference frame is presented. The layered Lagrangian transport model (LLTM) for suspended sediment performs laterally averaged concentration. The elevations of nearly horizontal streamlines and the simulation time step are selected to optimize model stability and efficiency. The computational elements are parcels of water that are moved along the streamlines in the Lagrangian sense and are mixed with neighboring parcels. Three applications show that the LLTM can accurately simulate theoretical and empirical nonequilibrium suspended sediment distributions and slug injections of suspended sediment in a laboratory flume.

Numerical Simulations of Homogeneous Turbulence Using Lagrangian-Averaged Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Mohseni, Kamran; Shkoller, Steve; Kosovic, Branko; Marsden, Jerrold E.; Carati, Daniele; Wray, Alan; Rogallo, Robert

2000-01-01

The Lagrangian-averaged Navier-Stokes (LANS) equations are numerically evaluated as a turbulence closure. They are derived from a novel Lagrangian averaging procedure on the space of all volume-preserving maps and can be viewed as a numerical algorithm which removes the energy content from the small scales (smaller than some a priori fixed spatial scale alpha) using a dispersive rather than dissipative mechanism, thus maintaining the crucial features of the large scale flow. We examine the modeling capabilities of the LANS equations for decaying homogeneous turbulence, ascertain their ability to track the energy spectrum of fully resolved direct numerical simulations (DNS), compare the relative energy decay rates, and compare LANS with well-accepted large eddy simulation (LES) models.

Lagrangian coherent structures along atmospheric rivers.

PubMed

Garaboa-Paz, Daniel; Eiras-Barca, Jorge; Huhn, Florian; Pérez-Muñuzuri, Vicente

2015-06-01

We show that filamentous Atmospheric Rivers (ARs) over the Northern Atlantic Ocean are closely linked to attracting Lagrangian Coherent Structures (LCSs) in the large scale wind field. The detected LCSs represent lines of attraction in the evolving flow with a significant impact on all passive tracers. Using Finite-Time Lyapunov Exponents, we extract LCSs from a two-dimensional flow derived from water vapor flux of atmospheric reanalysis data and compare them to the three-dimensional LCS obtained from the wind flow. We correlate the typical filamentous water vapor patterns of ARs with LCSs and find that LCSs bound the filaments on the back side. Passive advective transport of water vapor in the AR from tropical latitudes is potentially possible.

On Lagrangian residual currents with applications in south San Francisco Bay, California

USGS Publications Warehouse

Cheng, Ralph T.; Casulli, Vincenzo

1982-01-01

The Lagrangian residual circulation has often been introduced as the sum of the Eulerian residual circulation and the Stokes' drift. Unfortunately, this definition of the Lagrangian residual circulation is conceptually incorrect because both the Eulerian residual circulation and the Stokes' drift are Eulerian variables. In this paper a classification of various residual variables are reviewed and properly defined. The Lagrangian residual circulation is then studied by means of a two-stage formulation of a computer model. The tidal circulation is first computed in a conventional Eulerian way, and then the Lagrangian residual circulation is determined by a method patterned after the method of markers and cells. To demonstrate properties of the Lagrangian residual circulation, application of this approach in South San Francisco Bay, California, is considered. With the aid of the model results, properties of the Eulerian and Lagrangian residual circulation are examined. It can be concluded that estimation of the Lagrangian residual circulation from Eulerian data may lead to unacceptable error, particularly in a tidal estuary where the tidal excursion is of the same order of magnitude as the length scale of the basin. A direction calculation of the Lagrangian residual circulation must be made and has been shown to be feasible.

An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.

Can lagrangian models reproduce the migration time of European eel obtained from otolith analysis?

NASA Astrophysics Data System (ADS)

Rodríguez-Díaz, L.; Gómez-Gesteira, M.

2017-12-01

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.

On tide-induced Lagrangian residual current and residual transport: 1. Lagrangian residual current

USGS Publications Warehouse

Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi

1986-01-01

Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a Lagrangian mean velocity than an Eulerian mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the Lagrangian residual current.

Lagrangian motion, coherent structures, and lines of persistent material strain.

PubMed

Samelson, R M

2013-01-01

Lagrangian motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating Lagrangian regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.

About non standard Lagrangians in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dimitrijevic, Dragoljub D.; Milosevic, Milan

A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.

Eulerian Lagrangian Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Gotovac, Hrvoje; Srzic, Veljko

2014-05-01

Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large

Bayesian Lagrangian Data Assimilation and Drifter Deployment Strategies

NASA Astrophysics Data System (ADS)

Dutt, A.; Lermusiaux, P. F. J.

2017-12-01

Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). Lagrangian Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such Lagrangian transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both Eulerian and Lagrangian variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-Lagrangian Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian variables (e.g. velocity, temperature, salinity, etc.) and Lagrangian variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.

An extended Lagrangian method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1993-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N

2018-02-13

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

PubMed

Craven, Galen T; Hernandez, Rigoberto

2016-02-07

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.

Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caramana, E.J.; Shashkov, M.J.

1997-12-31

The bane of Lagrangian hydrodynamics calculations is premature breakdown of the grid topology that results in severe degradation of accuracy and run termination often long before the assumption of Lagrangian zonal mass ceased to be valid. At short spatial grid scales this is usually referred to by the terms hourglass mode or keystone motion associated in particular with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respectively. At longer spatial scales relative to the grid spacing there is what is referred to ubiquitously as spurious vorticity, or the long-thin zone problem. In both cases the resultmore » is anomalous grid distortion and tangling that has nothing to do with the actual solution, as would be the case for turbulent flow. In this work the authors show how such motions can be eliminated by the proper use of subzonal Lagrangian masses, and associated densities and pressures. These subzonal masses arise in a natural way from the fact that they require the mass associated with the nodal grid point to be constant in time. This is addition to the usual assumption of constant, Lagrangian zonal mass in staggered grid hydrodynamics scheme. The authors show that with proper discretization of subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems. Finally the authors are presenting results of calculations of many test problems.« less

Next generation extended Lagrangian first principles molecular dynamics

NASA Astrophysics Data System (ADS)

Niklasson, Anders M. N.

2017-08-01

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

Next generation extended Lagrangian first principles molecular dynamics.

PubMed

Niklasson, Anders M N

2017-08-07

Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended Lagrangian framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended Lagrangian Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended Lagrangian Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended Lagrangian Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.

Upscaling mixing in porous media from an experimental quantification of pore scale Lagrangian deformation statistics

NASA Astrophysics Data System (ADS)

Turuban, R.; Jimenez-Martinez, J.; De Anna, P.; Tabuteau, H.; Meheust, Y.; Le Borgne, T.

2014-12-01

As dissolved chemical elements are transported in the subsurface, their mixing with other compounds and potential reactivity depends on the creation of local scale chemical gradients, which ultimately drive diffusive mass transfer and reaction. The distribution of concentration gradients is in turn shaped by the spatial gradients of flow velocity arising from the random distribution of solid grains. We present an experimental investigation of the relationship between the microscale flow stretching properties and the effective large scale mixing dynamics in porous media. We use a flow cell that models a horizontal quasi two-dimensional (2D) porous medium, the grains of which are cylinders randomly positioned between two glass plates [de Anna et al. 2013]. In this setup, we perform both non diffusive and diffusive transport tests, by injecting respectively microsphere solid tracers and a fluorescent dye. While the dye front propagates through the medium, it undergoes in time a kinematic stretching that is controlled by the flow heterogeneity, as it encounters stagnation zones and high velocity channels between the grains. The spatial distribution of the dye can then be described as a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching [Le Borgne et al., 2013]. We show that this representation allows predicting the temporal evolution of the mixing rate and the probability distribution of concentration gradients for a range of Peclet numbers. This upscaling framework hence provides a quantification of the dynamics of effective mixing from the microscale Lagrangian velocity statistics. References:[1] P. de Anna, J. Jimenez-Martinez, H. Tabuteau, R. Turuban, T. Le Borgne, M. Derrien,and Yves Méheust, Mixing and reaction kinetics in porous media : an experimental pore scale quantification, Environ. Sci. Technol. 48, 508-516, 2014. [2] Le Borgne, T., M. Dentz, E. Villermaux, Stretching, coalescence and mixing in porous

Form of the manifestly covariant Lagrangian

NASA Astrophysics Data System (ADS)

Johns, Oliver Davis

1985-10-01

The preferred form for the manifestly covariant Lagrangian function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' Lagrangian and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant Lagrangian theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' Lagrangian, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives Lagrangian theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' Lagrangian is a completely adequate basis for covariant Lagrangian theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the Lagrangian and other four-vector equations.

Lagrangian Assimilation of Satellite Data for Climate Studies in the Arctic

NASA Technical Reports Server (NTRS)

Lindsay, Ronald W.; Zhang, Jin-Lun; Stern, Harry

2004-01-01

Under this grant we have developed and tested a new Lagrangian model of sea ice. A Lagrangian model keeps track of material parcels as they drift in the model domain. Besides providing a natural framework for the assimilation of Lagrangian data, it has other advantages: 1) a model that follows material elements is well suited for a medium such as sea ice in which an element retains its identity for a long period of time; 2) model cells can be added or dropped as needed, allowing the spatial resolution to be increased in areas of high variability or dense observations; 3) ice from particular regions, such as the marginal seas, can be marked and traced for a long time; and 4) slip lines in the ice motion are accommodated more naturally because there is no internal grid. Our work makes use of these strengths of the Lagrangian formulation.

Extreme Lagrangian acceleration in confined turbulent flow.

PubMed

Kadoch, Benjamin; Bos, Wouter J T; Schneider, Kai

2008-05-09

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.

Seakeeping with the semi-Lagrangian particle finite element method

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

2017-07-01

The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

Transport induced by mean-eddy interaction: I. Theory, and relation to Lagrangian lobe dynamics

NASA Astrophysics Data System (ADS)

Ide, Kayo; Wiggins, Stephen

2015-02-01

In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of Lagrangian and Eulerian methods. The (Eulerian) boundaries across which we consider (Lagrangian) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of Lagrangian transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the Lagrangian lobes. We contrast the similarities and differences between the TIME and Lagrangian lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the Lagrangian transport theory is made.

Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics

DOE PAGES

Barlow, Andrew; Klima, Matej; Shashkov, Mikhail

2018-04-02

In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–Eulerian (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the Lagrangian stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less

Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in Lagrangian hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barlow, Andrew; Klima, Matej; Shashkov, Mikhail

In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–Eulerian (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the Lagrangian stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.

PubMed

Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian

2015-10-23

We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.

Lorentz Invariance of Gravitational Lagrangians in the Space of Reference Frames

NASA Astrophysics Data System (ADS)

Cognola, G.

1980-06-01

The recently proposed theories of gravitation in the space of reference frames S are based on a Lagrangian invariant with respect to the homogeneous Lorentz group. However, in theories of this kind, the Lorentz invariance is not a necessary consequence of some physical principles, as in the theories formulated in space-time, but rather a purely esthetic request. In the present paper, we give a systematic method for the construction of gravitational theories in the space S, without assuming a priori the Lorentz invariance of the Lagrangian. The Einstein-Cartan equations of gravitation are obtained requiring only that the Lagrangian is invariant under proper rotations and has particular transformation properties under space reflections and space-time dilatations

Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: A Lagrangian flow network perspective.

PubMed

Lindner, Michael; Donner, Reik V

2017-03-01

We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.

Extended Lagrangian Excited State Molecular Dynamics

DOE PAGES

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...

2018-01-09

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Extended Lagrangian Excited State Molecular Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Comparing Lagrangian and Eulerian models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM

NASA Astrophysics Data System (ADS)

Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.

2012-10-01

We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics

DOE PAGES

Niklasson, Anders M. N.; Cawkwell, Marc J.

2014-10-29

Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended Lagrangian under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.

An Extended Lagrangian Method

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

1995-01-01

A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.

Lagrangian averaging with geodesic mean

NASA Astrophysics Data System (ADS)

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Lagrangian averaging with geodesic mean.

PubMed

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Lagrangian Statistics of Slightly Buoyant Droplets in Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph

2006-11-01

This project examines the dynamics of slightly buoyant diesel droplets in isotropic turbulence using high speed in-line digital Holographic PIV. A cloud of droplets with specific gravity of 0.85 is injected into the central portion of an isotropic turbulence facility. The droplet trajectories are measured in a 50x50x50 mm̂3 sample volume using high speed in-line digital holography. An automated program has been developed to obtain accurate time history of droplet velocities. Data analysis determines the PDF of velocity and acceleration in three dimensions. The time histories enable us to calculate the three dimensional Lagrangian velocity autocorrelation function, and from them the diffusion coefficients. Due to buoyancy the vertical diffusion time scale exceeds the horizontal one by about 65% .The diffusion coefficients vary between 2.8 cm̂2/sec in the horizontal direction to 5.5 cm̂2/sec in the vertical direction. For droplets with size varying from 2 to 11 Kolmogorov scales there are no clear trends with size. The variations of diffusion rates for different turbulent intensities and the effect of finite window size are presently examined. For shorter time scales, when the diffusion need not be Fickian the three dimensional trajectories can be used to calculate the generalized dispersion tensor and measure the time elapsed for diffusion to become Fickian.

Tests of dynamic Lagrangian eddy viscosity models in Large Eddy Simulations of flow over three-dimensional bluff bodies

NASA Astrophysics Data System (ADS)

Tseng, Yu-Heng; Meneveau, Charles; Parlange, Marc B.

2004-11-01

Large Eddy Simulations (LES) of atmospheric boundary-layer air movement in urban environments are especially challenging due to complex ground topography. Typically in such applications, fairly coarse grids must be used where the subgrid-scale (SGS) model is expected to play a crucial role. A LES code using pseudo-spectral discretization in horizontal planes and second-order differencing in the vertical is implemented in conjunction with the immersed boundary method to incorporate complex ground topography, with the classic equilibrium log-law boundary condition in the new-wall region, and with several versions of the eddy-viscosity model: (1) the constant-coefficient Smagorinsky model, (2) the dynamic, scale-invariant Lagrangian model, and (3) the dynamic, scale-dependent Lagrangian model. Other planar-averaged type dynamic models are not suitable because spatial averaging is not possible without directions of statistical homogeneity. These SGS models are tested in LES of flow around a square cylinder and of flow over surface-mounted cubes. Effects on the mean flow are documented and found not to be major. Dynamic Lagrangian models give a physically more realistic SGS viscosity field, and in general, the scale-dependent Lagrangian model produces larger Smagorinsky coefficient than the scale-invariant one, leading to reduced distributions of resolved rms velocities especially in the boundary layers near the bluff bodies.

Lagrangian statistics and flow topology in forced two-dimensional turbulence.

PubMed

Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

2011-03-01

A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.

PubMed

Holzner, M; Morales, V L; Willmann, M; Dentz, M

2015-07-01

Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.

Spectral-clustering approach to Lagrangian vortex detection.

PubMed

Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George

2016-06-01

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.

Elimination of the Reaction Rate "Scale Effect": Application of the Lagrangian Reactive Particle-Tracking Method to Simulate Mixing-Limited, Field-Scale Biodegradation at the Schoolcraft (MI, USA) Site

NASA Astrophysics Data System (ADS)

Ding, Dong; Benson, David A.; Fernández-Garcia, Daniel; Henri, Christopher V.; Hyndman, David W.; Phanikumar, Mantha S.; Bolster, Diogo

2017-12-01

Measured (or empirically fitted) reaction rates at groundwater remediation sites are typically much lower than those found in the same material at the batch or laboratory scale. The reduced rates are commonly attributed to poorer mixing at the larger scales. A variety of methods have been proposed to account for this scaling effect in reactive transport. In this study, we use the Lagrangian particle-tracking and reaction (PTR) method to simulate a field bioremediation experiment at the Schoolcraft, MI site. A denitrifying bacterium, Pseudomonas Stutzeri strain KC (KC), was injected to the aquifer, along with sufficient substrate, to degrade the contaminant, carbon tetrachloride (CT), under anaerobic conditions. The PTR method simulates chemical reactions through probabilistic rules of particle collisions, interactions, and transformations to address the scale effect (lower apparent reaction rates for each level of upscaling, from batch to column to field scale). In contrast to a prior Eulerian reaction model, the PTR method is able to match the field-scale experiment using the rate coefficients obtained from batch experiments.

A new method to calibrate Lagrangian model with ASAR images for oil slick trajectory.

PubMed

Tian, Siyu; Huang, Xiaoxia; Li, Hongga

2017-03-15

Since Lagrangian model coefficients vary with different conditions, it is necessary to calibrate the model to obtain optimal coefficient combination for special oil spill accident. This paper focuses on proposing a new method to calibrate Lagrangian model with time series of Envisat ASAR images. Oil slicks extracted from time series images form a detected trajectory of special oil slick. Lagrangian model is calibrated by minimizing the difference between simulated trajectory and detected trajectory. mean center position distance difference (MCPD) and rotation difference (RD) of Oil slicks' or particles' standard deviational ellipses (SDEs) are calculated as two evaluations. The two parameters are taken to evaluate the performance of Lagrangian transport model with different coefficient combinations. This method is applied to Penglai 19-3 oil spill accident. The simulation result with calibrated model agrees well with related satellite observations. It is suggested the new method is effective to calibrate Lagrangian model. Copyright © 2016 Elsevier Ltd. All rights reserved.

Influence of compressibility on the Lagrangian statistics of vorticity-strain-rate interactions.

PubMed

Danish, Mohammad; Sinha, Sawan Suman; Srinivasan, Balaji

2016-07-01

The objective of this study is to investigate the influence of compressibility on Lagrangian statistics of vorticity and strain-rate interactions. The Lagrangian statistics are extracted from "almost" time-continuous data sets of direct numerical simulations of compressible decaying isotropic turbulence by employing a cubic spline-based Lagrangian particle tracker. We study the influence of compressibility on Lagrangian statistics of alignment in terms of compressibility parameters-turbulent Mach number, normalized dilatation-rate, and flow topology. In comparison to incompressible turbulence, we observe that the presence of compressibility in a flow field weakens the alignment tendency of vorticity toward the largest strain-rate eigenvector. Based on the Lagrangian statistics of alignment conditioned on dilatation and topology, we find that the weakened tendency of alignment observed in compressible turbulence is because of a special group of fluid particles that have an initially negligible dilatation-rate and are associated with stable-focus-stretching topology.

Comparing Lagrangian and Eulerian models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM

NASA Astrophysics Data System (ADS)

Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.

2012-01-01

We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.

A river-scale Lagrangian experiment examining controls on phytoplankton dynamics in the presence and absence of treated wastewater effluent high in ammonium

USGS Publications Warehouse

Kraus, Tamara; Carpenter, Kurt; Bergamaschi, Brian; Parker, Alexander; Stumpner, Elizabeth; Downing, Bryan D.; Travis, Nicole; Wilkerson, Frances; Kendall, Carol; Mussen, Timothy

2017-01-01

Phytoplankton are critical component of the food web in most large rivers and estuaries, and thus identifying dominant controls on phytoplankton abundance and species composition is important to scientists, managers, and policymakers. Recent studies from a variety of systems indicate that ammonium ( NH+4) in treated wastewater effluent decreases primary production and alters phytoplankton species composition. However, these findings are based mainly on laboratory and enclosure studies, which may not adequately represent natural systems. To test effects of effluent high in ammonium on phytoplankton at the ecosystem scale, we conducted whole-river–scale experiments by halting discharges to the Sacramento River from the regional wastewater treatment plant (WWTP), and used a Lagrangian approach to compare changes in phytoplankton abundance and species composition in the presence (+EFF) and absence (−EFF) of effluent. Over 5 d of downstream travel from 20 km above to 50 km below the WWTP, chlorophyll concentrations declined from 15–25 to ∼2.5 μg L−1, irrespective of effluent addition. Benthic diatoms were dominant in most samples. We found no significant difference in phytoplankton abundance or species composition between +EFF and −EFF conditions. Moreover, greatest declines in chlorophyll occurred upstream of the WWTP where NH+4 concentrations were low. Grazing by clams and zooplankton could not account for observed losses, suggesting other factors such as hydrodynamics and light limitation were responsible for phytoplankton declines. These results highlight the advantages of conducting ecosystem-scale, Lagrangian-based experiments to understand the dynamic and complex interplay between physical, chemical, and biological factors that control phytoplankton populations.

Generalized Lagrangian coherent structures

NASA Astrophysics Data System (ADS)

Balasuriya, Sanjeeva; Ouellette, Nicholas T.; Rypina, Irina I.

2018-06-01

The notion of a Lagrangian Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized Lagrangian Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.

Lagrangian fluid description with simple applications in compressible plasma and gas dynamics

NASA Astrophysics Data System (ADS)

Schamel, Hans

2004-03-01

The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D

Forecasting Future Sea Ice Conditions: A Lagrangian Approach

DTIC Science & Technology

2015-09-30

1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Forecasting Future Sea Ice Conditions: A Lagrangian ...GCMs participating in IPCC AR5 agree with observed source region patterns from the satellite- derived dataset. 4- Compare Lagrangian ice... Lagrangian sea-ice back trajectories to estimate thermodynamic and dynamic (advection) ice loss. APPROACH We use a Lagrangian trajectory model to

Lagrangian Timescales of Southern Ocean Upwelling in a Hierarchy of Model Resolutions

NASA Astrophysics Data System (ADS)

Drake, Henri F.; Morrison, Adele K.; Griffies, Stephen M.; Sarmiento, Jorge L.; Weijer, Wilbert; Gray, Alison R.

2018-01-01

In this paper we study upwelling pathways and timescales of Circumpolar Deep Water (CDW) in a hierarchy of models using a Lagrangian particle tracking method. Lagrangian timescales of CDW upwelling decrease from 87 years to 31 years to 17 years as the ocean resolution is refined from 1° to 0.25° to 0.1°. We attribute some of the differences in timescale to the strength of the eddy fields, as demonstrated by temporally degrading high-resolution model velocity fields. Consistent with the timescale dependence, we find that an average Lagrangian particle completes 3.2 circumpolar loops in the 1° model in comparison to 0.9 loops in the 0.1° model. These differences suggest that advective timescales and thus interbasin merging of upwelling CDW may be overestimated by coarse-resolution models, potentially affecting the skill of centennial scale climate change projections.

Stochastic modeling of Lagrangian accelerations

NASA Astrophysics Data System (ADS)

Reynolds, Andy

2002-11-01

It is shown how Sawford's second-order Lagrangian stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

Lagrangian predictability characteristics of an Ocean Model

NASA Astrophysics Data System (ADS)

Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia

2014-11-01

The Mediterranean Forecasting System (MFS) Ocean Model, provided by INGV, has been chosen as case study to analyze Lagrangian trajectory predictability by means of a dynamical systems approach. To this regard, numerical trajectories are tested against a large amount of Mediterranean drifter data, used as sample of the actual tracer dynamics across the sea. The separation rate of a trajectory pair is measured by computing the Finite-Scale Lyapunov Exponent (FSLE) of first and second kind. An additional kinematic Lagrangian model (KLM), suitably treated to avoid "sweeping"-related problems, has been nested into the MFS in order to recover, in a statistical sense, the velocity field contributions to pair particle dispersion, at mesoscale level, smoothed out by finite resolution effects. Some of the results emerging from this work are: (a) drifter pair dispersion displays Richardson's turbulent diffusion inside the [10-100] km range, while numerical simulations of MFS alone (i.e., without subgrid model) indicate exponential separation; (b) adding the subgrid model, model pair dispersion gets very close to observed data, indicating that KLM is effective in filling the energy "mesoscale gap" present in MFS velocity fields; (c) there exists a threshold size beyond which pair dispersion becomes weakly sensitive to the difference between model and "real" dynamics; (d) the whole methodology here presented can be used to quantify model errors and validate numerical current fields, as far as forecasts of Lagrangian dispersion are concerned.

Coherent Lagrangian swirls among submesoscale motions.

PubMed

Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G

2018-03-05

The emergence of coherent Lagrangian swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for Lagrangian coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent Lagrangian eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.

Alternative kinetic energy metrics for Lagrangian systems

NASA Astrophysics Data System (ADS)

Sarlet, W.; Prince, G.

2010-11-01

We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.

Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes

NASA Technical Reports Server (NTRS)

Adeniji-Fashola, A.; Chen, C. P.

1990-01-01

Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the Eulerian and Lagrangian modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.

Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

NASA Technical Reports Server (NTRS)

Melott, A. L.; Buchert, T.; Weib, A. G.

1995-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

NASA Technical Reports Server (NTRS)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

Implications of Lagrangian transport for coupled chemistry-climate simulations

NASA Astrophysics Data System (ADS)

Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.

2008-10-01

For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the Lagrangian transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-Lagrangian advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the Lagrangian transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is

A Lagrangian model for the age of tracer in surface water

NASA Astrophysics Data System (ADS)

Ding, Yu; Liu, Haifei; Yi, Yujun

The age of tracer is a spatio-temporal scale, indicating the transition time of solute particles, which is helpful to monitor and manage the pollutant leakage accidents. In this study, an effective Lagrangian model for the age of tracer is developed based on the lattice Boltzmann method in D2Q5 lattices. A tracer age problem in an asymmetrical circular reservoir is then employed as a benchmark test to verify this method. Then it is applied to computing the age of tracers under two different reservoir operation schemes in the Danjiangkou Reservoir, the drinking water source for the Middle Route of South-to-North Water Transfer Project.

Multi-Lagrangians for integrable systems

NASA Astrophysics Data System (ADS)

Nutku, Y.; Pavlov, M. V.

2002-03-01

We propose a general scheme to construct multiple Lagrangians for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 Lagrangians which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.

Real-time prediction of atmospheric Lagrangian coherent structures based on forecast data: An application and error analysis

NASA Astrophysics Data System (ADS)

BozorgMagham, Amir E.; Ross, Shane D.; Schmale, David G.

2013-09-01

The language of Lagrangian coherent structures (LCSs) provides a new means for studying transport and mixing of passive particles advected by an atmospheric flow field. Recent observations suggest that LCSs govern the large-scale atmospheric motion of airborne microorganisms, paving the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. In addition, having reliable predictions of the timing of hyperbolic LCSs may contribute to improved aerobiological sampling of microorganisms with unmanned aerial vehicles and LCS-based early warning systems. Chaotic atmospheric dynamics lead to unavoidable forecasting errors in the wind velocity field, which compounds errors in LCS forecasting. In this study, we reveal the cumulative effects of errors of (short-term) wind field forecasts on the finite-time Lyapunov exponent (FTLE) fields and the associated LCSs when realistic forecast plans impose certain limits on the forecasting parameters. Objectives of this paper are to (a) quantify the accuracy of prediction of FTLE-LCS features and (b) determine the sensitivity of such predictions to forecasting parameters. Results indicate that forecasts of attracting LCSs exhibit less divergence from the archive-based LCSs than the repelling features. This result is important since attracting LCSs are the backbone of long-lived features in moving fluids. We also show under what circumstances one can trust the forecast results if one merely wants to know if an LCS passed over a region and does not need to precisely know the passage time.

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

NASA Technical Reports Server (NTRS)

Felici, Helene Marie

1992-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Toroidal regularization of the guiding center Lagrangian

DOE PAGES

Burby, J. W.; Ellison, C. L.

2017-11-22

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Toroidal regularization of the guiding center Lagrangian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burby, J. W.; Ellison, C. L.

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Target Lagrangian kinematic simulation for particle-laden flows.

PubMed

Murray, S; Lightstone, M F; Tullis, S

2016-09-01

The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.

Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex

NASA Astrophysics Data System (ADS)

Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba

2017-07-01

In this paper we study the three-dimensional (3-D) Lagrangian structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using Lagrangian descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of Lagrangian transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the Lagrangian structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex Lagrangian patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.

The Monotonic Lagrangian Grid for Rapid Air-Traffic Evaluation

NASA Technical Reports Server (NTRS)

Kaplan, Carolyn; Dahm, Johann; Oran, Elaine; Alexandrov, Natalia; Boris, Jay

2010-01-01

The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.

Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks.

PubMed

Pietarila Graham, Jonathan; Mininni, Pablo D; Pouquet, Annick

2009-07-01

We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) alpha model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of approximately 200 when compared to a direct numerical simulation on a large grid of 1536;{3} points at the same Reynolds number.

Lagrangian numerical methods for ocean biogeochemical simulations

NASA Astrophysics Data System (ADS)

Paparella, Francesco; Popolizio, Marina

2018-05-01

We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

Lagrangian statistics across the turbulent-nonturbulent interface in a turbulent plane jet.

PubMed

Taveira, Rodrigo R; Diogo, José S; Lopes, Diogo C; da Silva, Carlos B

2013-10-01

Lagrangian statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of Lagrangian statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The Lagrangian statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using Eulerian statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.

Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.

PubMed

Krause, Katharina; Klopper, Wim

2016-01-28

A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.

Communication: A simplified coupled-cluster Lagrangian for polarizable embedding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu

A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.

A Chiang-type lagrangian in CP^2

NASA Astrophysics Data System (ADS)

Cannas da Silva, Ana

2018-03-01

We analyse a monotone lagrangian in CP^2 that is hamiltonian isotopic to the standard lagrangian RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This lagrangian thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.

Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang Wenbo; Mahalov, Alex

2013-03-15

We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma,more » hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.« less

Special Bohr-Sommerfeld Lagrangian submanifolds

NASA Astrophysics Data System (ADS)

Tyurin, N. A.

2016-12-01

We introduce a new notion in symplectic geometry, that of speciality for Lagrangian submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld Lagrangian submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.

Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct numerical simulations and Lagrangian averaged modeling.

PubMed

Graham, Jonathan Pietarila; Mininni, Pablo D; Pouquet, Annick

2005-10-01

We present direct numerical simulations and Lagrangian averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct numerical simulations. The alpha model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.

Three dimensional Lagrangian structures in the Antarctic Polar Vortex.

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen

2017-04-01

Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A

Dry intrusions: Lagrangian climatology and impact on the boundary layer

NASA Astrophysics Data System (ADS)

Raveh-Rubin, Shira; Wernli, Heini

2017-04-01

Dry air intrusions (DIs) are large-scale descending airstreams. A DI is typically referred to as a coherent airstream in the cold sector of an extratropical cyclone. Emerging evidence suggests that DIs are linked to severe surface wind gusts. However, there is yet no strict Lagrangian definition of DIs, and so their climatological frequency, dynamical characteristics as well as their seasonal and spatial distributions are unknown. Furthermore, the dynamical interaction between DIs and the planetary boundary layer is not fully understood. Here, we suggest a Lagrangian definition for DI air parcels, namely a minimum pressure increase along a trajectory of 400 hPa in 48 hours. Based on this criterion, the open questions are addressed by: (i) a novel global Lagrangian climatology for the ECMWF ERA-Interim reanalysis dataset for the years 1979-2014; (ii) a case study illustrating the interaction between DIs and the boundary layer. We find that DIs occur predominantly in winter. DIs coherently descend from the upper troposphere (their stratospheric origin is small), to the mid- and low levels, where they mix with their environment and diverge. Different physical characteristics typify DIs in the different regions and seasons. Finally, we demonstrate the different mechanisms by which DIs can destabilize the boundary layer and facilitate the formation of strong surface winds.

Network-based study of Lagrangian transport and mixing

NASA Astrophysics Data System (ADS)

Padberg-Gehle, Kathrin; Schneide, Christiane

2017-10-01

Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows - the Bickley jet as well as the Antarctic stratospheric polar vortex.

Differential geometry based solvation model II: Lagrangian formulation.

PubMed

Chen, Zhan; Baker, Nathan A; Wei, G W

2011-12-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of

Differential geometry based solvation model II: Lagrangian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics.

PubMed

Glavatskiy, K S

2015-05-28

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such that there exists an "integral of evolution" which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.

Automated detection of Lagrangian eddies and coherent transport of heat and salinity in the Agulhas leakage

NASA Astrophysics Data System (ADS)

Huhn, Florian; Haller, George

2014-05-01

Haller and Beron-Vera(2013) have recently introduced a new objective method to detect coherent Lagrangian eddies in turbulence. They find that closed null-geodesics of a generalized Green-Lagrange strain tensor act as coherent Lagrangian eddy boundaries, showing near-zero and uniform material stretching. We make use of this method to develop an automated detection procedure for coherent Lagrangian eddies in large-scale ocean data. We apply our results to a recent 3D general circulation model, the Southern Ocean State Estimate (SOSE), with focus on the South Atlantic Ocean and the inter-ocean exchange between the Indian and Atlantic ocean. We detect a large number of coherent Lagrangian eddies and present statistics of their properties. The largest and most circular eddy boundaries represent Lagrangian Agulhas rings. Circular regions inside these rings with higher temperature and salinity than the surrounding waters can be explained by the coherent eddy boundaries that enclose and isolate the eddy interiors. We compare eddy boundaries at different depths with eddy boundaries obtained from geostrophic velocities derived from the model's sea surface height (SSH). The transport of mass, heat and salinity enclosed by coherent eddies through a section in the Cape basin is quantified and compared to the non-coherent transport by the background flow.

Comparison of updated Lagrangian FEM with arbitrary Lagrangian Eulerian method for 3D thermo-mechanical extrusion of a tube profile

NASA Astrophysics Data System (ADS)

Kronsteiner, J.; Horwatitsch, D.; Zeman, K.

2017-10-01

Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

Quasi Real Time Cruise Deployment Guidance to Coherent Regions Using Lagrangian Methods

NASA Astrophysics Data System (ADS)

Dehghani Ashkezari, M.; Barone, B.; Follows, M. J.; Hill, C. N.; Wilson, S. T.; Karl, D. M.

2016-02-01

We describe Lagrangian strategies that were used to help plan a field experiment in the North Pacific Subtropical Gyre in July 2015 close to Station ALOHA. The field study, part of the Simons Collaboration on Ocean Processes and Ecology (SCOPE), aimed to characterize diel changes in the composition and activity of the surface ocean microbial community. The study required forecasting a coherent water mass would remain relatively isolated from neighboring waters over 10 days. To this end, we used near-real-time remote-sensed altimetric data with 0.25 degree resolution (provided by Colorado Center for Astrodynamics Research) to compute particle trajectories and Finite-Time Lyapunov Exponent (FTLE) techniques to pinpoint the candidate coherent regions and exclude undesirable, highly dispersive regimes. We will demonstrate the utility of the approach, which was successful at the identification of the coherent region as evidenced by the trajectories of Surface Velocity Program drifters. It accurately identified a poorly suited field of strong transport close to Station ALOHA and identified a well suited region, associated with an anti-cylonic eddy that provided an ideal context for the field campaign. This talk will describe the methodology and the results from the Summer 2015 expedition as well as the potential to apply the approach more broadly.

Lagrangian transport properties of pulmonary interfacial flows

PubMed Central

Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.

2012-01-01

Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame. PMID:23049141

A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes

NASA Astrophysics Data System (ADS)

Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.

2016-01-01

An approach for Eulerian-Lagrangian large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian and Lagrangian frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted Eulerian and Lagrangian velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.

Getting Things Sorted With Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team

2014-11-01

The dispersion of a tracer in a fluid flow is influenced by the Lagrangian motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of Lagrangian Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.

Lagrangian or Eulerian; real or Fourier? Not all approaches to large-scale structure are created equal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tassev, Svetlin, E-mail: tassev@astro.princeton.edu

We present a pedagogical systematic investigation of the accuracy of Eulerian and Lagrangian perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theorymore » to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by Eulerian Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.« less

Chiral Lagrangian with broken scale: Testing the restoration of symmetries in astrophysics and in the laboratory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonanno, Luca; Drago, Alessandro

2009-04-15

We study matter at high density and temperature using a chiral Lagrangian in which the breaking of scale invariance is regulated by the value of a scalar field, called dilaton [E. K. Heide, S. Rudaz, and P. J. Ellis, Nucl. Phys. A571, 713 (1994); G. W. Carter, P. J. Ellis, and S. Rudaz, Nucl. Phys. A603, 367 (1996); G. W. Carter, P. J. Ellis, and S. Rudaz, Nucl. Phys. A618, 317 (1997); G. W. Carter and P. J. Ellis, Nucl. Phys. A628, 325 (1998)]. We provide a phase diagram describing the restoration of chiral and scale symmetries. We show thatmore » chiral symmetry is restored at large temperatures, but at low temperatures it remains broken at all densities. We also show that scale invariance is more easily restored at low rather than large baryon densities. The masses of vector-mesons scale with the value of the dilaton and their values initially slightly decrease with the density but then they increase again for densities larger than {approx}3{rho}{sub 0}. The pion mass increases continuously with the density and at {rho}{sub 0} and T=0 its value is {approx}30 MeV larger than in the vacuum. We show that the model is compatible with the bounds stemming from astrophysics, as, e.g., the one associated with the maximum mass of a neutron star. The most striking feature of the model is a very significant softening at large densities, which manifests also as a strong reduction of the adiabatic index. Although the softening has probably no consequence for supernova explosion via the direct mechanism, it could modify the signal in gravitational waves associated with the merging of two neutron stars.« less

Lagrangian Hotspots of In-Use NOX Emissions from Transit Buses.

PubMed

Kotz, Andrew J; Kittelson, David B; Northrop, William F

2016-06-07

In-use, spatiotemporal NOX emissions were measured from a conventional powertrain transit bus and a series electric hybrid bus over gradients of route kinetic intensity and ambient temperature. This paper introduces a new method for identifying NOX emissions hotspots along a bus route using high fidelity Lagrangian vehicle data to explore spatial interactions that may influence emissions production. Our study shows that the studied transit buses emit higher than regulated emissions because on-route operation does not accurately represent the range of engine operation tested according to regulatory standards. Using the Lagrangian hotspot detection, we demonstrate that NOX hotspots occurred at bus stops, during cold starts, on inclines, and for accelerations. On the selected routes, bus stops resulted in 3.3 times the route averaged emissions factor in grams/km without significant dependence on bus type or climate. The buses also emitted 2.3 times the route averaged NOX emissions factor at the beginning of each route due to cold selective catalytic reduction aftertreatment temperature. The Lagrangian hotspot detection technique demonstrated here could be employed in future connected vehicles empowered by advances in computational power, data storage capability, and improved sensor technology to optimize emissions as a function of spatial location.

Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.

2015-12-01

Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.

Lagrangian formulation of irreversible thermodynamics and the second law of thermodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Glavatskiy, K. S.

We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called “mirror-image” system. The Lagrangian is symmetric in time and therefore compatible with microscopic reversibility. The evolution equations in the normal and mirror-imaged systems are decoupled and describe therefore independent irreversible evolution of each of the systems. The second law of thermodynamics follows from a symmetry of the Lagrangian. Entropy increase in the normal system is balanced by the entropy decrease in the mirror-image system, such thatmore » there exists an “integral of evolution” which is a constant. The derivation relies on the property of local equilibrium, which states that the local relations between the thermodynamic quantities in non-equilibrium are the same as in equilibrium.« less

Lagrangian statistics of turbulent dispersion from 81923 direct numerical simulation of isotropic turbulence

NASA Astrophysics Data System (ADS)

Buaria, Dhawal; Yeung, P. K.; Sawford, B. L.

2016-11-01

An efficient massively parallel algorithm has allowed us to obtain the trajectories of 300 million fluid particles in an 81923 simulation of isotropic turbulence at Taylor-scale Reynolds number 1300. Conditional single-particle statistics are used to investigate the effect of extreme events in dissipation and enstrophy on turbulent dispersion. The statistics of pairs and tetrads, both forward and backward in time, are obtained via post-processing of single-particle trajectories. For tetrads, since memory of shape is known to be short, we focus, for convenience, on samples which are initially regular, with all sides of comparable length. The statistics of tetrad size show similar behavior as the two-particle relative dispersion, i.e., stronger backward dispersion at intermediate times with larger backward Richardson constant. In contrast, the statistics of tetrad shape show more robust inertial range scaling, in both forward and backward frames. However, the distortion of shape is stronger for backward dispersion. Our results suggest that the Reynolds number reached in this work is sufficient to settle some long-standing questions concerning Lagrangian scale similarity. Supported by NSF Grants CBET-1235906 and ACI-1036170.

A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain

NASA Astrophysics Data System (ADS)

Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.

2018-05-01

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (finite-difference in time and finite-element in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity finite element space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

Diagnosing isopycnal diffusivity in an eddying, idealized midlatitude ocean basin via Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT)

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.; Maltrud, Mathew E.; ...

2015-08-01

Isopycnal diffusivity due to stirring by mesoscale eddies in an idealized, wind-forced, eddying, midlatitude ocean basin is computed using Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT). Simulation is performed via LIGHT within the Model for Prediction across Scales Ocean (MPAS-O). Simulations are performed at 4-, 8-, 16-, and 32-km resolution, where the first Rossby radius of deformation (RRD) is approximately 30 km. Scalar and tensor diffusivities are estimated at each resolution based on 30 ensemble members using particle cluster statistics. Each ensemble member is composed of 303 665 particles distributed across five potential density surfaces. Diffusivity dependence upon modelmore » resolution, velocity spatial scale, and buoyancy surface is quantified and compared with mixing length theory. The spatial structure of diffusivity ranges over approximately two orders of magnitude with values of O(10 5) m 2 s –1 in the region of western boundary current separation to O(10 3) m 2 s –1 in the eastern region of the basin. Dominant mixing occurs at scales twice the size of the first RRD. Model resolution at scales finer than the RRD is necessary to obtain sufficient model fidelity at scales between one and four RRD to accurately represent mixing. Mixing length scaling with eddy kinetic energy and the Lagrangian time scale yield mixing efficiencies that typically range between 0.4 and 0.8. In conclusion, a reduced mixing length in the eastern region of the domain relative to the west suggests there are different mixing regimes outside the baroclinic jet region.« less

Lagrangian formulation and symmetrical description of liquid dynamics.

PubMed

Trachenko, K

2017-12-01

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

Lagrangian formulation and symmetrical description of liquid dynamics

NASA Astrophysics Data System (ADS)

Trachenko, K.

2017-12-01

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k -space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k -space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

Direct Lagrangian tracking simulations of particles in vertically-developing atmospheric clouds

NASA Astrophysics Data System (ADS)

Onishi, Ryo; Kunishima, Yuichi

2017-11-01

We have been developing the Lagrangian Cloud Simulator (LCS), which follows the so-called Euler-Lagrangian framework, where flow motion and scalar transportations (i.e., temperature and humidity) are computed with the Euler method and particle motion with the Lagrangian method. The LCS simulation considers the hydrodynamic interaction between approaching particles for robust collision detection. This leads to reliable simulations of collision growth of cloud droplets. Recently the activation process, in which aerosol particles become tiny liquid droplets, has been implemented in the LCS. The present LCS can therefore consider the whole warm-rain precipitation processes -activation, condensation, collision and drop precipitation. In this talk, after briefly introducing the LCS, we will show kinematic simulations using the LCS for quasi-one dimensional domain, i.e., vertically elongated 3D domain. They are compared with one-dimensional kinematic simulations using a spectral-bin cloud microphysics scheme, which is based on the Euler method. The comparisons show fairly good agreement with small discrepancies, the source of which will be presented. The Lagrangian statistics, obtained for the first time for the vertical domain, will be the center of discussion. This research was supported by MEXT as ``Exploratory Challenge on Post-K computer'' (Frontiers of Basic Science: Challenging the Limits).

Uncovering the Geometry of Barrierless Reactions Using Lagrangian Descriptors.

PubMed

Junginger, Andrej; Hernandez, Rigoberto

2016-03-03

Transition-state theories describing barrierless chemical reactions, or more general activated problems, are often hampered by the lack of a saddle around which the dividing surface can be constructed. For example, the time-dependent transition-state trajectory uncovering the nonrecrossing dividing surface in thermal reactions in the framework of the Langevin equation has relied on perturbative approaches in the vicinity of the saddle. We recently obtained an alternative approach using Lagrangian descriptors to construct time-dependent and recrossing-free dividing surfaces. This is a nonperturbative approach making no reference to a putative saddle. Here we show how the Lagrangian descriptor can be used to obtain the transition-state geometry of a dissipated and thermalized reaction across barrierless potentials. We illustrate the method in the case of a 1D Brownian motion for both barrierless and step potentials; however, the method is not restricted and can be directly applied to different kinds of potentials and higher dimensional systems.

Lagrangian statistics in compressible isotropic homogeneous turbulence

NASA Astrophysics Data System (ADS)

Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi

2011-11-01

In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the Lagrangian point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the Eulerian field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a Lagrangian module for tracking the tracers and recording the data. The Lagrangian probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The Lagrangian structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

NASA Astrophysics Data System (ADS)

Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander

2017-12-01

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.

Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash

NASA Technical Reports Server (NTRS)

Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

2012-01-01

In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in FLASH

NASA Astrophysics Data System (ADS)

Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

2012-08-01

In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

Identification and Lagrangian analysis of oceanographic structures favorable for fishery of neon flying squid ( Ommastrephes bartramii) in the South Kuril area

NASA Astrophysics Data System (ADS)

Budyansky, M. V.; Prants, S. V.; Samko, E. V.; Uleysky, M. Yu.

2017-09-01

Based on the AVISO velocity field, we compute daily synoptic Lagrangian maps in the South Kuril area for the fishery seasons of 1998, 1999, and 2001-2005 from available catching data on neon flying squid (NFS). With the help of drift maps for artificial particles, we found that the majority of NFS fishing grounds featuring maximum catches are situated near large-scale Lagrangian intrusions: tongues of water penetrating the surrounding water of other Lagrangian properties. It is shown that the NFS catch locations tend to accumulate at places where waters with different magnitudes of certain Lagrangian indicators converge, mix, and produce filaments, swirls, and tendrils typical of chaotic advection. Potential NFS fishing grounds are mainly located near (1) Lagrangian intrusions of the Subarctic front, (2) intrusions of Okhotsk Sea and Oyashio waters around mesoscale anticyclones east of Hokkaido with subsequent penetration of catch locations inside eddies and (3) intrusions of subtropical waters into the central part of the South Kuril area due to interaction with eddies of different size and polarity. Possible reasons for increased biological production and fishery in the vicinity of Lagrangian intrusions are discussed.

GPU-accelerated computing for Lagrangian coherent structures of multi-body gravitational regimes

NASA Astrophysics Data System (ADS)

Lin, Mingpei; Xu, Ming; Fu, Xiaoyu

2017-04-01

Based on a well-established theoretical foundation, Lagrangian Coherent Structures (LCSs) have elicited widespread research on the intrinsic structures of dynamical systems in many fields, including the field of astrodynamics. Although the application of LCSs in dynamical problems seems straightforward theoretically, its associated computational cost is prohibitive. We propose a block decomposition algorithm developed on Compute Unified Device Architecture (CUDA) platform for the computation of the LCSs of multi-body gravitational regimes. In order to take advantage of GPU's outstanding computing properties, such as Shared Memory, Constant Memory, and Zero-Copy, the algorithm utilizes a block decomposition strategy to facilitate computation of finite-time Lyapunov exponent (FTLE) fields of arbitrary size and timespan. Simulation results demonstrate that this GPU-based algorithm can satisfy double-precision accuracy requirements and greatly decrease the time needed to calculate final results, increasing speed by approximately 13 times. Additionally, this algorithm can be generalized to various large-scale computing problems, such as particle filters, constellation design, and Monte-Carlo simulation.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

PubMed

Buican, Matthew; Laczko, Zoltan

2018-02-23

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories

NASA Astrophysics Data System (ADS)

Buican, Matthew; Laczko, Zoltan

2018-02-01

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us Lagrangians for particular observables in certain subsectors of many "non-Lagrangian" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.

A Constructive Approach to Regularity of Lagrangian Trajectories for Incompressible Euler Flow in a Bounded Domain

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Frisch, Uriel

2017-04-01

The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.

An adaptive reconstruction for Lagrangian, direct-forcing, immersed-boundary methods

NASA Astrophysics Data System (ADS)

Posa, Antonio; Vanella, Marcos; Balaras, Elias

2017-12-01

Lagrangian, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the Lagrangian grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of Lagrangian IB, and Eulerian grids. With this approach, the density of surface Lagrangian markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying Eulerian grid. The markers are not stored and the Lagrangian data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any Lagrangian, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

NASA Astrophysics Data System (ADS)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-01

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory.

PubMed

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE PAGES

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...

2017-03-28

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Performance of extended Lagrangian schemes for molecular dynamics simulations with classical polarizable force fields and density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less

Recording High Resolution 3D Lagrangian Motions In Marine Dinoflagellates using Digital Holographic Microscopic Cinematography

NASA Astrophysics Data System (ADS)

Sheng, J.; Malkiel, E.; Katz, J.; Place, A. R.; Belas, R.

2006-11-01

Detailed data on swimming behavior and locomotion for dense population of dinoflagellates constitutes a key component to understanding cell migration, cell-cell interactions and predator-prey dynamics, all of which affect algae bloom dynamics. Due to the multi-dimensional nature of flagellated cell motions, spatial-temporal Lagrangian measurements of multiple cells in high concentration are very limited. Here we present detailed data on 3D Lagrangian motions for three marine dinoflagellates: Oxyrrhis marina, Karlodinium veneficum, and Pfiesteria piscicida, using digital holographic microscopic cinematography. The measurements are performed in a 5x5x25mm cuvette with cell densities varying from 50,000 ˜ 90,000 cells/ml. Approximately 200-500 cells are tracked simultaneously for 12s at 60fps in a sample volume of 1x1x5 mm at a spatial resolution of 0.4x0.4x2 μm. We fully resolve the longitudinal flagella (˜200nm) along with the Lagrangian trajectory of each organism. Species dependent swimming behavior are identified and categorized quantitatively by velocities, radii of curvature, and rotations of pitch. Statistics on locomotion, temporal & spatial scales, and diffusion rate show substantial differences between species. The scaling between turning radius and cell dimension can be explained by a distributed stokeslet model for a self-propelled body.

A Lagrangian Analysis of a Developing and Non-Developing Disturbance Observed During the PREDICT Experiment

DTIC Science & Technology

2012-12-03

paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time- dependent flows...the low- to mid- level embryonic vortex from adverse conditions, while the 1The glossary on NOAA’s Hurricane Research Division’s web - site uses...wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation

Stochastic Simulation of Lagrangian Particle Transport in Turbulent Flows

NASA Astrophysics Data System (ADS)

Sun, Guangyuan

This dissertation presents the development and validation of the One Dimensional Turbulence (ODT) multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent-particle mixing and transport at low computational cost. The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes. The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle-eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively. The Type-IC model combines the features of the Type-I and -C models. The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet. Particle dispersion, dispersion coefficients, and velocity statistics are predicted and compared with experimental data. The models accurately reproduces the experimental data sets and capture particle inertial effects and trajectory crossing effect. A new adjustable particle parameter is introduced into the ODT model, and sensitivity analysis is performed to facilitate parameter estimation and selection. A novel algorithm of the two-way momentum coupling between the particle and carrier phases is developed in the ODT multiphase model. Momentum exchange between the phases is accounted for through particle source terms in the viscous diffusion. The source term is implemented in eddy events through a new kernel transformation and an iterative procedure is required for eddy selection. This model is applied to a particle-laden turbulent jet flow, and simulation results are compared with experimental measurements. The effect of particle addition on the velocities of the gas phase is investigated. The development of

A Theoretical Framework for Lagrangian Descriptors

NASA Astrophysics Data System (ADS)

Lopesino, C.; Balibrea-Iniesta, F.; García-Garrido, V. J.; Wiggins, S.; Mancho, A. M.

This paper provides a theoretical background for Lagrangian Descriptors (LDs). The goal of achieving rigorous proofs that justify the ability of LDs to detect invariant manifolds is simplified by introducing an alternative definition for LDs. The definition is stated for n-dimensional systems with general time dependence, however we rigorously prove that this method reveals the stable and unstable manifolds of hyperbolic points in four particular 2D cases: a hyperbolic saddle point for linear autonomous systems, a hyperbolic saddle point for nonlinear autonomous systems, a hyperbolic saddle point for linear nonautonomous systems and a hyperbolic saddle point for nonlinear nonautonomous systems. We also discuss further rigorous results which show the ability of LDs to highlight additional invariants sets, such as n-tori. These results are just a simple extension of the ergodic partition theory which we illustrate by applying this methodology to well-known examples, such as the planar field of the harmonic oscillator and the 3D ABC flow. Finally, we provide a thorough discussion on the requirement of the objectivity (frame-invariance) property for tools designed to reveal phase space structures and their implications for Lagrangian descriptors.

Nonconservative Lagrangian Mechanics: Purely Causal Equations of Motion

NASA Astrophysics Data System (ADS)

Dreisigmeyer, David W.; Young, Peter M.

2015-06-01

This work builds on the Volterra series formalism presented in Dreisigmeyer and Young (J Phys A 36: 8297, 2003) to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle.

JY1 time scale: a new Kalman-filter time scale designed at NIST

NASA Astrophysics Data System (ADS)

Yao, Jian; Parker, Thomas E.; Levine, Judah

2017-11-01

We report on a new Kalman-filter hydrogen-maser time scale (i.e. JY1 time scale) designed at the National Institute of Standards and Technology (NIST). The JY1 time scale is composed of a few hydrogen masers and a commercial Cs clock. The Cs clock is used as a reference clock to ease operations with existing data. Unlike other time scales, the JY1 time scale uses three basic time-scale equations, instead of only one equation. Also, this time scale can detect a clock error (i.e. time error, frequency error, or frequency drift error) automatically. These features make the JY1 time scale stiff and less likely to be affected by an abnormal clock. Tests show that the JY1 time scale deviates from the UTC by less than  ±5 ns for ~100 d, when the time scale is initially aligned to the UTC and then is completely free running. Once the time scale is steered to a Cs fountain, it can maintain the time with little error even if the Cs fountain stops working for tens of days. This can be helpful when we do not have a continuously operated fountain or when the continuously operated fountain accidentally stops, or when optical clocks run occasionally.

Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

NASA Astrophysics Data System (ADS)

Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n

In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

NASA Astrophysics Data System (ADS)

Cornille, Brian; White, Dan

2017-10-01

We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

Scalable Methods for Eulerian-Lagrangian Simulation Applied to Compressible Multiphase Flows

NASA Astrophysics Data System (ADS)

Zwick, David; Hackl, Jason; Balachandar, S.

2017-11-01

Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the Eulerian-Lagrangian method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for Eulerian-Lagrangian simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.

Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

DTIC Science & Technology

2015-09-30

Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

Establishing Lagrangian Connections between Observations within Air Masses Crossing the Atlantic during the ICARTT Experiment

NASA Technical Reports Server (NTRS)

Methven, J.; Arnold, S. R.; Stohl, A.; Evans, M. J.; Avery, M.; Law, K.; Lewis, A. C.; Monks, P. S.; Parrish, D.; Reeves, C.;

A majorized Newton-CG augmented Lagrangian-based finite element method for 3D restoration of geological models

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.

Euler-Lagrangian computation for estuarine hydrodynamics

USGS Publications Warehouse

Cheng, Ralph T.

1983-01-01

The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.

The Gaussian streaming model and convolution Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; Castorina, Emanuele; White, Martin

2016-12-05

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less

The Gaussian streaming model and convolution Lagrangian effective field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vlah, Zvonimir; Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less

Parcels v0.9: prototyping a Lagrangian ocean analysis framework for the petascale age

NASA Astrophysics Data System (ADS)

Lange, Michael; van Sebille, Erik

2017-11-01

As ocean general circulation models (OGCMs) move into the petascale age, where the output of single simulations exceeds petabytes of storage space, tools to analyse the output of these models will need to scale up too. Lagrangian ocean analysis, where virtual particles are tracked through hydrodynamic fields, is an increasingly popular way to analyse OGCM output, by mapping pathways and connectivity of biotic and abiotic particulates. However, the current software stack of Lagrangian ocean analysis codes is not dynamic enough to cope with the increasing complexity, scale and need for customization of use-cases. Furthermore, most community codes are developed for stand-alone use, making it a nontrivial task to integrate virtual particles at runtime of the OGCM. Here, we introduce the new Parcels code, which was designed from the ground up to be sufficiently scalable to cope with petascale computing. We highlight its API design that combines flexibility and customization with the ability to optimize for HPC workflows, following the paradigm of domain-specific languages. Parcels is primarily written in Python, utilizing the wide range of tools available in the scientific Python ecosystem, while generating low-level C code and using just-in-time compilation for performance-critical computation. We show a worked-out example of its API, and validate the accuracy of the code against seven idealized test cases. This version 0.9 of Parcels is focused on laying out the API, with future work concentrating on support for curvilinear grids, optimization, efficiency and at-runtime coupling with OGCMs.

Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

NASA Astrophysics Data System (ADS)

Kuropatenko, V. F.; Shestakovskaya, E. S.

2016-10-01

It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

A semi-Lagrangian approach to the shallow water equation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad

1993-01-01

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

Renormalization in Coulomb-gauge QCD within the Lagrangian formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niegawa, A.

2006-08-15

We study renormalization of Coulomb-gauge QCD within the Lagrangian, second-order, formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analysis, we show that, in the strict Coulomb gauge, g{sup 2}D{sup 00} is invariant under renormalization. (D{sup 00} is the time-time component of the gluon propagator.)

Ensemble Pulsar Time Scale

NASA Astrophysics Data System (ADS)

Yin, Dong-shan; Gao, Yu-ping; Zhao, Shu-hong

2017-07-01

Millisecond pulsars can generate another type of time scale that is totally independent of the atomic time scale, because the physical mechanisms of the pulsar time scale and the atomic time scale are quite different from each other. Usually the pulsar timing observations are not evenly sampled, and the internals between two data points range from several hours to more than half a month. Further more, these data sets are sparse. All this makes it difficult to generate an ensemble pulsar time scale. Hence, a new algorithm to calculate the ensemble pulsar time scale is proposed. Firstly, a cubic spline interpolation is used to densify the data set, and make the intervals between data points uniform. Then, the Vondrak filter is employed to smooth the data set, and get rid of the high-frequency noises, and finally the weighted average method is adopted to generate the ensemble pulsar time scale. The newly released NANOGRAV (North American Nanohertz Observatory for Gravitational Waves) 9-year data set is used to generate the ensemble pulsar time scale. This data set includes the 9-year observational data of 37 millisecond pulsars observed by the 100-meter Green Bank telescope and the 305-meter Arecibo telescope. It is found that the algorithm used in this paper can reduce effectively the influence caused by the noises in pulsar timing residuals, and improve the long-term stability of the ensemble pulsar time scale. Results indicate that the long-term (> 1 yr) stability of the ensemble pulsar time scale is better than 3.4 × 10-15.

Extended hamiltonian formalism and Lorentz-violating lagrangians

NASA Astrophysics Data System (ADS)

Colladay, Don

2017-09-01

A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant lagrangian and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the lagrangian. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the lagrangians and the field-theoretic solutions to the Dirac equation is also established for a special case.

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bo, Wurigen; Shashkov, Mikhail

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

DOE PAGES

Bo, Wurigen; Shashkov, Mikhail

2015-07-21

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

Lagrangian Formulation of a Magnetostatic Field in the Presence of a Minimal Length Scale Based on the Kempf Algebra

NASA Astrophysics Data System (ADS)

Moayedi, S. K.; Setare, M. R.; Khosropour, B.

2013-11-01

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β‧)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length (\\triangle Xi)\\min = \\hbar √ {Dβ +β '}, \\forall i\\in \\{1, 2, ..., D\\}. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β‧ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee-Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot-Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19 m. The relationship between magnetostatics with a minimal length and the Gaete-Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.

We present an essentially Lagrangian hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedron meshes. The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on Lagrangian CCH work [8, 19, 37, 38, 44] and recent Lagrangian SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2014-10-28

We present an essentially Lagrangian hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedron meshes. The scheme reduces to a purely Lagrangian approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially Lagrangian for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic scheme (SGH) or with a cell-centered hydrodynamic (CCH) scheme. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on Lagrangian CCH work [8, 19, 37, 38, 44] and recent Lagrangian SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

NASA Technical Reports Server (NTRS)

Buchert, T.; Melott, A. L.; Weiss, A. G.

1993-01-01

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.

PubMed

Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas

2015-07-14

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.

Parallel Decomposition of the Fictitious Lagrangian Algorithm and its Accuracy for Molecular Dynamics Simulations of Semiconductors.

NASA Astrophysics Data System (ADS)

Yeh, Mei-Ling

We have performed a parallel decomposition of the fictitious Lagrangian method for molecular dynamics with tight-binding total energy expression into the hypercube computer. This is the first time in literature that the dynamical simulation of semiconducting systems containing more than 512 silicon atoms has become possible with the electrons treated as quantum particles. With the utilization of the Intel Paragon system, our timing analysis predicts that our code is expected to perform realistic simulations on very large systems consisting of thousands of atoms with time requirements of the order of tens of hours. Timing results and performance analysis of our parallel code are presented in terms of calculation time, communication time, and setup time. The accuracy of the fictitious Lagrangian method in molecular dynamics simulation is also investigated, especially the energy conservation of the total energy of ions. We find that the accuracy of the fictitious Lagrangian scheme in small silicon cluster and very large silicon system simulations is good for as long as the simulations proceed, even though we quench the electronic coordinates to the Born-Oppenheimer surface only in the beginning of the run. The kinetic energy of electrons does not increase as time goes on, and the energy conservation of the ionic subsystem remains very good. This means that, as far as the ionic subsystem is concerned, the electrons are on the average in the true quantum ground states. We also tie up some odds and ends regarding a few remaining questions about the fictitious Lagrangian method, such as the difference between the results obtained from the Gram-Schmidt and SHAKE method of orthonormalization, and differences between simulations where the electrons are quenched to the Born -Oppenheimer surface only once compared with periodic quenching.

Parent formulation at the Lagrangian level

NASA Astrophysics Data System (ADS)

Grigoriev, Maxim

2011-07-01

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV-BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang-Mills theory, and gravity.

Assimilating Eulerian and Lagrangian data in traffic-flow models

NASA Astrophysics Data System (ADS)

Xia, Chao; Cochrane, Courtney; DeGuire, Joseph; Fan, Gaoyang; Holmes, Emma; McGuirl, Melissa; Murphy, Patrick; Palmer, Jenna; Carter, Paul; Slivinski, Laura; Sandstede, Björn

2017-05-01

Data assimilation of traffic flow remains a challenging problem. One difficulty is that data come from different sources ranging from stationary sensors and camera data to GPS and cell phone data from moving cars. Sensors and cameras give information about traffic density, while GPS data provide information about the positions and velocities of individual cars. Previous methods for assimilating Lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in Lagrangian coordinates. These approaches make it hard to assimilate both Eulerian density and Lagrangian positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and Lagrangian data. We show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble Kalman or particle filters are used. We also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models.

Lagrangian descriptors of driven chemical reaction manifolds.

PubMed

Craven, Galen T; Junginger, Andrej; Hernandez, Rigoberto

2017-08-01

The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.148301], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

Lagrangian displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.

PubMed

Ma, Chi; Varghese, Tomy

2012-04-01

Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.

Advances in time-scale algorithms

NASA Technical Reports Server (NTRS)

Stein, S. R.

1993-01-01

The term clock is usually used to refer to a device that counts a nearly periodic signal. A group of clocks, called an ensemble, is often used for time keeping in mission critical applications that cannot tolerate loss of time due to the failure of a single clock. The time generated by the ensemble of clocks is called a time scale. The question arises how to combine the times of the individual clocks to form the time scale. One might naively be tempted to suggest the expedient of averaging the times of the individual clocks, but a simple thought experiment demonstrates the inadequacy of this approach. Suppose a time scale is composed of two noiseless clocks having equal and opposite frequencies. The mean time scale has zero frequency. However if either clock fails, the time-scale frequency immediately changes to the frequency of the remaining clock. This performance is generally unacceptable and simple mean time scales are not used. First, previous time-scale developments are reviewed and then some new methods that result in enhanced performance are presented. The historical perspective is based upon several time scales: the AT1 and TA time scales of the National Institute of Standards and Technology (NIST), the A.1(MEAN) time scale of the US Naval observatory (USNO), the TAI time scale of the Bureau International des Poids et Measures (BIPM), and the KAS-1 time scale of the Naval Research laboratory (NRL). The new method was incorporated in the KAS-2 time scale recently developed by Timing Solutions Corporation. The goal is to present time-scale concepts in a nonmathematical form with as few equations as possible. Many other papers and texts discuss the details of the optimal estimation techniques that may be used to implement these concepts.

Heavy precipitation episodes in the Western Mediterranean : Use of a semi-Lagrangian advection model for the fine-scale description of upper-level troughs

NASA Astrophysics Data System (ADS)

Gauthier, N.; Claud, C.; Funatsu, B. M.; Chaboureau, J.-P.; Argence, S.; Lambert, D.; Richard, E.; Hauchecorne, A.; Arbogast, P.; Maynard, K.

2009-09-01

Heavy precipitation events over the Mediterranean Sea are generally associated with upper-level troughs. The mesoscale structures of such troughs are however not well reproduced by the atmospheric analyses due to inappropriate spatial resolution. We propose here to use a semi-Lagrangian advection model called MIMOSA (Modélisation Isentrope du transport Méso-échelle de l'Ozone Stratosphérique par Advection) initially developed to describe stratospheric filaments, to calculate fine-scale Potential Vorticity (PV) fields on isentropic surfaces near the tropopause. After a description of MIMOSA, we will focus on the model-generated PV fields for several high impact weather cases that occurred over the Western Mediterreanean Sea. We will demonstrate the ability of MIMOSA to resolve fine scale structures of upper-level troughs considering the Algiers' flash flood, which occurred on November 2001, and then a heavy precipitation event over southeast France on the 5-6 September 2005. Finally, with a PV inversion method, we will show the impact of the fine scales PV structures as depicted by MIMOSA to improve the numerical simulation of a « hurricane » that hit Italy in September 2006, both in terms of surface pressure and precipitation forecasts.

Hamiltonian stability for weighted measure and generalized Lagrangian mean curvature flow

NASA Astrophysics Data System (ADS)

Kajigaya, Toru; Kunikawa, Keita

2018-06-01

In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of Lagrangian submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a Lagrangian submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized Lagrangian mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial Lagrangian submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable Lagrangian submanifold, then the generalized MCF converges exponentially fast to an f-minimal Lagrangian submanifold.

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

NASA Technical Reports Server (NTRS)

Peng, Y. K. M.

1974-01-01

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.

Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

NASA Astrophysics Data System (ADS)

Bertachini, A.

) Guess a final regularized time f and integrate the regularized equations of motion from 0 = 0 until f; iii) Check the final position rf obtained from the numerical integration with the prescribed final position and the final real time with the specified time of flight. If there is an agreement (difference less than a specified error allowed) the solution is found and the process can stop here. If there is no agreement, an increment in the initial guessed velocity Vi and in the guessed final regularized time is made and the process goes back to step i). The method used to find the increment in the guessed variables is the standard gradient method, as described in Press et. al., 1989. The routines available in this reference are also used in this research with minor modifications. After that this algorithm is implemented, the Lambert's three-body problem between the Earth and the Lagrangian points is solved for several values of the time of flight. Since the regularized system is used to solve this problem, there is no need to specify the final position of M3 as lying in an primary's parking orbit (to avoid the singularity). Then, to make a comparison with previous papers (Broucke, 1979 and Prado, 1996) the centre of the primary is used as the final position for M3. The results are organized in plots of the energy and the initial flight path angle (the control to be used) in the rotating frame against the time of flight. The definition of the angle is such that the zero is in the "x" axis, (pointing to the positive direction) and it increases in the counter-clock-wise sense. This problem, as well as the Lambert's original version, has two solutions for a given transfer time: one in the counter-clock-wise direction and one in the clock-wise direction in the inertial frame. In this paper, emphasis is given in finding the families with the smallest possible energy (and velocity), although many other families do exist. Broucke, R., (1979) Travelling Between the Lagrange

Cochlear Modeling Using Time-Averaged Lagrangian" Method:. Comparison with VBM, PST, and ZC Measurements

NASA Astrophysics Data System (ADS)

Yoon, Y.; Kim, N.; Puria, S.; Steele, C. R.

2009-02-01

In this work, basilar membrane velocity (VBM), scala tympani intracochlear pressure (PST), and cochlear input impedances (Zc) for gerbil and chinchilla are implemented using a three-dimensional hydro-dynamic cochlear model using 1) time-averaged Lagrangian, 2) push-pull mechanism in active case, and 3) the complex anatomy of cochlear scalae by micro computed tomography (μCT) scanning and 3-D reconstructions of gerbil and chinchilla temporal bones. The objective of this work is to compare the calculations and the physiological measurements of gerbil and chinchilla cochlear such as VBM (Ren and Nuttall [1]), PST (Olson [2]), and ZC (Decraemer et al. [3], Songer and Rosowski [4], Ruggero et al. [5]) with present model. A WKB asymptotic method combined with Fourier series expansions is used to provide an efficient simulation. VBM and PST simulation results for the gerbil cochlea show good agreement both in the magnitude and the phase for the physiological measurements without larger phase excursion. ZC simulation from the gerbil and chinchilla model show reasonably good agreement with measurement.

Vortex dynamics and Lagrangian statistics in a model for active turbulence.

PubMed

James, Martin; Wilczek, Michael

2018-02-14

Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the Eulerian and the Lagrangian frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.

Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.

Lagrangian coherent structures are associated with fluctuations in airborne microbial populations

NASA Astrophysics Data System (ADS)

Tallapragada, P.; Ross, S. D.; Schmale, D. G.

2011-09-01

Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.

Extended Lagrangian formulation of charge-constrained tight-binding molecular dynamics.

PubMed

Cawkwell, M J; Coe, J D; Yadav, S K; Liu, X-Y; Niklasson, A M N

2015-06-09

The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended Lagrangian molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of numerical noise during trajectories was also investigated.

Functional integral for non-Lagrangian systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

2010-02-01

A functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The approach, which we call “stringy quantization,” is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -κq˙A. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.

Quantization of Non-Lagrangian Systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.

The S-Lagrangian and a theory of homeostasis in living systems

NASA Astrophysics Data System (ADS)

Sandler, U.; Tsitolovsky, L.

2017-04-01

A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-Lagrangian, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-Lagrangian. Additionally, we reveal that plausible assumptions about S-Lagrangian features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.

Forms of null Lagrangians in field theories of continuum mechanics

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Radaev, Yu. N.

2012-02-01

The divergence representation of a null Lagrangian that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null Lagrangian can contain up to 15 independent elements in total. The general form of a null Lagrangian in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null Lagrangian for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null Lagrangians are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids

DOE PAGES

Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas

2015-06-26

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less

A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories

NASA Astrophysics Data System (ADS)

Li, Wenliang

2018-04-01

We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.

3-D Lagrangian-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis

NASA Astrophysics Data System (ADS)

Cheng, Huai-yu; Long, Xin-ping; Ji, Bin; Liu, Qi; Bai, Xiao-rui

2018-02-01

In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D Lagrangian technology is developed, which can provide the particle tracks and the 3-D Lagrangian coherent structures (LCSs). Combined with the traditional methods based on the Eulerian viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D Lagrangian technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D Lagrangian technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D Lagrangian technologies indicates the advantages of the latter. It is demonstrated that the 3-D Lagrangian technology is a promising tool in the investigation of complex cavitating flows.

Leading-order classical Lagrangians for the nonminimal standard-model extension

NASA Astrophysics Data System (ADS)

Reis, J. A. A. S.; Schreck, M.

2018-03-01

In this paper, we derive the general leading-order classical Lagrangian covering all fermion operators of the nonminimal standard-model extension (SME). Such a Lagrangian is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the Lagrangian obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.

Reynolds and Prandtl number scaling of viscous heating in isotropic turbulence

NASA Astrophysics Data System (ADS)

Pushkarev, Andrey; Balarac, Guillaume; Bos, Wouter J. T.

2017-08-01

Viscous heating is investigated using high-resolution direct numerical simulations. Scaling relations are derived and verified for different values of the Reynolds and Prandtl numbers. The scaling of the heat fluctuations is shown to depend on Lagrangian correlation times and on the scaling of dissipation-rate fluctuations. The convergence of the temperature spectrum to asymptotic scaling is observed to be slow, due to the broadband character of the temperature production spectrum and the slow convergence of the dissipation-rate spectrum to its asymptotic form.

Lagrangian condensation microphysics with Twomey CCN activation

NASA Astrophysics Data System (ADS)

Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna

2018-01-01

We report the development of a novel Lagrangian microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional Eulerian method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses Lagrangian super-droplets to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the Lagrangian warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation

Lagrangian methods in nonlinear plasma wave interaction

NASA Technical Reports Server (NTRS)

Crawford, F. W.

1980-01-01

Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-Lagrangian methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable Lagrangian densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.

Using Lagrangian Coherent Structures to understand coastal water quality

NASA Astrophysics Data System (ADS)

Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.

2012-09-01

The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a Lagrangian circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.

A continuous time random walk model for Darcy-scale anomalous transport in heterogeneous porous media.

NASA Astrophysics Data System (ADS)

Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco

2017-04-01

Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is

Integration over families of Lagrangian submanifolds in BV formalism

NASA Astrophysics Data System (ADS)

Mikhailov, Andrei

2018-03-01

Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.

An updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluids

NASA Astrophysics Data System (ADS)

Tu, Qingsong; Li, Shaofan

2017-11-01

In this work, we have developed an updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics formulation proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not formulated with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update Lagrangian particle hydrodynamics formulation converges to the conventional local fluid mechanics formulation; (2) the non-local updated Lagrangian particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the formulation, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust.

Symmetries in Lagrangian Dynamics

ERIC Educational Resources Information Center

Ferrario, Carlo; Passerini, Arianna

2007-01-01

In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

PubMed

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

ATLAS - A new Lagrangian transport and mixing model with detailed stratospheric chemistry

NASA Astrophysics Data System (ADS)

Wohltmann, I.; Rex, M.; Lehmann, R.

2009-04-01

We present a new global Chemical Transport Model (CTM) with full stratospheric chemistry and Lagrangian transport and mixing called ATLAS. Lagrangian models have some crucial advantages over Eulerian grid-box based models, like no numerical diffusion, no limitation of the time step of the model by the CFL criterion, conservation of mixing ratios by design and easy parallelization of code. The transport module is based on a trajectory code developed at the Alfred Wegener Institute. The horizontal and vertical resolution, the vertical coordinate system (pressure, potential temperature, hybrid coordinate) and the time step of the model are flexible, so that the model can be used both for process studies and long-time runs over several decades. Mixing of the Lagrangian air parcels is parameterized based on the local shear and strain of the flow with a method similar to that used in the CLaMS model, but with some modifications like a triangulation that introduces no vertical layers. The stratospheric chemistry module was developed at the Institute and includes 49 species and 170 reactions and a detailed treatment of heterogenous chemistry on polar stratospheric clouds. We present an overview over the model architecture, the transport and mixing concept and some validation results. Comparison of model results with tracer data from flights of the ER2 aircraft in the stratospheric polar vortex in 1999/2000 which are able to resolve fine tracer filaments show that excellent agreement with observed tracer structures can be achieved with a suitable mixing parameterization.

Lagrangian dynamics of the mistral during the HyMeX SOP2

NASA Astrophysics Data System (ADS)

Drobinski, P.; Alonzo, B.; Basdevant, C.; Cocquerez, P.; Doerenbecher, A.; Fourrié, N.; Nuret, M.

2017-02-01

The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the Lagrangian documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the Lagrangian formulation of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.

Lagrangian dynamics of the mistral during the HyMeX SOP2

NASA Astrophysics Data System (ADS)

Drobinski, Philippe; Alonzo, Bastien; Basdevant, Claude; Cocquerez, Philippe; Fourrié, Nadia; Nuret, Mathieu

2017-04-01

The mistral refers to a severe wind blowing over the Gulf of Lions after being channeled in the Rhone valley. It influences the western Mediterranean climate as it brings cold and dry continental air over the warm western Mediterranean, generating intense air-sea heat exchanges and sea surface cooling, inducing the formation of the western Mediterranean deep water that moves into the Atlantic Ocean. The mistral is frequently observed to extend as far as a few hundred kilometers from the coast, and its fine-scale dynamics over the sea is still only partially understood as finely resolved observations in time and space are lacking. The boundary layer pressurized balloons (BLPB) developed by the Centre National d'Etudes Spatiales and deployed during HyMeX SOP2 allowed the Lagrangian documentation of the mistral events that occurred between beginning of February to mid-March 2013. Analyzed in synergy with the AROME-WMED weather forecast model, all the terms of the Lagrangian formulation of the momentum conservation equation could be quantified showing three different regions: (1) an injection zone where the mistral flow is directed toward the center of the Genoa cyclone due to a strong zonal pressure gradient, enhanced friction, and entrainment in the mountain wake; (2) an ejection zone where the flow is deflected outward of the cyclone due to either the nonnegligible inertia pseudoforce or an inertial oscillation caused by a sudden friction decrease; and (3) a region of geostrophic deceleration due to the weakening of the pressure gradient.

V-ONSET: Introducing turbulent multiphase flow facility focusing on Lagrangian interfacial transfer dynamics

NASA Astrophysics Data System (ADS)

Salibindla, Ashwanth; Masuk, Ashik Ullah Mohammad; Ni, Rui

2017-11-01

We have designed and constructed a new vertical water tunnel, V-ONSET, to investigate interfacial mass, momentum and energy transfer between two phases in a Lagrangian frame. This system features an independent control of mean flow and turbulence level. The mean flow opposes the rising/falling velocity of the second phase, ``suspending'' the particles and increasing tracking time in the view area. Strong turbulence is generated by shooting 88 digitally-controlled water jets into the test section. The second phase, either bubbles or oil droplets, can be introduced into the test section through a capillary island. In addition to this flow control system, V-ONSET comes with a 3D two-phase visualization system, consisting of high-speed cameras, two-colored LED system, and in-house Lagrangian particle tracking algorithm. This enables us to acquire the Lagrangian evolution of both phases and the interfacial transfer dynamics in between, paving the way for new closure models for two-phase simulations. Financial support for this project was provided by National Science Foundation under Grant Number: 1653389 and 1705246.

Correlational signatures of time-reversal symmetry breaking in two-dimensional flow

NASA Astrophysics Data System (ADS)

Hogg, Charlie; Ouellette, Nicholas

2015-11-01

Classical turbulence theories posit that broken spatial symmetries should be (statistically) restored at small scales. But since turbulent flows are inherently dissipative, time reversal symmetry is expected to remain broken throughout the cascade. However, the precise dynamical signature of this broken symmetry is not well understood. Recent work has shed new light on this fundamental question by considering the Lagrangian structure functions of power. Here, we take a somewhat different approach by studying the Lagrangian correlation functions of velocity and acceleration. We measured these correlations using particle tracking velocimetry in a quasi-two-dimensional electromagnetically driven flow that displayed net inverse energy transfer. We show that the correlation functions of the velocity and acceleration magnitudes are not symmetric in time, and that the degree of asymmetry can be related to the flux of energy between scales, suggesting that the asymmetry has a dynamical origin.

Lagrangian solution of supersonic real gas flows

NASA Technical Reports Server (NTRS)

Loh, Ching-Yuen; Liou, Meng-Sing

1993-01-01

The present extention of a Lagrangian approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the Lagrangian form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.

Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico.

PubMed

Duran, R; Beron-Vera, F J; Olascoaga, M J

2018-03-26

We construct a climatology of Lagrangian coherent structures (LCSs)-the concealed skeleton that shapes transport-with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. The cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, showing that a climatological velocity can preserve meaningful transport information. The quasi-steady transport patterns revealed by the cLCSs agree well with aspects of the GoM circulation described in several previous observational and numerical studies. For example, the cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact are regions of maximal attraction. We also show that cLCSs are remarkably accurate at identifying transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus it is shown that computing cLCSs is an efficient and meaningful way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.

Lagrangian Approach to Study Catalytic Fluidized Bed Reactors

NASA Astrophysics Data System (ADS)

Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration

2013-03-01

Lagrangian approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a Lagrangian approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The Lagrangian perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the Lagrangian approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)

The Lagrangian-Hamiltonian formalism for higher order field theories

NASA Astrophysics Data System (ADS)

Vitagliano, Luca

2010-06-01

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.

Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems

NASA Astrophysics Data System (ADS)

Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso

2011-09-01

The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

Near-Surface Monsoonal Circulation of the Vietnam East Sea from Lagrangian Drifters

DTIC Science & Technology

2015-09-30

Sea from Lagrangian Drifters Luca Centurioni Scripps Institution of Oceanography 9500 Gilman Drive Mail Code 0213 La Jolla, California 92103...Contribute to the study of coastal and open ocean current systems in sparsely sampled regions such us the South China Sea (SCS), using a Lagrangian ...We intend to make new Lagrangian and Eulerian observations to measure the seasonal circulation 1) in the coastal waters of Vietnam and 2) in the SCS

Experimental Investigation of Lagrangian Statistics of Motion of Diesel Oil Droplets and Fluid Particles in Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Gopalan, Balaji; Malkiel, Edwin; Katz, Joseph

2007-11-01

Lagrangian motion in isotropic turbulence of slightly buoyant diesel oil droplets (specific gravity 0.85 and size 0.6-1.1 mm) and almost neutrally buoyant, 50 μm tracer particles are studied using high speed, in-line digital holographic cinematography. Droplets and particles are injected into a 50x50x70 mm^3 sample volume located at the center of a nearly isotropic turbulence facility, and data are obtained for Reλ of 190, 195 and 214. The turbulence is characterized by 2D PIV measurements at different planes. An automated tracking program has been used for measuring velocity time history of more than 22000 droplet tracks and 15000 particle tracks. Analysis compares probability density functions (PDF) of Lagrangian velocity and acceleration, spectra, as well as velocity and acceleration autocorrelation functions of droplets with those of particles. For most of the present conditions, rms values of horizontal droplet velocity exceed those of the fluid. The rms values of droplet vertical velocity are higher than those of the fluid only for the highest turbulence level. PDFs of droplet velocity have nearly Gaussian distributions, justifying use of Taylor's (1921) model to calculate diffusion parameters. The fluid particle diffusion coefficient exceeds that of the droplet primarily because the fluid diffusion timescale is higher than that of the droplet. For all droplet sizes and Reynolds numbers, the diffusion coefficient, calculated using Taylor's model, scaled by quiescent rise velocity and turbulence integral length scale, is a monotonically increasing function of the turbulence level normalized by droplet quiescent rise velocity.

Unsteady force estimation using a Lagrangian drift-volume approach

NASA Astrophysics Data System (ADS)

McPhaden, Cameron J.; Rival, David E.

2018-04-01

A novel Lagrangian force estimation technique for unsteady fluid flows has been developed, using the concept of a Darwinian drift volume to measure unsteady forces on accelerating bodies. The construct of added mass in viscous flows, calculated from a series of drift volumes, is used to calculate the reaction force on an accelerating circular flat plate, containing highly-separated, vortical flow. The net displacement of fluid contained within the drift volumes is, through Darwin's drift-volume added-mass proposition, equal to the added mass of the plate and provides the reaction force of the fluid on the body. The resultant unsteady force estimates from the proposed technique are shown to align with the measured drag force associated with a rapid acceleration. The critical aspects of understanding unsteady flows, relating to peak and time-resolved forces, often lie within the acceleration phase of the motions, which are well-captured by the drift-volume approach. Therefore, this Lagrangian added-mass estimation technique opens the door to fluid-dynamic analyses in areas that, until now, were inaccessible by conventional means.

Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tronko, Natalia; Brizard, Alain J.

A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center Lagrangian constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less

A new Lagrangian method for real gases at supersonic speed

NASA Technical Reports Server (NTRS)

Loh, C. Y.; Liou, Meng-Sing

1992-01-01

With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the Lagrangian description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the Lagrangian level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.

Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean.

PubMed

Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan

2015-08-01

Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.

Evaluating the assumption of power-law late time scaling of breakthrough curves in highly heterogeneous media

NASA Astrophysics Data System (ADS)

Pedretti, Daniele

2017-04-01

Power-law (PL) distributions are widely adopted to define the late-time scaling of solute breakthrough curves (BTCs) during transport experiments in highly heterogeneous media. However, from a statistical perspective, distinguishing between a PL distribution and another tailed distribution is difficult, particularly when a qualitative assessment based on visual analysis of double-logarithmic plotting is used. This presentation aims to discuss the results from a recent analysis where a suite of statistical tools was applied to evaluate rigorously the scaling of BTCs from experiments that generate tailed distributions typically described as PL at late time. To this end, a set of BTCs from numerical simulations in highly heterogeneous media were generated using a transition probability approach (T-PROGS) coupled to a finite different numerical solver of the flow equation (MODFLOW) and a random walk particle tracking approach for Lagrangian transport (RW3D). The T-PROGS fields assumed randomly distributed hydraulic heterogeneities with long correlation scales creating solute channeling and anomalous transport. For simplicity, transport was simulated as purely advective. This combination of tools generates strongly non-symmetric BTCs visually resembling PL distributions at late time when plotted in double log scales. Unlike other combination of modeling parameters and boundary conditions (e.g. matrix diffusion in fractures), at late time no direct link exists between the mathematical functions describing scaling of these curves and physical parameters controlling transport. The results suggest that the statistical tests fail to describe the majority of curves as PL distributed. Moreover, they suggest that PL or lognormal distributions have the same likelihood to represent parametrically the shape of the tails. It is noticeable that forcing a model to reproduce the tail as PL functions results in a distribution of PL slopes comprised between 1.2 and 4, which are the

Lagrangian Observations and Modeling of Marine Larvae

NASA Astrophysics Data System (ADS)

Paris, Claire B.; Irisson, Jean-Olivier

2017-04-01

Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a Lagrangian platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed Lagrangian behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source Lagrangian tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive Lagrangian trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.

Lagrangian coherent structures during combustion instability in a premixed-flame backward-step combustor.

PubMed

Sampath, Ramgopal; Mathur, Manikandan; Chakravarthy, Satyanarayanan R

2016-12-01

This paper quantitatively examines the occurrence of large-scale coherent structures in the flow field during combustion instability in comparison with the flow-combustion-acoustic system when it is stable. For this purpose, the features in the recirculation zone of the confined flow past a backward-facing step are studied in terms of Lagrangian coherent structures. The experiments are conducted at a Reynolds number of 18600 and an equivalence ratio of 0.9 of the premixed fuel-air mixture for two combustor lengths, the long duct corresponding to instability and the short one to the stable case. Simultaneous measurements of the velocity field using time-resolved particle image velocimetry and the CH^{*} chemiluminescence of the flame along with pressure time traces are obtained. The extracted ridges of the finite-time Lyapunov exponent (FTLE) fields delineate dynamically distinct regions of the flow field. The presence of large-scale vortical structures and their modulation over different time instants are well captured by the FTLE ridges for the long combustor where high-amplitude acoustic oscillations are self-excited. In contrast, small-scale vortices signifying Kelvin-Helmholtz instability are observed in the short duct case. Saddle-type flow features are found to separate the distinct flow structures for both combustor lengths. The FTLE ridges are found to align with the flame boundaries in the upstream regions, whereas farther downstream, the alignment is weaker due to dilatation of the flow by the flame's heat release. Specifically, the FTLE ridges encompass the flame curl-up for both the combustor lengths, and thus act as the surrogate flame boundaries. The flame is found to propagate upstream from an earlier vortex roll-up to a newer one along the backward-time FTLE ridge connecting the two structures.

Lagrangians for generalized Argyres-Douglas theories

NASA Astrophysics Data System (ADS)

Benvenuti, Sergio; Giacomelli, Simone

2017-10-01

We continue the study of Lagrangian descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.

COLA with scale-dependent growth: applications to screened modified gravity models

NASA Astrophysics Data System (ADS)

Winther, Hans A.; Koyama, Kazuya; Manera, Marc; Wright, Bill S.; Zhao, Gong-Bo

2017-08-01

We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely f(R) gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to ΛCDM even when using a fairly small number of COLA time steps.

Estimates of Lagrangian particle transport by wave groups: forward transport by Stokes drift and backward transport by the return flow

NASA Astrophysics Data System (ADS)

van den Bremer, Ton S.; Taylor, Paul H.

2014-11-01

Although the literature has examined Stokes drift, the net Lagrangian transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the Eulerian return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the Lagrangian transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal Lagrangian transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which Lagrangian particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.

Eulerian and Lagrangian approaches to multidimensional condensation and collection

NASA Astrophysics Data System (ADS)

Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.

2017-06-01

Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.