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.

Lagrangian large eddy simulations of boundary layer clouds on ERA-Interim and ERA5 trajectories

NASA Astrophysics Data System (ADS)

Kazil, J.; Feingold, G.; Yamaguchi, T.

2017-12-01

This exploratory study examines Lagrangian large eddy simulations of boundary layer clouds along wind trajectories from the ERA-Interim and ERA5 reanalyses. The study is motivated by the need for statistically representative sets of high resolution simulations of cloud field evolution in realistic meteorological conditions. The study will serve as a foundation for the investigation of biomass burning effects on the transition from stratocumulus to shallow cumulus clouds in the South-East Atlantic. Trajectories that pass through a location with radiosonde data (St. Helena) and which exhibit a well-defined cloud structure and evolution were identified in satellite imagery, and sea surface temperature and atmospheric vertical profiles along the trajectories were extracted from the reanalysis data sets. The System for Atmospheric Modeling (SAM) simulated boundary layer turbulence and cloud properties along the trajectories. Mean temperature and moisture (in the free troposphere) and mean wind speed (at all levels) were nudged towards the reanalysis data. Atmospheric and cloud properties in the large eddy simulations were compared with those from the reanalysis products, and evaluated with satellite imagery and radiosonde data. Simulations using ERA-Interim data and the higher resolution ERA5 data are contrasted.

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.

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

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.

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.

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

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.

A combined Eulerian-Lagrangian two-phase analysis of the SSME HPOTP nozzle plug trajectories

NASA Technical Reports Server (NTRS)

Garcia, Robert; Mcconnaughey, P. K.; Dejong, F. J.; Sabnis, J. S.; Pribik, D.

1989-01-01

As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs Lagrangian tracking of the particle through the Eulerian flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.

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.

A combined Eulerian-Lagrangian two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results

NASA Technical Reports Server (NTRS)

Mcconnaughey, P. K.; Garcia, R.; Dejong, F. J.; Sabnis, J. S.; Pribik, D. A.

1989-01-01

An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a Lagrangian method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.

Experimental design for drifting buoy Lagrangian test

NASA Technical Reports Server (NTRS)

Saunders, P. M.

1975-01-01

A test of instrumentation fabricated to measure the performance of a free drifting buoy as a (Lagrangian) current meter is described. Specifically it is proposed to distinguish between the trajectory of a drogued buoy and the trajectory of the water at the level of the drogue by measuring the flow relative to the drogue.

Evaluation of the HF-Radar network system around Taiwan using normalized cumulative Lagrangian separation.

NASA Astrophysics Data System (ADS)

Fredj, Erick; Kohut, Josh; Roarty, Hugh; Lai, Jian-Wu

2017-04-01

The Lagrangian separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as over continental shelves and the adjacent deep ocean. A skill score described in detail by (Lui et.al. 2011) was applied to estimate the cumulative Lagrangian separation distances normalized by the associated cumulative trajectory lengths. In contrast, the Lagrangian separation distance alone gives a misleading result. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional Eulerian-based velocity nor a Lagrangian based probability density function may be estimated. The skill score assesses The Taiwan Ocean Radar Observing System (TOROS) performance. TOROS consists of 17 SeaSonde type radars around the Taiwan Island. The currents off Taiwan are significantly influenced by the nearby Kuroshio current. The main stream of the Kuroshio flows along the east coast of Taiwan to the north throughout the year. Sometimes its branch current also bypasses the south end of Taiwan and goes north along the west coast of Taiwan. The Kuroshio is also prone to seasonal change in its speed of flow, current capacity, distribution width, and depth. The evaluations of HF-Radar National Taiwanese network performance using Lagrangian drifter records demonstrated the high quality and robustness of TOROS HF-Radar data using a purely trajectory-based non-dimensional index. Yonggang Liu and Robert H. Weisberg, "Evaluation of trajectory modeling in different dynamic regions using normalized cumulative Lagrangian separation", Journal of Geophysical Research, Vol. 116, C09013, doi:10.1029/2010JC006837, 2011

A Satellite-Based Lagrangian View on Phytoplankton Dynamics.

PubMed

Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan

2018-01-03

The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter-the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.

A Satellite-Based Lagrangian View on Phytoplankton Dynamics

NASA Astrophysics Data System (ADS)

Lehahn, Yoav; d'Ovidio, Francesco; Koren, Ilan

2018-01-01

The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter—the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.

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.

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.

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.

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.

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.

On Integral Invariants for Effective 3-D Motion Trajectory Matching and Recognition.

PubMed

Shao, Zhanpeng; Li, Youfu

2016-02-01

Motion trajectories tracked from the motions of human, robots, and moving objects can provide an important clue for motion analysis, classification, and recognition. This paper defines some new integral invariants for a 3-D motion trajectory. Based on two typical kernel functions, we design two integral invariants, the distance and area integral invariants. The area integral invariants are estimated based on the blurred segment of noisy discrete curve to avoid the computation of high-order derivatives. Such integral invariants for a motion trajectory enjoy some desirable properties, such as computational locality, uniqueness of representation, and noise insensitivity. Moreover, our formulation allows the analysis of motion trajectories at a range of scales by varying the scale of kernel function. The features of motion trajectories can thus be perceived at multiscale levels in a coarse-to-fine manner. Finally, we define a distance function to measure the trajectory similarity to find similar trajectories. Through the experiments, we examine the robustness and effectiveness of the proposed integral invariants and find that they can capture the motion cues in trajectory matching and sign recognition satisfactorily.

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.

Source apportion of atmospheric particulate matter: a joint Eulerian/Lagrangian approach.

PubMed

Riccio, A; Chianese, E; Agrillo, G; Esposito, C; Ferrara, L; Tirimberio, G

2014-12-01

PM2.5 samples were collected during an annual monitoring campaign (January 2012-January 2013) in the urban area of Naples, one of the major cities in Southern Italy. Samples were collected by means of a standard gravimetric sampler (Tecora Echo model) and characterized from a chemical point of view by ion chromatography. As a result, 143 samples together with their ionic composition have been collected. We extend traditional source apportionment techniques, usually based on multivariate factor analysis, interpreting the chemical analysis results within a Lagrangian framework. The Hybrid Single-Particle Lagrangian Integrated Trajectory Model (HYSPLIT) model was used, providing linkages to the source regions in the upwind areas. Results were analyzed in order to quantify the relative weight of different source types/areas. Model results suggested that PM concentrations are strongly affected not only by local emissions but also by transboundary emissions, especially from the Eastern and Northern European countries and African Saharan dust episodes.

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.

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.

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Scale-by-scale contributions to Lagrangian particle acceleration

NASA Astrophysics Data System (ADS)

Lalescu, Cristian C.; Wilczek, Michael

2017-11-01

Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. Lagrangian particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on Lagrangian statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the Lagrangian tracer acceleration as the short time limit of the Lagrangian velocity increment, we also quantify the influence of filtering on Lagrangian intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

Collaborative Visual Seafloor Imaging using a Photographic AUV and a Lagrangian Imaging Float

NASA Astrophysics Data System (ADS)

Friedman, A.; Pizarro, O.; Roman, C.; Toohey, L.; Snyder, W.; Johnson-Roberson, M.; Iscar, E.; Williams, S. B.

2016-02-01

High resolution seafloor imaging from mobile autonomous platforms has become a valuable tool for habitat classification, stock assessment and seafloor exploration. This abstract addresses the concept of joint seafloor survey planning using both navigable and drifting platforms, and presents results from an experiment using a bottom surveying AUV and a drifting Lagrangian camera float. We consider two classes of vehicles; one which is able to self propel and execute structured surveys, and one which is Lagrangian and moves only with the currents. The navigable vehicle is the more capable and the more expensives asset of the two. The Lagrangian platforms is a low cost imaging tool that can actively control its altitude above the seafloor to obtain high quality images but can not otherwise control its trajectory over the bottom. When used together the vehicles offer several scenarios for joint operations. When used in an exploratory manner the Lagrangian float is an inexpensive way to collect images from an unknown area. Depending on the collected images, a follow on structured survey with the navigable AUV can collect additional information if the cost is acceptable given the need and prior data. When used simultaneously the drifting float can guide the AUV trajectory over an area. When both platforms are equipped with acoustic tracking and communications the AUV trajectory can be automatically redirected to follow the Lagrangian float using one of many patterns. This capability allows for surveys that are potentially more representative of the near bottom oceanographic conditions at the desired location. Results will be presented from a cruise to Scott Reef, Australia, where both platforms were used as part of a coral habitat monitoring project.

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

Lateral eddy diffusivity estimates from simulated and observed drifter trajectories: a case study for the Agulhas Current system

NASA Astrophysics Data System (ADS)

Rühs, Siren; Zhurbas, Victor; Durgadoo, Jonathan V.; Biastoch, Arne

2017-04-01

The Lagrangian description of fluid motion by sets of individual particle trajectories is extensively used to characterize connectivity between distinct oceanic locations. One important factor influencing the connectivity is the average rate of particle dispersal, generally quantified as Lagrangian diffusivity. In addition to Lagrangian observing programs, Lagrangian analyses are performed by advecting particles with the simulated flow field of ocean general circulation models (OGCMs). However, depending on the spatio-temporal model resolution, not all scale-dependent processes are explicitly resolved in the simulated velocity fields. Consequently, the dispersal of advective Lagrangian trajectories has been assumed not to be sufficiently diffusive compared to observed particle spreading. In this study we present a detailed analysis of the spatially variable lateral eddy diffusivity characteristics of advective drifter trajectories simulated with realistically forced OGCMs and compare them with estimates based on observed drifter trajectories. The extended Agulhas Current system around South Africa, known for its intricate mesoscale dynamics, serves as a test case. We show that a state-of-the-art eddy-resolving OGCM indeed features theoretically derived dispersion characteristics for diffusive regimes and realistically represents Lagrangian eddy diffusivity characteristics obtained from observed surface drifter trajectories. The estimates for the maximum and asymptotic lateral single-particle eddy diffusivities obtained from the observed and simulated drifter trajectories show a good agreement in their spatial pattern and magnitude. We further assess the sensitivity of the simulated lateral eddy diffusivity estimates to the temporal and lateral OGCM output resolution and examine the impact of the different eddy diffusivity characteristics on the Lagrangian connectivity between the Indian Ocean and the South Atlantic.

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.;

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

2018-05-01

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration." Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

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

Lagrangian photochemical modeling studies of the 1987 Antarctic spring vortex. I - Comparison with AAOE observations

NASA Technical Reports Server (NTRS)

Jones, R. L.; Austin, J.; Mckenna, D. S.; Anderson, J. G.; Fahey, D. W.; Farmer, C. B.; Vedder, J. F.

1989-01-01

Results from the Lagrangian photochemical model integrated along computed air parcel trajectories intersected by the ER-2 aircraft are presented and compared with AAOE observations. According to the model, the BrO observations made from the ER-2 within the dehydrated denitrified region are consistent with there being approximately 5 parts per trillion by volume of BrO(y) at 428 K in spring. Within the high ClO region, ozone destruction rates are expected to exceed 2 percent/d with approximately 80 percent due to the ClO dimer mechanism.

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.

Lagrangian Trajectory Modeling of Lunar Dust Particles

NASA Technical Reports Server (NTRS)

Lane, John E.; Metzger, Philip T.; Immer, Christopher D.

2008-01-01

Apollo landing videos shot from inside the right LEM window, provide a quantitative measure of the characteristics and dynamics of the ejecta spray of lunar regolith particles beneath the Lander during the final 10 [m] or so of descent. Photogrammetry analysis gives an estimate of the thickness of the dust layer and angle of trajectory. In addition, Apollo landing video analysis divulges valuable information on the regolith ejecta interactions with lunar surface topography. For example, dense dust streaks are seen to originate at the outer rims of craters within a critical radius of the Lander during descent. The primary intent of this work was to develop a mathematical model and software implementation for the trajectory simulation of lunar dust particles acted on by gas jets originating from the nozzle of a lunar Lander, where the particle sizes typically range from 10 micron to 500 micron. The high temperature, supersonic jet of gas that is exhausted from a rocket engine can propel dust, soil, gravel, as well as small rocks to high velocities. The lunar vacuum allows ejected particles to travel great distances unimpeded, and in the case of smaller particles, escape velocities may be reached. The particle size distributions and kinetic energies of ejected particles can lead to damage to the landing spacecraft or to other hardware that has previously been deployed in the vicinity. Thus the primary motivation behind this work is to seek a better understanding for the purpose of modeling and predicting the behavior of regolith dust particle trajectories during powered rocket descent and ascent.

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.

High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

NASA Technical Reports Server (NTRS)

Scott, James R.; Martini, Michael C.

2008-01-01

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems.

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.

Experimental Evaluation of an Integrated Datalink and Automation-Based Strategic Trajectory Concept

NASA Technical Reports Server (NTRS)

Mueller, Eric

2007-01-01

This paper presents research on the interoperability of trajectory-based automation concepts and technologies with modern Flight Management Systems and datalink communication available on many of today s commercial aircraft. A tight integration of trajectory-based ground automation systems with the aircraft Flight Management System through datalink will enable mid-term and far-term benefits from trajectory-based automation methods. A two-way datalink connection between the trajectory-based automation resident in the Center/TRACON Automation System and the Future Air Navigation System-1 integrated FMS/datalink in NASA Ames B747-400 Level D simulator has been established and extensive simulation of the use of datalink messages to generate strategic trajectories completed. A strategic trajectory is defined as an aircraft deviation needed to solve a conflict or honor a route request and then merge the aircraft back to its nominal preferred trajectory using a single continuous trajectory clearance. Engineers on the ground side of the datalink generated lateral and vertical trajectory clearances and transmitted them to the Flight Management System of the 747; the airborne automation then flew the new trajectory without human intervention, requiring the flight crew only to review and to accept the trajectory. This simulation established the protocols needed for a significant majority of the trajectory change types required to solve a traffic conflict or deviate around weather. This demonstration provides a basis for understanding the requirements for integration of trajectory-based automation with current Flight Management Systems and datalink to support future National Airspace System operations.

Chaotic trajectories in the standard map. The concept of anti-integrability

NASA Astrophysics Data System (ADS)

Aubry, Serge; Abramovici, Gilles

1990-07-01

A rigorous proof is given in the standard map (associated with a Frenkel-Kontorowa model) for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k > k0. These chaotic trajectories (with finite entropy per site) are coded by integer sequences { mi} such that the sequence bi = |m i+1 + m i-1-2m i| be bounded by some integer b. The bound k0 in k depends on b and can be lowered for coding sequences { mi} fulfilling more restrictive conditions. The obtained chaotic trajectories correspond to stationary configurations of the Frenkel-Kontorowa model with a finite (non-zero) photon gap (called gap parameter in dimensionless units). This property implies that the trajectory (or the configuration { ui}) can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration. A non-zero gap parameter implies that the Lyapunov coefficient is strictly positive (when it is defined). In addition, the existence of dilating and contracting manifolds is proven for these chaotic trajectories. “Exotic” trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems. The concept of anti-integrability emerges from these theorems. In the anti-integrable limit which can be only defined for a discrete time dynamical system, the coordinates of the trajectory at time i do not depend on the coordinates at time i - 1. Thus, at this singular limit, the existence of chaotic trajectories is trivial and the dynamical system reduces to a Bernoulli shift. It is well known that the KAM tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit (under certain conditions). In a similar way, it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti-integrable limits (also under certain conditions).

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.

Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

2014-02-01

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon's sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon's gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.

Trajectory errors of different numerical integration schemes diagnosed with the MPTRAC advection module driven by ECMWF operational analyses

NASA Astrophysics Data System (ADS)

Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars

2018-02-01

The accuracy of trajectory calculations performed by Lagrangian particle dispersion models (LPDMs) depends on various factors. The optimization of numerical integration schemes used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration schemes of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration scheme with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the numerical scheme, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six numerical schemes fall into three distinct groups, which mostly depend on the numerical order of the scheme. Schemes of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration

Homing by path integration when a locomotion trajectory crosses itself.

PubMed

Yamamoto, Naohide; Meléndez, Jayleen A; Menzies, Derek T

2014-01-01

Path integration is a process with which navigators derive their current position and orientation by integrating self-motion signals along a locomotion trajectory. It has been suggested that path integration becomes disproportionately erroneous when the trajectory crosses itself. However, there is a possibility that this previous finding was confounded by effects of the length of a traveled path and the amount of turns experienced along the path, two factors that are known to affect path integration performance. The present study was designed to investigate whether the crossover of a locomotion trajectory truly increases errors of path integration. In an experiment, blindfolded human navigators were guided along four paths that varied in their lengths and turns, and attempted to walk directly back to the beginning of the paths. Only one of the four paths contained a crossover. Results showed that errors yielded from the path containing the crossover were not always larger than those observed in other paths, and the errors were attributed solely to the effects of longer path lengths or greater degrees of turns. These results demonstrated that path crossover does not always cause significant disruption in path integration processes. Implications of the present findings for models of path integration are discussed.

Accuracy Progressive Calculation of Lagrangian Trajectories from Gridded Velocity Field

DTIC Science & Technology

2014-01-01

traced (Vries and Doos 2001). The two types of velocity are convertible. Routine ocean data 36 assimilation systems (Galanis et al. 2006; Lozano et...1b) 54 The position of each fluid particle, R(t) = [x(t), y(t), z(t)], is specified in the Lagrangian system . 55 The connection...coordinate 233 system at the southwest corner (Fig. 6). The x*- and y*- axes point eastward and northward, 234 respectively. Here, the superscript

Sensitivity Analysis of a Lagrangian Sea Ice Model

NASA Astrophysics Data System (ADS)

Rabatel, Matthias; Rampal, Pierre; Bertino, Laurent; Carrassi, Alberto; Jones, Christopher K. R. T.

2017-04-01

Large changes in the Arctic sea ice have been observed in the last decades in terms of the ice thickness, extension and drift. Understanding the mechanisms behind these changes is of paramount importance to enhance our modeling and forecasting capabilities. For 40 years, models have been developed to describe the non-linear dynamical response of the sea ice to a number of external and internal factors. Nevertheless, there still exists large deviations between predictions and observations. There are related to incorrect descriptions of the sea ice response and/or to the uncertainties about the different sources of information: parameters, initial and boundary conditions and external forcing. Data assimilation (DA) methods are used to combine observations with models, and there is nowadays an increasing interest of DA for sea-ice models and observations. We consider here the state-of-the art sea-ice model, neXtSIM te{Rampal2016a}, which is based on a time-varying Lagrangian mesh and makes use of the Elasto-Brittle rheology. Our ultimate goal is designing appropriate DA scheme for such a modelling facility. This contribution reports about the first milestone along this line: a sensitivity analysis in order to quantify forecast error to guide model development and to set basis for further Lagrangian DA methods. Specific features of the sea-ice dynamics in relation to the wind are thus analysed. Virtual buoys are deployed across the Arctic domain and their trajectories of motion are analysed. The simulated trajectories are also compared to real buoys trajectories observed. The model response is also compared with that one from a model version not including internal forcing to highlight the role of the rheology. Conclusions and perspectives for the general DA implementation are also discussed. \\bibitem{Rampal2016a} P. Rampal, S. Bouillon, E. Ólason, and M. Morlighem. ne{X}t{SIM}: a new {L}agrangian sea ice model. The Cryosphere, 10 (3): 1055-1073, 2016.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state.

PubMed

Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H

2015-10-01

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

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.

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.

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

Lagrangian analysis of premixed turbulent combustion in hydrogen-air flames

NASA Astrophysics Data System (ADS)

Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2016-11-01

Lagrangian analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the numerical algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct numerical simulations (DNS) of non-reacting homogeneous isotropic turbulence. The Lagrangian analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.

Lagrangian drifter design for the determination of surface currents by remote sensing. [for pollution trajectory determination in estuaries

NASA Technical Reports Server (NTRS)

Gordon, H. H.; Munday, J. C., Jr.

1977-01-01

In estuaries, the interaction of wind, tidal current, and mixing of fresh and saline water produces a variable depth profile of current, with foam lines and convergence zones between water types. Careful measurement of surface currents via Lagrangian drifters requires a drifter design appropriate to both the depth of current to be measured and the tide and wind conditions of interest. The use of remote sensing to track drifters contributes additional constraints on drifter design. Several designs of biodegradable drifters which emit uranine dye plumes, resolvable in aerial imagery to 1:60,000 scale, were tested for wind drag in field conditions against data from calibrated current meters. A 20 cm-vaned wooden drifter and a window shade drifter set to 1.5 m depth had negligible wind drag in winds to 8 m/sec. Prediction of oil slick trajectories using surface current data and a wind factor should be approached cautiously, as surface current data may be wind-contaminated, while the usual 3.5% wind factor is appropriate only for currents measured at depth.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

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

Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less

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.

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.

A Generalized Eulerian-Lagrangian Analysis, with Application to Liquid Flows with Vapor Bubbles

NASA Technical Reports Server (NTRS)

Dejong, Frederik J.; Meyyappan, Meyya

1993-01-01

Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined Eulerian-Lagrangian technique, in which Eulerian conservation equations are solved for the liquid phase, while Lagrangian equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the Lagrangian analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.

Integrating palliative care into the trajectory of cancer care

PubMed Central

Hui, David; Bruera, Eduardo

2016-01-01

Over the past five decades, palliative care has evolved from serving patients at the end of life into a highly specialized discipline focused on delivering supportive care to patients with life-limiting illnesses throughout the disease trajectory. A growing body of evidence is now available to inform the key domains in the practice of palliative care, including symptom management, psychosocial care, communication, decision-making, and end-of-life care. Findings from multiple studies indicate that integrating palliative care early in the disease trajectory can result in improvements in quality of life, symptom control, patient and caregiver satisfaction, quality of end-of-life care, survival, and costs of care. In this narrative Review, we discuss various strategies to integrate oncology and palliative care by optimizing clinical infrastructures, processes, education, and research. The goal of integration is to maximize patient access to palliative care and, ultimately, to improve patient outcomes. We provide a conceptual model for the integration of supportive and/or palliative care with primary and oncological care. We end by discussing how health-care systems and institutions need to tailor integration based on their resources, size, and the level of primary palliative care available. PMID:26598947

Lagrangian evolution of the marine boundary layer from the Cloud System Evolution in the Trades (CSET) campaign

NASA Astrophysics Data System (ADS)

Mohrmann, J.; Ghate, V. P.; McCoy, I. L.; Bretherton, C. S.; Wood, R.; Minnis, P.; Palikonda, R.

2017-12-01

The Cloud System Evolution in the Trades (CSET) field campaign took place July/August 2015 to study the evolution of clouds, precipitation, and aerosols in the stratocumulus-to-cumulus (Sc-Cu) transition region of the northeast Pacific marine boundary layer (MBL). Aircraft observations sampled across a wide range of cloud and aerosol conditions. The sampling strategy, where MBL airmasses were sampled with the NSF/NCAR Gulfstream-V (HIAPER) and resampled then at their advected location two days later, resulted in a dataset of 14 paired flights suitable for Lagrangian analysis. This analysis shows that Lagrangian coherence of long-lived species (namely CO and O3) across 48 hours are high, but that of subcloud aerosol, MBL depth, and cloud properties is limited. Geostationary satellite retrievals are compared against aircraft observations; these are combined with reanalysis data and HYSPLIT trajectories to document the Lagrangian evolution of cloud fraction, cloud droplet number concentration, liquid water path, estimated inversion strength (EIS), and MBL depth, which are used to expand upon and validate the aircraft-based analysis. Many of the trajectories sampled by the aircraft show a clear Sc-Cu transition. Although satellite cloud fraction and EIS were found to be strongly spatiotemporally correlated, changes in MBL cloud fraction along trajectories did not correlate with any measure of EIS forcing.

Rapid Calculation of Spacecraft Trajectories Using Efficient Taylor Series Integration

NASA Technical Reports Server (NTRS)

Scott, James R.; Martini, Michael C.

2011-01-01

A variable-order, variable-step Taylor series integration algorithm was implemented in NASA Glenn's SNAP (Spacecraft N-body Analysis Program) code. SNAP is a high-fidelity trajectory propagation program that can propagate the trajectory of a spacecraft about virtually any body in the solar system. The Taylor series algorithm's very high order accuracy and excellent stability properties lead to large reductions in computer time relative to the code's existing 8th order Runge-Kutta scheme. Head-to-head comparison on near-Earth, lunar, Mars, and Europa missions showed that Taylor series integration is 15.8 times faster than Runge- Kutta on average, and is more accurate. These speedups were obtained for calculations involving central body, other body, thrust, and drag forces. Similar speedups have been obtained for calculations that include J2 spherical harmonic for central body gravitation. The algorithm includes a step size selection method that directly calculates the step size and never requires a repeat step. High-order Taylor series integration algorithms have been shown to provide major reductions in computer time over conventional integration methods in numerous scientific applications. The objective here was to directly implement Taylor series integration in an existing trajectory analysis code and demonstrate that large reductions in computer time (order of magnitude) could be achieved while simultaneously maintaining high accuracy. This software greatly accelerates the calculation of spacecraft trajectories. At each time level, the spacecraft position, velocity, and mass are expanded in a high-order Taylor series whose coefficients are obtained through efficient differentiation arithmetic. This makes it possible to take very large time steps at minimal cost, resulting in large savings in computer time. The Taylor series algorithm is implemented primarily through three subroutines: (1) a driver routine that automatically introduces auxiliary variables and

Establishing Lagrangian connections between observations within air masses crossing the Atlantic during the International Consortium for Atmospheric Research on Transport and Transformation experiment

NASA Astrophysics Data System (ADS)

Methven, J.; Arnold, S. R.; Stohl, A.; Evans, M. J.; Avery, M.; Law, K.; Lewis, A. C.; Monks, P. S.; Parrish, D. D.; Reeves, C. E.; Schlager, H.; Atlas, E.; Blake, D. R.; Coe, H.; Crosier, J.; Flocke, F. M.; Holloway, J. S.; Hopkins, J. R.; McQuaid, J.; Purvis, R.; Rappenglück, B.; Singh, H. B.; Watson, N. M.; Whalley, L. K.; Williams, P. I.

2006-12-01

The ITCT-Lagrangian-2K4 (Intercontinental Transport and Chemical Transformation) experiment was conceived with an aim to quantify the effects of photochemistry and mixing on the transformation of air masses in the free troposphere away from emissions. To this end, attempts were made to intercept and sample air masses several times during their journey across the North Atlantic using four aircraft based in New Hampshire (USA), Faial (Azores) and Creil (France). This article begins by describing forecasts from two Lagrangian models that were used to direct the aircraft into target air masses. A novel technique then identifies Lagrangian matches between flight segments. Two independent searches are conducted: for Lagrangian model matches and for pairs of whole air samples with matching hydrocarbon fingerprints. The information is filtered further by searching for matching hydrocarbon samples that are linked by matching trajectories. The quality of these "coincident matches" is assessed using temperature, humidity and tracer observations. The technique pulls out five clear Lagrangian cases covering a variety of situations and these are examined in detail. The matching trajectories and hydrocarbon fingerprints are shown, and the downwind minus upwind differences in tracers are discussed.

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.

A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.

PubMed

Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu

2017-10-01

The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

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.

Development of Multistep and Degenerate Variational Integrators for Applications in Plasma Physics

NASA Astrophysics Data System (ADS)

Ellison, Charles Leland

Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. This dissertation uses a systematic procedure for constructing geometric integrators --- known as variational integration --- to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically multistep methods. Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator

Lagrangian transport near perturbed periodic lines in three-dimensional unsteady flows

NASA Astrophysics Data System (ADS)

Speetjens, Michel

2015-11-01

Periodic lines formed by continuous strings of periodic points are key organizing entities in the Lagrangian flow topology of certain three-dimensional (3D) time-periodic flows. Such lines generically consist of elliptic and/or hyperbolic points and thus give rise to 3D flow topologies made up of families of concentric closed trajectories embedded in chaotic regions. Weak perturbation destroys the periodic lines and causes said trajectories to coalesce into families of concentric tubes. However, emergence of isolated periodic points near the disintegrating periodic lines and/or partitioning of the original lines into elliptic and hyperbolic segments interrupt the tube formation. This yields incomplete tubes that interact with the (chaotic) environment through their open ends, resulting in intricate and essentially 3D flow topologies These phenomena have been observed in various realistic flows yet the underlying mechanisms are to date only partially understood. This study deepens insight into the (perturbed) Lagrangian dynamics of these flows by way of a linearized representation of the equations of motion near the periodic lines. Predictions on the basis of this investigation are in full (qualitative) agreement with observed behavior in the actual flows

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.

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.

Do Assimilated Drifter Velocities Improve Lagrangian Predictability in an Operational Ocean Model?

DTIC Science & Technology

2015-05-01

extended Kalman filter . Molcard et al. (2005) used a statistical method to cor- relate model and drifter velocities. Taillandier et al. (2006) describe the... temperature and salinity observations. Trajectory angular differ- ences are also reduced. 1. Introduction The importance of Lagrangian forecasts was seen... Temperature , salinity, and sea surface height (SSH, measured along-track by satellite altimeters) observa- tions are typically assimilated in

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.

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)].

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

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

Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloring

NASA Astrophysics Data System (ADS)

Schlueter-Kuck, Kristy; Dabiri, John

2017-11-01

In recent years, there has been a proliferation of techniques that aim to characterize fluid flow kinematics on the basis of Lagrangian trajectories of collections of tracer particles. Most of these techniques depend on presence of tracer particles that are initially closely-spaced, in order to compute local gradients of their trajectories. In many applications, the requirement of close tracer spacing cannot be satisfied, especially when the tracers are naturally occurring and their distribution is dictated by the underlying flow. Moreover, current methods often focus on determination of the boundaries of coherent sets, whereas in practice it is often valuable to identify the complete set of trajectories that are coherent with an individual trajectory of interest. We extend the concept of Coherent Structure Coloring to achieve identification of the coherent set associated with individual Lagrangian trajectories. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Importantly, although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems. This work was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

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.

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.

Eulerian-Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry.

PubMed

Umeyama, Motohiko

2012-04-13

This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an Eulerian scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the Eulerian velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.

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.

Determination of NH3 emissions from confined areas using backward Lagrangian stochastic dispersion modelling

NASA Astrophysics Data System (ADS)

Häni, Christoph; Neftel, Albrecht; Sintermann, Jörg

2016-04-01

a line integrated vertical concentration profile downwind of the source. The inclusion of the deposition process is necessary for a consistent interpretation of the measurements. References Flesch, T.K., Wilson, J.D., Harper, L.A., Crenna, B.P., Sharpe, R.R., 2004. Deducing ground-to-air emissions from observed trace gas concentrations: A field trial. J. Appl. Meteorol. 43 (3), 487-502. Wilson, J.D., Flesch, T.K., Crenna, B.P., 2012. Estimating Surface-Air Gas Fluxes by Inverse Dispersion Using a Backward Lagrangian Stochastic Trajectory Model, in: Lin, J., Brunner, D., Gerbig, C., Stohl, A., Luhar, A., Webley, P. (Eds.), Lagrangian Modeling of the Atmosphere. American Geophysical Union, Washington, D. C., pp. 149-162.

High-Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

NASA Technical Reports Server (NTRS)

Scott, James R.; Martini, Michael C.

2010-01-01

It has been known for some time that Taylor series (TS) integration is among the most efficient and accurate numerical methods in solving differential equations. However, the full benefit of the method has yet to be realized in calculating spacecraft trajectories, for two main reasons. First, most applications of Taylor series to trajectory propagation have focused on relatively simple problems of orbital motion or on specific problems and have not provided general applicability. Second, applications that have been more general have required use of a preprocessor, which inevitably imposes constraints on computational efficiency. The latter approach includes the work of Berryman et al., who solved the planetary n-body problem with relativistic effects. Their work specifically noted the computational inefficiencies arising from use of a preprocessor and pointed out the potential benefit of manually coding derivative routines. In this Engineering Note, we report on a systematic effort to directly implement Taylor series integration in an operational trajectory propagation code: the Spacecraft N-Body Analysis Program (SNAP). The present Taylor series implementation is unique in that it applies to spacecraft virtually anywhere in the solar system and can be used interchangeably with another integration method. SNAP is a high-fidelity trajectory propagator that includes force models for central body gravitation with N X N harmonics, other body gravitation with N X N harmonics, solar radiation pressure, atmospheric drag (for Earth orbits), and spacecraft thrusting (including shadowing). The governing equations are solved using an eighth-order Runge-Kutta Fehlberg (RKF) single-step method with variable step size control. In the present effort, TS is implemented by way of highly integrated subroutines that can be used interchangeably with RKF. This makes it possible to turn TS on or off during various phases of a mission. Current TS force models include central body

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.

Path integral learning of multidimensional movement trajectories

NASA Astrophysics Data System (ADS)

André, João; Santos, Cristina; Costa, Lino

2013-10-01

This paper explores the use of Path Integral Methods, particularly several variants of the recent Path Integral Policy Improvement (PI2) algorithm in multidimensional movement parametrized policy learning. We rely on Dynamic Movement Primitives (DMPs) to codify discrete and rhythmic trajectories, and apply the PI2-CMA and PIBB methods in the learning of optimal policy parameters, according to different cost functions that inherently encode movement objectives. Additionally we merge both of these variants and propose the PIBB-CMA algorithm, comparing all of them with the vanilla version of PI2. From the obtained results we conclude that PIBB-CMA surpasses all other methods in terms of convergence speed and iterative final cost, which leads to an increased interest in its application to more complex robotic problems.

Alternative Transfer to the Earth-Moon Lagrangian Points L4 and L5 Using Lunar Gravity assist

NASA Astrophysics Data System (ADS)

Salazar, Francisco; Winter, Othon; Macau, Elbert; Bertachini de Almeida Prado, Antonio Fernando

2012-07-01

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies transfer orbits in the planar restricted three-body problem. To avoid solving a two-boundary problem, the patched-conic approximation is used to find initial conditions to transfer a spacecraft between an Earth circular parking orbit and the Lagrangian points L4, L5 (in the Earth-Moon system), such that a swing-by maneuver is applied using the lunar gravity. We also found orbits that can be used to make a tour to the Lagrangian points L4, L5 based on the theorem of image trajectories. Keywords: Stable Lagrangian points, L4, L5, Three-Body problem, Patched Conic, Swing-by

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.

Lagrangian Vortices in Developing Tropical Cyclones

DTIC Science & Technology

2015-06-25

45 −6 −4 −2 0 2 4 6 8 10 Hyperbolic trajectory Vortex core Shear sheath Lagrangian...5 10 15 20 25 30 35 40 45 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 × 10−9 (a) P13LP16E P17L 700 hPa 700 hPa 4590804102 100 80 60 40 20 0 0 5 10...15 20 25 30 35 40 45 −8 −6 −4 −2 0 2 4 6 8 10(b) Figure 4. The (a) OW (s−2) and (b) OWLag (radians) fields for the Atlantic development region at

Advances in Quantum Trajectory Approaches to Dynamics

NASA Astrophysics Data System (ADS)

Askar, Attila

2001-03-01

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)

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.

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.

An airborne perfluorocarbon tracer system and its first application for a Lagrangian experiment

NASA Astrophysics Data System (ADS)

Ren, Y.; Baumann, R.; Schlager, H.

2015-01-01

A perfluorocarbon tracer system (PERTRAS), specifically designed for Lagrangian aircraft experiments, has been developed by the Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center, DLR). It consists of three main parts: a tracer release unit (RU), an adsorption tube sampler (ATS), and a tracer analytical system. The RU was designed for airborne tracer release experiments; meanwhile, it can be used on various platforms for different experimental purposes (here research vessel). PERTRAS was for the first time applied in the field campaign Stratospheric ozone: Halogen Impacts in a Varying Atmosphere (SHIVA) in November 2011. An amount of 8.8 kg perfluoromethylcyclopentane (PMCP) was released aboard the research vessel Sonne (RV Sonne) near the operational site of this campaign, Miri, Malaysia, on 21 November. The tracer samples collected using the ATS onboard the DLR research aircraft Falcon were analyzed in the laboratory using a thermal desorber-gas chromatography-mass spectrometry (TD-GC-MS) system. Guided by forecasts calculated with the Lagrangian model Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT), 64 tracer samples were collected onboard the Falcon approximately 5 and 25 h after the release, mostly with a time resolution of 1 min. Enhanced PMCP concentrations relative to ambient PMCP background values (mean: 6.62 fmol mol-1) were detected during three intersects of the fresh tracer plume (age 5 h), with a maximum value of 301.33 fmol mol-1. This indicates that the fresh tracer plume was successfully intercepted at the forecast position. During the second flight, 25 h after the release, the center of tracer plume was not detected by the sampling system due to a faster advection of the plume than forecast. The newly developed PERTRAS system has been successfully deployed for the first time. The instrumental setup and comparisons between the measurements and HYSPLIT simulations are presented in this study.

An airborne perfluorocarbon tracer system and its first application for a Lagrangian experiment

NASA Astrophysics Data System (ADS)

Ren, Y.; Baumann, R.; Schlager, H.

2014-07-01

A perfluorocarbon tracer system (PERTRAS), specifically designed for Lagrangian aircraft experiments, has been developed by the Deutsches Zentrum für Luft- und Raumfahrt (German Aerospace Center, DLR). It consists of three main parts: a tracer release unit (RU), an adsorption tube sampler (ATS) and a tracer analytical system. The RU was designed for airborne tracer release experiments; meanwhile, it can be used on various platforms for different experimental purpose (here research vessel). PERTRAS was for the first time applied in the field campaign Stratospheric ozone: halogen Impacts in a Varying Atmosphere (SHIVA) in November 2011. An amount of 8.8 kg perfluoromethylcyclopentane (PMCP) was released aboard the research vessel Sonne (RV Sonne) near the operational site of this campaign, Miri, Malaysia, on 21 November. The tracer samples collected using the ATS on board the DLR research aircraft Falcon were analyzed in the laboratory using a thermal desorber/gas chromatography/mass spectrometry (TD/GC/MS) system. Guided by forecasts calculated with the Lagrangian model, Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT), 64 tracer samples were collected onboard the Falcon approximately 5 and 25 h after the release, respectively, mostly with a time resolution of 1 min. Enhanced PMCP concentrations relative to ambient PMCP background values (mean: 6.62 fmol mol-1) were detected during three intersects of the fresh tracer plume (age 5 h), with a maximum value of 301.33 fmol mol-1. This indicates that the fresh tracer plume was successfully intercepted at the forecasted position. During the second flight, 25 h after the release, the center of tracer plume was not detected by the sampling system due to a faster advection of the plume than forecasted. The newly developed PERTRAS system has been successfully deployed for the first time. The instrumental set-up and comparisons between the measurements and HYSPLIT simulations are presented in this study.

Regional Influences of Marcellus Shale Natural Gas Activity: Back-trajectory Analysis of Baltimore/Washington Ethane Concentrations

NASA Astrophysics Data System (ADS)

Vinciguerra, T.; Chittams, A.; Dadzie, J.; Deskins, T.; Goncalves, V.; M'Bagui Matsanga, C.; Zakaria, R.; Ehrman, S.; Dickerson, R. R.

2015-12-01

Over the past several years, the combined utilization of hydraulic fracturing and horizontal drilling has led to a rapid increase in natural gas production, especially from the Marcellus Shale. To explore the impact of this activity downwind on regions with no natural gas production, the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) Model was used to generate 48-hour back-trajectories for summer, daytime hours from the years 2007-2014 in the Baltimore, MD and Washington, D.C. areas where hourly ethane measurements are available from Photochemical Assessment Monitoring Stations (PAMS). For each of the years investigated, unconventional well counts were obtained for counties in the surrounding states of Pennsylvania, Ohio, West Virginia, and Virginia, and counties exceeding a threshold of 0.05 wells/km2 were designated as counties with a high density of wells. The back-trajectories for each year were separated into two groups: those which passed through counties containing a high density of wells, and those which did not. Back-trajectories passing through high-density counties were further screened by applying a height criterion where trajectories beyond 10% above the mixing layer were excluded. Preliminary results indicate that air parcels with back-trajectories passing within the boundary layer of counties with a high density of unconventional natural gas wells correspond to significantly greater concentrations of observed ethane at these downwind monitors.

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.

Evaluation of the Monotonic Lagrangian Grid and Lat-Long Grid for Air Traffic Management

NASA Technical Reports Server (NTRS)

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

2011-01-01

The Air Traffic Monotonic Lagrangian Grid (ATMLG) is used to simulate a 24 hour period of air traffic flow in the National Airspace System (NAS). During this time period, there are 41,594 flights over the United States, and the flight plan information (departure and arrival airports and times, and waypoints along the way) are obtained from an Federal Aviation Administration (FAA) Enhanced Traffic Management System (ETMS) dataset. Two simulation procedures are tested and compared: one based on the Monotonic Lagrangian Grid (MLG), and the other based on the stationary Latitude-Longitude (Lat- Long) grid. Simulating one full day of air traffic over the United States required the following amounts of CPU time on a single processor of an SGI Altix: 88 s for the MLG method, and 163 s for the Lat-Long grid method. We present a discussion of the amount of CPU time required for each of the simulation processes (updating aircraft trajectories, sorting, conflict detection and resolution, etc.), and show that the main advantage of the MLG method is that it is a general sorting algorithm that can sort on multiple properties. We discuss how many MLG neighbors must be considered in the separation assurance procedure in order to ensure a five-mile separation buffer between aircraft, and we investigate the effect of removing waypoints from aircraft trajectories. When aircraft choose their own trajectory, there are more flights with shorter duration times and fewer CD&R maneuvers, resulting in significant fuel savings.

Mean-Lagrangian formalism and covariance of fluid turbulence.

PubMed

Ariki, Taketo

2017-05-01

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.

Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities

NASA Technical Reports Server (NTRS)

Bendiksen, Oddvar O.

1994-01-01

This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.

Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.

PubMed

Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi

2017-10-11

We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nosé-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.

Lagrangian mixed layer modeling of the western equatorial Pacific

NASA Technical Reports Server (NTRS)

Shinoda, Toshiaki; Lukas, Roger

1995-01-01

Processes that control the upper ocean thermohaline structure in the western equatorial Pacific are examined using a Lagrangian mixed layer model. The one-dimensional bulk mixed layer model of Garwood (1977) is integrated along the trajectories derived from a nonlinear 1 1/2 layer reduced gravity model forced with actual wind fields. The Global Precipitation Climatology Project (GPCP) data are used to estimate surface freshwater fluxes for the mixed layer model. The wind stress data which forced the 1 1/2 layer model are used for the mixed layer model. The model was run for the period 1987-1988. This simple model is able to simulate the isothermal layer below the mixed layer in the western Pacific warm pool and its variation. The subduction mechanism hypothesized by Lukas and Lindstrom (1991) is evident in the model results. During periods of strong South Equatorial Current, the warm and salty mixed layer waters in the central Pacific are subducted below the fresh shallow mixed layer in the western Pacific. However, this subduction mechanism is not evident when upwelling Rossby waves reach the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific due to episodes of strong wind and light precipitation associated with the El Nino-Southern Oscillation. Comparison of the results between the Lagrangian mixed layer model and a locally forced Eulerian mixed layer model indicated that horizontal advection of salty waters from the central Pacific strongly affects the upper ocean salinity variation in the western Pacific, and that this advection is necessary to maintain the upper ocean thermohaline structure in this region.

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.

Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy

USDA-ARS?s Scientific Manuscript database

When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...

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.

Lagrangian methods for blood damage estimation in cardiovascular devices--How numerical implementation affects the results.

PubMed

Marom, Gil; Bluestein, Danny

2016-01-01

This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of Lagrangian models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.

Lagrangian methods for blood damage estimation in cardiovascular devices - How numerical implementation affects the results

PubMed Central

Marom, Gil; Bluestein, Danny

2016-01-01

Summary This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using Lagrangian methods with Eulerian computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of Lagrangian models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed. PMID:26679833

The simultaneous integration of many trajectories using nilpotent normal forms

NASA Technical Reports Server (NTRS)

Grayson, Matthew A.; Grossman, Robert

1990-01-01

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Lagrangian transport simulations of volcanic sulfur dioxide emissions: impact of meteorological data products

NASA Astrophysics Data System (ADS)

Hoffmann, Lars; Rößler, Thomas; Griessbach, Sabine; Heng, Yi; Stein, Olaf

2017-04-01

Sulfur dioxide (SO2) emissions from strong volcanic eruptions are an important natural cause for climate variations. We applied our new Lagrangian transport model Massive-Parallel Trajectory Calculations (MPTRAC) to perform simulations for three case studies of volcanic eruption events. The case studies cover the eruptions of Grímsvötn, Iceland, Puyehue-Cordón Caulle, Chile, and Nabro, Eritrea, in May and June 2011. We used SO2 observations of the Atmospheric Infrared Sounder (AIRS/Aqua) and a backward trajectory approach to initialize the simulations. Besides validation of the new model, the main goal of our study was a comparison of simulations with different meteorological data products. We considered three reanalyses (ERA-Interim, MERRA, and NCAR/NCEP) and the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analysis. Qualitatively, the SO2 distributions from the simulations compare well with the AIRS data, but also with Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) aerosol observations. Transport deviations and the critical success index (CSI) are analyzed to evaluate the simulations quantitatively. During the first 5 or 10 days after the eruptions we found the best performance for the ECMWF analysis (CSI range of 0.25 - 0.31), followed by ERA-Interim (0.25 - 0.29), MERRA (0.23 - 0.27), and NCAR/NCEP (0.21 - 0.23). High temporal and spatial resolution of the meteorological data does lead to improved performance of Lagrangian transport simulations of volcanic emissions in the upper troposphere and lower stratosphere. Reference: Hoffmann L., Rößler, T., Griessbach, S., Heng, Y., and Stein, O., Lagrangian transport simulations of volcanic sulfur dioxide emissions: impact of meteorological data products, J. Geophys. Res., 121(9), 4651-4673, doi:10.1002/2015JD023749, 2016.

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.

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.

GPU acceleration of Eulerian-Lagrangian particle-laden turbulent flow simulations

NASA Astrophysics Data System (ADS)

Richter, David; Sweet, James; Thain, Douglas

2017-11-01

The Lagrangian point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the Eulerian flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.

The Trapping Index: How to integrate the Eulerian and the Lagrangian approach for the computation of the transport time scales of semi-enclosed basins.

PubMed

Cucco, Andrea; Umgiesser, Georg

2015-09-15

In this work, we investigated if the Eulerian and the Lagrangian approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The Eulerian and Lagrangian TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an Eulerian only or from a Lagrangian only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.

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

Non-recursive augmented Lagrangian algorithms for the forward and inverse dynamics of constrained flexible multibodies

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Ledesma, Ragnar

1993-01-01

A technique is presented for solving the inverse dynamics of flexible planar multibody systems. This technique yields the non-causal joint efforts (inverse dynamics) as well as the internal states (inverse kinematics) that produce a prescribed nominal trajectory of the end effector. A non-recursive global Lagrangian approach is used in formulating the equations for motion as well as in solving the inverse dynamics equations. Contrary to the recursive method previously presented, the proposed method solves the inverse problem in a systematic and direct manner for both open-chain as well as closed-chain configurations. Numerical simulation shows that the proposed procedure provides an excellent tracking of the desired end effector trajectory.

Modelling environmentally friendly fairways using Lagrangian trajectories: a case study for the Gulf of Finland, the Baltic Sea

NASA Astrophysics Data System (ADS)

Soomere, Tarmo; Berezovski, Mihhail; Quak, Ewald; Viikmäe, Bert

2011-10-01

We address possibilities of minimising environmental risks using statistical features of current-driven propagation of adverse impacts to the coast. The recently introduced method for finding the optimum locations of potentially dangerous activities (Soomere et al. in Proc Estonian Acad Sci 59:156-165, 2010) is expanded towards accounting for the spatial distributions of probabilities and times for reaching the coast for passively advecting particles released in different sea areas. These distributions are calculated using large sets of Lagrangian trajectories found from Eulerian velocity fields provided by the Rossby Centre Ocean Model with a horizontal resolution of 2 nautical miles for 1987-1991. The test area is the Gulf of Finland in the northeastern Baltic Sea. The potential gain using the optimum fairways from the Baltic Proper to the eastern part of the gulf is an up to 44% decrease in the probability of coastal pollution and a similar increase in the average time for reaching the coast. The optimum fairways are mostly located to the north of the gulf axis (by 2-8 km on average) and meander substantially in some sections. The robustness of this approach is quantified as the typical root mean square deviation (6-16 km) between the optimum fairways specified from different criteria. Drastic variations in the width of the `corridors' for almost optimal fairways (2-30 km for the average width of 15 km) signifies that the sensitivity of the results with respect to small changes in the environmental criteria largely varies in different parts of the gulf.

The radiative versus entraining effects of overlying humidity on the Lagrangian evolution of subtropical stratocumulus

NASA Astrophysics Data System (ADS)

Eastman, R. M.; Wood, R.

2017-12-01

This study observes the 24-hour Lagrangian evolution of stratocumulus cloud amount and PBL depth in four eastern subtropical ocean basins: the NE Pacific, SE Pacific, SE Atlantic, and E Indian. Nearly 170,000 trajectories are computed using the 2-D wind field at 925mb and cloud properties are sampled along these trajectories twice daily as the A-Train satellite constellation passes overhead. Concurrent measurements of the overlying humidity and temperature profiles are interpolated from the ERA-Interim reanalysis grids. Cloud properties are sampled by MODIS and a measure of planetary boundary layer (PBL) depth is calculated using MODIS cloud top temperatures, CALIPSO lidar observations of cloud top heights, and ERA-Interim sea surface temperatures. High humidity overlying the PBL can reduce cloud top cooling by counteracting radiative cooling and by reducing evaporation within the entrainment zone. Both of these effects can slow the entrainment rate and change cloud evolution. To discern which effect is more important the humidity profile is broken into two distinct components: the specific humidity directly above the inversion, which is entraining into the boundary layer, and the column of specific humidity above that layer, which is radiatively interacting with the PBL, but not directly entraining. These two measures of humidity are compared in the Lagrangian framework. Results suggest that humidity above the PBL has a stronger effect on the Lagrangian PBL deepening rate compared to lower tropospheric stability. A comparison of PBL deepening rates driven by the entraining humidity versus the radiating humidity shows that the radiative effects of overlying humidity are dominant with respect to entrainment. However, the entraining effects of humidity are more important in prolonging cloud lifetime.

Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

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

Anderson, R W; Pember, R B; Elliott, N S

2001-10-22

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less

Integrated Vehicle and Trajectory Design of Small Spacecraft with Electric Propulsion for Earth and Interplanetary Missions

NASA Technical Reports Server (NTRS)

Spangelo, Sara; Dalle, Derek; Longmier, Benjamin

2015-01-01

This paper investigates the feasibility of Earth-transfer and interplanetary mission architectures for miniaturized spacecraft using emerging small solar electric propulsion technologies. Emerging small SEP thrusters offer significant advantages relative to existing technologies and will enable U-class systems to perform trajectory maneuvers with significant Delta V requirements. The approach in this paper is unique because it integrates trajectory design with vehicle sizing and accounts for the system and operational constraints of small U-class missions. The modeling framework includes integrated propulsion, orbit, energy, and external environment dynamics and systems-level power, energy, mass, and volume constraints. The trajectory simulation environment models orbit boosts in Earth orbit and flyby and capture trajectories to interplanetary destinations. A family of small spacecraft mission architectures are studied, including altitude and inclination transfers in Earth orbit and trajectories that escape Earth orbit and travel to interplanetary destinations such as Mercury, Venus, and Mars. Results are presented visually to show the trade-offs between competing performance objectives such as maximizing available mass and volume for payloads and minimizing transfer time. The results demonstrate the feasibility of using small spacecraft to perform significant Earth and interplanetary orbit transfers in less than one year with reasonable U-class mass, power, volume, and mission durations.

Transformation of Deep Water Masses Along Lagrangian Upwelling Pathways in the Southern Ocean

NASA Astrophysics Data System (ADS)

Tamsitt, V.; Abernathey, R. P.; Mazloff, M. R.; Wang, J.; Talley, L. D.

2018-03-01

Upwelling of northern deep waters in the Southern Ocean is fundamentally important for the closure of the global meridional overturning circulation and delivers carbon and nutrient-rich deep waters to the sea surface. We quantify water mass transformation along upwelling pathways originating in the Atlantic, Indian, and Pacific and ending at the surface of the Southern Ocean using Lagrangian trajectories in an eddy-permitting ocean state estimate. Recent related work shows that upwelling in the interior below about 400 m depth is localized at hot spots associated with major topographic features in the path of the Antarctic Circumpolar Current, while upwelling through the surface layer is more broadly distributed. In the ocean interior upwelling is largely isopycnal; Atlantic and to a lesser extent Indian Deep Waters cool and freshen while Pacific deep waters are more stable, leading to a homogenization of water mass properties. As upwelling water approaches the mixed layer, there is net strong transformation toward lighter densities due to mixing of freshwater, but there is a divergence in the density distribution as Upper Circumpolar Deep Water tends become lighter and dense Lower Circumpolar Deep Water tends to become denser. The spatial distribution of transformation shows more rapid transformation at eddy hot spots associated with major topography where density gradients are enhanced; however, the majority of cumulative density change along trajectories is achieved by background mixing. We compare the Lagrangian analysis to diagnosed Eulerian water mass transformation to attribute the mechanisms leading to the observed transformation.

Lagrangian Particle Tracking Simulation for Warm-Rain Processes in Quasi-One-Dimensional Domain

NASA Astrophysics Data System (ADS)

Kunishima, Y.; Onishi, R.

2017-12-01

Conventional cloud simulations are based on the Euler method and compute each microphysics process in a stochastic way assuming infinite numbers of particles within each numerical grid. They therefore cannot provide the Lagrangian statistics of individual particles in cloud microphysics (i.e., aerosol particles, cloud particles, and rain drops) nor discuss the statistical fluctuations due to finite number of particles. We here simulate the entire precipitation process of warm-rain, with tracking individual particles. We use the Lagrangian Cloud Simulator (LCS), which is based on the Euler-Lagrangian framework. In that framework, flow motion and scalar transportation are computed with the Euler method, and particle motion with the Lagrangian one. The LCS tracks particle motions and collision events individually with considering the hydrodynamic interaction between approaching particles with a superposition method, that is, it can directly represent the collisional growth of cloud particles. It is essential for trustworthy collision detection to take account of the hydrodynamic interaction. In this study, we newly developed a stochastic model based on the Twomey cloud condensation nuclei (CCN) activation for the Lagrangian tracking simulation and integrated it into the LCS. Coupling with the Euler computation for water vapour and temperature fields, the initiation and condensational growth of water droplets were computed in the Lagrangian way. We applied the integrated LCS for a kinematic simulation of warm-rain processes in a vertically-elongated domain of, at largest, 0.03×0.03×3000 (m3) with horizontal periodicity. Aerosol particles with a realistic number density, 5×107 (m3), were evenly distributed over the domain at the initial state. Prescribed updraft at the early stage initiated development of a precipitating cloud. We have confirmed that the obtained bulk statistics fairly agree with those from a conventional spectral-bin scheme for a vertical column

Challenges in Achieving Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Cate, Karen Tung

2012-01-01

In the past few years much of the global ATM research community has proposed advanced systems based on Trajectory-Based Operations (TBO). The concept of TBO uses four-dimensional aircraft trajectories as the base information for managing safety and capacity. Both the US and European advanced ATM programs call for the sharing of trajectory data across different decision support tools for successful operations. However, the actual integration of TBO systems presents many challenges. Trajectory predictors are built to meet the specific needs of a particular system and are not always compatible with others. Two case studies are presented which examine the challenges of introducing a new concept into two legacy systems in regards to their trajectory prediction software. The first case describes the issues with integrating a new decision support tool with a legacy operational system which overlap in domain space. These tools perform similar functions but are driven by different requirements. The difference in the resulting trajectories can lead to conflicting advisories. The second case looks at integrating this same new tool with a legacy system originally developed as an integrated system, but diverged many years ago. Both cases illustrate how the lack of common architecture concepts for the trajectory predictors added cost and complexity to the integration efforts.

LINKING THE CMAQ AND HYSPLIT MODELING SYSTEM INTERFACE PROGRAM AND EXAMPLE APPLICATION

EPA Science Inventory

A new software tool has been developed to link the Eulerian-based Community Multiscale Air Quality (CMAQ) modeling system with the Lagrangian-based HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) model. Both models require many of the same hourly meteorological...

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.

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.

Lagrangian formulation of the general relativistic Poynting-Robertson effect

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio

2018-04-01

We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a Lagrangian formulation; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic Lagrangian formulation to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.

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.

3D Air Quality and the Clean Air Interstate Rule: Lagrangian Sampling of CMAQ Model Results to Aid Regional Accountability Metrics

NASA Technical Reports Server (NTRS)

Fairlie, T. D.; Szykman, Jim; Pierce, Robert B.; Gilliland, A. B.; Engel-Cox, Jill; Weber, Stephanie; Kittaka, Chieko; Al-Saadi, Jassim A.; Scheffe, Rich; Dimmick, Fred;

Improved estimation of PM2.5 using Lagrangian satellite-measured aerosol optical depth

NASA Astrophysics Data System (ADS)

Olivas Saunders, Rolando

Suspended particulate matter (aerosols) with aerodynamic diameters less than 2.5 mum (PM2.5) has negative effects on human health, plays an important role in climate change and also causes the corrosion of structures by acid deposition. Accurate estimates of PM2.5 concentrations are thus relevant in air quality, epidemiology, cloud microphysics and climate forcing studies. Aerosol optical depth (AOD) retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument has been used as an empirical predictor to estimate ground-level concentrations of PM2.5 . These estimates usually have large uncertainties and errors. The main objective of this work is to assess the value of using upwind (Lagrangian) MODIS-AOD as predictors in empirical models of PM2.5. The upwind locations of the Lagrangian AOD were estimated using modeled backward air trajectories. Since the specification of an arrival elevation is somewhat arbitrary, trajectories were calculated to arrive at four different elevations at ten measurement sites within the continental United States. A systematic examination revealed trajectory model calculations to be sensitive to starting elevation. With a 500 m difference in starting elevation, the 48-hr mean horizontal separation of trajectory endpoints was 326 km. When the difference in starting elevation was doubled and tripled to 1000 m and 1500m, the mean horizontal separation of trajectory endpoints approximately doubled and tripled to 627 km and 886 km, respectively. A seasonal dependence of this sensitivity was also found: the smallest mean horizontal separation of trajectory endpoints was exhibited during the summer and the largest separations during the winter. A daily average AOD product was generated and coupled to the trajectory model in order to determine AOD values upwind of the measurement sites during the period 2003-2007. Empirical models that included in situ AOD and upwind AOD as predictors of PM2.5 were generated by

"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.

A Lagrangian analysis of a sudden stratospheric warming - Comparison of a model simulation and LIMS observations

NASA Technical Reports Server (NTRS)

Pierce, R. B.; Remsberg, Ellis E.; Fairlie, T. D.; Blackshear, W. T.; Grose, William L.; Turner, Richard E.

1992-01-01

Lagrangian area diagnostics and trajectory techniques are used to investigate the radiative and dynamical characteristics of a spontaneous sudden warming which occurred during a 2-yr Langley Research Center model simulation. The ability of the Langley Research Center GCM to simulate the major features of the stratospheric circulation during such highly disturbed periods is illustrated by comparison of the simulated warming to the observed circulation during the LIMS observation period. The apparent sink of vortex area associated with Rossby wave-breaking accounts for the majority of the reduction of the size of the vortex and also acts to offset the radiatively driven increase in the area occupied by the 'surf zone'. Trajectory analysis of selected material lines substantiates the conclusions from the area diagnostics.

Lagrangian transport in a class of three-dimensional buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2017-11-01

The study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure of the Lagrangian flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).

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

Gravitational Lagrangians, Mach's Principle, and the Equivalence Principle in an Expanding Universe

NASA Astrophysics Data System (ADS)

Essén, Hanno

2014-08-01

Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach's principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.

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.

Homogeneous and heterogeneous chemistry along air parcel trajectories

NASA Technical Reports Server (NTRS)

Jones, R. L.; Mckenna, D. L.; Poole, L. R.; Solomon, S.

1990-01-01

The study of coupled heterogeneous and homogeneous chemistry due to polar stratospheric clouds (PSC's) using Lagrangian parcel trajectories for interpretation of the Airborne Arctic Stratosphere Experiment (AASE) is discussed. This approach represents an attempt to quantitatively model the physical and chemical perturbation to stratospheric composition due to formation of PSC's using the fullest possible representation of the relevant processes. Further, the meteorological fields from the United Kingdom Meteorological office global model were used to deduce potential vorticity and inferred regions of PSC's as an input to flight planning during AASE.

Integrating the Base of Aircraft Data (BADA) in CTAS Trajectory Synthesizer

NASA Technical Reports Server (NTRS)

Abramson, Michael; Ali, Kareem

2012-01-01

The Center-Terminal Radar Approach Control (TRACON) Automation System (CTAS), developed at NASA Ames Research Center for assisting controllers in the management and control of air traffic in the extended terminal area, supports the modeling of more than four hundred aircraft types. However, 90% of them are supported indirectly by mapping them to one of a relatively few aircraft types for which CTAS has detailed drag and engine thrust models. On the other hand, the Base of Aircraft Data (BADA), developed and maintained by Eurocontrol, supports more than 300 aircraft types, about one third of which are directly supported, i.e. they have validated performance data. All these data were made available for CTAS by integrating BADA version 3.8 into CTAS Trajectory Synthesizer (TS). Several validation tools were developed and used to validate the integrated code and to evaluate the accuracy of trajectory predictions generated using CTAS "native" and BADA Aircraft Performance Models (APM) comparing them with radar track data. Results of these comparisons indicate that the two models have different strengths and weaknesses. The BADA APM can improve the accuracy of CTAS predictions at least for some aircraft types, especially small aircraft, and for some flight phases, especially climb.

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.

High-volume rainfall events in Calgary, Alberta, Canada and their relationship to HYSPLIT back trajectories and chemical constituents

NASA Astrophysics Data System (ADS)

Ge, C.; Norman, A. L.; Stenhouse, K. J.; Jansens, B.; Beamish, S.

2016-12-01

The Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model created by the Air Resources Laboratory at the National Oceanic and Atmospheric Administration (NOAA) in the United States is utilized for modelling air mass back-trajectories (AMBT) for weather systems. In this study, the HYSPLIT model was used to analyze weather systems in Calgary, Alberta over an 8 year period. It was found that setting the level 1 height input of the model to examine air masses at 3000 meters above ground level (AGL) more accurately represents true back-trajectories of intense precipitation events than 500 mbar pressure. This study utilizes 3000m AMBT to analyze weather systems from 2008 to 2016 in Calgary, and classifies these events on the basis of their geographic origin. A variety of precipitation characteristics were measured, such as the concentration of insoluble components as well as anion and cation concentrations. Interpretation of storm formation, and its relationship to constituents of precipitation found to be important to droplet activation in clouds - such as insoluble components and sulfate - are explored. Particularly, this study focused on the geographic origin of large precipitation events of 15 mm and over, and whether these events had distinct attributes associated with the insoluble and sulfate components and/or formation at southern latitudes in the North Pacific.

Lagrangian Approach to Jet Mixing and Optimization of the Reactor for Production of Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Povitsky, Alex; Salas, Manuel D.

2001-01-01

This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process for the production of carbon nanotubes from gaseous carbon oxide, The goal is to achieve rapid and uniform heating of catalyst particles by an optimal arrangement of jets. A mixed Eulerian and Lagrangian approach is implemented to track the temperature of catalyst particles along their trajectories as a function of time. The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor configuration is explained in terms of features of particle trajectories. The trajectories most exposed to the hot jets appear to be the most problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor configuration with three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.

Identification of individual coherent sets associated with flow trajectories using coherent structure coloring

NASA Astrophysics Data System (ADS)

Schlueter-Kuck, Kristy L.; Dabiri, John O.

2017-09-01

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data are available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.

Integrating Technology in the Classroom: Factors That Account for Teachers' Regressive Developmental Trajectories

ERIC Educational Resources Information Center

Looi, Chee-Kit; Chen, Wenli; Chen, Fang-Hao

2014-01-01

In this article, we studied the developmental trajectories of three teachers as they integrated GroupScribbles (GS) technology in their classroom lessons over a semester period of about 5 months. Coherency diagrams were used to capture the complex interplay of a teacher's knowledge (K), goals (G) and beliefs (B) in leveraging technology…

Lagrangian Transport Model Forecasts as Useful Support of the Flight Planning During the Intercontinental Transport and Chemical Transformation 2002 (ITCT 2k2) Measurement Campaign

NASA Astrophysics Data System (ADS)

Forster, C.; Cooper, O.; Stohl, A.; Eckhardt, S.; James, P.; Dunlea, E.; Nicks, D. K.; Holloway, J. S.; Hübler, G.; Parrish, D. D.; Ryerson, T. B.; Trainer, M.

2002-12-01

In this study, the Lagrangian tracer transport model FLEXPART is shown to be a useful forecasting tool for the flight planning during the ITCT 2k2 (Intercontinental Transport and Chemical Transformation 2002) aircraft measurement campaign. The advantages of this model are that it requires only a short computation time, has a finer spatial resolution and does not suffer numerical diffusion compared to chemistry transport models (CTMs). It is a compromise between simple trajectory calculations and complex CTMs that makes best use of available computer hardware. During the campaign FLEXPART provided three-day forecasts for four different anthropogenic CO tracers: Asian, North American, Japanese, and European. The forecasts were based on data from the Aviation model (AVN) of the National Center for Environmental Prediction (NCEP) and relied on the EDGAR emission inventory for the base year 1990. In two case studies, the forecast abilities of FLEXPART are analysed and discussed by comparing the forecasts with measurement data, results from the post analysis modelling, infrared satellite images, and backward trajectories calculated with two different Lagrangian trajectory models. It is shown that intercontinental transport and dispersion of pollution plumes were qualitatively well predicted, and the aircraft could successfully be directed into the polluted air masses.

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.

Dispersion upscaling from a pore scale characterization of Lagrangian velocities

NASA Astrophysics Data System (ADS)

Turuban, Régis; de Anna, Pietro; Jiménez-Martínez, Joaquín; Tabuteau, Hervé; Méheust, Yves; Le Borgne, Tanguy

2013-04-01

Mixing and reactive transport are primarily controlled by the interplay between diffusion, advection and reaction at pore scale. Yet, how the distribution and spatial correlation of the velocity field at pore scale impact these processes is still an open question. Here we present an experimental investigation of the distribution and correlation of pore scale velocities and its relation with upscaled dispersion. We use a quasi two-dimensional (2D) horizontal set up, consisting of two glass plates filled with cylinders representing the grains of the porous medium : the cell is built by soft lithography technique, wich allows for full control of the system geometry. The local velocity field is quantified from particle tracking velocimetry using microspheres that are advected with the pore scale flow. Their displacement is purely advective, as the particle size is chosen large enough to avoid diffusion. We thus obtain particle trajectories as well as lagrangian velocities in the entire system. The measured velocity field shows the existence of a network of preferential flow paths in channels with high velocities, as well as very low velocity in stagnation zones, with a non Gaussian distribution. Lagrangian velocities are long range correlated in time, which implies a non-fickian scaling of the longitudinal variance of particle positions. To upscale this process we develop an effective transport model, based on correlated continous time random walk, which is entirely parametrized by the pore scale velocity distribution and correlation. The model predictions are compared with conservative tracer test data for different Peclet numbers. Furthermore, we investigate the impact of different pore geometries on the distribution and correlation of Lagrangian velocities and we discuss the link between these properties and the effective dispersion behavior.

A novel approach to Lagrangian sampling of marine boundary layer cloud and aerosol in the northeast Pacific: case studies from CSET

NASA Astrophysics Data System (ADS)

Mohrmann, J.; Albrecht, B. A.; Bretherton, C. S.; Ghate, V. P.; Zuidema, P.; Wood, R.

2015-12-01

The Cloud System Evolution in the Trades (CSET) field campaign took place during July/August 2015 with the purpose of characterizing the cloud, aerosol and thermodynamic properties of the northeast Pacific marine boundary layer. One major science goal of the campaign was to observe a Lagrangian transition from thin stratocumulus (Sc) upwind near California to trade cumulus (Cu) nearer to Hawaii. Cloud properties were observed from the NSF/NCAR Gulfstream V research plane (GV) using the HIAPER Cloud Radar (HCR) and the HIAPER Spectral Resolution Lidar (HSRL), among other instrumentation. Aircraft observations were complemented by a suite of satellite-derived products. To observe a the evolution of airmasses over the course of two days, upwind regions were sampled on an outbound flight to from Sacramento, CA, to Kona, HI. The sampled airmasses were then tracked using HYSPLIT trajectories based on GFS model forecasts, and the return flight to California was planned to intercept those airmasses, using satellite observation to track cloud evolution in the interim. This approach required that trajectories were reasonably stable up to 3 days prior to final sampling, and also that forecast trajectories were in agreement with post-flight analysis and visual cloud feature tracking. The extent to which this was realised, and hence the validity of this new approach to Lagrangian airmass observation, is assessed here. We also present results showing that a Sc-Cu airmass transition was consistently observed during the CSET study using measurements from research flights and satellite.

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

Eulerian-Lagrangian CFD modelling of pesticide dust emissions from maize planters

NASA Astrophysics Data System (ADS)

Devarrewaere, Wouter; Foqué, Dieter; Nicolai, Bart; Nuyttens, David; Verboven, Pieter

2018-07-01

An Eulerian-Lagrangian 3D computational fluid dynamics (CFD) model of pesticide dust drift from precision vacuum planters in field conditions was developed. Tractor and planter models were positioned in an atmospheric computational domain, representing the field and its edges. Physicochemical properties of dust abraded from maize seeds (particle size, shape, porosity, density, a.i. content), dust emission rates and exhaust air velocity values at the planter fan outlets were measured experimentally and implemented in the model. The wind profile, the airflow pattern around the machines and the dust dispersion were computed. Various maize sowing scenarios with different wind conditions, dust properties, planter designs and vacuum pressures were simulated. Dust particle trajectories were calculated by means of Lagrangian particle tracking, considering nonspherical particle drag, gravity and turbulent dispersion. The dust dispersion model was previously validated with wind tunnel data. In this study, simulated pesticide concentrations in the air and on the soil in the different sowing scenarios were compared and discussed. The model predictions were similar to experimental literature data in terms of concentrations and drift distance. Pesticide exposure levels to bees during flight and foraging were estimated from the simulated concentrations. The proposed CFD model can be used in risk assessment studies and in the evaluation of dust drift mitigation measures.

The general setting for the zero-flux condition: The lagrangian and zero-flux conditions that give the heisenberg equation of motion.

PubMed

Anderson, James S M; Ayers, Paul W

2018-06-30

Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero-flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, "reasonable"). For any reasonable Lagrangian for the electronic wave function and any two-component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

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.

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.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Lagrangian clustering detection of internal wave boluses

NASA Astrophysics Data System (ADS)

Allshouse, M.; Salvador Vieira, G.; Swinney, H. L.

2016-02-01

The shoaling of internal waves on a continental slope or shelf produces boluses that travel up the slope with the wave. The boluses are regions of trapped fluid that are transported along with the wave, unlike fluid in the bulk that is temporarily pertubed by a passing wave. Boluses have been observed to transport oxygen-depleted water and induce rapid changes in temperature (Walter et al, JGR, 2012), both of which have potential ramifications for marine biology. Several previous studies have investigated boluses in systems with two layers of different density (e.g., Helfrich, JFM, 1992, and Sutherland et al., JGR, 2013). We conduct laboratory and computational studies of bolus generation and material transport in continuously stratified fluids with a pycnocline, as in the oceans. Our laboratory experiments in a 4 m long tank are complemented by 2-dimensional direct numerical simulations of the Navier-Stokes equations. Efforts have been made to identify boluses with Eularian measures in the past, but a Lagrangian perspective is necessary to objectively identify the bolus over its lifespan. Here we use a Lagrangian based coherent structure method relying on trajectory clustering using the fuzzy c-means approach (Froyland and Padberg-Gehle, Chaos, 2015). The objective detection of a bolus enables examination of the volume, distance traveled, and increased available potential energy of a bolus, as a function of the stratification, wave properties, and the angle of the sloping topography. The decay of a bolus through turbulent mixing is investigated by locating where the Richardson number drops below ¼, where velocity shear overcomes the tendency of a stratified fluid to remain stratified. (supported by ONR MURI grant N000141110701)

Reaction Analysis of Shocked Nitromethane using Extended Lagrangian Born-Oppenheimer Molecular Dynamics

NASA Astrophysics Data System (ADS)

Perriot, Romain; Kober, Ed; Mniszewski, Sue; Martinez, Enrique; Niklasson, Anders; Yang, Ping; McGrane, Shawn; Cawkwell, Marc

2017-06-01

Characterizing the complex, rapid reactions of energetic materials under conditions of high temperatures and pressures presents strong experimental and computational challenges. The recently developed extended Lagrangian Born-Oppenheimer molecular dynamics formalism enables the long-term conservation of the total energy in microcanonical trajectories, and using a density functional tight binding formulation provides good chemical accuracy. We use this combined approach to study the evolution of temperature, pressure, and chemical species in shock-compressed liquid nitromethane over hundreds of picoseconds. The chemical species seen in nitromethane under shock compression are compared with those seen under static high temperature conditions. A reduced-order representation of the complex sequence of chemical reactions that characterize this system has been developed from the molecular dynamics simulations by focusing on classes of chemical reactions rather than specific molecular species. Time-resolved infra-red vibrational spectra were also computed from the molecular trajectories and compared to the chemical analysis. These spectra provide a time history of the species present in the system that can be compared directly with recent experiments at LANL.

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.

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.

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

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.

Development of a new integrated local trajectory planning and tracking control framework for autonomous ground vehicles

NASA Astrophysics Data System (ADS)

Li, Xiaohui; Sun, Zhenping; Cao, Dongpu; Liu, Daxue; He, Hangen

2017-03-01

This study proposes a novel integrated local trajectory planning and tracking control (ILTPTC) framework for autonomous vehicles driving along a reference path with obstacles avoidance. For this ILTPTC framework, an efficient state-space sampling-based trajectory planning scheme is employed to smoothly follow the reference path. A model-based predictive path generation algorithm is applied to produce a set of smooth and kinematically-feasible paths connecting the initial state with the sampling terminal states. A velocity control law is then designed to assign a speed value at each of the points along the generated paths. An objective function considering both safety and comfort performance is carefully formulated for assessing the generated trajectories and selecting the optimal one. For accurately tracking the optimal trajectory while overcoming external disturbances and model uncertainties, a combined feedforward and feedback controller is developed. Both simulation analyses and vehicle testing are performed to verify the effectiveness of the proposed ILTPTC framework, and future research is also briefly discussed.

Flash trajectory imaging of target 3D motion

NASA Astrophysics Data System (ADS)

Wang, Xinwei; Zhou, Yan; Fan, Songtao; He, Jun; Liu, Yuliang

2011-03-01

We present a flash trajectory imaging technique which can directly obtain target trajectory and realize non-contact measurement of motion parameters by range-gated imaging and time delay integration. Range-gated imaging gives the range of targets and realizes silhouette detection which can directly extract targets from complex background and decrease the complexity of moving target image processing. Time delay integration increases information of one single frame of image so that one can directly gain the moving trajectory. In this paper, we have studied the algorithm about flash trajectory imaging and performed initial experiments which successfully obtained the trajectory of a falling badminton. Our research demonstrates that flash trajectory imaging is an effective approach to imaging target trajectory and can give motion parameters of moving targets.

Learning and Inferring "Dark Matter" and Predicting Human Intents and Trajectories in Videos.

PubMed

Xie, Dan; Shu, Tianmin; Todorovic, Sinisa; Zhu, Song-Chun

2018-07-01

This paper presents a method for localizing functional objects and predicting human intents and trajectories in surveillance videos of public spaces, under no supervision in training. People in public spaces are expected to intentionally take shortest paths (subject to obstacles) toward certain objects (e.g., vending machine, picnic table, dumpster etc.) where they can satisfy certain needs (e.g., quench thirst). Since these objects are typically very small or heavily occluded, they cannot be inferred by their visual appearance but indirectly by their influence on people's trajectories. Therefore, we call them "dark matter", by analogy to cosmology, since their presence can only be observed as attractive or repulsive "fields" in the public space. A person in the scene is modeled as an intelligent agent engaged in one of the "fields" selected depending his/her intent. An agent's trajectory is derived from an Agent-based Lagrangian Mechanics. The agents can change their intents in the middle of motion and thus alter the trajectory. For evaluation, we compiled and annotated a new dataset. The results demonstrate our effectiveness in predicting human intent behaviors and trajectories, and localizing and discovering distinct types of "dark matter" in wide public spaces.

Development and evaluation of the Screening Trajectory Ozone Prediction System (STOPS, version 1.0)

NASA Astrophysics Data System (ADS)

Czader, B. H.; Percell, P.; Byun, D.; Choi, Y.

2014-11-01

A hybrid Lagrangian-Eulerian modeling tool has been developed using the Eulerian framework of the Community Multiscale Air Quality (CMAQ) model. It is a moving nest that utilizes saved original CMAQ simulation results to provide boundary conditions, initial conditions, as well as emissions and meteorological parameters necessary for a simulation. Given that these file are available, this tool can run independently from the CMAQ whole domain simulation and it is designed to simulate source - receptor relationship upon changes in emissions. In this tool, the original CMAQ's horizontal domain is reduced to a small sub-domain that follows a trajectory defined by the mean mixed-layer wind. It has the same vertical structure and physical and chemical interactions as CMAQ except advection calculation. The advantage of this tool compared to other Lagrangian models is its capability of utilizing realistic boundary conditions that change with space and time as well as detailed chemistry treatment. The correctness of the algorithms and the overall performance was evaluated against CMAQ simulation results. Its performance depends on the atmospheric conditions occurring during the simulation period with the comparisons being most similar to CMAQ results under uniform wind conditions. The mean bias varies between -0.03 and -0.78 and the slope is between 0.99 and 1.01 for different analyzed cases. For complicated meteorological condition, such as wind circulation, the simulated mixing ratios deviate from CMAQ values as a result of Lagrangian approach of using mean wind for its movement, but are still close, with the mean varying between 0.07 and -4.29 and slope varying between 0.95 and 1.063 for different analyzed cases. For historical reasons this hybrid Lagrangian - Eulerian tool is named the Screening Trajectory Ozone Prediction System (STOPS) but its use is not limited to ozone prediction as similarly to CMAQ it can simulate concentrations of many species, including

Development and evaluation of the Screening Trajectory Ozone Prediction System (STOPS, version 1.0)

NASA Astrophysics Data System (ADS)

Czader, B. H.; Percell, P.; Byun, D.; Kim, S.; Choi, Y.

2015-05-01

A hybrid Lagrangian-Eulerian based modeling tool has been developed using the Eulerian framework of the Community Multiscale Air Quality (CMAQ) model. It is a moving nest that utilizes saved original CMAQ simulation results to provide boundary conditions, initial conditions, as well as emissions and meteorological parameters necessary for a simulation. Given that these files are available, this tool can run independently of the CMAQ whole domain simulation, and it is designed to simulate source-receptor relationships upon changes in emissions. In this tool, the original CMAQ's horizontal domain is reduced to a small sub-domain that follows a trajectory defined by the mean mixed-layer wind. It has the same vertical structure and physical and chemical interactions as CMAQ except advection calculation. The advantage of this tool compared to other Lagrangian models is its capability of utilizing realistic boundary conditions that change with space and time as well as detailed chemistry treatment. The correctness of the algorithms and the overall performance was evaluated against CMAQ simulation results. Its performance depends on the atmospheric conditions occurring during the simulation period, with the comparisons being most similar to CMAQ results under uniform wind conditions. The mean bias for surface ozone mixing ratios varies between -0.03 and -0.78 ppbV and the slope is between 0.99 and 1.01 for different analyzed cases. For complicated meteorological conditions, such as wind circulation, the simulated mixing ratios deviate from CMAQ values as a result of the Lagrangian approach of using mean wind for its movement, but are still close, with the mean bias for ozone varying between 0.07 and -4.29 ppbV and the slope varying between 0.95 and 1.06 for different analyzed cases. For historical reasons, this hybrid Lagrangian-Eulerian based tool is named the Screening Trajectory Ozone Prediction System (STOPS), but its use is not limited to ozone prediction as

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, Rutwig

2017-03-01

Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

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

Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es

Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

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.

3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

NASA Technical Reports Server (NTRS)

Douglass, A.

2005-01-01

The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

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.

Severity of Mental Health Impairment and Trajectories of Improvement in an Integrated Primary Care Clinic

ERIC Educational Resources Information Center

Bryan, Craig J.; Corso, Meghan L.; Corso, Kent A.; Morrow, Chad E.; Kanzler, Kathryn E.; Ray-Sannerud, Bobbie

2012-01-01

Objective: To model typical trajectories for improvement among patients treated in an integrated primary care behavioral health service, multilevel models were used to explore the relationship between baseline mental health impairment level and eventual mental health functioning across follow-up appointments. Method: Data from 495 primary care…

Spatial variability of hailfalls in France: an analysis of air mass retro-trajectories

NASA Astrophysics Data System (ADS)

Hermida, Lucía; Merino, Andrés; Sánchez, José Luis; Berthet, Claude; Dessens, Jean; López, Laura; Fernández-González, Sergio; Gascón, Estíbaliz; García-Ortega, Eduardo

2014-05-01

Hail is the main meteorological risk in south-west France, with the strongest hailfalls being concentrated in just a few days. Specifically, this phenomenon occurs most often and with the greatest severity in the Midi-Pyrénées area. Previous studies have revealed the high spatial variability of hailfall in this part of France, even leading to different characteristics being recorded on hailpads that were relatively close together. For this reason, an analysis of the air mass trajectories was carried out at ground level and at altitude, which subsequently led to the formation of the hail recorded by these hailpads. It is already known that in the study zone, the trajectories of the storms usually stretch for long distances and are oriented towards the east, leading to hailstones with diameters in excess of 3 cm, and without any change in direction above 3 km. We analysed different days with hail precipitation where there was at least one stone with a diameter of 3 cm or larger. Using the simulations from these days, an analysis of the backward trajectories of the air masses was carried out. We used the HYSPLIT (Hybrid Single Particle Lagrangian Integrated Trajectory Model) to determine the origin of the air masses, and tracked them toward each of the hailpads that were hit during the day studied. The height of the final points was the height of the impacted hailpads. Similarly, the backward trajectories for different heights were also established. Finally, the results show how storms that affect neighbouring hailpads come from very different air masses; and provide a deeper understanding of the high variability that affects the characteristics of hailfalls. Acknowledgements The authors would like to thank the Regional Government of Castile-León for its financial support through the project LE220A11-2. This study was supported by the following grants: GRANIMETRO (CGL2010-15930); MICROMETEO (IPT-310000-2010-22).

Lagrangian based methods for coherent structure detection

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

Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu; Peacock, Thomas, E-mail: tomp@mit.edu

There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other twomore » approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.« less

Lagrangian based methods for coherent structure detection

NASA Astrophysics Data System (ADS)

Allshouse, Michael R.; Peacock, Thomas

2015-09-01

There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.

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.

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.

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 3D tracking of fluorescent microscopic objects in motion

NASA Astrophysics Data System (ADS)

Darnige, T.; Figueroa-Morales, N.; Bohec, P.; Lindner, A.; Clément, E.

2017-05-01

We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.

Lagrangian 3D tracking of fluorescent microscopic objects in motion.

PubMed

Darnige, T; Figueroa-Morales, N; Bohec, P; Lindner, A; Clément, E

2017-05-01

We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.

A Lagrangian subgrid-scale model with dynamic estimation of Lagrangian time scale for large eddy simulation of complex flows

NASA Astrophysics Data System (ADS)

Verma, Aman; Mahesh, Krishnan

2012-08-01

The dynamic Lagrangian averaging approach for the dynamic Smagorinsky model for large eddy simulation is extended to an unstructured grid framework and applied to complex flows. The Lagrangian time scale is dynamically computed from the solution and does not need any adjustable parameter. The time scale used in the standard Lagrangian model contains an adjustable parameter θ. The dynamic time scale is computed based on a "surrogate-correlation" of the Germano-identity error (GIE). Also, a simple material derivative relation is used to approximate GIE at different events along a pathline instead of Lagrangian tracking or multi-linear interpolation. Previously, the time scale for homogeneous flows was computed by averaging along directions of homogeneity. The present work proposes modifications for inhomogeneous flows. This development allows the Lagrangian averaged dynamic model to be applied to inhomogeneous flows without any adjustable parameter. The proposed model is applied to LES of turbulent channel flow on unstructured zonal grids at various Reynolds numbers. Improvement is observed when compared to other averaging procedures for the dynamic Smagorinsky model, especially at coarse resolutions. The model is also applied to flow over a cylinder at two Reynolds numbers and good agreement with previous computations and experiments is obtained. Noticeable improvement is obtained using the proposed model over the standard Lagrangian model. The improvement is attributed to a physically consistent Lagrangian time scale. The model also shows good performance when applied to flow past a marine propeller in an off-design condition; it regularizes the eddy viscosity and adjusts locally to the dominant flow features.

A Lagrangian dynamic subgrid-scale model turbulence

NASA Technical Reports Server (NTRS)

Meneveau, C.; Lund, T. S.; Cabot, W.

1994-01-01

A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic Lagrangian time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

Mass and tracer transport within oceanic Lagrangian coherent vortices as diagnosed in a global mesoscale eddying climate model

NASA Astrophysics Data System (ADS)

Tarshish, Nathaniel; Abernathey, Ryan; Dufour, Carolina; Frenger, Ivy; Griffies, Stephen

2017-04-01

Transient ocean mesoscale fluctuations play a central role in the global climate system, transporting climate relevant tracers such as heat and carbon. In satellite observations and numerical simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on Eulerian identification methods, in which vortices are identified by selecting closed contours of Eulerian fields (e.g. sea surface height, or the Okubo-Weiss parameter) that satisfy geometric criteria and anomaly thresholds. In contrast, recent studies employ Lagrangian analysis of virtual particle trajectories initialized within the selected Eulerian contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the Eulerian field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between Eulerian and Lagrangian analyses for the detection of vortices. To do so, we use GFDL's CM2.6 coupled climate model with 5-10km horizontal grid spacing. We identify coherent vortices in CM2.6 by implementing the Rotationally Coherent Lagrangian Vortex (RCLV) framework, which recently emerged from dynamical systems theory. This approach involves the numerical advection of millions of Lagrangian particles and guarantees material coherence by construction. We compute the statistics, spatial distribution, and lifetimes of coherent vortices in addition to calculating the associated mass and tracer transports. We offer compelling evidence that Eulerian vortex methods are poorly suited to answer questions of mass and tracer transport.

A high order cell-centered semi-Lagrangian scheme for multi-dimensional kinetic simulations of neutral gas flows

NASA Astrophysics Data System (ADS)

Güçlü, Y.; Hitchon, W. N. G.

2012-04-01

The term 'Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of final cells. As such the CS is a 'forward-trajectory' semi-Lagrangian scheme. For multi-dimensional simulations of neutral gas flows, the cell-centered version of this semi-Lagrangian (CCSL) scheme has advantages over other options due to its implementation simplicity, low memory requirements, and easier treatment of boundary conditions. The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2nd order remapping that takes place at the end of each time step. By means of a modified equation analysis, it is shown that a high order estimate of the remapping error can be obtained a priori, and a small correction to the final position of the cells can be applied upon remapping, in order to achieve full compensation of this error. The resulting scheme is 4th order accurate in space while retaining the desirable properties of the CS: it is conservative and positivity-preserving, and the overall algorithm complexity is not appreciably increased. Two monotone (i.e. non-oscillating) versions of the fourth order CCSL-CS are also presented: one uses a common flux-limiter approach; the other uses a non-polynomial reconstruction to evaluate the derivatives of the density function. The method is illustrated in simple one- and two-dimensional examples, and a fully 3D solution of the Boltzmann equation describing expansion of a gas into vacuum through a cylindrical tube.

Fingerprints of heavy scales in electroweak effective Lagrangians

NASA Astrophysics Data System (ADS)

Pich, Antonio; Rosell, Ignasi; Santos, Joaquín; Sanz-Cillero, Juan José

2017-04-01

The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2) L ⊗ SU(2) R → SU(2) L+ R , which couples the known particle fields to heavier states with bosonic quantum numbers J P = 0± and 1±. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.

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.

Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

NASA Astrophysics Data System (ADS)

Richardson, S. I. Heath; Baggaley, A. W.; Hill, N. A.

2018-02-01

We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotactic swimming microorganisms and identify phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor-Green and Arnold-Beltrami-Childress (ABC) flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical "plumelike" structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. Furthermore, studies of Lyapunov exponents reveal that, as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.

Paracas dust storms: Sources, trajectories and associated meteorological conditions

NASA Astrophysics Data System (ADS)

Briceño-Zuluaga, F.; Castagna, A.; Rutllant, J. A.; Flores-Aqueveque, V.; Caquineau, S.; Sifeddine, A.; Velazco, F.; Gutierrez, D.; Cardich, J.

2017-09-01

Dust storms that develop along the Pisco-Ica desert in Southern Peru, locally known as ;Paracas; winds have ecological, health and economic repercussions. Here we identify dust sources through MODIS (Moderate Resolution Imaging Spectroradiometer) imagery and analyze HYSPLIT (Hybrid Single Particles Lagrangian Integrated Trajectory) model trajectories and dispersion patterns, along with concomitant synoptic-scale meteorological conditions from National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis (NCEP/NCAR). Additionally, surface pressure data from the hourly METeorological Aerodrome Report (METAR) at Arica (18.5°S, 70.3°W) and Pisco (13.7°S, 76.2°W) were used to calculate Alongshore (sea-level) Pressure Gradient (APG) anomalies during Paracas dust storms, their duration and associated wind-speeds and wind directions. This study provides a review on the occurrence and strength of the Paracas dust storms as reported in the Pisco airfield for five-year period and their correspondence with MODIS true-color imagery in terms of dust-emission source areas. Our results show that most of the particle fluxes moving into the Ica-Pisco desert area during Paracas wind events originate over the coastal zone, where strong winds forced by steep APGs develop as the axis of a deep mid-troposphere trough sets in along north-central Chile. Direct relationships between Paracas wind intensity, number of active dust-emission sources and APGs are also documented, although the scarcity of simultaneous METAR/MODIS data for clearly observed MODIS dust plumes prevents any significant statistical inference. Synoptic-scale meteorological composites from NCEP/NCAR reanalysis data show that Paracas wind events (steep APGs) are mostly associated with the strengthening of anticyclonic conditions in northern Chile, that can be attributed to cold air advection associated with the incoming trough. Compared to the MODIS images, HYSPLIT outputs were able

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.

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

Systematic Review: A Reevaluation and Update of the Integrative (Trajectory) Model of Pediatric Medical Traumatic Stress.

PubMed

Price, Julia; Kassam-Adams, Nancy; Alderfer, Melissa A; Christofferson, Jennifer; Kazak, Anne E

2016-01-01

The objective of this systematic review is to reevaluate and update the Integrative Model of Pediatric Medical Traumatic Stress (PMTS; Kazak et al., 2006), which provides a conceptual framework for traumatic stress responses across pediatric illnesses and injuries. Using established systematic review guidelines, we searched PsycINFO, Cumulative Index to Nursing and Allied Health Literature, and PubMed (producing 216 PMTS papers published since 2005), extracted findings for review, and organized and interpreted findings within the Integrative Model framework. Recent PMTS research has included additional pediatric populations, used advanced longitudinal modeling techniques, clarified relations between parent and child PMTS, and considered effects of PMTS on health outcomes. Results support and extend the model's five assumptions, and suggest a sixth assumption related to health outcomes and PMTS. Based on new evidence, the renamed Integrative Trajectory Model includes phases corresponding with medical events, adds family-centered trajectories, reaffirms a competency-based framework, and suggests updated assessment and intervention implications. © The Author 2015. Published by Oxford University Press on behalf of the Society of Pediatric Psychology. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Optimal sensor locations for the backward Lagrangian stochastic technique in measuring lagoon gas emission

USDA-ARS?s Scientific Manuscript database

This study evaluated the impact of gas concentration and wind sensor locations on the accuracy of the backward Lagrangian stochastic inverse-dispersion technique (bLS) for measuring gas emission rates from a typical lagoon environment. Path-integrated concentrations (PICs) and 3-dimensional (3D) wi...

Air-breathing hypersonic vehicle guidance and control studies; An integrated trajectory/control analysis methodology: Phase 1

NASA Technical Reports Server (NTRS)

Hattis, Philip D.; Malchow, Harvey L.

1991-01-01

A tool which generates optimal trajectory/control histories in an integrated manner is generically adapted to the treatment of single-stage-to-orbit air-breathing hypersonic vehicles. The methodology is implemented as a two point boundary value problem solution technique. Its use permits an assessment of an entire near-minimum-fuel trajectory and desired control strategy from takeoff to orbit while satisfying physically derived inequality constraints and while achieving efficient propulsive mode phasing. A simpler analysis strategy that partitions the trajectory into several boundary condition matched segments is also included to construct preliminary trajectory and control history representations with less computational burden than is required for the overall flight profile assessment. A demonstration was accomplished using a tabulated example (winged-cone accelerator) vehicle model that is combined with a newly developed multidimensional cubic spline data smoothing routine. A constrained near-fuel-optimal trajectory, imposing a dynamic pressure limit of 1000 psf, was developed from horizontal takeoff to 20,000 ft/sec relative air speed while aiming for a polar orbit. Previously unspecified propulsive discontinuities were located. Flight regimes demanding rapid attitude changes were identified, dictating control effector and closed-loop controller authority was ascertained after evaluating effector use for vehicle trim. Also, inadequacies in vehicle model representations and specific subsystem models with insufficient fidelity were determined based on unusual control characteristics and/or excessive sensitivity to uncertainty.

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.

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.

Gravity, Time, and Lagrangians

NASA Astrophysics Data System (ADS)

Huggins, Elisha

2010-11-01

Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one subtract potential energy from kinetic energy?) In this paper we discuss a thought experiment that relates gravity and time. Then we use a Feynman thought experiment to explain the minus sign in the Lagrangian. Our surprise was that these two topics are related.

Minimum impulse three-body trajectories.

NASA Technical Reports Server (NTRS)

D'Amario, L.; Edelbaum, T. N.

1973-01-01

A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.

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.

Statistical Decoupling of a Lagrangian Fluid Parcel in Newtonian Cosmology

NASA Astrophysics Data System (ADS)

Wang, Xin; Szalay, Alex

2016-03-01

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differential equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.

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.

Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins.

PubMed

Junginger, Andrej; Duvenbeck, Lennart; Feldmaier, Matthias; Main, Jörg; Wunner, Günter; Hernandez, Rigoberto

2017-08-14

In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all times. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS) between these states often exhibits a nontrivial time-dependence. The so-called transition state (TS) trajectory has been seen to define a DS which is free of recrossings in a large number of one-dimensional reactions across time-dependent barriers and thus, allows one to determine exact reaction rates. A fundamental challenge to applying this method is the construction of the TS trajectory itself. The minimization of Lagrangian descriptors (LDs) provides a general and powerful scheme to obtain that trajectory even when perturbation theory fails. Both approaches encounter possible breakdowns when the overall potential is bounded, admitting the possibility of returns to the barrier long after the trajectories have reached the product or reactant wells. Such global dynamics cannot be captured by perturbation theory. Meanwhile, in the LD-DS approach, it leads to the emergence of additional local minima which make it difficult to extract the optimal branch associated with the desired TS trajectory. In this work, we illustrate this behavior for a time-dependent double-well potential revealing a self-similar structure of the LD, and we demonstrate how the reflections and side-minima can be addressed by an appropriate modification of the LD associated with the direct rate across the barrier.

Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

NASA Astrophysics Data System (ADS)

Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander

2016-02-01

We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated

Optimal trajectories from the Earth-Moon L1 and L3 points to deflect hazardous asteroids and comets.

PubMed

Maccone, Claudio

2004-05-01

Software code named asteroff was recently created by the author to simulate the deflection of hazardous asteroids off of their collision course with the Earth. This code was both copyrighted and patented to avoid unauthorized use of ideas that could possibly be vital to construct a planetary defense system in the vicinity of the Earth. Having so said, the basic ideas and equations underlying the asteroff simulation code are openly described in this paper. A system of two space bases housing missiles is proposed to achieve the planetary defense of the Earth against dangerous asteroids and comets, collectively called impactors herein. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L(1) (between the Earth and the Moon) and L(3) (in the direction opposite to the Moon from the Earth). We show that placing missile bases at L(1) and L(3) would enable those missiles to deflect the trajectory of impactors by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. One additional remark is that the theory developed in this paper is just a beginning for a wider set of future research. In fact, we only develop the Keplerian analytical theory for the optimal planetary defense achievable from the Earth-Moon Lagrangian points L(1) and L(3). Much more sophisticated analytical refinements would be needed to: (1) take into account many perturbation forces of all kinds acting on both the impactors and missiles shot from L(1) and L(3); (2) add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L(4) and L(5) of the Earth-Moon System or from the surface of the

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.

Rapid Design of Gravity Assist Trajectories

NASA Technical Reports Server (NTRS)

Carrico, J.; Hooper, H. L.; Roszman, L.; Gramling, C.

1991-01-01

Several International Solar Terrestrial Physics (ISTP) missions require the design of complex gravity assisted trajectories in order to investigate the interaction of the solar wind with the Earth's magnetic field. These trajectories present a formidable trajectory design and optimization problem. The philosophy and methodology that enable an analyst to design and analyse such trajectories are discussed. The so called 'floating end point' targeting, which allows the inherently nonlinear multiple body problem to be solved with simple linear techniques, is described. The combination of floating end point targeting with analytic approximations with a Newton method targeter to achieve trajectory design goals quickly, even for the very sensitive double lunar swingby trajectories used by the ISTP missions, is demonstrated. A multiconic orbit integration scheme allows fast and accurate orbit propagation. A prototype software tool, Swingby, built for trajectory design and launch window analysis, is described.

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.

ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

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

Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

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.

Markov Chain Monte Carlo from Lagrangian Dynamics.

PubMed

Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark

2015-04-01

Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper.

A Lagrangian trajectory view on transport and mixing processes between the eye, eyewall, and environment using a high resolution simulation of Hurricane Bonnie (1998)

NASA Technical Reports Server (NTRS)

Cram, Thomas A.; Persing, John; Montgomery, Michael T.; Braun, Scott A.

2006-01-01

The transport and mixing characteristics of a large sample of air parcels within a mature and vertically sheared hurricane vortex is examined. Data from a high-resolution (2 km grid spacing) numerical simulation of "real-case" Hurricane Bonnie (1998) is used to calculate Lagrangian trajectories of air parcels in various subdomains of the hurricane (namely, the eye, eyewall, and near-environment) to study the degree of interaction (transport and mixing) between these subdomains. It is found that 1) there is transport and mixing from the low-level eye to the eyewall that carries high- Be air which can enhance the efficiency of the hurricane heat engine; 2) a portion of the low-level inflow of the hurricane bypasses the eyewall to enter the eye, that both replaces the mass of the low-level eye and lingers for a sufficient time (order 1 hour) to acquire enhanced entropy characteristics through interaction with the ocean beneath the eye; 3) air in the mid- to upper-level eye is exchanged with the eyewall such that more than half the air of the eye is exchanged in five hours in this case of a sheared hurricane; and 4) that one-fifth of the mass in the eyewall at a height of 5 km has an origin in the mid- to upper-level environment where thet(sub e) is much less than in the eyewall, which ventilates the ensemble average eyewall theta(sub e) by about 1 K. Implications of these findings to the problem of hurricane intensity forecasting are discussed.

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.

A Lagrangian particle method with remeshing for tracer transport on the sphere

DOE PAGES

Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...

2017-03-30

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

A Lagrangian particle method with remeshing for tracer transport on the sphere

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

Bosler, Peter Andrew; Kent, James; Krasny, Robert

A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.« less

The Water Vapor Source and Transport Characteristic of Rainy Seasons in Eastern China Base on Lagrangian Method

NASA Astrophysics Data System (ADS)

Shi, Y.; Jiang, Z.; Liu, Z.; Li, L.

2017-12-01

The Hybrid Single-Particle Lagrangian Integrated Trajectory platform is employed in this studyto simulate trajectories of air parcels in the different rainy seasons in East China from 1961 to 2010,with the purpose of investigating general and specific characteristics of moisture sources and the eventual relationship withprecipitation in each rainy season.The moisture transport andsource-sink characteristics of different rainy seasons have evident differences. The results show that the frontal pre-rainy season is mainly influenced bywinter monsoon system, and the precipitation is strongly affected by water vapor from Pacific Ocean (PO) and East China (EC). Afterthe onset of South China Sea Summer Monsoon (SCSMS), the moisture from Pacific Ocean decreases and from Indian Ocean monsoon area increases. Afterwards, with the northward of the rain belt, the parcels from Southwest region (South China Sea (SCS), Indian Ocean (IO) andIndo-China Peninsula and Indian Peninsula(IP)) decrease and from North region (EC, Eurasia (EA) and PO) increase. Besides, most of the land areas are water vapor sink region and most of sea areas are water vapor source region. Before the onset of SCSMS, EC and PO are two main water vapor source areas.After the onset of SCSMS, the source from PO decreasesand Indian monsoon area becomes the main vapor source region. IP is the main water vapor sink area for all four rainy seasons.As for moisture circulation characteristics, the results of vertical structure of water vapor transport indicate that the maximum water vapor transport in west and east boundaries is located in mid-troposphere and in south and north boundaries is at low-troposphere. The spatiotemporal analysis of moisture trajectory based onmultivariate empirical orthogonal function (MVEOF) indicates that the first mode has close relationship with the precipitation in North China and PDO pattern; the second mode is closely related with the precipitation in Yangtze-Huaihe river basin and

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.

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 Photochemical Box-Model Calculations of Asian Pacific Rim Outflow During TRACE-P

NASA Astrophysics Data System (ADS)

Hamlin, A.; Crawford, J.; Olson, J.; Avery, M.; Sachse, G.; Barrick, J.; Blake, D.; Tan, D.; Sandholm, S.; Kondo, Y.; Singh, H.; Eisele, F.; Zondlo, M.; Flocke, F.; Talbot, R.

2006-12-01

NASA's TRACE-P (TRAnsport and Chemical Evolution over the Pacific) mission was conducted over the northwestern Pacific February-April, 2001. During two transit flights across the Pacific, extensive pollution was observed from an Asian outflow event that split into two branches over the central Pacific, one subsiding and moving southward over the central Pacific and the other continuing eastward in the upper troposphere. The subsiding branch was observed as a widespread stagnant pollution layer between 2 and 4 km over the central Pacific during transit flights from Kona, HI to Guam. In this region, high levels of O3 (70 ppbv), CO (217 ppbv), and NOx (114 pptv) were well in excess of typical values observed during TRACE-P along the Asian coast. Evidence suggests that the subsiding branch experienced extensive photochemical processing compared to the branch that remained at altitude. To examine the processes controlling the chemical evolution of ozone and its precursors in this outflow event, data collected during the TRACE-P mission have been combined with lagrangian photochemical box model calculations. One of the largest sources of uncertainty in these calculations was associated with predicted water vapor levels along the transport trajectories calculated using the HYSPLIT model. Water vapor levels predicted by HYSPLIT trajectory calculations in the subsiding layer ranged from 3390 to 4880 ppm, while the median level observed in the pollution layer was only 637 ppm. Simulations of ozone production and associated radical chemistry differed dramatically when using water vapor levels based on trajectory calculations versus observed water vapor levels. Levels of PAN and HO2NO2, NOx reservoir species, are also influenced by uncertainties in temperature along the trajectories. These results highlight the importance of accurately representing the humidification and warming of subsiding air masses in 3-D chemical- transport models.

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.

Movement and collision of Lagrangian particles in hydro-turbine intakes: a case study

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

Romero-Gomez, Pedro; Richmond, Marshall C.

Studies of the stress/survival of migratory fish during downstream passage through operating hydro-turbines are normally conducted to determine the fish-friendliness of units. One field approach consisting of recording extreme hydraulics with autonomous sensors is largely sensitive to the conditions of sensor release and the initial trajectories at the turbine intake. This study applies a modelling strategy based on flow simulations using computational fluid dynamics and Lagrangian particle tracking to represent the travel of live fish and autonomous sensor devices through hydro-turbine intakes. For the flow field calculation, the simulations were conducted with both a time-averaging turbulence model and an eddy-resolvingmore » technique. For the particle tracking calculation, different modelling assumptions for turbulence forcing, mass formulation, buoyancy, and release condition were tested. The modelling assumptions are evaluated with respect to data sets collected using a laboratory physical model and an autonomous sensor device deployed at Ice Harbor Dam (Snake River, State of Washington, U.S.A.) at the same discharge and release point as in the present computer simulations. We found an acceptable agreement between the simulated results and observed data and discuss relevant features of Lagrangian particle movement that are critical in turbine design and in the experimental design of field studies.« less

The Monotonic Lagrangian Grid for Fast Air-Traffic Evaluation

NASA Technical Reports Server (NTRS)

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

2010-01-01

This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. 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. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.

Extending geometrical optics: A Lagrangian theory for vector waves

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2017-03-16

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Extending geometrical optics: A Lagrangian theory for vector waves

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

Ruiz, D. E.; Dodin, I. Y.

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wavemore » spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. Here, this work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.« less

Extending geometrical optics: A Lagrangian theory for vector waves

NASA Astrophysics Data System (ADS)

Ruiz, D. E.

2016-10-01

Even diffraction aside, the commonly known equations of geometrical optics (GO) are not entirely accurate. GO considers wave rays as classical particles, which are completely described by their coordinates and momenta, but rays have another degree of freedom, namely, polarization. As a result, wave rays can behave as particles with spin. A well-known example of polarization dynamics is wave-mode conversion, which can be interpreted as rotation of the (classical) ``wave spin.'' However, there are other less-known manifestations of the wave spin, such as polarization precession and polarization-driven bending of ray trajectories. This talk presents recent advances in extending and reformulating GO as a first-principle Lagrangian theory, whose effective-gauge Hamiltonian governs both mentioned polarization phenomena simultaneously. Examples and numerical results are presented. When applied to classical waves, the theory correctly predicts the polarization-driven divergence of left- and right- polarized electromagnetic waves in isotropic media, such as dielectrics and nonmagnetized plasmas. In the case of particles with spin, the formalism also yields a point-particle Lagrangian model for the Dirac electron, i.e. the relativistic spin-1/2 electron, which includes both the Stern-Gerlach spin potential and the Bargmann-Michel-Telegdi spin precession. Additionally, the same theory contributes, perhaps unexpectedly, to the understanding of ponderomotive effects in both wave and particle dynamics; e.g., the formalism allows to obtain the ponderomotive Hamiltonian for a Dirac electron interacting with an arbitrarily large electromagnetic laser field with spin effects included. Supported by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, by the U.S. DOE through Contract No. DE-AC02-09CH11466, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.

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.

STATISTICAL DECOUPLING OF A LAGRANGIAN FLUID PARCEL IN NEWTONIAN COSMOLOGY

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

Wang, Xin; Szalay, Alex, E-mail: xwang@cita.utoronto.ca

The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the nonlinear evolution of various cosmic objects, e.g., dark matter halos, in the context of Lagrangian fluid dynamics, since fluid parcels with given initial density and shape may evolve differently depending on their environments. In this paper, we provide a statistical solution that could decouple this environmental dependence. After deriving the evolution equation for the probability distribution of the matter field, our method produces a set of closed ordinary differentialmore » equations whose solution is uniquely determined by the initial condition of the fluid element. Mathematically, it corresponds to the projected characteristic curve of the transport equation of the density-weighted probability density function (ρPDF). Consequently it is guaranteed that the one-point ρPDF would be preserved by evolving these local, yet nonlinear, curves with the same set of initial data as the real system. Physically, these trajectories describe the mean evolution averaged over all environments by substituting the tidal tensor with its conditional average. For Gaussian distributed dynamical variables, this mean tidal tensor is simply proportional to the velocity shear tensor, and the dynamical system would recover the prediction of the Zel’dovich approximation (ZA) with the further assumption of the linearized continuity equation. For a weakly non-Gaussian field, the averaged tidal tensor could be expanded perturbatively as a function of all relevant dynamical variables whose coefficients are determined by the statistics of the field.« less

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.

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

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.

Professional Development to Support TPACK Technology Integration: The Initial Learning Trajectories of Thirteen Fifth- and Sixth-Grade Educators

ERIC Educational Resources Information Center

Morsink, Paul M.; Hagerman, Michelle Schira; Heintz, Anne; Boyer, D. Matthew; Harris, Robin; Kereluik, Kristen; Hartman, Douglas K.; Wood, Anne; White, Amber; Woodruff, Carmen; Anderson, Tracey; Goldstein, Shelly; Hamm, Beth; Lewis, Cindy; Lewis, Paul; Mitchell, Cindy; Murphy, Jill; Rogers, Lyn; Sherrieb, Anne; Siegler, Tammy; Withey, Kevin

2011-01-01

This study examined the initial learning trajectories of 13 upper elementary teachers as they developed technological, pedagogical, and content knowledge during a 7-month professional development program to integrate technology into classroom practice. The program was collaborative and non-prescriptive; teachers worked on self-chosen summer…

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

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.

Uncertainty and dispersion in air parcel trajectories near the tropical tropopause

NASA Astrophysics Data System (ADS)

Bergman, John; Jensen, Eric; Pfister, Leonhard; Bui, Thoapaul

2016-04-01

The Tropical Tropopause Layer (TTL) is important as the gateway to the stratosphere for chemical constituents produced at the Earth's surface. As such, understanding the processes that transport air through the upper tropical troposphere is important for a number of current scientific issues such as the impact of stratospheric water vapor on the global radiative budget and the depletion of ozone by both anthropogenically- and naturally-produced halocarbons. Compared to the lower troposphere, transport in the TTL is relatively unaffected by turbulent motion. Consequently, Lagrangian particle models are thought to provide reasonable estimates of parcel pathways through the TTL. However, there are complications that make trajectory analyses difficult to interpret; uncertainty in the wind data used to drive these calculations and trajectory dispersion being among the most important. These issues are examined using ensembles of backward air parcel trajectories that are initially tightly grouped near the tropical tropopause using three approaches: A Monte Carlo ensemble, in which different members use identical resolved wind fluctuations but different realizations of stochastic, multi-fractal simulations of unresolved winds, perturbed initial location ensembles, in which members use identical resolved wind fields but initial locations are displaced 2° in latitude and longitude, and a multi-model ensemble that uses identical initial conditions but different resolved wind fields and/or trajectory formulations. Comparisons among the approaches distinguish, to some degree, physical dispersion from that due to data uncertainty and the impact of unresolved wind fluctuations from that of resolved variability.

Trajectory-Based Loads for the Ares I-X Test Flight Vehicle

NASA Technical Reports Server (NTRS)

Vause, Roland F.; Starr, Brett R.

2011-01-01

In trajectory-based loads, the structural engineer treats each point on the trajectory as a load case. Distributed aero, inertial, and propulsion forces are developed for the structural model which are equivalent to the integrated values of the trajectory model. Free-body diagrams are then used to solve for the internal forces, or loads, that keep the applied aero, inertial, and propulsion forces in dynamic equilibrium. There are several advantages to using trajectory-based loads. First, consistency is maintained between the integrated equilibrium equations of the trajectory analysis and the distributed equilibrium equations of the structural analysis. Second, the structural loads equations are tied to the uncertainty model for the trajectory systems analysis model. Atmosphere, aero, propulsion, mass property, and controls uncertainty models all feed into the dispersions that are generated for the trajectory systems analysis model. Changes in any of these input models will affect structural loads response. The trajectory systems model manages these inputs as well as the output from the structural model over thousands of dispersed cases. Large structural models with hundreds of thousands of degrees of freedom would execute too slowly to be an efficient part of several thousand system analyses. Trajectory-based loads provide a means for the structures discipline to be included in the integrated systems analysis. Successful applications of trajectory-based loads methods for the Ares I-X vehicle are covered in this paper. Preliminary design loads were based on 2000 trajectories using Monte Carlo dispersions. Range safety loads were tied to 8423 malfunction turn trajectories. In addition, active control system loads were based on 2000 preflight trajectories using Monte Carlo dispersions.

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.

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.

a Marker-Based Eulerian-Lagrangian Method for Multiphase Flow with Supersonic Combustion Applications

NASA Astrophysics Data System (ADS)

Fan, Xiaofeng; Wang, Jiangfeng

2016-06-01

The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.

Survey of optimization techniques for nonlinear spacecraft trajectory searches

NASA Technical Reports Server (NTRS)

Wang, Tseng-Chan; Stanford, Richard H.; Sunseri, Richard F.; Breckheimer, Peter J.

1988-01-01

Mathematical analysis of the optimal search of a nonlinear spacecraft trajectory to arrive at a set of desired targets is presented. A high precision integrated trajectory program and several optimization software libraries are used to search for a converged nonlinear spacecraft trajectory. Several examples for the Galileo Jupiter Orbiter and the Ocean Topography Experiment (TOPEX) are presented that illustrate a variety of the optimization methods used in nonlinear spacecraft trajectory searches.

A Lagrangian particle model to predict the airborne spread of foot-and-mouth disease virus

NASA Astrophysics Data System (ADS)

Mayer, D.; Reiczigel, J.; Rubel, F.

Airborne spread of bioaerosols in the boundary layer over a complex terrain is simulated using a Lagrangian particle model, and applied to modelling the airborne spread of foot-and-mouth disease (FMD) virus. Two case studies are made with study domains located in a hilly region in the northwest of the Styrian capital Graz, the second largest town in Austria. Mountainous terrain as well as inhomogeneous and time varying meteorological conditions prevent from application of so far used Gaussian dispersion models, while the proposed model can handle these realistically. In the model, trajectories of several thousands of particles are computed and the distribution of virus concentration near the ground is calculated. This allows to assess risk of infection areas with respect to animal species of interest, such as cattle, swine or sheep. Meteorological input data like wind field and other variables necessary to compute turbulence were taken from the new pre-operational version of the non-hydrostatic numerical weather prediction model LMK ( Lokal-Modell-Kürzestfrist) running at the German weather service DWD ( Deutscher Wetterdienst). The LMK model provides meteorological parameters with a spatial resolution of about 2.8 km. To account for the spatial resolution of 400 m used by the Lagrangian particle model, the initial wind field is interpolated upon the finer grid by a mass consistent interpolation method. Case studies depict a significant influence of local wind systems on the spread of virus. Higher virus concentrations at the upwind side of the hills and marginal concentrations in the lee are well observable, as well as canalization effects by valleys. The study demonstrates that the Lagrangian particle model is an appropriate tool for risk assessment of airborne spread of virus by taking into account the realistic orographic and meteorological conditions.

Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points

NASA Astrophysics Data System (ADS)

Bertachini, A.

The well-known Lagrangian points that appear in the planar restricted three-body problem (Szebehely, 1967) are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L1, L2 and L3) are always unstable and the triangular points (L4 and L5) are stable in the present case studied (Sun-Earth system). They are all very good points to locate a space-station, since they require a small amount of V (and fuel), the control to be used for station-keeping. The triangular points are specially good for this purpose, since they are stable equilibrium points. In this paper, the planar restricted three-body problem is regularized (using Lemaître regularization) and combined with numerical integration and gradient methods to solve the two point boundary value problem (the Lambert's three-body problem). This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Sun-Earth system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude and direction of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth. This paper is a continuation of two previous papers that studied transfers in the Earth-Moon system: Broucke (1979), that studied transfer orbits between the Lagrangian points and the Moon and Prado (1996), that studied transfer orbits between the Lagrangian points and the Earth. So, the equations of motion are: whereis the pseudo-potential given by: To solve the TPBVP in the regularized variables the following steps are used: i) Guess a initial velocity Vi, so together with the initial prescribed position ri the complete initial state is known; ii

Using the Lagrangian Method to Track Trajectories of Fog And Mist in the Monterey Bay

DTIC Science & Technology

2017-12-01

inversions (Koračin et al. 2014). During these extensive research experiments (Pilié et al. 1979) the role of the Eastern Pacific High was the...the inversion , which then lifts and eventually erodes the marine layer (Koračin et al. 2005). 22 Figure 13. Trajectories from a thermal low lead... inversion characteristics support fog and stratus conditions. Figure 20. Annotation of “L” for June 1, which classifies “Local” wind conditions

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.

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

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.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity

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.

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 particle drift and surface deformation in a rotating wave on a free liquid surface

NASA Astrophysics Data System (ADS)

Fontana, Paul W.; Francois, Nicolas; Xia, Hua; Punzmann, Horst; Shats, Michael

2017-11-01

A nonlinear model of a rotating wave on the free surface of a liquid is presented. The flow is assumed to be inviscid and irrotational. The wave is constructed as a superposition of two perpendicular, monochromatic standing Stokes waves and is standing-wave-like, but with ``antinodes'' or cells consisting of rotating surface gradients of alternating polarity. Lagrangian fluid particle trajectories show a rotational drift about each cell in the direction of wave rotation, corresponding to a rotating Stokes drift. Each cell therefore has a circulating flow and localized angular momentum even though the Eulerian flow is irrotational. Meanwhile, the wave sets up a static displacement of the free surface, making a trough in each cell. This static surface gradient provides a centripetal force that may account for additional rotation seen in experiments.

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.

Real-time trajectory optimization on parallel processors

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1993-01-01

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

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 analysis of mid-latitude stratospheric ozone variability and long-term trends.

NASA Astrophysics Data System (ADS)

Koch, G.; Wernli, H.; Staehelin, J.; Peter, T.

2002-05-01

A systematic Lagrangian investigation is performed of wintertime high-resolution stratospheric ozone soundings at Payerne, Switzerland, from January 1970 to March 2001. For every ozone sounding, 10-day backward trajectories have been calculated on 16 isentropic levels using NCEP reanalysis data. Both the minimum/maximum latitude and potential vorticity (PV) averaged along the trajectories are used as indicators of the air parcels' ``origin''. The importance of transport for the understandin g of single ozone profiles is confirmed by a statistical analysis which shows that negative/positive ozone deviations gener ally coincide with transport from regions with climatologically low/high ozone values. The stable relationship between PV and ozone for the 32 year period indicates either no direct chemical impact or no temporal change of this impact. In the upper layer the PV-ozone relationship changes significantly after 1987 and a separate trend analysis for air masses transported from the polar, midlatitude and subtropical regions shows negative ozone trends in all three categories (with a maximum for the polar region). This is not direct evidence for, but would be in agreement with, an increased chemical ozone depletion in the Arctic since the late 1980s. The reasons for the negative trend in the mid-stratospheric air masses with subtropical origin that are in qualitative agreement with recent satellite observations are presently unknown.

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.

Eulerian and Lagrangian methods for vortex tracking in 2D and 3D flows

NASA Astrophysics Data System (ADS)

Huang, Yangzi; Green, Melissa

2014-11-01

Coherent structures are a key component of unsteady flows in shear layers. Improvement of experimental techniques has led to larger amounts of data and requires of automated procedures for vortex tracking. Many vortex criteria are Eulerian, and identify the structures by an instantaneous local swirling motion in the field, which are indicated by closed or spiral streamlines or pathlines in a reference frame. Alternatively, a Lagrangian Coherent Structures (LCS) analysis is a Lagrangian method based on the quantities calculated along fluid particle trajectories. In the current work, vortex detection is demonstrated on data from the simulation of two cases: a 2D flow with a flat plate undergoing a 45 ° pitch-up maneuver and a 3D wall-bounded turbulence channel flow. Vortices are visualized and tracked by their centers and boundaries using Γ1, the Q criterion, and LCS saddle points. In the cases of 2D flow, saddle points trace showed a rapid acceleration of the structure which indicates the shedding from the plate. For channel flow, saddle points trace shows that average structure convection speed exhibits a similar trend as a function of wall-normal distance as the mean velocity profile, and leads to statistical quantities of vortex dynamics. Dr. Jeff Eldredge and his research group at UCLA are gratefully acknowledged for sharing the database of simulation for the current research. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.

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.

Trajectories for High Specific Impulse High Specific Power Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, Tara; Adams, Robert B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Flight times and deliverable masses for electric and fusion propulsion systems are difficult to approximate. Numerical integration is required for these continuous thrust systems. Many scientists are not equipped with the tools and expertise to conduct interplanetary and interstellar trajectory analysis for their concepts. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. An analytical method derived in the companion paper was also evaluated. The accuracy of this method is discussed in the paper.

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.

Residual sweeping errors in turbulent particle pair diffusion in a Lagrangian diffusion model.

PubMed

Malik, Nadeem A

2017-01-01

Thomson, D. J. & Devenish, B. J. [J. Fluid Mech. 526, 277 (2005)] and others have suggested that sweeping effects make Lagrangian properties in Kinematic Simulations (KS), Fung et al [Fung J. C. H., Hunt J. C. R., Malik N. A. & Perkins R. J. J. Fluid Mech. 236, 281 (1992)], unreliable. However, such a conclusion can only be drawn under the assumption of locality. The major aim here is to quantify the sweeping errors in KS without assuming locality. Through a novel analysis based upon analysing pairs of particle trajectories in a frame of reference moving with the large energy containing scales of motion it is shown that the normalized integrated error [Formula: see text] in the turbulent pair diffusivity (K) due to the sweeping effect decreases with increasing pair separation (σl), such that [Formula: see text] as σl/η → ∞; and [Formula: see text] as σl/η → 0. η is the Kolmogorov turbulence microscale. There is an intermediate range of separations 1 < σl/η < ∞ in which the error [Formula: see text] remains negligible. Simulations using KS shows that in the swept frame of reference, this intermediate range is large covering almost the entire inertial subrange simulated, 1 < σl/η < 105, implying that the deviation from locality observed in KS cannot be atributed to sweeping errors. This is important for pair diffusion theory and modeling. PACS numbers: 47.27.E?, 47.27.Gs, 47.27.jv, 47.27.Ak, 47.27.tb, 47.27.eb, 47.11.-j.

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.

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.

Optimal trajectories of aircraft and spacecraft

NASA Technical Reports Server (NTRS)

Miele, A.

1990-01-01

Work done on algorithms for the numerical solutions of optimal control problems and their application to the computation of optimal flight trajectories of aircraft and spacecraft is summarized. General considerations on calculus of variations, optimal control, numerical algorithms, and applications of these algorithms to real-world problems are presented. The sequential gradient-restoration algorithm (SGRA) is examined for the numerical solution of optimal control problems of the Bolza type. Both the primal formulation and the dual formulation are discussed. Aircraft trajectories, in particular, the application of the dual sequential gradient-restoration algorithm (DSGRA) to the determination of optimal flight trajectories in the presence of windshear are described. Both take-off trajectories and abort landing trajectories are discussed. Take-off trajectories are optimized by minimizing the peak deviation of the absolute path inclination from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. Abort landing trajectories are optimized by minimizing the peak drop of altitude from a reference value. The survival capability of an aircraft in a severe windshear is discussed, and the optimal trajectories are found to be superior to both constant pitch trajectories and maximum angle of attack trajectories. Spacecraft trajectories, in particular, the application of the primal sequential gradient-restoration algorithm (PSGRA) to the determination of optimal flight trajectories for aeroassisted orbital transfer are examined. Both the coplanar case and the noncoplanar case are discussed within the frame of three problems: minimization of the total characteristic velocity; minimization of the time integral of the square of the path inclination; and minimization of the peak heating rate. The solution of the second problem is called nearly-grazing solution, and its merits are pointed out as a useful

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.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

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…

Iso-chemical potential trajectories in the P-T plane for He II

NASA Technical Reports Server (NTRS)

Maytal, B.; Nissen, J. A.; Van Sciver, S. W.

1990-01-01

Trajectories of constant chemical potential in the P-T plane serve as an integral formulation of London's equation. The trajectories are useful for analysis and synthesis of fountain effect pump performance. A family of trajectories is generated from available numerical codes.

Constrained Multi-Level Algorithm for Trajectory Optimization

NASA Astrophysics Data System (ADS)

Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi

The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in

Integrated direct/indirect adaptive robust motion trajectory tracking control of pneumatic cylinders

NASA Astrophysics Data System (ADS)

Meng, Deyuan; Tao, Guoliang; Zhu, Xiaocong

2013-09-01

This paper studies the precision motion trajectory tracking control of a pneumatic cylinder driven by a proportional-directional control valve. An integrated direct/indirect adaptive robust controller is proposed. The controller employs a physical model based indirect-type parameter estimation to obtain reliable estimates of unknown model parameters, and utilises a robust control method with dynamic compensation type fast adaptation to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. Due to the use of projection mapping, the robust control law and the parameter adaption algorithm can be designed separately. Since the system model uncertainties are unmatched, the recursive backstepping technology is adopted to design the robust control law. Extensive comparative experimental results are presented to illustrate the effectiveness of the proposed controller and its performance robustness to parameter variations and sudden disturbances.

Modeling NIF experimental designs with adaptive mesh refinement and Lagrangian hydrodynamics

NASA Astrophysics Data System (ADS)

Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.

2006-06-01

Incorporation of adaptive mesh refinement (AMR) into Lagrangian hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary Lagrangian-Eulerian (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.

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.

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.

On Markov modelling of near-wall turbulent shear flow

NASA Astrophysics Data System (ADS)

Reynolds, A. M.

1999-11-01

The role of Reynolds number in determining particle trajectories in near-wall turbulent shear flow is investigated in numerical simulations using a second-order Lagrangian stochastic (LS) model (Reynolds, A.M. 1999: A second-order Lagrangian stochastic model for particle trajectories in inhomogeneous turbulence. Quart. J. Roy. Meteorol. Soc. (In Press)). In such models, it is the acceleration, velocity and position of a particle rather than just its velocity and position which are assumed to evolve jointly as a continuous Markov process. It is found that Reynolds number effects are significant in determining simulated particle trajectories in the viscous sub-layer and the buffer zone. These effects are due almost entirely to the change in the Lagrangian integral timescale and are shown to be well represented in a first-order LS model by Sawford's correction footnote Sawford, B.L. 1991: Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys Fluids, 3, 1577-1586). This is found to remain true even when the Taylor-Reynolds number R_λ ~ O(0.1). This is somewhat surprising because the assumption of a Markovian evolution for velocity and position is strictly applicable only in the large Reynolds number limit because then the Lagrangian acceleration autocorrelation function approaches a delta function at the origin, corresponding to an uncorrelated component in the acceleration, and hence a Markov process footnote Borgas, M.S. and Sawford, B.L. 1991: The small-scale structure of acceleration correlations and its role in the statistical theory of turbulent dispersion. J. Fluid Mech. 288, 295-320.

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.

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

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.

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.

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.

A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

NASA Astrophysics Data System (ADS)

Cazes, F.; Coret, M.; Combescure, A.

2013-06-01

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

Coherent structure coloring: identification of coherent structures from sparse flow trajectories using graph theory

NASA Astrophysics Data System (ADS)

Schlueter, Kristy; Dabiri, John

2016-11-01

Coherent structure identification is important in many fluid dynamics applications, including transport phenomena in ocean flows and mixing and diffusion in turbulence. However, many of the techniques currently available for measuring such flows, including ocean drifter datasets and particle tracking velocimetry, only result in sparse velocity data. This is often insufficient for the use of current coherent structure detection algorithms based on analysis of the deformation gradient. Here, we present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number. The method, based on principles used in graph coloring algorithms, examines a measure of the kinematic dissimilarity of all pairs of flow trajectories, either measured experimentally, e.g. using particle tracking velocimetry; or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data is available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than is required by existing methods. This research was supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

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

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

Predicting seed dispersal using a Lagrangian Stochastic Model

NASA Astrophysics Data System (ADS)

Hsieh, C. I.; Chen, C. W.; Su, M. D.

2017-12-01

Migration and expansion of a plant species are determined by longdistance dispersion (LDD). A more sophisticated mechanical dispersion model is needed for mimicking LDD of wind-driven seeds. This study simulated seed dispersion trajectories in canopy turbulence by using the Lagrangian stochastic dispersion model under varying atmospheric stabilities in conjunction with the effects of turbulent kinetic energy dissipation rate intermittency. The effects of friction velocity, seed release height, and seed terminal velocity were also studied. The results showed that both the unstable atmosphere and the inclusion of the dissipation rate intermittency in the model could increase seeds' LDD. The number of seeds that escape the canopy volume by dissipation intermittency is increased under unstable atmospheric conditions. As a result, more seeds can be transported a further distance. When dissipation intermittency is included under astrong unstable atmosphere, the peak location of dispersal kernel tends to be closer to the source. Contrasting this, under both neutral and stable conditions when LDD of both are similar, the peak location will be further away from the source. However higher friction velocity, higher seed release height, and lower seed terminal velocity will all increase the LDD of seeds irregardless of atmospheric conditions. The change of LDD due to change in friction velocity, seed release height, or the seed terminal velocity, would be heightened under unstable conditions

Geometrically derived difference formulae for the numerical integration of trajectory problems

NASA Technical Reports Server (NTRS)

Mcleod, R. J. Y.; Sanz-Serna, J. M.

1982-01-01

An initial value problem for the autonomous system of ordinary differential equations dy/dt = f(y), where y is a vector, is considered. In a number of practical applications the interest lies in obtaining the curve traced by the solution y. These applications include the computation of trajectories in mechanical problems. The term 'trajectory problem' is employed to refer to these cases. Lambert and McLeod (1979) have introduced a method involving local rotation of the axes in the y-plane for the two-dimensional case. The present investigation continues the study of difference schemes specifically derived for trajectory problems. A simple geometrical way of constructing such methods is presented, and the local accuracy of the schemes is investigated. A circularly exact, fixed-step predictor-corrector algorithm is defined, and a variable-step version of a circularly exact algorithm is presented.

Quantum caustics in resonance-fluorescence trajectories

NASA Astrophysics Data System (ADS)

Naghiloo, M.; Tan, D.; Harrington, P. M.; Lewalle, P.; Jordan, A. N.; Murch, K. W.

2017-11-01

We employ phase-sensitive amplification to perform homodyne detection of the resonance fluorescence from a driven superconducting artificial atom. Entanglement between the emitter and its fluorescence allows us to track the individual quantum state trajectories of the emitter conditioned on the outcomes of the field measurements. We analyze the ensemble properties of these trajectories by considering trajectories that connect specific initial and final states. By applying the stochastic path-integral formalism, we calculate equations of motion for the most-likely path between two quantum states and compare these predicted paths to experimental data. Drawing on the mathematical similarity between the action formalism of the most-likely quantum paths and ray optics, we study the emergence of caustics in quantum trajectories: places where multiple extrema in the stochastic action occur. We observe such multiple most-likely paths in experimental data and find these paths to be in reasonable quantitative agreement with theoretical calculations.

Hyper-X Post-Flight Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Tartabini, Paul V.; Blanchard, RobertC.; Kirsch, Michael; Toniolo, Matthew D.

2004-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X{43A/Hyper{X high speed research vehicle, and its implementation for the reconstruction and analysis of ight test data. Extended Kalman ltering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the ltering routines. Additionally, smoothing algorithms have been implemented in which the nal value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from ight data.

Trajectory Optimization: OTIS 4

NASA Technical Reports Server (NTRS)

Riehl, John P.; Sjauw, Waldy K.; Falck, Robert D.; Paris, Stephen W.

2010-01-01

The latest release of the Optimal Trajectories by Implicit Simulation (OTIS4) allows users to simulate and optimize aerospace vehicle trajectories. With OTIS4, one can seamlessly generate optimal trajectories and parametric vehicle designs simultaneously. New features also allow OTIS4 to solve non-aerospace continuous time optimal control problems. The inputs and outputs of OTIS4 have been updated extensively from previous versions. Inputs now make use of objectoriented constructs, including one called a metastring. Metastrings use a greatly improved calculator and common nomenclature to reduce the user s workload. They allow for more flexibility in specifying vehicle physical models, boundary conditions, and path constraints. The OTIS4 calculator supports common mathematical functions, Boolean operations, and conditional statements. This allows users to define their own variables for use as outputs, constraints, or objective functions. The user-defined outputs can directly interface with other programs, such as spreadsheets, plotting packages, and visualization programs. Internally, OTIS4 has more explicit and implicit integration procedures, including high-order collocation methods, the pseudo-spectral method, and several variations of multiple shooting. Users may switch easily between the various methods. Several unique numerical techniques such as automated variable scaling and implicit integration grid refinement, support the integration methods. OTIS4 is also significantly more user friendly than previous versions. The installation process is nearly identical on various platforms, including Microsoft Windows, Apple OS X, and Linux operating systems. Cross-platform scripts also help make the execution of OTIS and post-processing of data easier. OTIS4 is supplied free by NASA and is subject to ITAR (International Traffic in Arms Regulations) restrictions. Users must have a Fortran compiler, and a Python interpreter is highly recommended.

Towards Assessing the Human Trajectory Planning Horizon

PubMed Central

Nitsch, Verena; Meinzer, Dominik; Wollherr, Dirk

2016-01-01

Mobile robots are envisioned to cooperate closely with humans and to integrate seamlessly into a shared environment. For locomotion, these environments resemble traversable areas which are shared between multiple agents like humans and robots. The seamless integration of mobile robots into these environments requires accurate predictions of human locomotion. This work considers optimal control and model predictive control approaches for accurate trajectory prediction and proposes to integrate aspects of human behavior to improve their performance. Recently developed models are not able to reproduce accurately trajectories that result from sudden avoidance maneuvers. Particularly, the human locomotion behavior when handling disturbances from other agents poses a problem. The goal of this work is to investigate whether humans alter their trajectory planning horizon, in order to resolve abruptly emerging collision situations. By modeling humans as model predictive controllers, the influence of the planning horizon is investigated in simulations. Based on these results, an experiment is designed to identify, whether humans initiate a change in their locomotion planning behavior while moving in a complex environment. The results support the hypothesis, that humans employ a shorter planning horizon to avoid collisions that are triggered by unexpected disturbances. Observations presented in this work are expected to further improve the generalizability and accuracy of prediction methods based on dynamic models. PMID:27936015

Towards Assessing the Human Trajectory Planning Horizon.

PubMed

Carton, Daniel; Nitsch, Verena; Meinzer, Dominik; Wollherr, Dirk

2016-01-01

Mobile robots are envisioned to cooperate closely with humans and to integrate seamlessly into a shared environment. For locomotion, these environments resemble traversable areas which are shared between multiple agents like humans and robots. The seamless integration of mobile robots into these environments requires accurate predictions of human locomotion. This work considers optimal control and model predictive control approaches for accurate trajectory prediction and proposes to integrate aspects of human behavior to improve their performance. Recently developed models are not able to reproduce accurately trajectories that result from sudden avoidance maneuvers. Particularly, the human locomotion behavior when handling disturbances from other agents poses a problem. The goal of this work is to investigate whether humans alter their trajectory planning horizon, in order to resolve abruptly emerging collision situations. By modeling humans as model predictive controllers, the influence of the planning horizon is investigated in simulations. Based on these results, an experiment is designed to identify, whether humans initiate a change in their locomotion planning behavior while moving in a complex environment. The results support the hypothesis, that humans employ a shorter planning horizon to avoid collisions that are triggered by unexpected disturbances. Observations presented in this work are expected to further improve the generalizability and accuracy of prediction methods based on dynamic models.

From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for Finite Lagrangian Data

NASA Astrophysics Data System (ADS)

Koltai, Péter; Renger, D. R. Michiel

2018-06-01

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.

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.

Huygens probe entry, descent, and landing trajectory reconstruction using the Program to Optimize Simulated Trajectories II

NASA Astrophysics Data System (ADS)

Striepe, Scott Allen

The objectives of this research were to develop a reconstruction capability using the Program to Optimize Simulated Trajectories II (POST2), apply this capability to reconstruct the Huygens Titan probe entry, descent, and landing (EDL) trajectory, evaluate the newly developed POST2 reconstruction module, analyze the reconstructed trajectory, and assess the pre-flight simulation models used for Huygens EDL simulation. An extended Kalman filter (EKF) module was developed and integrated into POST2 to enable trajectory reconstruction (especially when using POST2-based mission specific simulations). Several validation cases, ranging from a single, constant parameter estimate to multivariable estimation cases similar to an actual mission flight, were executed to test the POST2 reconstruction module. Trajectory reconstruction of the Huygens entry probe at Titan was accomplished using accelerometer measurements taken during flight to adjust an estimated state (e.g., position, velocity, parachute drag, wind velocity, etc.) in a POST2-based simulation developed to support EDL analyses and design prior to entry. Although the main emphasis of the trajectory reconstruction was to evaluate models used in the NASA pre-entry trajectory simulation, the resulting reconstructed trajectory was also assessed to provide an independent evaluation of the ESA result. Major findings from this analysis include: Altitude profiles from this analysis agree well with other NASA and ESA results but not with Radar data, whereas a scale factor of about 0.93 would bring the radar measurements into compliance with these results; entry capsule aerodynamics predictions (axial component only) were well within 3-sigma bounds established pre-flight for most of the entry when compared to reconstructed values; Main parachute drag of 9% to 19% above ESA model was determined from the reconstructed trajectory; based on the tilt sensor and accelerometer data, the conclusion from this assessment was that the

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.

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Gravity, Time, and Lagrangians

ERIC Educational Resources Information Center

Huggins, Elisha

2010-01-01

Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…

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.

Goddard trajectory determination subsystem: Mathematical specifications

NASA Technical Reports Server (NTRS)

Wagner, W. E. (Editor); Velez, C. E. (Editor)

1972-01-01

The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

Halo orbit transfer trajectory design using invariant manifold in the Sun-Earth system accounting radiation pressure and oblateness

NASA Astrophysics Data System (ADS)

Srivastava, Vineet K.; Kumar, Jai; Kushvah, Badam Singh

2018-01-01

In this paper, we study the invariant manifold and its application in transfer trajectory problem from a low Earth parking orbit to the Sun-Earth L1 and L2-halo orbits with the inclusion of radiation pressure and oblateness. Invariant manifold of the halo orbit provides a natural entrance to travel the spacecraft in the solar system along some specific paths due to its strong hyperbolic character. In this regard, the halo orbits near both collinear Lagrangian points are computed first. The manifold's approximation near the nominal halo orbit is computed using the eigenvectors of the monodromy matrix. The obtained local approximation provides globalization of the manifold by applying backward time propagation to the governing equations of motion. The desired transfer trajectory well suited for the transfer is explored by looking at a possible intersection between the Earth's parking orbit of the spacecraft and the manifold.

Parallel Aircraft Trajectory Optimization with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Falck, Robert D.; Gray, Justin S.; Naylor, Bret

2016-01-01

Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.

Longitudinal trajectories of bicultural identity integration in recently immigrated Hispanic adolescents: Links with mental health and family functioning.

PubMed

Schwartz, Seth J; Unger, Jennifer B; Baezconde-Garbanati, Lourdes; Benet-Martínez, Verónica; Meca, Alan; Zamboanga, Byron L; Lorenzo-Blanco, Elma I; Des Rosiers, Sabrina E; Oshri, Assaf; Sabet, Raha F; Soto, Daniel W; Pattarroyo, Monica; Huang, Shi; Villamar, Juan A; Lizzi, Karina M; Szapocznik, José

2015-12-01

This study examined, in a sample of recently immigrated Hispanic adolescents in Miami and Los Angeles, the extent to which bicultural identity integration (BII; involving the ability to synthesise one's heritage and receiving cultural streams and to identify as a member of both cultures) is best understood as a developmental construct that changes over time or as an individual-difference construct that is largely stable over time. We were also interested in the extent to which these trajectories predicted mental health and family functioning. Recent-immigrant 9th graders (N = 302) were assessed 6 times from 9th to 12th grade. Latent class growth analyses using the first 5 timepoints identified 2 trajectory classes-one with lower BII scores over time and another with higher BII scores over time. Higher heritage and US identity at baseline predicted membership in the higher BII class. At the 6th study timepoint, lower BII adolescents reported significantly poorer self-esteem, optimism, prosocial behaviour and family relationships compared with their higher BII counterparts. These findings are discussed in terms of further research on the over-time trajectory of biculturalism, and on the need to develop interventions to promote BII as a way of facilitating well-being and positive family functioning. © 2015 International Union of Psychological Science.

Simulation of Trajectories for High Specific Impulse Deep Space Exploration

NASA Technical Reports Server (NTRS)

Polsgrove, Tara; Adams, Robert B.; Brady, Hugh J. (Technical Monitor)

2002-01-01

Difficulties in approximating flight times and deliverable masses for continuous thrust propulsion systems have complicated comparison and evaluation of proposed propulsion concepts. These continuous thrust propulsion systems are of interest to many groups, not the least of which are the electric propulsion and fusion communities. Several charts plotting the results of well-known trajectory simulation codes were developed and are contained in this paper. These charts illustrate the dependence of time of flight and payload ratio on jet power, initial mass, specific impulse and specific power. These charts are intended to be a tool by which people in the propulsion community can explore the possibilities of their propulsion system concepts. Trajectories were simulated using the tools VARITOP and IPOST. VARITOP is a well known trajectory optimization code that involves numerical integration based on calculus of variations. IPOST has several methods of trajectory simulation; the one used in this paper is Cowell's method for full integration of the equations of motion. The analytical method derived in the companion paper was also used to simulate the trajectory. The accuracy of this method is discussed in the paper.

Steepest Ascent Low/Non-Low-Frequency Ratio in Empirical Mode Decomposition to Separate Deterministic and Stochastic Velocities From a Single Lagrangian Drifter

NASA Astrophysics Data System (ADS)

Chu, Peter C.

2018-03-01

SOund Fixing And Ranging (RAFOS) floats deployed by the Naval Postgraduate School (NPS) in the California Current system from 1992 to 2001 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) are used to study 2-D turbulent characteristics. Each drifter trajectory is adaptively decomposed using the empirical mode decomposition (EMD) into a series of intrinsic mode functions (IMFs) with corresponding specific scale for each IMF. A new steepest ascent low/non-low-frequency ratio is proposed in this paper to separate a Lagrangian trajectory into low-frequency (nondiffusive, i.e., deterministic) and high-frequency (diffusive, i.e., stochastic) components. The 2-D turbulent (or called eddy) diffusion coefficients are calculated on the base of the classical turbulent diffusion with mixing length theory from stochastic component of a single drifter. Statistical characteristics of the calculated 2-D turbulence length scale, strength, and diffusion coefficients from the NPS RAFOS data are presented with the mean values (over the whole drifters) of the 2-D diffusion coefficients comparable to the commonly used diffusivity tensor method.

Users manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

Schoellhamer, D.H.; Jobson, H.E.

1986-01-01

A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)

Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling.

PubMed

Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F

2014-02-01

Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations - such as missing the Lagrangian parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified Lagrangian" sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data

Taylor dispersion in two-dimensional bacterial turbulence

NASA Astrophysics Data System (ADS)

Huang, Yongxiang; Ou, Wenyu; Chen, Ming; Lu, Zhiming; Jiang, Nan; Liu, Yulu; Qiu, Xiang; Zhou, Quan

2017-05-01

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. The two-regime power-law behavior for short and long time evolutions was identified experimentally, which was separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be 0.94 and 0.97 for short and long time evolutions, respectively. For the case without the mean velocity effect, the values were 0.88 and 0.58. Moreover, very weak intermittency correction was detected. All measured Hurst numbers were above 1/2, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food.

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.

Hyper-X Mach 10 Trajectory Reconstruction

NASA Technical Reports Server (NTRS)

Karlgaard, Christopher D.; Martin, John G.; Tartabini, Paul V.; Thornblom, Mark N.

2005-01-01

This paper discusses the formulation and development of a trajectory reconstruction tool for the NASA X-43A/Hyper-X high speed research vehicle, and its implementation for the reconstruction and analysis of flight test data. Extended Kalman filtering techniques are employed to reconstruct the trajectory of the vehicle, based upon numerical integration of inertial measurement data along with redundant measurements of the vehicle state. The equations of motion are formulated in order to include the effects of several systematic error sources, whose values may also be estimated by the filtering routines. Additionally, smoothing algorithms have been implemented in which the final value of the state (or an augmented state that includes other systematic error parameters to be estimated) and covariance are propagated back to the initial time to generate the best-estimated trajectory, based upon all available data. The methods are applied to the problem of reconstructing the trajectory of the Hyper-X vehicle from data obtained during the Mach 10 test flight, which occurred on November 16th 2004.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

PubMed

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888

Programmers manual for a one-dimensional Lagrangian transport model

USGS Publications Warehouse

Schoellhamer, D.H.; Jobson, H.E.

1986-01-01

A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program codes. The Programmers Manual is intended for the model user who needs to modify code either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)

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

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

Management trajectories in the type 2 diabetes Integrated Delivery System project in Taiwan: accounting for behavioral therapy, nutrition education and therapeutics.

PubMed

Chang, Hsing-Yi; Wahlqvist, Mark L; Liu, Wen-Ling; Lee, Meei-Shyuan; Shin, Shyi-Jang; Li, Yu-Sheng; Chang, Chih-Jen; Chang, Chwen-Tzuei; Fuh, Mao-Tsu; Yang, Hung-Jen; Tai, Tong-Yuan; Hsu, Chih-Cheng

2014-01-01

Glycated hemoglobin (HbA1c) assessment is basic to diabetes management. Little is done to describe the whole spectrum of the trajectory, its related temporal patterns of metabolic indices, and comorbidities. This was a longitudinal study. In the Diabetes Management through Integrated Delivery System project in Taiwan, enrollees had diabetes, but no major comorbidities. They were randomized into intensive or conventional education (health, diet and exercise) groups. HbA1c was classified by a groupbased trajectory model on the basis of repeated six-monthly measurements. We analyzed data from 1091 subjects who had at least two measurements on HbA1c. HbA1c exhibited three distinct ranges of low (42-53 mmol/mol), intermediate (64-75 mmol/mol) and high (97 mmol/mol), all of which persisted for 4.5 years regardless of receiving intensive education or not. Temporal changes and a time-group interaction were found for triglycerides, total cholesterol, HDL-C and LDL-C. The high trajectory was associated with the major co-morbidities of retinopathy, nephropathy, neuropathy, stroke, hypoglycemia, and ketoacidosis. Patients in the intensive education group (62.4%), which were equally distributed in the three trajectories, had significantly lower HbA1cs (-0.14%= -1.5 mmol/mol, p=0.026). The intermediate trajectory patients with intensive education had HbA1cs higher than the low trajectory patients with conventional education (β=0.189, p=0.033). Though not significant, a similar pattern was found for DM education in the high group (β=0.223, p=0.154). Novel strategies beyond current education and pharmacotherapeutic regimens are needed to lower HbA1c at least 11 mmol/mol for the high HbA1c group to minimize comorbidities.

Identifying Lagrangian fronts with favourable fishery conditions

NASA Astrophysics Data System (ADS)

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

2014-08-01

Lagrangian fronts (LFs) in the ocean are defined as boundaries between surface waters with strongly different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps for displacements of synthetic tracers and other Lagrangian indicators. We use Pacific saury catch and location data for a number of commercial fishery seasons in the region of the northwest Pacific with one of the richest fishery in the world. It is shown statistically that the saury fishing grounds with maximal catches are not randomly distributed over the region but located mainly along the sharp LFs where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts in altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions LF locations may serve as good indicators of potential fishing grounds. Possible biophysical reasons for saury aggregation near sharp LFs are discussed. We propose a mechanism for effective export of nutrient rich waters based on stretching of material lines in the vicinity of hyperbolic objects in the ocean. The developed method, based on identifying LFs in any velocity fields, is quite general and may be applied to find potential fishing grounds for the other pelagic fish.

Trajectory Design Tools for Libration and Cis-Lunar Environments

NASA Technical Reports Server (NTRS)

Folta, David C.; Webster, Cassandra M.; Bosanac, Natasha; Cox, Andrew; Guzzetti, Davide; Howell, Kathleen C.

2016-01-01

Innovative trajectory design tools are required to support challenging multi-body regimes with complex dynamics, uncertain perturbations, and the integration of propulsion influences. Two distinctive tools, Adaptive Trajectory Design and the General Mission Analysis Tool have been developed and certified to provide the astrodynamics community with the ability to design multi-body trajectories. In this paper we discuss the multi-body design process and the capabilities of both tools. Demonstrable applications to confirmed missions, the Lunar IceCube Cubesat lunar mission and the Wide-Field Infrared Survey Telescope (WFIRST) Sun-Earth L2 mission, are presented.

Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian Approaches

NASA Astrophysics Data System (ADS)

Hong, Soon-Tae; Kim, Yong-Wan; Park, Young-Jai

We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first-class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the Lagrangian approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed Lagrangian from the above extended action.

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).

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

Resonance fluorescence trajectories in superconducting qubit

NASA Astrophysics Data System (ADS)

Naghiloo, Mahdi; Tan, Dian; Harrington, Patrick; Lewalle, Philippe; Jordan, Andrew; Murch, Kater

We employ phase-sensitive amplification to perform homodyne detection of the resonance fluorescence from a driven superconducting artificial atom. Entanglement between the emitter and its fluorescence allows us to track the individual quantum state trajectories of the emitter. We analyze the ensemble properties of these trajectories by considering paths that connect specific initial and final states. By applying a stochastic path integral formalism, we calculate equations of motion for the most likely path between two quantum states and compare these predicted paths to experimental data. Drawing on the mathematical similarity between the action formalism of the most likely quantum paths and ray optics, we study the emergence of caustics in quantum trajectories-situations where multiple extrema in the stochastic action occur. We observe such multiple most likely paths in experimental data and find these paths to be in reasonable quantitative agreement with theoretical calculations. Supported by the John Templeton Foundation.

Definition ofthe Design Trajectory and Entry Flight Corridor for the NASA Orion Exploration Mission 1 Entry Trajectory Using an Integrated Approach and Optimization

NASA Technical Reports Server (NTRS)

McNamara, Luke W.; Braun, Robert D.

2014-01-01

One of the key design objectives of NASA's Orion Exploration Mission 1 (EM- 1) is to execute a guided entry trajectory demonstrating GN&C capability. The focus of this paper is defining the flyable entry corridor for EM-1 taking into account multiple subsystem constraints such as complex aerothermal heating constraints, aerothermal heating objectives, landing accuracy constraints, structural load limits, Human-System-Integration-Requirements, Service Module debris disposal limits and other flight test objectives. During the EM-1 Design Analysis Cycle 1 design challenges came up that made defining the flyable entry corridor for the EM-1 mission critical to mission success. This document details the optimization techniques that were explored to use with the 6-DOF ANTARES simulation to assist in defining the design entry interface state and entry corridor with respect to key flight test constraints and objectives.

Fluctuating observation time ensembles in the thermodynamics of trajectories

NASA Astrophysics Data System (ADS)

Budini, Adrián A.; Turner, Robert M.; Garrahan, Juan P.

2014-03-01

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This ‘thermodynamics of trajectories’ approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there are a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show how the LD functions that describe an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates can be mapped to those of the fixed-time ensemble. We discuss how the correspondence between generalized ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.

Estimating the Temporal Domain when the Discount of the Net Evaporation Term Affects the Resulting Net Precipitation Pattern in the Moisture Budget Using a 3-D Lagrangian Approach

PubMed Central

Castillo, Rodrigo; Nieto, Raquel; Drumond, Anita; Gimeno, Luis

2014-01-01

The Lagrangian FLEXPART model has been used during the last decade to detect moisture sources that affect the climate in different regions of the world. While most of these studies provided a climatological perspective on the atmospheric branch of the hydrological cycle in terms of precipitation, none assessed the minimum temporal domain for which the climatological approach is valid. The methodology identifies the contribution of humidity to the moisture budget in a region by computing the changes in specific humidity along backward (or forward) trajectories of air masses over a period of ten days beforehand (afterwards), thereby allowing the calculation of monthly, seasonal and annual averages. The current study calculates as an example the climatological seasonal mean and variance of the net precipitation for regions in which precipitation exceeds evaporation (E-P<0) for the North Atlantic moisture source region using different time periods, for winter and summer from 1980 to 2000. The results show that net evaporation (E-P>0) can be discounted after when the integration of E-P is done without affecting the general net precipitation patterns when it is discounted in a monthly or longer time scale. PMID:24893002

Numerical analysis of the asymptotic two-point boundary value solution for N-body trajectories.

NASA Technical Reports Server (NTRS)

Lancaster, J. E.; Allemann, R. A.

1972-01-01

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical boundary value solution applicable to a broad class of trajectory problems. In addition, the earlier first-order solutions have been extended to second-order to determine if improved accuracy is possible. Comparisons between the asymptotic solution and numerical integration for several lunar and interplanetary trajectories show that the asymptotic solution is generally quite accurate. Also, since no iterations are required, a solution to the boundary value problem is obtained in a fraction of the time required for numerically integrated solutions.

Developmental Trajectories of Agency and Communion in Moral Motivation

ERIC Educational Resources Information Center

Walker, Lawrence J.; Frimer, Jeremy A.

2015-01-01

How does moral motivation develop across the life span? Previous research has indicated that moral exemplars have integrated the typically oppositional motives of agency and communion. The present research maps developmental trajectories in these motives that may lead to this end-point integration. Participants were 140 Canadians comprising four…

Simulating oil droplet dispersal from the Deepwater Horizon spill with a Lagrangian approach

USGS Publications Warehouse

North, Elizabeth W.; Schlag, Zachary; Adams, E. Eric; Sherwood, Christopher R.; He, Ruoying; Hyun, Hoon; Socolofsky, Scott A.

2011-01-01

An analytical multiphase plume model, combined with time-varying flow and hydrographic fields generated by the 3-D South Atlantic Bight and Gulf of Mexico model (SABGOM) hydrodynamic model, were used as input to a Lagrangian transport model (LTRANS), to simulate transport of oil droplets dispersed at depth from the recent Deepwater Horizon MC 252 oil spill. The plume model predicts a stratification-dominated near field, in which small oil droplets detrain from the central plume containing faster rising large oil droplets and gas bubbles and become trapped by density stratification. Simulated intrusion (trap) heights of ∼ 310–370 m agree well with the midrange of conductivity-temperature-depth observations, though the simulated variation in trap height was lower than observed, presumably in part due to unresolved variability in source composition (percentage oil versus gas) and location (multiple leaks during first half of spill). Simulated droplet trajectories by the SABGOM-LTRANS modeling system showed that droplets with diameters between 10 and 50 μm formed a distinct subsurface plume, which was transported horizontally and remained in the subsurface for >1 month. In contrast, droplets with diameters ≥90 μm rose rapidly to the surface. Simulated trajectories of droplets ≤50 μm in diameter were found to be consistent with field observations of a southwest-tending subsurface plume in late June 2010 reported by Camilli et al. [2010]. Model results suggest that the subsurface plume looped around to the east, with potential subsurface oil transport to the northeast and southeast. Ongoing work is focusing on adding degradation processes to the model to constrain droplet dispersal.

Nonpolynomial Lagrangian approach to regular black holes

NASA Astrophysics Data System (ADS)

Colléaux, Aimeric; Chinaglia, Stefano; Zerbini, Sergio

We present a review on Lagrangian models admitting spherically symmetric regular black holes (RBHs), and cosmological bounce solutions. Nonlinear electrodynamics, nonpolynomial gravity, and fluid approaches are explained in details. They consist respectively in a gauge invariant generalization of the Maxwell-Lagrangian, in modifications of the Einstein-Hilbert action via nonpolynomial curvature invariants, and finally in the reconstruction of density profiles able to cure the central singularity of black holes. The nonpolynomial gravity curvature invariants have the special property to be second-order and polynomial in the metric field, in spherically symmetric spacetimes. Along the way, other models and results are discussed, and some general properties that RBHs should satisfy are mentioned. A covariant Sakharov criterion for the absence of singularities in dynamical spherically symmetric spacetimes is also proposed and checked for some examples of such regular metric fields.

The augmented Lagrangian method for parameter estimation in elliptic systems

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Kunisch, Karl

1990-01-01

In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.

Unconventional Constraints on Nitrogen Chemistry using DC3 Observations and Trajectory-based Chemical Modeling

NASA Astrophysics Data System (ADS)

Shu, Q.; Henderson, B. H.

2017-12-01

Chemical transport models underestimate nitrogen dioxide observations in the upper troposphere (UT). Previous research in the UT succeeded in combining model predictions with field campaign measurements to demonstrate that the nitric acid formation rate (HO + NO2 → HNO3 (R1)) is overestimated by 22% (Henderson et al., 2012). A subsequent publication (Seltzer et al., 2015) demonstrated that single chemical constraint alters ozone and aerosol formation/composition. This work attempts to replicate previous chemical constraints with newer observations and a different modeling framework. We apply the previously successful constraint framework to Deep Convection Clouds and Chemistry (DC3). DC3 is a more recent field campaign where simulated nitrogen imbalances still exist. Freshly convected air parcels, identified in the DC3 dataset, as initial coordinates to initiate Lagrangian trajectories. Along each trajectory, we simulate the air parcel chemical state. Samples along the trajectories will form ensembles that represent possible realizations of UT air parcels. We then apply Bayesian inference to constrain nitrogen chemistry and compare results to the existing literature. Our anticipated results will confirm overestimation of HNO3 formation rate in previous work and provide further constraints on other nitrogen reaction rate coefficients that affect terminal products from NOx. We will particularly focus on organic nitrate chemistry that laboratory literature has yet to fully address. The results will provide useful insights into nitrogen chemistry that affects climate and human health.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Evaluation of wastewater contaminant transport in surface waters using verified Lagrangian sampling

USGS Publications Warehouse

Antweiler, Ronald C.; Writer, Jeffrey H.; Murphy, Sheila F.

2014-01-01

Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. Lagrangian sampling, which in theory samples the same water parcel as it moves downstream (the Lagrangian parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise Lagrangian sampling is difficult, and small deviations – such as missing the Lagrangian parcel by less than 1 h – can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed “verified Lagrangian” sampling, which can be used to determine if the Lagrangian parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the Lagrangian parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2–4 h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we

Route Sanitizer: Connected Vehicle Trajectory De-Identification Tool

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

Carter, Jason M; Ferber, Aaron E

Route Sanitizer is ORNL's connected vehicle moving object database de-identification tool and a graphical user interface to ORNL's connected vehicle de-identification algorithm. It uses the Google Chrome (soon to be Electron) platform so it will run on different computing platforms. The basic de-identification strategy is record redaction: portions of a vehicle trajectory (e.g. sequences of precise temporal spatial records) are removed. It does not alter retained records. The algorithm uses custom techniques to find areas within trajectories that may be considered private, then it suppresses those in addition to enough of the trajectory surrounding those locations to protect against "inferencemore » attacks" in a mathematically sound way. Map data is integrated into the process to make this possible.« less

Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows

NASA Astrophysics Data System (ADS)

Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs

2017-11-01

A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

S-Lagrangian dynamics of many-body systems and behavior of social groups: Dominance and hierarchy formation

NASA Astrophysics Data System (ADS)

Sandler, U.

2017-11-01

In this paper, we extend our generalized Lagrangian dynamics (i.e., S-Lagrangian dynamics, which can be applied equally to physical and non-physical systems as per Sandler (2014)) to many-body systems. Unlike common Lagrangian dynamics, this is not a trivial task. For many-body systems with S-dependent Lagrangians, the Lagrangian and the corresponding Hamiltonian or energy become vector functions, conjugated momenta become second-order tensors, and the system inevitably develops a hierarchical structure, even if all bodies initially have similar status and Lagrangians. As an application of our theory, we consider dominance and hierarchy formation, which is present in almost all communities of living species. As a biological basis for this application, we assume that the primary motivation of a groups activity is to attempt to cope with stress arising as pressure from the environment and from intrinsic unmet needs of individuals. It has been shown that the S-Lagrangian approach to a group's evolution naturally leads to formation of linear or despotic dominance hierarchies, depending on differences between individuals in coping with stress. That is, individuals that cope more readily with stress take leadership roles during the evolution. Experimental results in animal groups which support our assumption and findings are considered.

The need for social support provided by the non-profit cancer societies throughout different phases in the cancer trajectory and its integration into public healthcare.

PubMed

Yli-Uotila, Tiina; Kaunonen, Marja; Pylkkänen, Liisa; Suominen, Tarja

2016-04-01

To describe the phases of the cancer trajectory when social support, in the form of electronic counselling services, as provided by the non-profit cancer societies, is needed, as well as how these services are integrated into the cancer care in public healthcare. In this descriptive qualitative study a purposive sample of patients with cancer (n = 12) were interviewed. The data were content analysed inductively. Social support was needed when emotional well-being was weakened, when the body broke, when the care pathway induced unawareness, and when empowerment needed strengthening. There was no need for social support when well-being was considered in balance. The electronic counselling services were integrated into cancer care by supporting the patient with cancer emotionally, developing the informational expertise of the patient with cancer, expanding the opportunities for support, and supporting public healthcare. Integration required improvements to the actions of the patients and various actors involved in the healthcare system. There was no integration due to the health status of the patient and the sufficiency of the primary support sources. The received social support was not integrated into the actual cancer treatment process of the patient with cancer in the public healthcare system. The phases of support needed in the cancer trajectory as defined by the patient differ from the traditional biomedical phases of treatment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Lagrangians and Systems They Describe-How Not to Treat Dissipation in Quantum Mechanics.

ERIC Educational Resources Information Center

Ray, John R.

1979-01-01

The author argues that a Lagrangian that yields equations of motion for a damped simple harmonic oscillator does not describe this system, but a completely different physical system, and constructs a physical system that the Lagrangian describes and derives some of its properties. (Author/GA)

Lagrangian pathways of upwelling in the Southern Ocean

NASA Astrophysics Data System (ADS)

Viglione, Giuliana A.; Thompson, Andrew F.

2016-08-01

The spatial and temporal variability of upwelling into the mixed layer in the Southern Ocean is studied using a 1/10° ocean general circulation model. Virtual drifters are released in a regularly spaced pattern across the Southern Ocean at depths of 250, 500, and 1000 m during both summer and winter months. The drifters are advected along isopycnals for a period of 4 years, unless they outcrop into the mixed layer, where lateral advection and a parameterization of vertical mixing are applied. The focus of this study is on the discrete exchange between the model mixed layer and the interior. Localization of interior-mixed layer exchange occurs downstream of major topographic features across the Indian and Pacific basins, creating "hotspots" of outcropping. Minimal outcropping occurs in the Atlantic basin, while 59% of drifters outcrop in the Pacific sector and in Drake Passage (the region from 140° W to 40° W), a disproportionately large amount even when considering the relative basin sizes. Due to spatial and temporal variations in mixed layer depth, the Lagrangian trajectories provide a statistical measure of mixed layer residence times. For each exchange into the mixed layer, the residence time has a Rayleigh distribution with a mean of 30 days; the cumulative residence time of the drifters is 261 ± 194 days, over a period of 4 years. These results suggest that certain oceanic gas concentrations, such as CO2 and 14C, will likely not reach equilibrium with the atmosphere before being resubducted.

Dynamics of Multibody Systems Near Lagrangian Points

NASA Astrophysics Data System (ADS)

Wong, Brian

This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term

Geometric Lagrangian approach to the physical degree of freedom count in field theory

NASA Astrophysics Data System (ADS)

Díaz, Bogar; Montesinos, Merced

2018-05-01

To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.

What is integrability of discrete variational systems?

PubMed

Boll, Raphael; Petrera, Matteo; Suris, Yuri B

2014-02-08

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z -invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d -dimensional pluri-Lagrangian problem can be described as follows: given a d -form [Formula: see text] on an m -dimensional space (called multi-time, m > d ), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals [Formula: see text] for any d -dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler-Lagrange equations for a discrete pluri-Lagrangian problem with d =2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations.

What is integrability of discrete variational systems?

PubMed Central

Boll, Raphael; Petrera, Matteo; Suris, Yuri B.

2014-01-01

We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. PMID:24511254

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.

A non-conventional discontinuous Lagrangian for viscous flow

PubMed Central

Marner, F.

2017-01-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier–Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier–Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided. PMID:28386415

A non-conventional discontinuous Lagrangian for viscous flow.

PubMed

Scholle, M; Marner, F

2017-02-01

Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.

Particle trajectory computer program for icing analysis of axisymmetric bodies

NASA Technical Reports Server (NTRS)

Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.

1982-01-01

General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.

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).

Back-trajectory modelling and DNA-based species-specific detection methods allow tracking of fungal spore transport in air masses.

PubMed

Grinn-Gofroń, Agnieszka; Sadyś, Magdalena; Kaczmarek, Joanna; Bednarz, Aleksandra; Pawłowska, Sylwia; Jedryczka, Malgorzata

2016-11-15

Recent advances in molecular detection of living organisms facilitate the introduction of novel methods to studies of the transport of fungal spores over large distances. Monitoring the migration of airborne fungi using microscope based spore identification is limited when different species produce very similar spores. In our study, DNA-based monitoring with the use of species-specific probes allowed us to track the aerial movements of two important fungal pathogens of oilseed rape (Brassica napus L.), i.e., Leptosphaeria maculans and Leptosphaeria biglobosa, which have identical spore shape and size. The fungi were identified using dual-labelled fluorescent probes that were targeted to a β-tubulin gene fragment of either Leptosphaeria species. Spore identification by Real-Time PCR techniques capable of detecting minute amounts of DNA of selected fungal species was combined with back-trajectory analysis, allowing the tracking of past movements of air masses using the Hybrid Single Particle Lagrangian Integrated Trajectory model. Over a study period spanning the previous decade (2006-2015) we investigated two specific events relating to the long distance transport of Leptosphaeria spp. spores to Szczecin in North-West Poland. Based on the above mentioned methods and the results obtained with the additional spore sampler located in nearby Szczecin, and operating at the ground level in an oilseed rape field, we have demonstrated that on both occasions the L. biglobosa spores originated from the Jutland Peninsula. This is the first successful attempt to combine analysis of back-trajectories of air masses with DNA-based identification of economically important pathogens of oilseed rape in Europe. In our studies, the timing of L. biglobosa ascospore dispersal in the air was unlikely to result in the infection of winter oilseed rape grown as a crop plant. However, the fungus could infect other host plants, such as vegetable brassicas, cruciferous weeds, spring rapeseed

A Lagrangian discontinuous Galerkin hydrodynamic method

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

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

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

A Lagrangian discontinuous Galerkin hydrodynamic method

DOE PAGES

Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.

2017-12-11

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less

Trajectory optimization for an asymmetric launch vehicle. M.S. Thesis - MIT

NASA Technical Reports Server (NTRS)

Sullivan, Jeanne Marie

1990-01-01

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Lagrangian methods in the analysis of nonlinear wave interactions in plasma

NASA Technical Reports Server (NTRS)

Galloway, J. J.

1972-01-01

An averaged-Lagrangian method is developed for obtaining the equations which describe the nonlinear interactions of the wave (oscillatory) and background (nonoscillatory) components which comprise a continuous medium. The method applies to monochromatic waves in any continuous medium that can be described by a Lagrangian density, but is demonstrated in the context of plasma physics. The theory is presented in a more general and unified form by way of a new averaged-Lagrangian formalism which simplifies the perturbation ordering procedure. Earlier theory is extended to deal with a medium distributed in velocity space and to account for the interaction of the background with the waves. The analytic steps are systematized, so as to maximize calculational efficiency. An assessment of the applicability and limitations of the method shows that it has some definite advantages over other approaches in efficiency and versatility.

Lagrangian chaos in three- dimensional steady buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2016-11-01

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).

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.

Power corrections to the HTL effective Lagrangian of QED

NASA Astrophysics Data System (ADS)

Carignano, Stefano; Manuel, Cristina; Soto, Joan

2018-05-01

We present compact expressions for the power corrections to the hard thermal loop (HTL) Lagrangian of QED in d space dimensions. These are corrections of order (L / T) 2, valid for momenta L ≪ T, where T is the temperature. In the limit d → 3 we achieve a consistent regularization of both infrared and ultraviolet divergences, which respects the gauge symmetry of the theory. Dimensional regularization also allows us to witness subtle cancellations of infrared divergences. We also discuss how to generalize our results in the presence of a chemical potential, so as to obtain the power corrections to the hard dense loop (HDL) Lagrangian.

Effect of VSR invariant Chern-Simons Lagrangian on photon polarization

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

Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj, E-mail: acnayak@iitk.ac.in, E-mail: ravindkv@iitk.ac.in, E-mail: pkjain@iitk.ac.in

2015-07-01

We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.

Effect of VSR invariant Chern-Simons Lagrangian on photon polarization

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

Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj

We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.

Oceanic Flights and Airspace: Improving Efficiency by Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Fernandes, Alicia Borgman; Rebollo, Juan; Koch, Michael

2016-01-01

Oceanic operations suffer from multiple inefficiencies, including pre-departure planning that does not adequately consider uncertainty in the proposed trajectory, restrictions on the routes that a flight operator can choose for an oceanic crossing, time-consuming processes and procedures for amending en route trajectories, and difficulties exchanging data between Flight Information Regions (FIRs). These inefficiencies cause aircraft to fly suboptimal trajectories, burning fuel and time that could be conserved. A concept to support integration of existing and emerging capabilities and concepts is needed to transition to an airspace system that employs Trajectory Based Operations (TBO) to improve efficiency and safety in oceanic operations. This paper describes such a concept and the results of preliminary activities to evaluate the concept, including a stakeholder feedback activity, user needs analysis, and high level benefits analysis.

Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians

NASA Astrophysics Data System (ADS)

Ćaǧatay Uçgun, Filiz; Esen, Oǧul; Gümral, Hasan

2018-01-01

We present Skinner-Rusk and Hamiltonian formalisms of second order degenerate Clément and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed to obtain Hamiltonian realizations of Lagrangian theories. The Gotay-Nester-Hinds algorithm is used to investigate Skinner-Rusk formalisms of these systems.

Trajectory mapping of middle atmospheric water vapor by a mini network of NDACC instruments

NASA Astrophysics Data System (ADS)

Lainer, M.; Kämpfer, N.; Tschanz, B.; Nedoluha, G. E.; Ka, S.; Oh, J. J.

2015-08-01

The important task to observe the global coverage of middle atmospheric trace gases like water vapor or ozone usually is accomplished by satellites. Climate and atmospheric studies rely upon the knowledge of trace gas distributions throughout the stratosphere and mesosphere. Many of these gases are currently measured from satellites, but it is not clear whether this capability will be maintained in the future. This could lead to a significant knowledge gap of the state of the atmosphere. We explore the possibilities of mapping middle atmospheric water vapor in the Northern Hemisphere by using Lagrangian trajectory calculations and water vapor profile data from a small network of five ground-based microwave radiometers. Four of them are operated within the frame of NDACC (Network for the Detection of Atmospheric Composition Change). Keeping in mind that the instruments are based on different hardware and calibration setups, a height-dependent bias of the retrieved water vapor profiles has to be expected among the microwave radiometers. In order to correct and harmonize the different data sets, the Microwave Limb Sounder (MLS) on the Aura satellite is used to serve as a kind of traveling standard. A domain-averaging TM (trajectory mapping) method is applied which simplifies the subsequent validation of the quality of the trajectory-mapped water vapor distribution towards direct satellite observations. Trajectories are calculated forwards and backwards in time for up to 10 days using 6 hourly meteorological wind analysis fields. Overall, a total of four case studies of trajectory mapping in different meteorological regimes are discussed. One of the case studies takes place during a major sudden stratospheric warming (SSW) accompanied by the polar vortex breakdown; a second takes place after the reformation of stable circulation system. TM cases close to the fall equinox and June solstice event from the year 2012 complete the study, showing the high potential of a

Trajectory mapping of middle atmospheric water vapor by a mini network of NDACC instruments

NASA Astrophysics Data System (ADS)

Lainer, M.; Kämpfer, N.; Tschanz, B.; Nedoluha, G. E.; Ka, S.; Oh, J. J.

2015-04-01

The important task to observe the global coverage of middle atmospheric trace gases like water vapor or ozone usually is accomplished by satellites. Climate and atmospheric studies rely upon the knowledge of trace gas distributions throughout the stratosphere and mesosphere. Many of these gases are currently measured from satellites, but it is not clear whether this capability will be maintained in the future. This could lead to a significant knowledge gap of the state of the atmosphere. We explore the possibilities of mapping middle atmospheric water vapor in the Northern Hemisphere by using Lagrangian trajectory calculations and water vapor profile data from a small network of five ground-based microwave radiometers. Four of them are operated within the frame of NDACC (Network for the Detection of Atmospheric Composition Change). Keeping in mind that the instruments are based on different hardware and calibration setups, a height dependent bias of the retrieved water vapor profiles has to be expected among the microwave radiometers. In order to correct and harmonize the different datasets, the Microwave Limb Sounder (MLS) on the Aura satellite is used to serve as a kind of travelling standard. A domain-averaging TM (trajectory mapping) method is applied which simplifies the subsequent validation of the quality of the trajectory mapped water vapor distribution towards direct satellite observations. Trajectories are calculated forwards and backwards in time for up to 10 days using 6 hourly meteorological wind analysis fields. Overall, a total of four case studies of trajectory mapping in different meteorological regimes are discussed. One of the case studies takes place during a major sudden stratospheric warming (SSW) accompanied by the polar vortex breakdown, a second takes place after the reformation of stable circulation system. TM cases close to the fall equinox and June solstice event from the year 2012 complete the study, showing the high potential of a

Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1998-01-01

Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.

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 space consistency relation for large scale structure

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

Horn, Bart; Hui, Lam; Xiao, Xiao

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

Lagrangian space consistency relation for large scale structure

DOE PAGES

Horn, Bart; Hui, Lam; Xiao, Xiao

2015-09-29

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

Lagrangian flows within reflecting internal waves at a horizontal free-slip surface

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

Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.

In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less

Examination of Eulerian and Lagrangian Coordinate Systems.

ERIC Educational Resources Information Center

Remillard, Wilfred J.

1978-01-01

Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)

The analysis of control trajectories using symbolic and database computing

NASA Technical Reports Server (NTRS)

Grossman, Robert

1995-01-01

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Statistical scaling of pore-scale Lagrangian velocities in natural porous media.

PubMed

Siena, M; Guadagnini, A; Riva, M; Bijeljic, B; Pereira Nunes, J P; Blunt, M J

2014-08-01

We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.

Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.

2013-08-01

In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S2 is constructed.

Simulations of High Speed Fragment Trajectories

NASA Astrophysics Data System (ADS)

Yeh, Peter; Attaway, Stephen; Arunajatesan, Srinivasan; Fisher, Travis

2017-11-01

Flying shrapnel from an explosion are capable of traveling at supersonic speeds and distances much farther than expected due to aerodynamic interactions. Predicting the trajectories and stable tumbling modes of arbitrary shaped fragments is a fundamental problem applicable to range safety calculations, damage assessment, and military technology. Traditional approaches rely on characterizing fragment flight using a single drag coefficient, which may be inaccurate for fragments with large aspect ratios. In our work we develop a procedure to simulate trajectories of arbitrary shaped fragments with higher fidelity using high performance computing. We employ a two-step approach in which the force and moment coefficients are first computed as a function of orientation using compressible computational fluid dynamics. The force and moment data are then input into a six-degree-of-freedom rigid body dynamics solver to integrate trajectories in time. Results of these high fidelity simulations allow us to further understand the flight dynamics and tumbling modes of a single fragment. Furthermore, we use these results to determine the validity and uncertainty of inexpensive methods such as the single drag coefficient model.

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.

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.

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

Notes on integral identities for 3d supersymmetric dualities

NASA Astrophysics Data System (ADS)

Aghaei, Nezhla; Amariti, Antonio; Sekiguchi, Yuta

2018-04-01

Four dimensional N=2 Argyres-Douglas theories have been recently conjectured to be described by N=1 Lagrangian theories. Such models, once reduced to 3d, should be mirror dual to Lagrangian N=4 theories. This has been numerically checked through the matching of the partition functions on the three sphere. In this article, we provide an analytic derivation for this result in the A 2 n-1 case via hyperbolic hypergeometric integrals. We study the D 4 case as well, commenting on some open questions and possible resolutions. In the second part of the paper we discuss other integral identities leading to the matching of the partition functions in 3d dual pairs involving higher monopole superpotentials.

Variations in the water vapor distribution and the associated effects on fog and haze events over Xi'an based on Raman lidar data and back trajectories.

PubMed

Wang, Yufeng; Zhang, Jing; Fu, Qiang; Song, Yuehui; Di, Huige; Li, Bo; Hua, Dengxin

2017-10-01

A combination of more than two years of water vapor lidar data with back trajectory analysis using the hybrid single-particle Lagrangian integrated trajectory (HYSPLIT) model was used to study the long-range transport of air masses and the water vapor distribution characteristics and variations over Xi'an, China (34.233° N, 108.911° E), which is a typical city in Northwest China. High-quality profiles of the water vapor density were derived from a multifunction Raman lidar system built in Xi'an, and more than 2000 sets of profiles with >400 nighttime observations from October 2013 to July 2016 were collected and used for statistical and quantitative analyses. The vertical variations in the water vapor content were discussed. A mutation height of the water vapor exists at 2-4 km with a high occurrence rate of ∼60% during the autumn and winter seasons. This height reflects a distinct stratification in the water vapor content. Additionally, the atmospheric water vapor content was mainly concentrated in the lower troposphere, and the proportion of the water vapor content at 0.5-5 km accounted for 80%-90% of the total water vapor below 10 km. Obvious seasonal variations were observed, including large water vapor content during the spring and summer and small content during the autumn and winter. Combined with back trajectory analysis, the results showed that markedly different water vapor transport pathways contribute to seasonal variations in the water vapor content. South and southeast airflows dominated during the summer, with 30% of the 84 trajectories originating from these areas; however, the air masses during the winter originated from the north and local regions (64.3%) and from the northwest (27%). In addition, we discussed variations in the water vapor during fog and haze weather conditions during the winter. A considerable enhancement in the mean water vapor density at 0.5-3 km exhibited a clear positive correlation (correlation coefficient >0.8) with

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.

Sigma decomposition: the CP-odd Lagrangian

NASA Astrophysics Data System (ADS)

Hierro, I. M.; Merlo, L.; Rigolin, S.

2016-04-01

In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.

Matter Lagrangian of particles and fluids

NASA Astrophysics Data System (ADS)

Avelino, P. P.; Sousa, L.

2018-03-01

We consider a model where particles are described as localized concentrations of energy, with fixed rest mass and structure, which are not significantly affected by their self-induced gravitational field. We show that the volume average of the on-shell matter Lagrangian Lm describing such particles, in the proper frame, is equal to the volume average of the trace T of the energy-momentum tensor in the same frame, independently of the particle's structure and constitution. Since both Lm and T are scalars, and thus independent of the reference frame, this result is also applicable to collections of moving particles and, in particular, to those which can be described by a perfect fluid. Our results are expected to be particularly relevant in the case of modified theories of gravity with nonminimal coupling to matter where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, such as f (R ,Lm) and f (R ,T ) gravity. In particular, they indicate that, in this context, f (R ,Lm) theories may be regarded as a subclass of f (R ,T ) gravity.

A variable resolution nonhydrostatic global atmospheric semi-implicit semi-Lagrangian model

NASA Astrophysics Data System (ADS)

Pouliot, George Antoine

2000-10-01

The objective of this project is to develop a variable-resolution finite difference adiabatic global nonhydrostatic semi-implicit semi-Lagrangian (SISL) model based on the fully compressible nonhydrostatic atmospheric equations. To achieve this goal, a three-dimensional variable resolution dynamical core was developed and tested. The main characteristics of the dynamical core can be summarized as follows: Spherical coordinates were used in a global domain. A hydrostatic/nonhydrostatic switch was incorporated into the dynamical equations to use the fully compressible atmospheric equations. A generalized horizontal variable resolution grid was developed and incorporated into the model. For a variable resolution grid, in contrast to a uniform resolution grid, the order of accuracy of finite difference approximations is formally lost but remains close to the order of accuracy associated with the uniform resolution grid provided the grid stretching is not too significant. The SISL numerical scheme was implemented for the fully compressible set of equations. In addition, the generalized minimum residual (GMRES) method with restart and preconditioner was used to solve the three-dimensional elliptic equation derived from the discretized system of equations. The three-dimensional momentum equation was integrated in vector-form to incorporate the metric terms in the calculations of the trajectories. Using global re-analysis data for a specific test case, the model was compared to similar SISL models previously developed. Reasonable agreement between the model and the other independently developed models was obtained. The Held-Suarez test for dynamical cores was used for a long integration and the model was successfully integrated for up to 1200 days. Idealized topography was used to test the variable resolution component of the model. Nonhydrostatic effects were simulated at grid spacings of 400 meters with idealized topography and uniform flow. Using a high

The Improvement of Efficiency in the Numerical Computation of Orbit Trajectories

NASA Technical Reports Server (NTRS)

Dyer, J.; Danchick, R.; Pierce, S.; Haney, R.

1972-01-01

An analysis, system design, programming, and evaluation of results are described for numerical computation of orbit trajectories. Evaluation of generalized methods, interaction of different formulations for satellite motion, transformation of equations of motion and integrator loads, and development of efficient integrators are also considered.

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

Feedback Integrators

NASA Astrophysics Data System (ADS)

Chang, Dong Eui; Jiménez, Fernando; Perlmutter, Matthew

2016-12-01

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves the first integrals of the system. The idea is that given an initial point in the manifold we extend the dynamics from the manifold to its ambient Euclidean space and then modify the dynamics outside the intersection of the manifold and the level sets of the first integrals containing the initial point such that the intersection becomes a unique local attractor of the resultant dynamics. While the modified dynamics theoretically produces the same trajectory as the original dynamics, it yields a numerical trajectory that stably remains on the manifold and preserves the first integrals. The big merit of our method is that the modified dynamics can be integrated with any ordinary numerical integrator such as Euler or Runge-Kutta. We illustrate this method by applying it to three famous problems: the free rigid body, the Kepler problem and a perturbed Kepler problem with rotational symmetry. We also carry out simulation studies to demonstrate the excellence of our method and make comparisons with the standard projection method, a splitting method and Störmer-Verlet schemes.

Trajectory of the arctic as an integrated system

USGS Publications Warehouse

Hinzman, Larry; Deal, Clara; McGuire, Anthony David; Mernild, Sebastian H.; Polyakov, Igor V.; Walsh, John E.

2013-01-01

Although much remains to be learned about the Arctic and its component processes, many of the most urgent scientific, engineering, and social questions can only be approached through a broader system perspective. Here, we address interactions between components of the Arctic System and assess feedbacks and the extent to which feedbacks (1) are now underway in the Arctic; and (2) will shape the future trajectory of the Arctic system. We examine interdependent connections among atmospheric processes, oceanic processes, sea-ice dynamics, marine and terrestrial ecosystems, land surface stocks of carbon and water, glaciers and ice caps, and the Greenland ice sheet. Our emphasis on the interactions between components, both historical and anticipated, is targeted on the feedbacks, pathways, and processes that link these different components of the Arctic system. We present evidence that the physical components of the Arctic climate system are currently in extreme states, and that there is no indication that the system will deviate from this anomalous trajectory in the foreseeable future. The feedback for which the evidence of ongoing changes is most compelling is the surface albedo-temperature feedback, which is amplifying temperature changes over land (primarily in spring) and ocean (primarily in autumn-winter). Other feedbacks likely to emerge are those in which key processes include surface fluxes of trace gases, changes in the distribution of vegetation, changes in surface soil moisture, changes in atmospheric water vapor arising from higher temperatures and greater areas of open ocean, impacts of Arctic freshwater fluxes on the meridional overturning circulation of the ocean, and changes in Arctic clouds resulting from changes in water vapor content.

Trajectory of the Arctic as an integrated system.

PubMed

Hinzman, Larry D; Deal, Clara J; McGuire, A David; Mernild, Sebastian H; Polyakov, Igor V; Walsh, John E

2013-12-01

Although much remains to be learned about the Arctic and its component processes, many of the most urgent scientific, engineering, and social questions can only be approached through a broader system perspective. Here, we address interactions between components of the Arctic system and assess feedbacks and the extent to which feedbacks (1) are now underway in the Arctic and (2) will shape the future trajectory of the Arctic system. We examine interdependent connections among atmospheric processes, oceanic processes, sea-ice dynamics, marine and terrestrial ecosystems, land surface stocks of carbon and water, glaciers and ice caps, and the Greenland ice sheet. Our emphasis on the interactions between components, both historical and anticipated, is targeted on the feedbacks, pathways, and processes that link these different components of the Arctic system. We present evidence that the physical components of the Arctic climate system are currently in extreme states, and that there is no indication that the system will deviate from this anomalous trajectory in the foreseeable future. The feedback for which the evidence of ongoing changes is most compelling is the surface albedo-temperature feedback, which is amplifying temperature changes over land (primarily in spring) and ocean (primarily in autumn-winter). Other feedbacks likely to emerge are those in which key processes include surface fluxes of trace gases, changes in the distribution of vegetation, changes in surface soil moisture, changes in atmospheric water vapor arising from higher temperatures and greater areas of open ocean, impacts of Arctic freshwater fluxes on the meridional overturning circulation of the ocean, and changes in Arctic clouds resulting from changes in water vapor content.

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 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 space consistency relation for large scale structure

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

Horn, Bart; Hui, Lam; Xiao, Xiao, E-mail: bh2478@columbia.edu, E-mail: lh399@columbia.edu, E-mail: xx2146@columbia.edu

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias and Riotto and Peloso and Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

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.

Impact of rheology on probabilistic forecasts of sea ice trajectories: application for search and rescue operations in the Arctic

NASA Astrophysics Data System (ADS)

Rabatel, Matthias; Rampal, Pierre; Carrassi, Alberto; Bertino, Laurent; Jones, Christopher K. R. T.

2018-03-01

We present a sensitivity analysis and discuss the probabilistic forecast capabilities of the novel sea ice model neXtSIM used in hindcast mode. The study pertains to the response of the model to the uncertainty on winds using probabilistic forecasts of ice trajectories. neXtSIM is a continuous Lagrangian numerical model that uses an elasto-brittle rheology to simulate the ice response to external forces. The sensitivity analysis is based on a Monte Carlo sampling of 12 members. The response of the model to the uncertainties is evaluated in terms of simulated ice drift distances from their initial positions, and from the mean position of the ensemble, over the mid-term forecast horizon of 10 days. The simulated ice drift is decomposed into advective and diffusive parts that are characterised separately both spatially and temporally and compared to what is obtained with a free-drift model, that is, when the ice rheology does not play any role in the modelled physics of the ice. The seasonal variability of the model sensitivity is presented and shows the role of the ice compactness and rheology in the ice drift response at both local and regional scales in the Arctic. Indeed, the ice drift simulated by neXtSIM in summer is close to the one obtained with the free-drift model, while the more compact and solid ice pack shows a significantly different mechanical and drift behaviour in winter. For the winter period analysed in this study, we also show that, in contrast to the free-drift model, neXtSIM reproduces the sea ice Lagrangian diffusion regimes as found from observed trajectories. The forecast capability of neXtSIM is also evaluated using a large set of real buoy's trajectories and compared to the capability of the free-drift model. We found that neXtSIM performs significantly better in simulating sea ice drift, both in terms of forecast error and as a tool to assist search and rescue operations, although the sources of uncertainties assumed for the present

NextGen Far-Term Concept Exploration for Integrated Gate-to-Gate Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Johnson, Sally C.; Barmore, Bryan E.

2016-01-01

NASA is currently conducting concept exploration studies toward the definition of a far-term, gate-to-gate concept for Trajectory-Based Operations. This paper presents a basic architectural framework for the far-term concept and discusses some observations about implementation of trajectory-based operations in the National Airspace System. Within the concept, operators and service providers collaboratively negotiate aircraft trajectories, providing agile, optimized, aircraft-specific routing to meet service provider gate-to-gate flow-management constraints and increasing capacity by smoothly and effectively combining flight-deck-based and ground-based metering, merging, and spacing in a mixed-equipage environment. The far-term TBO concept is intended to influence the direction of mid-term TBO research and to inform the definition of stable requirements and standards for TBO communications infrastructure and user equipage.

Detailed description of the HP-9825A HFRMP trajectory processor (TRAJ)

NASA Technical Reports Server (NTRS)

Kindall, S. M.; Wilson, S. W.

1979-01-01

The computer code for the trajectory processor of the HP-9825A High Fidelity Relative Motion Program is described in detail. The processor is a 12-degrees-of-freedom trajectory integrator which can be used to generate digital and graphical data describing the relative motion of the Space Shuttle Orbiter and a free-flying cylindrical payload. Coding standards and flow charts are given and the computational logic is discussed.

Mexican-origin Adolescents' Educational Expectation Trajectories: Intersection of Nativity, Sex, and Socioeconomic Status

PubMed Central

Perez-Brena, Norma J.; Delgado, Melissa Y.; Rodríguez De Jesús, Sue A.; Updegraff, Kimberly A.; Umaña-Taylor, Adriana J.

2017-01-01

Expectancy value theory and a cultural-ecological framework are integrated in this study to examine the trajectories of 246 Mexican-origin adolescents' (Mage = 12.52, SDage = 0.58; 51% girls, 62% U.S.-born) educational expectations across eight years. Findings from a multilevel growth model revealed that early adolescents expected to complete a post-bachelor's degree, but expectations declined in middle adolescence and improved in late adolescence. This pattern was more pronounced for immigrant, compared to U.S-born, adolescents. Higher socioeconomic status was associated with higher expectations. Boys and girls differed in their trajectories, such that boys showed a curvilinear trajectory and girls showed a stable trajectory. Nativity moderated these sex differences. Immigrant boys showed curvilinear trajectories that dipped in middle adolescence and immigrant girls showed a declining trajectory. In contrast, U.S.-born boys and girls showed linear and stable trajectories. The discussion addresses suggestions for targeted interventions with at-risk subgroups during a sensitive period in adolescence. PMID:29242673

Mexican-origin Adolescents' Educational Expectation Trajectories: Intersection of Nativity, Sex, and Socioeconomic Status.

PubMed

Perez-Brena, Norma J; Delgado, Melissa Y; Rodríguez De Jesús, Sue A; Updegraff, Kimberly A; Umaña-Taylor, Adriana J

2017-01-01

Expectancy value theory and a cultural-ecological framework are integrated in this study to examine the trajectories of 246 Mexican-origin adolescents' (M age = 12.52, SD age = 0.58; 51% girls, 62% U.S.-born) educational expectations across eight years. Findings from a multilevel growth model revealed that early adolescents expected to complete a post-bachelor's degree, but expectations declined in middle adolescence and improved in late adolescence. This pattern was more pronounced for immigrant, compared to U.S-born, adolescents. Higher socioeconomic status was associated with higher expectations. Boys and girls differed in their trajectories, such that boys showed a curvilinear trajectory and girls showed a stable trajectory. Nativity moderated these sex differences. Immigrant boys showed curvilinear trajectories that dipped in middle adolescence and immigrant girls showed a declining trajectory. In contrast, U.S.-born boys and girls showed linear and stable trajectories. The discussion addresses suggestions for targeted interventions with at-risk subgroups during a sensitive period in adolescence.

Numerical Study on the Particle Trajectory Tracking in a Micro-UV Bio-Fluorescence Sensor.

PubMed

Byeon, Sun-Seok; Cho, Moon-Young; Lee, Jong-Chul; Kim, Youn-Jea

2015-03-01

A micro-UV bio-fluorescence sensor was developed to detect primary biological aerosols including bacteria, bacterial spores, fungal spores, pollens, viruses, algae, etc. In order to effectively detect the bio-particles in a micro-UV bio-fluorescence sensor, numerical calculations were performed to adjust for appropriate flow conditions of the sensor by regulating the sample aerosols and sheath flow. In particular, a CFD-based model of hydrodynamic processes was developed by computing the trajectory of particles using commercially available ANSYS CFX-14 software and the Lagrangian tracking model. The established model was evaluated with regard to the variation of sheath flow rate and particle size. Results showed that the sheath flow was changed rapidly at the end of nozzle tip, but the sample particles moved near the center of aerosol jet for aerodynamic focusing with little deviation from the axis.

SENS-5D trajectory and wind-sensitivity calculations for unguided rockets

NASA Technical Reports Server (NTRS)

Singh, R. P.; Huang, L. C. P.; Cook, R. A.

1975-01-01

A computational procedure is described which numerically integrates the equations of motion of an unguided rocket. Three translational and two angular (roll discarded) degrees of freedom are integrated through the final burnout; and then, through impact, only three translational motions are considered. Input to the routine is: initial time, altitude and velocity, vehicle characteristics, and other defined options. Input format has a wide range of flexibility for special calculations. Output is geared mainly to the wind-weighting procedure, and includes summary of trajectory at burnout, apogee and impact, summary of spent-stage trajectories, detailed position and vehicle data, unit-wind effects for head, tail and cross winds, coriolis deflections, range derivative, and the sensitivity curves (the so called F(Z) and DF(Z) curves). The numerical integration procedure is a fourth-order, modified Adams-Bashforth Predictor-Corrector method. This method is supplemented by a fourth-order Runge-Kutta method to start the integration at t=0 and whenever error criteria demand a change in step size.

Impact trajectories of the asteroid Apophis in the 21st century

NASA Astrophysics Data System (ADS)

Sokolov, L. L.; Bashakov, A. A.; Borisova, T. P.; Petrov, N. A.; Pitjev, N. P.; Shaidulin, V. S.

2012-07-01

The asteroid Apophis is one of the most hazardous near-Earth asteroids. As a result of the scattering of Apophis' potential trajectories after its close approach in 2029, and its possible approach in 2036, there are many dangerous trajectories including impact trajectories after 2036. The purpose of this study is to identify and investigate these trajectories. We use the Everhart integrator; the DE405, DE423, and EPM2008 ephemerides; and two sets of initial data for Apophis (those collected by NASA in 2006 and by the IAA in 2010). More than 50 possible encounters in this century are presented, including 13 encounters between 2036 and 2050. The minimum geocentric distances obtained using a different ephemeris and initial conditions differ little between themselves. Analogous results in (Yeomans et al., 2009) are consistent with our results.

Ascent trajectory dispersion analysis for WTR heads-up space shuttle trajectory

NASA Technical Reports Server (NTRS)

1986-01-01

The results of a Space Transportation System ascent trajectory dispersion analysis are discussed. The purpose is to provide critical trajectory parameter values for assessing the Space Shuttle in a heads-up configuration launched from the Western Test Range (STR). This analysis was conducted using a trajectory profile based on a launch from the WTR in December. The analysis consisted of the following steps: (1) nominal trajectories were simulated under the conditions as specified by baseline reference mission guidelines; (2) dispersion trajectories were simulated using predetermined parametric variations; (3) requirements for a system-related composite trajectory were determined by a root-sum-square (RSS) analysis of the positive deviations between values of the aerodynamic heating indicator (AHI) generated by the dispersion and nominal trajectories; (4) using the RSS assessment as a guideline, the system related composite trajectory was simulated by combinations of dispersion parameters which represented major contributors; (5) an assessment of environmental perturbations via a RSS analysis was made by the combination of plus or minus 2 sigma atmospheric density variation and 95% directional design wind dispersions; (6) maximum aerodynamic heating trajectories were simulated by variation of dispersion parameters which would emulate the summation of the system-related RSS and environmental RSS values of AHI. The maximum aerodynamic heating trajectories were simulated consistent with the directional winds used in the environmental analysis.

Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.

PubMed

Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P

2015-08-01

Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

Firing rate dynamics in the hippocampus induced by trajectory learning.

PubMed

Ji, Daoyun; Wilson, Matthew A

2008-04-30

The hippocampus is essential for spatial navigation, which may involve sequential learning. However, how the hippocampus encodes new sequences in familiar environments is unknown. To study the impact of novel spatial sequences on the activity of hippocampal neurons, we monitored hippocampal ensembles while rats learned to switch from two familiar trajectories to a new one in a familiar environment. Here, we show that this novel spatial experience induces two types of changes in firing rates, but not locations of hippocampal place cells. First, place-cell firing rates on the two familiar trajectories start to change before the actual behavioral switch to the new trajectory. Second, repeated exposure on the new trajectory is associated with an increased dependence of place-cell firing rates on immediate past locations. The result suggests that sequence encoding in the hippocampus may involve integration of information about the recent past into current state.

Firing Rate Dynamics in the Hippocampus Induced by Trajectory Learning

PubMed Central

Wilson, Matthew A.

2008-01-01

The hippocampus is essential for spatial navigation, which may involve sequential learning. However, how the hippocampus encodes new sequences in familiar environments is unknown. To study the impact of novel spatial sequences on the activity of hippocampal neurons, we monitored hippocampal ensembles while rats learned to switch from two familiar trajectories to a new one in a familiar environment. Here, we show that this novel spatial experience induces two types of changes in firing rates, but not locations of hippocampal place cells. First, place-cell firing rates on the two familiar trajectories start to change before the actual behavioral switch to the new trajectory. Second, repeated exposure on the new trajectory is associated with an increased dependence of place-cell firing rates on immediate past locations. The result suggests that sequence encoding in the hippocampus may involve integration of information about the recent past into current state. PMID:18448645

A SPACE TRAJECTORY RADIATION EXPOSURE PROCEDURE FOR CISLUNAR MISSIONS

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

Cranford, W.; Falkenbury, R.F.; Miller, R.A.

1962-07-31

The Space Trajectory Radiation Exposure Procedure (STREP) is designed for use in computing the timeintegrated spectra for any specified trajectory in cislunar space for any combination of the several components of space radiations. These components include Van Allen protons and electrons; solar-flare protons, electrons, heavy particles, and gamma radiation; cosmic protons and heavy particles; albedo neutrons, and aurora borealis gamma radiation. The program can also be used to calculate the accumulated dose behind a thin vehicle skin at any time after the start of the mission. The technique of interpolation for intermediate points along the prescribed space trajectory is describedmore » in detail. The method of representation of the space radiation data as input for the calculation of the dose and time-integrated spectra is discussed. (auth)« less

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

Time dependent semiclassical tunneling through one dimensional barriers using only real valued trajectories

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

Herman, Michael F.

2015-10-28

The time independent semiclassical treatment of barrier tunneling has been understood for a very long time. Several semiclassical approaches to time dependent tunneling through barriers have also been presented. These typically involve trajectories for which the position variable is a complex function of time. In this paper, a method is presented that uses only real valued trajectories, thus avoiding the complications that can arise when complex trajectories are employed. This is accomplished by expressing the time dependent wave packet as an integration over momentum. The action function in the exponent in this expression is expanded to second order in themore » momentum. The expansion is around the momentum, p{sub 0{sup *}}, at which the derivative of the real part of the action is zero. The resulting Gaussian integral is then taken. The stationary phase approximation requires that the derivative of the full action is zero at the expansion point, and this leads to a complex initial momentum and complex tunneling trajectories. The “pseudo-stationary phase” approximation employed in this work results in real values for the initial momentum and real valued trajectories. The transmission probabilities obtained are found to be in good agreement with exact quantum results.« less

Lagrangian particle method for compressible fluid dynamics

NASA Astrophysics Data System (ADS)

Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang

2018-06-01

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

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.

Effective Lagrangians and Current Algebra in Three Dimensions

NASA Astrophysics Data System (ADS)

Ferretti, Gabriele

In this thesis we study three dimensional field theories that arise as effective Lagrangians of quantum chromodynamics in Minkowski space with signature (2,1) (QCD3). In the first chapter, we explain the method of effective Langrangians and the relevance of current algebra techniques to field theory. We also provide the physical motivations for the study of QCD3 as a toy model for confinement and as a theory of quantum antiferromagnets (QAF). In chapter two, we derive the relevant effective Lagrangian by studying the low energy behavior of QCD3, paying particular attention to how the global symmetries are realized at the quantum level. In chapter three, we show how baryons arise as topological solitons of the effective Lagrangian and also show that their statistics depends on the number of colors as predicted by the quark model. We calculate mass splitting and magnetic moments of the soliton and find logarithmic corrections to the naive quark model predictions. In chapter four, we drive the current algebra of the theory. We find that the current algebra is a co -homologically non-trivial generalization of Kac-Moody algebras to three dimensions. This fact may provide a new, non -perturbative way to quantize the theory. In chapter five, we discuss the renormalizability of the model in the large-N expansion. We prove the validity of the non-renormalization theorem and compute the critical exponents in a specific limiting case, the CP^ {N-1} model with a Chern-Simons term. Finally, chapter six contains some brief concluding remarks.

Simulated trajectories error analysis program, version 2. Volume 2: Programmer's manual

NASA Technical Reports Server (NTRS)

Vogt, E. D.; Adams, G. L.; Working, M. M.; Ferguson, J. B.; Bynum, M. R.

1971-01-01

A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.

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.

Optimal design of a lagrangian observing system for hydrodynamic surveys in coastal areas

NASA Astrophysics Data System (ADS)

Cucco, Andrea; Quattrocchi, Giovanni; Antognarelli, Fabio; Satta, Andrea; Maicu, Francesco; Ferrarin, Christian; Umgiesser, Georg

2014-05-01

The optimization of ocean observing systems is a pressing need for scientific research. In particular, the improvement of ocean short-term observing networks is achievable by reducing the cost-benefit ratio of the field campaigns and by increasing the quality of measurements. Numerical modeling is a powerful tool for determining the appropriateness of a specific observing system and for optimizing the sampling design. This is particularly true when observations are carried out in coastal areas and lagoons where, the use satellites is prohibitive due to the water shallowness. For such areas, numerical models are the most efficient tool both to provide a preliminary assess of the local physical environment and to make short -term predictions above its change. In this context, a test case experiment was carried out within an enclosed shallow water areas, the Cabras Lagoon (Sardinia, Italy). The aim of the experiment was to explore the optimal design for a field survey based on the use of coastal lagrangian buoys. A three-dimensional hydrodynamic model based on the finite element method (SHYFEM3D, Umgiesser et al., 2004) was implemented to simulate the lagoon water circulation. The model domain extent to the whole Cabras lagoon and to the whole Oristano Gulf, including the surrounding coastal area. Lateral open boundary conditions were provided by the operational ocean model system WMED and only wind forcing, provided by SKIRON atmospheric model (Kallos et al., 1997), was considered as surface boundary conditions. The model was applied to provide a number of ad hoc scenarios and to explore the efficiency of the short-term hydrodynamic survey. A first field campaign was carried out to investigate the lagrangian circulation inside the lagoon under the main wind forcing condition (Mistral wind from North-West). The trajectories followed by the lagrangian buoys and the estimated lagrangian velocities were used to calibrate the model parameters and to validate the

Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

USGS Publications Warehouse

Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil

1984-01-01

The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

The general form of the coupled Horndeski Lagrangian that allows cosmological scaling solutions

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

Gomes, Adalto R.; Amendola, Luca, E-mail: argomes.ufma@gmail.com, E-mail: l.amendola@thphys.uni-heidelberg.de

We consider the general scalar field Horndeski Lagrangian coupled to dark matter. Within this class of models, we present two results that are independent of the particular form of the model. First, we show that in a Friedmann-Robertson-Walker metric the Horndeski Lagrangian coincides with the pressure of the scalar field. Second, we employ the previous result to identify the most general form of the Lagrangian that allows for cosmological scaling solutions, i.e. solutions where the ratio of dark matter to field density and the equation of state remain constant. Scaling solutions of this kind may help solving the coincidence problemmore » since in this case the presently observed ratio of matter to dark energy does not depend on initial conditions, but rather on the theoretical parameters.« less

Stanley Corrsin Award Lecture: Lagrangian Measurements in Turbulence: From Fundamentals to Applications

NASA Astrophysics Data System (ADS)

Bodenschatz, Eberhard

2014-11-01

In my talk I shall present results from particle tracking experiments in turbulence. After a short review of the history of the field, I shall summarize the most recent technological advances that range form low and high-density particle tracking to direct measurements of the Lagrangian evolution of vorticity. I shall embark on a journey that describes the discoveries made possible by this new technology in the last 15 years. I present results that challenge our understanding of turbulence and show how Lagrangian particle tracking can help us ask questions on turbulent flows that so far were hidden. I shall show how Lagrangian particle tracking may provide important insights into the reversibility of turbulent flows, on vorticity generation, the energy cascade and turbulent mixing. I shall describe the consequences of inertial particle transport on rain formation and end with an outlook on how Lagrangian particle tracking experiments on non-stationary flows in real-world situations may provide high quality data that can support real world engineering problems. I am very thankful for the support by Cornell University, the National Science Foundation, the Research Corporation, the Alfred P. Sloan Foundation, the Kavli Institute for Theoretical Physics, the German Research Foundation, the European Union and the Max Planck Society. I very gratefully acknowledge the excellent partnership with many colleagues in the field of fluid mechanics and turbulence.

Cloud System Evolution in the Trades (CSET): Airborne sampling of Lagrangian airmass evolution in the Northeast Pacific stratocumulus-cumulus transition

NASA Astrophysics Data System (ADS)

Bretherton, Christopher; Wood, Robert; Albrecht, Bruce; Zuidema, Paquita; Ghate, Virendra; Mohrmann, Johannes; Oh, Kuan-Ting; Blossey, Peter

2017-04-01

The CSET field study in July-August 2015 over the Northeast Pacific ocean was motivated by a need for more in-situ sampling of the subtropical stratocumulus to cumulus (Sc-Cu) transition zones. One goal was comprehensive documentation of observational cases suitable for detailed intercomparison with large-eddy simulation models run following Lagrangian air columns and global models run in a hindcast mode. A second goal was to understand the role of aerosol and precipitation processes in this transition. The U.S. National Science Foundation G-V, equipped with cloud, aerosol, turbulence probes, a multispectral lidar, a cloud radar, and dropsondes, flew seven missions consisting of an outbound leg from northern California to Hawaii and a return leg two days later. Each mission was based on forecast air trajectories within the boundary layer; the goal was to sample a 2000-km long vertical curtain of boundary-layer air on the outbound leg and resample the advected position of that curtain on the return leg, using ramped sawtooths. In this way, most missions successfully captured the Lagrangian Sc-Cu transition. While CSET sampled diverse aerosol conditions, including the interaction of the boundary layer with smoke plumes from massive forest fires, lower tropospheric stability was the primary control on cloud cover. Mesoscale cloud organization was ubiquitous. Toward Hawaii, clusters of 2 km deep precipitating shallow cumulus and patchy thin stratiform 'veil cloud' with extremely low droplet concentrations were embedded in ultraclean layers at the trade inversion. These were separated by drier regions of suppressed convection. LES and parcel modeling plausibly explain these features.

Mid-Term Probabilistic Forecast of Oil Spill Trajectories

NASA Astrophysics Data System (ADS)

Castanedo, S.; Abascal, A. J.; Cardenas, M.; Medina, R.; Guanche, Y.; Mendez, F. J.; Camus, P.

2012-12-01

There is increasing concern about the threat posed by oil spills to the coastal environment. This is reflected in the promulgation of various national and international standards among which are those that require companies whose activities involves oil spill risk, to have oil pollution emergency plans or similar arrangements for responding promptly and effectively to oil pollution incidents. Operational oceanography systems (OOS) that provide decision makers with oil spill trajectory forecasting, have demonstrated their usefulness in recent accidents (Castanedo et al., 2006). In recent years, many national and regional OOS have been setup focusing on short-term oil spill forecast (up to 5 days). However, recent accidental marine oil spills (Prestige in Spain, Deep Horizon in Gulf of Mexico) have revealed the importance of having larger prediction horizons (up to 15 days) in regional-scale areas. In this work, we have developed a methodology to provide probabilistic oil spill forecast based on numerical modelling and statistical methods. The main components of this approach are: (1) Use of high resolution long-term (1948-2009) historical hourly data bases of wind, wind-induced currents and astronomical tide currents obtained using state-of-the-art numerical models; (2) classification of representative wind field patterns (n=100) using clustering techniques based on PCA and K-means algorithms (Camus et al., 2011); (3) determination of the cluster occurrence probability and the stochastic matrix (matrix of transition of probability or Markov matrix), p_ij, (probability of moving from a cluster "i" to a cluster "j" in one time step); (4) Initial state for mid-term simulations is obtained from available wind forecast using nearest-neighbors analog method; (5) 15-days Stochastic Markov Chain simulations (m=1000) are launched; (6) Corresponding oil spill trajectories are carried out by TESEO Lagrangian transport model (Abascal et al., 2009); (7) probability maps are

Second order upwind Lagrangian particle method for Euler equations

DOE PAGES

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

2016-06-01

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Second order upwind Lagrangian particle method for Euler equations

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

Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin

A new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Rossby wave breaking and Lagrangian structures inside the Antarctic stratospheric polar vortex during Vorcore and Concordiasi campaigns

NASA Astrophysics Data System (ADS)

de la Camara, Alvaro; Mechoso, Carlos R.; Mancho, Ana M.; Serrano, Encarna; Ide, Kayo

2013-04-01

The trajectories in the lower stratosphere of isopycnic balloons released from Antarctica by international field campaigns during the southern springs of 2005 and 2010 showed events of latitudinal transport inside the stratospheric polar vortex, both away and towards the poleward flank of the polar night jet. The present work applies trajectory-based diagnostic techniques to examine mechanisms at work during such events. Reverse domain filling calculations of potential vorticity (PV) fields from ECMWF ERA-Interim data set during the events show irreversible filamentation of the PV fields in the inner side of the polar night jet, which is a signature of planetary (Rossby) wave breaking. Balloons motions during the events are fairly consistent with the PV filaments. Events of both large (~15° of arch length) and small (~5° of arch length) balloon displacements from the vortex edge are associated to deep and shallow penetration into the core of the elongated PV contours. The function M is applied to study the configuration of Lagrangian coherent structures during the events. A close association is found between hyperbolic points and breaking waves inside the vortex. The geometric configuration of the invariant manifolds associated with the hyperbolic points helps to understand the apparent chaotic behavior of balloons motions, and to identify and analyze balloon transport events not captured by the Reverse Domain Filling calculations. The Antarctic polar vortex edge is an effective barrier to air parcel crossings. Rossby wave breaking inside the vortex, however, can contribute to tracer mixing inside the vortex and to occasional air crossings of the edge.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Lagrangian Particle Tracking in a Discontinuous Galerkin Method for Hypersonic Reentry Flows in Dusty Environments

NASA Astrophysics Data System (ADS)

Ching, Eric; Lv, Yu; Ihme, Matthias

2017-11-01

Recent interest in human-scale missions to Mars has sparked active research into high-fidelity simulations of reentry flows. A key feature of the Mars atmosphere is the high levels of suspended dust particles, which can not only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, increasing surface heat fluxes. Second-order finite-volume schemes are typically employed for hypersonic flow simulations, but such schemes suffer from a number of limitations. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other advantages. As such, a Lagrangian particle method is developed in a discontinuous Galerkin framework to enable the computation of particle-laden hypersonic flows. Two-way coupling between the carrier and disperse phases is considered, and an efficient particle search algorithm compatible with unstructured curved meshes is proposed. In addition, variable thermodynamic properties are considered to accommodate high-temperature gases. The performance of the particle method is demonstrated in several test cases, with focus on the accurate prediction of particle trajectories and heating augmentation. Financial support from a Stanford Graduate Fellowship and the NASA Early Career Faculty program are gratefully acknowledged.

Independent-Trajectory Thermodynamic Integration: a practical guide to protein-drug binding free energy calculations using distributed computing.

PubMed

Lawrenz, Morgan; Baron, Riccardo; Wang, Yi; McCammon, J Andrew

2012-01-01

The Independent-Trajectory Thermodynamic Integration (IT-TI) approach for free energy calculation with distributed computing is described. IT-TI utilizes diverse conformational sampling obtained from multiple, independent simulations to obtain more reliable free energy estimates compared to single TI predictions. The latter may significantly under- or over-estimate the binding free energy due to finite sampling. We exemplify the advantages of the IT-TI approach using two distinct cases of protein-ligand binding. In both cases, IT-TI yields distributions of absolute binding free energy estimates that are remarkably centered on the target experimental values. Alternative protocols for the practical and general application of IT-TI calculations are investigated. We highlight a protocol that maximizes predictive power and computational efficiency.

The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen Plateau

NASA Astrophysics Data System (ADS)

d'Ovidio, F.; Della Penna, A.; Trull, T. W.; Nencioli, F.; Pujol, M.-I.; Rio, M.-H.; Park, Y.-H.; Cotté, C.; Zhou, M.; Blain, S.

2015-10-01

Field campaigns are instrumental in providing ground truth for understanding and modeling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region hundreds of kilometers wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in situ measures are used to infer larger-scale budgets, one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back trajectories for the ship-sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using a model based on first-order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation-based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellites with the patterns of more than one hundred drifters, including some adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in situ biogeochemical surveys.

The biogeochemical structuring role of horizontal stirring: Lagrangian perspectives on iron delivery downstream of the Kerguelen plateau

NASA Astrophysics Data System (ADS)

d'Ovidio, F.; Della Penna, A.; Trull, T. W.; Nencioli, F.; Pujol, I.; Rio, M. H.; Park, Y.-H.; Cotté, C.; Zhou, M.; Blain, S.

2015-01-01

Field campaigns are instrumental in providing ground truth for understanding and modelling global ocean biogeochemical budgets. A survey however can only inspect a fraction of the global oceans, typically a region 100s km wide for a temporal window of the order of (at most) several weeks. This spatiotemporal domain is also the one in which the mesoscale activity induces through horizontal stirring a strong variability in the biogeochemical tracers, with ephemeral, local contrasts which can easily mask the regional and seasonal gradients. Therefore, whenever local in-situ measures are used to infer larger scale budgets one faces the challenge of identifying the mesoscale structuring effect, if not simply to filter it out. In the case of the KEOPS2 investigation of biogeochemical responses to natural iron fertilization, this problem was tackled by designing an adaptive sampling strategy based on regionally-optimized multisatellite products analyzed in real time by specifically designed Lagrangian diagnostics. This strategy identified the different mesoscale and stirring structures present in the region and tracked the dynamical frontiers among them. It also enabled back-trajectories for the ship sampled stations to be estimated, providing important insights into the timing and pathways of iron supply, which were explored further using model based on first order iron removal. This context was essential for the interpretation of the field results. The mesoscale circulation based strategy was also validated post-cruise by comparing the Lagrangian maps derived from satellite with the patterns of more than one hundred drifters adaptively released during KEOPS2 and a subsequent research voyage. The KEOPS2 strategy was adapted to the specific biogeochemical characteristics of the region, but its principles are general and will be useful for future in-situ biogeochemical surveys.

A new Lagrangian method for three-dimensional steady supersonic flows

NASA Technical Reports Server (NTRS)

Loh, Ching-Yuen; Liou, Meng-Sing

1993-01-01

In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.

Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity

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

Shabad, Anatoly E.; Usov, Vladimir V.

2011-05-15

In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum c=1, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we establish the positive convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants that are derivatives of the effective Lagrangian with respect to the field invariants. Violation of the general principles by the one-loop approximation in QED atmore » exponentially large magnetic field is analyzed, resulting in complex energy ghosts that signal the instability of the magnetized vacuum. Superluminal excitations (tachyons) appear, too, but for the magnetic field exceeding its instability threshold. Also other popular Lagrangians are tested to establish that the ones leading to spontaneous vacuum magnetization possess wrong convexity.« less

Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.

PubMed

Li, Xiaosheng; He, Xiaowei; Liu, Xuehui; Zhang, Jian J; Liu, Baoquan; Wu, Enhua

2016-08-01

We propose a semi-Lagrangian method for multiphase interface tracking. In contrast to previous methods, our method maintains an explicit polygonal mesh, which is reconstructed from an unsigned distance function and an indicator function, to track the interface of arbitrary number of phases. The surface mesh is reconstructed at each step using an efficient multiphase polygonization procedure with precomputed stencils while the distance and indicator function are updated with an accurate semi-Lagrangian path tracing from the meshes of the last step. Furthermore, we provide an adaptive data structure, multiphase distance tree, to accelerate the updating of both the distance function and the indicator function. In addition, the adaptive structure also enables us to contour the distance tree accurately with simple bisection techniques. The major advantage of our method is that it can easily handle topological changes without ambiguities and preserve both the sharp features and the volume well. We will evaluate its efficiency, accuracy and robustness in the results part with several examples.

Unambiguous formalism for higher order Lagrangian field theories

NASA Astrophysics Data System (ADS)

Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris

2009-11-01

The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.

Delivering Sound Energy along an Arbitrary Convex Trajectory

PubMed Central

Zhao, Sipei; Hu, Yuxiang; Lu, Jing; Qiu, Xiaojun; Cheng, Jianchun; Burnett, Ian

2014-01-01

Accelerating beams have attracted considerable research interest due to their peculiar properties and various applications. Although there have been numerous research on the generation and application of accelerating light beams, few results have been published on the generation of accelerating acoustic beams. Here we report on the experimental observation of accelerating acoustic beams along arbitrary convex trajectories. The desired trajectory is projected to the spatial phase profile on the boundary which is discretized and sampled spatially. The sound field distribution is formulated with the Green function and the integral equation method. Both the paraxial and the non-paraxial regimes are examined and observed in the experiments. The effect of obstacle scattering in the sound field is also investigated and the results demonstrate that the approach is robust against obstacle scattering. The realization of accelerating acoustic beams will have an impact on various applications where acoustic information and energy are required to be delivered along an arbitrary convex trajectory. PMID:25316353

Imaginary geometric phases of quantum trajectories in high-order terahertz sideband generation

NASA Astrophysics Data System (ADS)

Yang, Fan; Liu, Ren-Bao

2014-03-01

Quantum evolution of particles under strong fields can be described by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integral. The quantum trajectories are the key concept to understand the high-order terahertz siedeband generation (HSG) in semiconductors. Due to the nontrivial ``vacuum'' states of band materials, the quantum trajectories of optically excited electron-hole pairs in semiconductors can accumulate geometric phases under the driving of an elliptically polarized THz field. We find that the geometric phase of the stationary trajectory is generally complex with both real and imaginary parts. In monolayer MoS2, the imaginary parts of the geometric phase leads to a changing of the polarization ellipticity of the sideband. We further show that the imaginary part originates from the quantum interference of many trajectories with different phases. Thus the observation of the polarization ellipticity of the sideband shall be a good indication of the quantum nature of the stationary trajectory. This work is supported by Hong Kong RGC/GRF 401512 and the CUHK Focused Investments Scheme.

Identification of PM10 air pollution origins at a rural background site

NASA Astrophysics Data System (ADS)

Reizer, Magdalena; Orza, José A. G.

2018-01-01

Trajectory cluster analysis and concentration weighted trajectory (CWT) approach have been applied to investigate the origins of PM10 air pollution recorded at a rural background site in North-eastern Poland (Diabla Góra). Air mass back-trajectories used in this study have been computed with the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model for a 10-year period of 2006-2015. A cluster analysis grouped back-trajectories into 7 clusters. Most of the trajectories correspond to fast and moderately moving westerly and northerly flows (45% and 25% of the cases, respectively). However, significantly higher PM10 concentrations were observed for slow moving easterly (11%) and southerly (20%) air masses. The CWT analysis shows that high PM10 levels are observed at Diabla Góra site when air masses are originated and passed over the heavily industrialized areas in Central-Eastern Europe located to the south and south-east of the site.

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.

OPTIMAL AIRCRAFT TRAJECTORIES FOR SPECIFIED RANGE

NASA Technical Reports Server (NTRS)

Lee, H.

1994-01-01

For an aircraft operating over a fixed range, the operating costs are basically a sum of fuel cost and time cost. While minimum fuel and minimum time trajectories are relatively easy to calculate, the determination of a minimum cost trajectory can be a complex undertaking. This computer program was developed to optimize trajectories with respect to a cost function based on a weighted sum of fuel cost and time cost. As a research tool, the program could be used to study various characteristics of optimum trajectories and their comparison to standard trajectories. It might also be used to generate a model for the development of an airborne trajectory optimization system. The program could be incorporated into an airline flight planning system, with optimum flight plans determined at takeoff time for the prevailing flight conditions. The use of trajectory optimization could significantly reduce the cost for a given aircraft mission. The algorithm incorporated in the program assumes that a trajectory consists of climb, cruise, and descent segments. The optimization of each segment is not done independently, as in classical procedures, but is performed in a manner which accounts for interaction between the segments. This is accomplished by the application of optimal control theory. The climb and descent profiles are generated by integrating a set of kinematic and dynamic equations, where the total energy of the aircraft is the independent variable. At each energy level of the climb and descent profiles, the air speed and power setting necessary for an optimal trajectory are determined. The variational Hamiltonian of the problem consists of the rate of change of cost with respect to total energy and a term dependent on the adjoint variable, which is identical to the optimum cruise cost at a specified altitude. This variable uniquely specifies the optimal cruise energy, cruise altitude, cruise Mach number, and, indirectly, the climb and descent profiles. If the optimum

Trajectory Browser: An Online Tool for Interplanetary Trajectory Analysis and Visualization

NASA Technical Reports Server (NTRS)

Foster, Cyrus James

2013-01-01

The trajectory browser is a web-based tool developed at the NASA Ames Research Center for finding preliminary trajectories to planetary bodies and for providing relevant launch date, time-of-flight and (Delta)V requirements. The site hosts a database of transfer trajectories from Earth to planets and small-bodies for various types of missions such as rendezvous, sample return or flybys. A search engine allows the user to find trajectories meeting desired constraints on the launch window, mission duration and (Delta)V capability, while a trajectory viewer tool allows the visualization of the heliocentric trajectory and the detailed mission itinerary. The anticipated user base of this tool consists primarily of scientists and engineers designing interplanetary missions in the context of pre-phase A studies, particularly for performing accessibility surveys to large populations of small-bodies.

Hamiltonian vs Lagrangian Embedding of a Massive Spin-One Theory Involving Two-Form Field

NASA Astrophysics Data System (ADS)

Harikumar, E.; Sivakumar, M.

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge noninvariant theory involving antisymmetric tensor field. We apply the BFV-BRST generalized canonical approach to convert the model to a first class system and construct nilpotent BFV-BRST charge and a unitarizing Hamiltonian. The canonical analysis of the Stückelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant Stückelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.

Integrative Convergence in Neuroscience: Trajectories, Problems, and the Need for a Progressive Neurobioethics

NASA Astrophysics Data System (ADS)

Giordano, J.

The advanced integrative scientific convergence (AISC) model represents a viable approach to neuroscience. Beyond simple multi-disciplinarity, the AISC model unifies constituent scientific and technological fields to foster innovation, invention and new ways of addressing seemingly intractable questions. In this way, AISC can yield novel methods and foster new trajectories of knowledge and discovery, and yield new epistemologies. As stand-alone disciplines, each and all of the constituent fields generate practical and ethical issues, and their convergence may establish a unique set of both potential benefits and problems. To effectively attend to these contingencies requires pragmatic assessment of the actual capabilities and limits of neurofocal AISC, and an openness to what new knowledge and scientific/technological achievements may be produced, and how such outcomes can affect humanity, the human condition, society and the global environment. It is proposed that a progressive neurobioethics may be needed to establish both a meta-ethical framework upon which to structure ethical decisions, and a system and method of ethics that is inclusive, convergent and innovative, and in thus aligned with and meaningful to use of an AISC model in neuroscience.