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.

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

PubMed

Tian, Siyu; Huang, Xiaoxia; Li, Hongga

2017-03-15

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

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.

Target Lagrangian kinematic simulation for particle-laden flows.

PubMed

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

2016-09-01

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

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.

Multi-stream portrait of the Cosmic web

NASA Astrophysics Data System (ADS)

Ramachandra, Nesar; Shandarin, Sergei

2016-03-01

We report the results of the first study of the multi-stream environment of dark matter haloes in cosmological N-body simulations in the ΛCDM cosmology. The full dynamical state of dark matter can be described as a three-dimensional sub-manifold in six-dimensional phase space - the dark matter sheet. In our study we use a Lagrangian sub-manifold x = x (q , t) (where x and q are co-moving Eulerian and Lagrangian coordinates respectively), which is dynamically equivalent to the dark matter sheet but is more convenient for numerical analysis. Our major results can be summarized as follows. At the resolution of the simulation, the cosmic web represents a hierarchical structure: each halo is embedded in the filamentary framework of the web predominantly at the filament crossings, and each filament is embedded in the wall like fabric of the web at the wall crossings. Locally, each halo or sub-halo is a peak in the number of streams field. The number of streams in the neighbouring filaments is higher than in the neighbouring walls. The walls are regions where number of streams is equal to three or a few. Voids are uniquely defined by the local condition requiring to be a single-stream flow region.

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2013-01-01

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

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.

A kinematic wave model in Lagrangian coordinates incorporating capacity drop: Application to homogeneous road stretches and discontinuities

NASA Astrophysics Data System (ADS)

Yuan, Kai; Knoop, Victor L.; Hoogendoorn, Serge P.

2017-01-01

On freeways, congestion always leads to capacity drop. This means the queue discharge rate is lower than the pre-queue capacity. Our recent research findings indicate that the queue discharge rate increases with the speed in congestion, that is the capacity drop is strongly correlated with the congestion state. Incorporating this varying capacity drop into a kinematic wave model is essential for assessing consequences of control strategies. However, to the best of authors' knowledge, no such a model exists. This paper fills the research gap by presenting a Lagrangian kinematic wave model. "Lagrangian" denotes that the new model is solved in Lagrangian coordinates. The new model can give capacity drops accompanying both of stop-and-go waves (on homogeneous freeway section) and standing queues (at nodes) in a network. The new model can be applied in a network operation. In this Lagrangian kinematic wave model, the queue discharge rate (or the capacity drop) is a function of vehicular speed in traffic jams. Four case studies on links as well as at lane-drop and on-ramp nodes show that the Lagrangian kinematic wave model can give capacity drops well, consistent with empirical observations.

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.

Forecasting Future Sea Ice Conditions: A Lagrangian Approach

DTIC Science & Technology

2015-09-30

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

A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Ruthotto, Lars

2017-01-01

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

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.

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.

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.

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)

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.

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

PubMed

Holm, Darryl D.

2002-06-01

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

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.

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

Global tectonic reconstructions with continuously deforming and evolving rigid plates

NASA Astrophysics Data System (ADS)

Gurnis, Michael; Yang, Ting; Cannon, John; Turner, Mark; Williams, Simon; Flament, Nicolas; Müller, R. Dietmar

2018-07-01

Traditional plate reconstruction methodologies do not allow for plate deformation to be considered. Here we present software to construct and visualize global tectonic reconstructions with deforming plates within the context of rigid plates. Both deforming and rigid plates are defined by continuously evolving polygons. The deforming regions are tessellated with triangular meshes such that either strain rate or cumulative strain can be followed. The finite strain history, crustal thickness and stretching factor of points within the deformation zones are tracked as Lagrangian points. Integrating these tools within the interactive platform GPlates enables specialized users to build and refine deforming plate models and integrate them with other models in time and space. We demonstrate the integrated platform with regional reconstructions of Cenozoic western North America, the Mesozoic South American Atlantic margin, and Cenozoic southeast Asia, embedded within global reconstructions, using different data and reconstruction strategies.

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.

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

Method of and apparatus for modeling interactions

DOEpatents

Budge, Kent G.

2004-01-13

A method and apparatus for modeling interactions can accurately model tribological and other properties and accommodate topological disruptions. Two portions of a problem space are represented, a first with a Lagrangian mesh and a second with an ALE mesh. The ALE and Lagrangian meshes are constructed so that each node on the surface of the Lagrangian mesh is in a known correspondence with adjacent nodes in the ALE mesh. The interaction can be predicted for a time interval. Material flow within the ALE mesh can accurately model complex interactions such as bifurcation. After prediction, nodes in the ALE mesh in correspondence with nodes on the surface of the Lagrangian mesh can be mapped so that they are once again adjacent to their corresponding Lagrangian mesh nodes. The ALE mesh can then be smoothed to reduce mesh distortion that might reduce the accuracy or efficiency of subsequent prediction steps. The process, from prediction through mapping and smoothing, can be repeated until a terminal condition is reached.

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

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.

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 realistically reproduced which is an important step towards a more reliable projection of future changes, especially of stratospheric ozone.

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 better than the Kalman-based algorithm in strong shear flows. An important component of our research is the optimal predictor location problem; Where should floats be launched in order to minimize the Lagrangian prediction error? Preliminary Lagrangian sampling results for different flow scenarios will be presented.

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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...

A Skill Score of Trajectory Model Evaluation Using Reinitialized Series of Normalized Cumulative Lagrangian Separation

NASA Astrophysics Data System (ADS)

Liu, Y.; Weisberg, R. H.

2017-12-01

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 a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative Lagrangian separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the Lagrangian separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. 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.

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.

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

NASA Astrophysics Data System (ADS)

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

2004-11-01

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

Comparison between collective coordinate models for domain wall motion in PMA nanostrips in the presence of the Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Vandermeulen, J.; Nasseri, S. A.; Van de Wiele, B.; Durin, G.; Van Waeyenberge, B.; Dupré, L.

2018-03-01

Lagrangian-based collective coordinate models for magnetic domain wall (DW) motion rely on an ansatz for the DW profile and a Lagrangian approach to describe the DW motion in terms of a set of time-dependent collective coordinates: the DW position, the DW magnetization angle, the DW width and the DW tilting angle. Another approach was recently used to derive similar equations of motion by averaging the Landau-Lifshitz-Gilbert equation without any ansatz, and identifying the relevant collective coordinates afterwards. In this paper, we use an updated version of the semi-analytical equations to compare the Lagrangian-based collective coordinate models with micromagnetic simulations for field- and STT-driven (spin-transfer torque-driven) DW motion in Pt/CoFe/MgO and Pt/Co/AlOx nanostrips. Through this comparison, we assess the accuracy of the different models, and provide insight into the deviations of the models from simulations. It is found that the lack of terms related to DW asymmetry in the Lagrangian-based collective coordinate models significantly contributes to the discrepancy between the predictions of the most accurate Lagrangian-based model and the micromagnetic simulations in the field-driven case. This is in contrast to the STT-driven case where the DW remains symmetric.

Molecular properties via a subsystem density functional theory formulation: a common framework for electronic embedding.

PubMed

Höfener, Sebastian; Gomes, André Severo Pereira; Visscher, Lucas

2012-01-28

In this article, we present a consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT (WFT-in-DFT) and the DFT-based subsystem formulation of response theory (DFT-in-DFT) by Neugebauer [J. Neugebauer, J. Chem. Phys. 131, 084104 (2009)] as special cases. This formulation, which is based on the time-averaged quasi-energy formalism, makes use of the variation Lagrangian techniques to allow the use of non-variational (in particular: coupled cluster) wave-function-based methods. We show how, in the time-independent limit, we naturally obtain expressions for the ground-state DFT-in-DFT and WFT-in-DFT embedding via a local potential. We furthermore provide working equations for the special case in which coupled cluster theory is used to obtain the density and excitation energies of the active subsystem. A sample application is given to demonstrate the method. © 2012 American Institute of Physics

An Eulerian-Lagrangian description for fluvial coarse sediment transport: theory and verification with low-cost inertial sensors.

NASA Astrophysics Data System (ADS)

Maniatis, Georgios

2017-04-01

Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (Eulerian or Lagrangian) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general Eulerian-Lagrangian (E-L) model. This approach accounts for inertial characteristics of particles in a Lagrangian (particle fixed) frame, and for the hydrodynamics in an independent Eulerian frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D=75 mm (C) was released to roll freely in a (> threshold for entrainment) flow and over surfaces of different roughness. Finally, the coarser spherical and elliptical sensor- assemblies (A and B) were deployed in a steep mountain stream during active sediment transport flow conditions. The results include the calculation of the inertial acceleration, the instantaneous particle velocity and the total kinetic energy of the mobile particle (including the rotational component using gyroscope measurements). The comparison of the field deployments with the laboratory experiments suggests that E-L model can be generalised from laboratory to natural conditions. Overall, the inertia of individual coarse particles is a statistically significant effect for all the modes of sediment transport (entrainment, translation, deposition) in both natural and laboratory regimes. Maniatis et. al 2015: "Calculating the Explicit Probability of Entrainment Based on Inertial Acceleration Measurements", J. Hydraulic Engineering, 04016097

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

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)

Eulerian and Lagrangian Parameterization of the Oceanic Mixed Layer using Large Eddy Simulation and MPAS-Ocean

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

Van Roekel, Luke

We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that Eulerian-Lagrangian effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and Lagrangian particles will be utilized to better represent the movement of water into and out of the mixed layer.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

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.

Development of CO2 inversion system based on the adjoint of the global coupled transport model

NASA Astrophysics Data System (ADS)

Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon

2014-05-01

We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) Eulerian transport model (TM) and the Lagrangian plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the Lagrangian model FLEXPART. The Lagrangian component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the Lagrangian part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to Eulerian part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No code modification of Lagrangian model is required, making it applicable to combination of global NIES TM and any Lagrangian model; 2. Once run, the Lagrangian output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over limited regions close to the monitoring sites (using the LPDM part), and at coarse resolution for the rest of the globe (using the Eulerian part), minimizing aggregation errors and computation cost. The adjoint of the coupled high-resolution Eulerian-Lagrangian model will be incorporated into the PYVAR CO2 variational inverse system (Chevallier et al., 2005). Chevallier, F., Fisher, M., Peylin, P., Serrar, S., Bousquet, P., Bréon, F.-M., Chédin, A., and Ciais, P.: Inferring CO2 sources and sinks from satellite observations: method and application to TOVS data, J. Geophys. Res., 110, D24309, doi:10.1029/2005JD006390, 2005.

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.

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 into a variational inversion system designed to optimize surface fluxes of greenhouse gases.

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia

2018-05-01

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We constrained the parameters of the qDHOST model by requiring the validity of the Vainshtein screening mechanism inside the cosmic structures and the consistency with the recently established bounds on gravitational wave speed from GW170817/GRB170817A event. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

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.

NATIONAL AND REGIONAL AIR AND DEPOSITION MODELING OF STATIONARY AND MOBILE SOURCE EMISSIONS OF DIOXINS USING THE RELMAP MODELING SYSTEM

EPA Science Inventory

The purpose of this study is to estimate the atmospheric transport, fate and deposition flux of air releases of CDDs and CDFs from known sources within the continental United States using the Regional Lagrangian Model of Air Pollution (RELMAP). RELMAP is a Lagrangian air model th...

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.

APPLICATION OF BAYESIAN MONTE CARLO ANALYSIS TO A LAGRANGIAN PHOTOCHEMICAL AIR QUALITY MODEL. (R824792)

EPA Science Inventory

Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...

Modeling Sediment Transport Using a Lagrangian Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity

NASA Astrophysics Data System (ADS)

Garcia, M. H.

2016-12-01

Modeling Sediment Transport Using a Lagrangian Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity Som Dutta1, Paul Fischer2, Marcelo H. Garcia11Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 2Department of Computer Science and Department of MechSE, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 Since the seminal work of Niño and Garcia [1994], one-way coupled Lagrangian particle tracking has been used extensively for modeling sediment transport. Over time, the Lagrangian particle tracking method has been coupled with Eulerian flow simulations, ranging from Reynolds Averaged Navier-Stokes (RANS) based models to Detached Eddy Simulations (DES) [Escauriaza and Sotiropoulos, 2011]. Advent of high performance computing (HPC) platforms and faster algorithms have resulted in the work of Dutta et al. [2016], where Lagrangian particle tracking was coupled with high-resolution Large Eddy Simulations (LES) to model the complex and highly non-linear phenomenon of Bulle-Effect at diversions. Despite all the advancements in using Lagrangian particle tracking, there has not been a study that looks in detail at the limits of the model in the context of sediment transport, and also analyzes the sensitivity of the various force formulation in the force balance equation of the particles. Niño and Garcia [1994] did a similar analysis, but the vertical flow velocity distribution was modeled as the log-law. The current study extends the analysis by modeling the flow using high-resolution LES at a Reynolds number comparable to experiments of Niño et al. [1994]. Dutta et al., (2016), Large Eddy Simulation (LES) of flow and bedload transport at an idealized 90-degree diversion: insight into Bulle-Effect, River Flow 2016 - Constantinescu, Garcia & Hanes (Eds), Taylor & Francis Group, London, 101-109. Escauriaza and Sotiropoulos, (2011), Lagrangian model of bed-load transport in turbulent junction flows, Journal of Fluid Mechanics, 666,36-76. Niño and García, (1994), Gravel saltation: 2. Modeling, Water Resources Research, 30(6),1915-1924. Niño et al., (1994), Gravel saltation: 1. Experiments, Water Resources Research, 30(6), 1907-1914.

Annual Research Briefs, 1987

NASA Technical Reports Server (NTRS)

Moin, Parviz; Reynolds, William C.

1988-01-01

Lagrangian techniques have found widespread application to the prediction and understanding of turbulent transport phenomena and have yielded satisfactory results for different cases of shear flow problems. However, it must be kept in mind that in most experiments what is really available are Eulerian statistics, and it is far from obvious how to extract from them the information relevant to the Lagrangian behavior of the flow; in consequence, Lagrangian models still include some hypothesis for which no adequate supporting evidence was until now available. Direct numerical simulation of turbulence offers a new way to obtain Lagrangian statistics and so verify the validity of the current predictive models and the accuracy of their results. After the pioneering work of Riley (Riley and Patterson, 1974) in the 70's, some such results have just appeared in the literature (Lee et al, Yeung and Pope). The present contribution follows in part similar lines, but focuses on two particle statistics and comparison with existing models.

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.

A Nonlinear Multigrid Solver for an Atmospheric General Circulation Model Based on Semi-Implicit Semi-Lagrangian Advection of Potential Vorticity

NASA Technical Reports Server (NTRS)

McCormick, S.; Ruge, John W.

1998-01-01

This work represents a part of a project to develop an atmospheric general circulation model based on the semi-Lagrangian advection of potential vorticity (PC) with divergence as the companion prognostic variable.

Development and evaluation of GRAL-C dispersion model, a hybrid Eulerian-Lagrangian approach capturing NO-NO 2-O 3 chemistry

NASA Astrophysics Data System (ADS)

Oettl, Dietmar; Uhrner, Ulrich

2011-02-01

Based on two recent publications using Lagrangian dispersion models to simulate NO-NO 2-O 3 chemistry for industrial plumes, a similar modified approach was implemented using GRAL-C ( Graz Lagrangian Model with Chemistry) and tested on two urban applications. In the hybrid dispersion model GRAL-C, the transport and turbulent diffusion of primary species such as NO and NO 2 are treated in a Lagrangian framework while those of O 3 are treated in an Eulerian framework. GRAL-C was employed on a one year street canyon simulation in Berlin and on a four-day simulation during a winter season in Graz, the second biggest city in Austria. In contrast to Middleton D.R., Jones A.R., Redington A.L., Thomson D.J., Sokhi R.S., Luhana L., Fisher B.E.A. (2008. Lagrangian modelling of plume chemistry for secondary pollutants in large industrial plumes. Atmospheric Environment 42, 415-427) and Alessandrini S., Ferrero E. (2008. A Lagrangian model with chemical reactions: application in real atmosphere. Proceedings of the 12th Int. Conf. on Harmonization within atmospheric dispersion modelling for regulatory purposes. Croatian Meteorological Journal, 43, ISSN: 1330-0083, 235-239) the treatment of ozone was modified in order to facilitate urban scale simulations encompassing dense road networks. For the street canyon application, modelled daily mean NO x/NO 2 concentrations deviated by +0.4%/-15% from observations, while the correlations for NO x and NO 2 were 0.67 and 0.76 respectively. NO 2 concentrations were underestimated in summer, but were captured well for other seasons. In Graz a fair agreement for NO x and NO 2 was obtained between observed and modelled values for NO x and NO 2. Simulated diurnal cycles of NO 2 and O 3 matched observations reasonably well, although O 3 was underestimated during the day. A possible explanation here might lie in the non-consideration of volatile organic compounds (VOCs) chemistry.

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.

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.;

MatchingTools: A Python library for symbolic effective field theory calculations

NASA Astrophysics Data System (ADS)

Criado, Juan C.

2018-06-01

MatchingTools is a Python library for doing symbolic calculations in effective field theory. It provides the tools to construct general models by defining their field content and their interaction Lagrangian. Once a model is given, the heavy particles can be integrated out at the tree level to obtain an effective Lagrangian in which only the light particles appear. After integration, some of the terms of the resulting Lagrangian might not be independent. MatchingTools contains functions for transforming these terms to rewrite them in terms of any chosen set of operators.

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

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

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

Lagrangian formulation of the 2(2S+1)-component model and its connection with the skew symmetric/tensor description

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

Dvoeglazov, V.V.

1993-12-01

In the framework of the 2(2S + 1)-component theory for massless particles, the dynamical invariants have been derived from the Lagrangian density which is considered to be a 4-vector. A la Majorana interpretation of the 6-component spinors, the field operators of S=1 particles, as the left- and right-circularly polarized radiation, leads the author to the conserved quantities which are analogous to ones obtained by Lipkin and Sudbery. The scalar Lagrangian of this model is shown to be equivalent to the Lagrangian of a free massless field, introduced by Hayashi. As a consequence of a new {open_quotes}gauge{close_quotes} invariance this skew-symmetric fieldmore » describes physical particles with the longitudinal components only.« less

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...

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

NASA Astrophysics Data System (ADS)

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

2008-12-01

Time domain particle tracking is an emerging alternative to the conventional random walk particle tracking algorithm. With time domain particle tracking, particles are moved from node to node on one-dimensional pathways defined by streamlines of the groundwater flow field or by discrete subsurface features. The time to complete each deterministic segment is sampled from residence time distributions that include the effects of advection, longitudinal dispersion, a variety of kinetically controlled retention (sorption) processes, linear transformation, and temporal changes in groundwater velocities and sorption parameters. The simulation results in a set of arrival times at a monitoring location that can be post-processed with a kernel method to construct mass discharge (breakthrough) versus time. Implementation strategies differ for discrete flow (fractured media) systems and continuous porous media systems. The implementation strategy also depends on the scale at which hydraulic property heterogeneity is represented in the supporting flow model. For flow models that explicitly represent discrete features (e.g., discrete fracture networks), the sampling of residence times along segments is conceptually straightforward. For continuous porous media, such sampling needs to be related to the Lagrangian velocity field. Analytical or semi-analytical methods may be used to approximate the Lagrangian segment velocity distributions in aquifers with low-to-moderate variability, thereby capturing transport effects of subgrid velocity variability. If variability in hydraulic properties is large, however, Lagrangian velocity distributions are difficult to characterize and numerical simulations are required; in particular, numerical simulations are likely to be required for estimating the velocity integral scale as a basis for advective segment distributions. Aquifers with evolving heterogeneity scales present additional challenges. Large-scale simulations of radionuclide transport at two potential repository sites for high-level radioactive waste will be used to demonstrate the potential of the method. The simulations considered approximately 1000 source locations, multiple radionuclides with contrasting sorption properties, and abrupt changes in groundwater velocity associated with future glacial scenarios. Transport pathways linking the source locations to the accessible environment were extracted from discrete feature flow models that include detailed representations of the repository construction (tunnels, shafts, and emplacement boreholes) embedded in stochastically generated fracture networks. Acknowledgment The authors are grateful to SwRI Advisory Committee for Research, the Swedish Nuclear Fuel and Waste Management Company, and Posiva Oy for financial support.

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

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

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

NASA Astrophysics Data System (ADS)

Huhn, Florian; Haller, George

2014-05-01

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

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

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

SENSITIVITY ANALYSIS AND PRELIMINARY EVALUATION OF RELMAP (REGIONAL LAGRANGIAN MODEL OF AIR POLLUTION) INVOLVING FINE AND COURSE PARTICULATE MATTER

EPA Science Inventory

In response to the new, size-discriminate federal standards for Inhalable Particulate Matter, the Regional Lagrangian Model of Air Pollution (RELMAP) has been modified to include simple, linear parameterizations. As an initial step in the possible refinement, RELMAP has been subj...

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.

Solvability of the Initial Value Problem to the Isobe-Kakinuma Model for Water Waves

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe-Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t=0 is characteristic for the Isobe-Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

Lagrangian derivation of the two coupled field equations in the Janus cosmological model

NASA Astrophysics Data System (ADS)

Petit, Jean-Pierre; D'Agostini, G.

2015-05-01

After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.

Edgeworth streaming model for redshift space distortions

NASA Astrophysics Data System (ADS)

Uhlemann, Cora; Kopp, Michael; Haugg, Thomas

2015-09-01

We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N -body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc /h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc /h . To predict the scale-dependent functions entering the streaming model we employ convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarse-grained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse graining in Eulerian space features modified fluid dynamics different from dust while the coarse graining in Lagrangian space is performed in the initial conditions with subsequent single-streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N -body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.

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

Soltanian, Mohamad Reza; Sun, Alexander; Dai, Zhenxue

Yucca Mountain, Nevada, had been extensively investigated as a potential deep geologic repository for storing high-level nuclear wastes. Previous field investigations of stratified alluvial aquifer downstream of the site revealed that there is a hierarchy of sedimentary facies types. There is a corresponding log conductivity and reactive surface area subpopulations within each facies at each scale of sedimentary architecture. Here in this paper, we use a Lagrangian-based transport model in order to analyze radionuclide dispersion in the saturated alluvium of Fortymile Wash, Nevada. First, we validate the Lagrangian model using high-resolution flow and reactive transport simulations. Then, we used themore » validated model to investigate how each scale of sedimentary architecture may affect long-term radionuclide transport at Yucca Mountain. Results show that the reactive solute dispersion developed by the Lagrangian model matches the ensemble average of numerical simulations well. The link between the alluvium spatial variability and reactive solute dispersion at different spatiotemporal scales is demonstrated using the Lagrangian model. Finally, the longitudinal dispersivity of the reactive plume can be on the order of hundreds to thousands of meters, and it may not reach its asymptotic value even after 10,000 years of travel time and 2–3 km of travel distance.« less

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.

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.

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

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.

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.

Classical Lagrangians and Finsler structures for the nonminimal fermion sector of the standard model extension

NASA Astrophysics Data System (ADS)

Schreck, M.

2016-05-01

This article is devoted to finding classical point-particle equivalents for the fermion sector of the nonminimal standard model extension (SME). For a series of nonminimal operators, such Lagrangians are derived at first order in Lorentz violation using the algebraic concept of Gröbner bases. Subsequently, the Lagrangians serve as a basis for reanalyzing the results of certain kinematic tests of special relativity that were carried out in the past century. Thereby, a number of new constraints on coefficients of the nonminimal SME is obtained. In the last part of the paper we point out connections to Finsler geometry.

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.

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.

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.

Trispectrum from co-dimension 2(n) Galileons

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

Fasiello, Matteo, E-mail: mrf65@case.edu

2013-12-01

A generalized theory of multi-field Galileons has been recently put forward. This model stems from the ongoing effort to embed generic Galileon theories within brane constructions. Such an approach has proved very useful in connecting interesting and essential features of these theories with geometric properties of the branes embedding. We investigate the cosmological implications of a very restrictive multi-field Galileon theory whose leading interaction is solely quartic in the scalar field π and lends itself nicely to an interesting cosmology. The bispectrum is characterized by a naturally small amplitude (f{sub NL}∼<1) and an equilateral shape-function. The trispectrum of curvature fluctuationsmore » has features which are quite distinctive with respect to their P(X,φ) counterpart. We also show that, despite an absent cubic Lagrangian in the full theory, non-Gaussianities in this model cannot produce the combination of a small bispectrum alongside with a large trispectrum. We further expand on this point to draw a lesson on what having a symmetry in the full background independent theory entails at the level of fluctuations and vice-versa.« less

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

NASA Astrophysics Data System (ADS)

Gonzalez, M.

2018-04-01

The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

Recent progress in Lagrangian field theory and applications. Proceedings of the colloquium held at Marseille, France, June 24--28, 1974

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

Korthals-Altes, C.P.; de Rafael, E.; Stora, R.

1975-07-01

This Colloquium was devoted to recent developments in the study of Lagrangian models of quantum field theory: renormalized pertubation theories; supergauge fields; asymptotic freedom and infrared slavery in gauge field models involving quarks; gauge fields on lattices; and theory of critical exponents. Papers were abstracted separately for the database.

Constraints on non-Standard Model Higgs boson interactions in an effective Lagrangian using differential cross sections measured in the H→γγ decay channel at \\(\\sqrt{s} = 8\\) TeV with the ATLAS detector

DOE PAGES

Aad, G.

2015-12-02

The strength and tensor structure of the Higgs boson's interactions are investigated using an effective Lagrangian, which introduces additional CP-even and CP-odd interactions that lead to changes in the kinematic properties of the Higgs boson and associated jet spectra with respect to the Standard Model. We found that the parameters of the effective Lagrangian are probed using a fit to five differential cross sections previously measured by the ATLAS experiment in the H→γγ decay channel with an integrated luminosity of 20.3 fb -1 at \\(\\sqrt{s} = 8\\) TeV. In order to perform a simultaneous fit to the five distributions, themore » statistical correlations between them are determined by re-analysing the H→γγ candidate events in the proton–proton collision data. No significant deviations from the Standard Model predictions are observed and limits on the effective Lagrangian parameters are derived. These statistical correlations are made publicly available to allow for future analysis of theories with non-Standard Model interactions.« less

A novel approach to study effects of asymmetric stiffness on parametric instabilities of multi-rotor-system

NASA Astrophysics Data System (ADS)

Jain, Anuj Kumar; Rastogi, Vikas; Agrawal, Atul Kumar

2018-01-01

The main focus of this paper is to study effects of asymmetric stiffness on parametric instabilities of multi-rotor-system through extended Lagrangian formalism, where symmetries are broken in terms of the rotor stiffness. The complete insight of dynamic behaviour of multi-rotor-system with asymmetries is evaluated through extension of Lagrangian equation with a case study. In this work, a dynamic mathematical model of a multi-rotor-system through a novel approach of extension of Lagrangian mechanics is developed, where the system is having asymmetries due to varying stiffness. The amplitude and the natural frequency of the rotor are obtained analytically through the proposed methodology. The bond graph modeling technique is used for modeling the asymmetric rotor. Symbol-shakti® software is used for the simulation of the model. The effects of the stiffness of multi-rotor-system on amplitude and frequencies are studied using numerical simulation. Simulation results show a considerable agreement with the theoretical results obtained through extended Lagrangian formalism. It is further shown that amplitude of the rotor increases inversely the stiffness of the rotor up to a certain limit, which is also affirmed theoretically.

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

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

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

Constraints on non-Standard Model Higgs boson interactions in an effective Lagrangian using differential cross sections measured in the H→γγ decay channel at \\(\\sqrt{s} = 8\\) TeV with the ATLAS detector

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

Aad, G.

The strength and tensor structure of the Higgs boson's interactions are investigated using an effective Lagrangian, which introduces additional CP-even and CP-odd interactions that lead to changes in the kinematic properties of the Higgs boson and associated jet spectra with respect to the Standard Model. We found that the parameters of the effective Lagrangian are probed using a fit to five differential cross sections previously measured by the ATLAS experiment in the H→γγ decay channel with an integrated luminosity of 20.3 fb -1 at \\(\\sqrt{s} = 8\\) TeV. In order to perform a simultaneous fit to the five distributions, themore » statistical correlations between them are determined by re-analysing the H→γγ candidate events in the proton–proton collision data. No significant deviations from the Standard Model predictions are observed and limits on the effective Lagrangian parameters are derived. These statistical correlations are made publicly available to allow for future analysis of theories with non-Standard Model interactions.« less

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

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

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

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

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

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.

The exceptional sigma model

NASA Astrophysics Data System (ADS)

Arvanitakis, Alex S.; Blair, Chris D. A.

2018-04-01

We detail the construction of the exceptional sigma model, which describes a string propagating in the "extended spacetime" of exceptional field theory. This is to U-duality as the doubled sigma model is to T-duality. Symmetry specifies the Weylinvariant Lagrangian uniquely and we show how it reduces to the correct 10-dimensional string Lagrangians. We also consider the inclusion of a Fradkin-Tseytlin (or generalised dilaton) coupling as well as a reformulation with dynamical tension.

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

Arctic sea-ice diffusion from observed and simulated Lagrangian trajectories

NASA Astrophysics Data System (ADS)

Rampal, Pierre; Bouillon, Sylvain; Bergh, Jon; Ólason, Einar

2016-07-01

We characterize sea-ice drift by applying a Lagrangian diffusion analysis to buoy trajectories from the International Arctic Buoy Programme (IABP) dataset and from two different models: the standalone Lagrangian sea-ice model neXtSIM and the Eulerian coupled ice-ocean model used for the TOPAZ reanalysis. By applying the diffusion analysis to the IABP buoy trajectories over the period 1979-2011, we confirm that sea-ice diffusion follows two distinct regimes (ballistic and Brownian) and we provide accurate values for the diffusivity and integral timescale that could be used in Eulerian or Lagrangian passive tracers models to simulate the transport and diffusion of particles moving with the ice. We discuss how these values are linked to the evolution of the fluctuating displacements variance and how this information could be used to define the size of the search area around the position predicted by the mean drift. By comparing observed and simulated sea-ice trajectories for three consecutive winter seasons (2007-2011), we show how the characteristics of the simulated motion may differ from or agree well with observations. This comparison illustrates the usefulness of first applying a diffusion analysis to evaluate the output of modeling systems that include a sea-ice model before using these in, e.g., oil spill trajectory models or, more generally, to simulate the transport of passive tracers in sea ice.

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.

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.

Multi-phase CFD modeling of solid sorbent carbon capture system

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

Ryan, E. M.; DeCroix, D.; Breault, R.

2013-07-01

Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both Eulerian–Eulerian and Eulerian–Lagrangian multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD codes for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® Eulerian–Lagrangian simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA Eulerian–Lagrangian model is able to simulate the system given appropriate simplifying assumptions. FLUENT® Eulerian–Eulerian simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less

Multi-Phase CFD Modeling of Solid Sorbent Carbon Capture System

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

Ryan, Emily M.; DeCroix, David; Breault, Ronald W.

2013-07-30

Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both Eulerian-Eulerian and Eulerian-Lagrangian multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD codes for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® Eulerian-Lagrangian simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA Eulerian-Lagrangian model is able to simulate the system given appropriate simplifying assumptions. FLUENT® Eulerian-Eulerian simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less

Reactive transport in the complex heterogeneous alluvial aquifer of Fortymile Wash, Nevada

DOE PAGES

Soltanian, Mohamad Reza; Sun, Alexander; Dai, Zhenxue

2017-04-02

Yucca Mountain, Nevada, had been extensively investigated as a potential deep geologic repository for storing high-level nuclear wastes. Previous field investigations of stratified alluvial aquifer downstream of the site revealed that there is a hierarchy of sedimentary facies types. There is a corresponding log conductivity and reactive surface area subpopulations within each facies at each scale of sedimentary architecture. Here in this paper, we use a Lagrangian-based transport model in order to analyze radionuclide dispersion in the saturated alluvium of Fortymile Wash, Nevada. First, we validate the Lagrangian model using high-resolution flow and reactive transport simulations. Then, we used themore » validated model to investigate how each scale of sedimentary architecture may affect long-term radionuclide transport at Yucca Mountain. Results show that the reactive solute dispersion developed by the Lagrangian model matches the ensemble average of numerical simulations well. The link between the alluvium spatial variability and reactive solute dispersion at different spatiotemporal scales is demonstrated using the Lagrangian model. Finally, the longitudinal dispersivity of the reactive plume can be on the order of hundreds to thousands of meters, and it may not reach its asymptotic value even after 10,000 years of travel time and 2–3 km of travel distance.« less

Overshooting thunderstorm cloud top dynamics as approximated by a linear Lagrangian parcel model with analytic exact solutions

NASA Technical Reports Server (NTRS)

Schlesinger, Robert E.

1990-01-01

Results are presented from a linear Lagrangian entraining parcel model of an overshooting thunderstorm cloud top. The model, which is similar to that of Adler and Mack (1986), gives analytic exact solutions for vertical velocity and temperature by representing mixing with Rayleigh damping instead of nonlinearly. Model results are presented for various combinations of stratospheric lapse rate, drag intensity, and mixing strength. The results are compared to those of Adler and Mack.

Conformal model of gravitons

NASA Astrophysics Data System (ADS)

Donoghue, John F.

2017-08-01

In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running coupling. When running from high energy, the coupling gets large at a scale which can be called the Planck mass. If the Lorentz connection is confined at that scale, the low energy theory can have the Einstein Lagrangian induced at low energy through dimensional transmutation. However, in general there will be new divergences in such a theory and the Lagrangian basis should be expanded. I construct a conformally invariant model with a larger basis size which potentially may have the same property.

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.

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.

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

The Performance Improvement of the Lagrangian Particle Dispersion Model (LPDM) Using Graphics Processing Unit (GPU) Computing

DTIC Science & Technology

2017-08-01

access to the GPU for general purpose processing .5 CUDA is designed to work easily with multiple programming languages , including Fortran. CUDA is a...Using Graphics Processing Unit (GPU) Computing by Leelinda P Dawson Approved for public release; distribution unlimited...The Performance Improvement of the Lagrangian Particle Dispersion Model (LPDM) Using Graphics Processing Unit (GPU) Computing by Leelinda

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.

Hyperviscosity for unstructured ALE meshes

NASA Astrophysics Data System (ADS)

Cook, Andrew W.; Ulitsky, Mark S.; Miller, Douglas S.

2013-01-01

An artificial viscosity, originally designed for Eulerian schemes, is adapted for use in arbitrary Lagrangian-Eulerian simulations. Changes to the Eulerian model (dubbed 'hyperviscosity') are discussed, which enable it to work within a Lagrangian framework. New features include a velocity-weighted grid scale and a generalised filtering procedure, applicable to either structured or unstructured grids. The model employs an artificial shear viscosity for treating small-scale vorticity and an artificial bulk viscosity for shock capturing. The model is based on the Navier-Stokes form of the viscous stress tensor, including the diagonal rate-of-expansion tensor. A second-order version of the model is presented, in which Laplacian operators act on the velocity divergence and the grid-weighted strain-rate magnitude to ensure that the velocity field remains smooth at the grid scale. Unlike sound-speed-based artificial viscosities, the hyperviscosity model is compatible with the low Mach number limit. The new model outperforms a commonly used Lagrangian artificial viscosity on a variety of test problems.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

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

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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.

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.

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

NASA Astrophysics Data System (ADS)

Minier, Jean-Pierre; Chibbaro, Sergio; Pope, Stephen B.

2014-11-01

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.

Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint

NASA Technical Reports Server (NTRS)

Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.

1993-01-01

An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.

Modelling the propagation of smoke from a tanker fire in a built-up area.

PubMed

Brzozowska, Lucyna

2014-02-15

The paper presents the application of a Lagrangian particle model to problems connected with safety in road transport. Numerical simulations were performed for a hypothetical case of smoke emission from a tanker fire in a built-up area. Propagation of smoke was analysed for three wind directions. A diagnostic model was used to determine the air velocity field, whereas the dispersion of pollutants was analysed by means of a Lagrangian particle model (Brzozowska, 2013). The Idrisi Andes geographic information system was used to provide data on landforms and on their aerodynamic roughness. The presented results of computations and their analysis exemplify a possible application of the Lagrangian particle model: evaluation of mean (averaged over time) concentrations of pollutants and their distribution in the considered area (especially important due to the protection of people, animals and plants) and simulation of the propagation of harmful compounds in time as well as performing computations for cases of the potential effects of road incidents. Copyright © 2013 Elsevier B.V. All rights reserved.

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

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

Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less

A Lagrangian mixing frequency model for transported PDF modeling

NASA Astrophysics Data System (ADS)

Turkeri, Hasret; Zhao, Xinyu

2017-11-01

In this study, a Lagrangian mixing frequency model is proposed for molecular mixing models within the framework of transported probability density function (PDF) methods. The model is based on the dissipations of mixture fraction and progress variables obtained from Lagrangian particles in PDF methods. The new model is proposed as a remedy to the difficulty in choosing the optimal model constant parameters when using conventional mixing frequency models. The model is implemented in combination with the Interaction by exchange with the mean (IEM) mixing model. The performance of the new model is examined by performing simulations of Sandia Flame D and the turbulent premixed flame from the Cambridge stratified flame series. The simulations are performed using the pdfFOAM solver which is a LES/PDF solver developed entirely in OpenFOAM. A 16-species reduced mechanism is used to represent methane/air combustion, and in situ adaptive tabulation is employed to accelerate the finite-rate chemistry calculations. The results are compared with experimental measurements as well as with the results obtained using conventional mixing frequency models. Dynamic mixing frequencies are predicted using the new model without solving additional transport equations, and good agreement with experimental data is observed.

A METHOD FOR COUPLING DYNAMICAL AND COLLISIONAL EVOLUTION OF DUST IN CIRCUMSTELLAR DISKS: THE EFFECT OF A DEAD ZONE

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

Charnoz, Sebastien; Taillifet, Esther, E-mail: charnoz@cea.fr

Dust is a major component of protoplanetary and debris disks as it is the main observable signature of planetary formation. However, since dust dynamics are size-dependent (because of gas drag or radiation pressure) any attempt to understand the full dynamical evolution of circumstellar dusty disks that neglect the coupling of collisional evolution with dynamical evolution is thwarted because of the feedback between these two processes. Here, a new hybrid Lagrangian/Eulerian code is presented that overcomes some of these difficulties. The particles representing 'dust clouds' are tracked individually in a Lagrangian way. This system is then mapped on an Eulerian spatialmore » grid, inside the cells of which the local collisional evolutions are computed. Finally, the system is remapped back in a collection of discrete Lagrangian particles, keeping their number constant. An application example of dust growth in a turbulent protoplanetary disk at 1 AU is presented. First, the growth of dust is considered in the absence of a dead zone and the vertical distribution of dust is self-consistently computed. It is found that the mass is rapidly dominated by particles about a fraction of a millimeter in size. Then the same case with an embedded dead zone is investigated and it is found that coagulation is much more efficient and produces, in a short timescale, 1-10 cm dust pebbles that dominate the mass. These pebbles may then be accumulated into embryo-sized objects inside large-scale turbulent structures as shown recently.« less

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.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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.

Discrete-element simulation of sea-ice mechanics: Contact mechanics and granular jamming

NASA Astrophysics Data System (ADS)

Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.

2017-12-01

Lagrangian models of sea-ice dynamics offer several advantages to Eulerian continuum methods. Spatial discretization on the ice-floe scale is natural for Lagrangian models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in Eulerian models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum formulations, jamming occurs naturally in dense granular systems simulated in a Lagrangian framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-element framework for simulating Lagrangian sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.

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.

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.

Lagrange thermodynamic potential and intrinsic variables for He-3 He-4 dilute solutions

NASA Technical Reports Server (NTRS)

Jackson, H. W.

1983-01-01

For a two-fluid model of dilute solutions of He-3 in liquid He-4, a thermodynamic potential is constructed that provides a Lagrangian for deriving equations of motion by a variational procedure. This Lagrangian is defined for uniform velocity fields as a (negative) Legendre transform of total internal energy, and its primary independent variables, together with their thermodynamic conjugates, are identified. Here, similarities between relations in classical physics and quantum statistical mechanics serve as a guide for developing an alternate expression for this function that reveals its character as the difference between apparent kinetic energy and intrinsic internal energy. When the He-3 concentration in the mixtures tends to zero, this expression reduces to Zilsel's formula for the Lagrangian for pure liquid He-4. An investigation of properties of the intrinsic internal energy leads to the introduction of intrinsic chemical potentials along with other intrinsic variables for the mixtures. Explicit formulas for these variables are derived for a noninteracting elementary excitation model of the fluid. Using these formulas and others also derived from quantum statistical mechanics, another equivalent expression for the Lagrangian is generated.

Cloud Microphysics Parameterization in a Shallow Cumulus Cloud Simulated by a Largrangian Cloud Model

NASA Astrophysics Data System (ADS)

Oh, D.; Noh, Y.; Hoffmann, F.; Raasch, S.

2017-12-01

Lagrangian cloud model (LCM) is a fundamentally new approach of cloud simulation, in which the flow field is simulated by large eddy simulation and droplets are treated as Lagrangian particles undergoing cloud microphysics. LCM enables us to investigate raindrop formation and examine the parameterization of cloud microphysics directly by tracking the history of individual Lagrangian droplets simulated by LCM. Analysis of the magnitude of raindrop formation and the background physical conditions at the moment at which every Lagrangian droplet grows from cloud droplets to raindrops in a shallow cumulus cloud reveals how and under which condition raindrops are formed. It also provides information how autoconversion and accretion appear and evolve within a cloud, and how they are affected by various factors such as cloud water mixing ratio, rain water mixing ratio, aerosol concentration, drop size distribution, and dissipation rate. Based on these results, the parameterizations of autoconversion and accretion, such as Kessler (1969), Tripoli and Cotton (1980), Beheng (1994), and Kharioutdonov and Kogan (2000), are examined, and the modifications to improve the parameterizations are proposed.

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

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory

2012-10-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a Lagrangian Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat Eulerian and Lagrangian components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the Lagrangian approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

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.

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.

A Theoretically Consistent Framework for Modelling Lagrangian Particle Deposition in Plant Canopies

NASA Astrophysics Data System (ADS)

Bailey, Brian N.; Stoll, Rob; Pardyjak, Eric R.

2018-06-01

We present a theoretically consistent framework for modelling Lagrangian particle deposition in plant canopies. The primary focus is on describing the probability of particles encountering canopy elements (i.e., potential deposition), and provides a consistent means for including the effects of imperfect deposition through any appropriate sub-model for deposition efficiency. Some aspects of the framework draw upon an analogy to radiation propagation through a turbid medium with which to develop model theory. The present method is compared against one of the most commonly used heuristic Lagrangian frameworks, namely that originally developed by Legg and Powell (Agricultural Meteorology, 1979, Vol. 20, 47-67), which is shown to be theoretically inconsistent. A recommendation is made to discontinue the use of this heuristic approach in favour of the theoretically consistent framework developed herein, which is no more difficult to apply under equivalent assumptions. The proposed framework has the additional advantage that it can be applied to arbitrary canopy geometries given readily measurable parameters describing vegetation structure.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Quantization of Spontaneously Broken Gauge Theory Based on the Bft-Bfv Formalism

NASA Astrophysics Data System (ADS)

Kim, Yong-Wan; Park, Young-Jai

We quantize the spontaneously broken Abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We construct the BFT physical fields and obtain the firstclass observables including the Hamiltonian in terms of these fields. We also explicitly show that there are exact form invariances between the second-class and first-class quantities. Then, according to the BFV formalism, we derive the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first-class Lagrangian from the symmetry-broken second-class Lagrangian.

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.

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.

Minimal Cohomological Model of a Scalar Field on a Riemannian Manifold

NASA Astrophysics Data System (ADS)

Arkhipov, V. V.

2018-04-01

Lagrangians of the field-theory model of a scalar field are considered as 4-forms on a Riemannian manifold. The model is constructed on the basis of the Hodge inner product, this latter being an analog of the scalar product of two functions. Including the basis fields in the action of the terms with tetrads makes it possible to reproduce the Klein-Gordon equation and the Maxwell equations, and also the Einstein-Hilbert action. We conjecture that the principle of construction of the Lagrangians as 4-forms can give a criterion restricting possible forms of the field-theory models.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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.

Modeling Gas-Aerosol Processes during MILAGRO 2006

NASA Astrophysics Data System (ADS)

Zaveri, R. A.; Chapman, E. G.; Easter, R. C.; Fast, J. D.; Flocke, F.; Kleinman, L. I.; Madronich, S.; Springston, S. R.; Voss, P. B.; Weinheimer, A.

2007-12-01

Significant gas-aerosol interactions are expected in the Mexico City outflow due to formation of various semi- volatile secondary inorganic and organic gases that can partition into the particulate phase and due to various heterogeneous chemical processes. A number of T0-T1-T2 Lagrangian transport episodes during the MILAGRO campaign provide focused modeling opportunities to elucidate the roles of various chemical and physical processes in the evolution of the primary trace gases and aerosol particles emitted in Mexico City over a period of 4-8 hours. Additionally, one long-range Lagrangian transport episode on March 18-19, 2006, as characterized by the Controlled Meteorological (CMET) balloon trajectories, presents an excellent opportunity to model evolution of Mexico City pollutants over 26 hours. The key tools in our analysis of these Lagrangian episodes include a comprehensive Lagrangian box-model and the WRF-chem model based on the new Model for Simulating Aerosol Interactions and Chemistry (MOSAIC), which simulates gas-phase photochemistry, heterogeneous reactions, equilibrium particulate phase-state and water content, and dynamic gas-particle partitioning for size- resolved aerosols. Extensive gas, aerosol, and meteorological measurements onboard the G1 and C130 aircraft and T0, T1, and T2 ground sites will be used to initialize, constrain, and evaluate the models. For the long-range transport event, in-situ vertical profiles of wind vectors from repeated CMET balloon soundings in the Mexico City outflow will be used to nudge the winds in the WRF-chem simulation. Preliminary model results will be presented with the intention to explore further collaborative opportunities to use additional gas and particulate measurements to better constrain and evaluate the models.

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

PubMed

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

2018-03-26

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

Asymptotic stability of spectral-based PDF modeling for homogeneous turbulent flows

NASA Astrophysics Data System (ADS)

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2015-11-01

Engineering models of turbulence, based on one-point statistics, neglect spectral information inherent in a turbulence field. It is well known, however, that the evolution of turbulence is dictated by a complex interplay between the spectral modes of velocity. For example, for homogeneous turbulence, the pressure-rate-of-strain depends on the integrated energy spectrum weighted by components of the wave vectors. The Interacting Particle Representation Model (IPRM) (Kassinos & Reynolds, 1996) and the Velocity/Wave-Vector PDF model (Van Slooten & Pope, 1997) emulate spectral information in an attempt to improve the modeling of turbulence. We investigate the evolution and asymptotic stability of the IPRM using three different approaches. The first approach considers the Lagrangian evolution of individual realizations (idealized as particles) of the stochastic process defined by the IPRM. The second solves Lagrangian evolution equations for clusters of realizations conditional on a given wave vector. The third evolves the solution of the Eulerian conditional PDF corresponding to the aforementioned clusters. This last method avoids issues related to discrete particle noise and slow convergence associated with Lagrangian particle-based simulations.

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

PubMed

Ma, Chi; Varghese, Tomy

2012-04-01

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

Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian

NASA Astrophysics Data System (ADS)

Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.

2018-03-01

Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.

Lagrangian Sampling of 3-D Air Quality Model Results for Regional Transport Contributions to Sulfate Aerosol Concentrations at Baltimore, MD in Summer of 2004

EPA Science Inventory

The Lagrangian method provides estimates of the chemical and physical evolution of air arriving in the daytime boundary layer at Baltimore. Study results indicate a dominant role for regional transport contributions of those days when sulfate air pollution is highest in Baltimor...

Lagrangian ocean analysis: Fundamentals and practices

DOE PAGES

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

2017-11-24

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

Lagrangian ocean analysis: Fundamentals and practices

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Lagrangian ocean analysis: Fundamentals and practices

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

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

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

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.

Smoothed particle hydrodynamics method from a large eddy simulation perspective

NASA Astrophysics Data System (ADS)

Di Mascio, A.; Antuono, M.; Colagrossi, A.; Marrone, S.

2017-03-01

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier-Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filtering, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

Lagrangian formulation for penny-shaped and Perkins-Kern geometry models

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

Lee, W.S.

1989-09-01

This paper discusses basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models developed with a Lagrangian formulation combined with a virtual-work analysis. The Lagrangian formulation yields a pair of nonlinear equations in R/sub f/ or L/sub f/ and b/sub f/, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved numerically. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, canmore » be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry.« less

Insights into the physico-chemical evolution of pyrogenic organic carbon emissions from biomass burning using coupled Lagrangian-Eulerian simulations

NASA Astrophysics Data System (ADS)

Suciu, L. G.; Griffin, R. J.; Masiello, C. A.

2017-12-01

Wildfires and prescribed burning are important sources of particulate and gaseous pyrogenic organic carbon (PyOC) emissions to the atmosphere. These emissions impact atmospheric chemistry, air quality and climate, but the spatial and temporal variabilities of these impacts are poorly understood, primarily because small and fresh fire plumes are not well predicted by three-dimensional Eulerian chemical transport models due to their coarser grid size. Generally, this results in underestimation of downwind deposition of PyOC, hydroxyl radical reactivity, secondary organic aerosol formation and ozone (O3) production. However, such models are very good for simulation of multiple atmospheric processes that could affect the lifetimes of PyOC emissions over large spatiotemporal scales. Finer resolution models, such as Lagrangian reactive plumes models (or plume-in-grid), could be used to trace fresh emissions at the sub-grid level of the Eulerian model. Moreover, Lagrangian plume models need background chemistry predicted by the Eulerian models to accurately simulate the interactions of the plume material with the background air during plume aging. Therefore, by coupling the two models, the physico-chemical evolution of the biomass burning plumes can be tracked from local to regional scales. In this study, we focus on the physico-chemical changes of PyOC emissions from sub-grid to grid levels using an existing chemical mechanism. We hypothesize that finer scale Lagrangian-Eulerian simulations of several prescribed burns in the U.S. will allow more accurate downwind predictions (validated by airborne observations from smoke plumes) of PyOC emissions (i.e., submicron particulate matter, organic aerosols, refractory black carbon) as well as O3 and other trace gases. Simulation results could be used to optimize the implementation of additional PyOC speciation in the existing chemical mechanism.

Modeling shockwaves and impact phenomena with Eulerian peridynamics

DOE PAGES

Silling, Stewart A.; Parks, Michael L.; Kamm, James R.; ...

2017-05-09

Most previous development of the peridynamic theory has assumed a Lagrangian formulation, in which the material model refers to an undeformed reference configuration. Here, an Eulerian form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the Lagrangian form unsuitable. The Eulerian capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The Eulerian and Lagrangian contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less

Modeling shockwaves and impact phenomena with Eulerian peridynamics

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

Silling, Stewart A.; Parks, Michael L.; Kamm, James R.

Most previous development of the peridynamic theory has assumed a Lagrangian formulation, in which the material model refers to an undeformed reference configuration. Here, an Eulerian form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the Lagrangian form unsuitable. The Eulerian capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The Eulerian and Lagrangian contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less

LAGRANGIAN MODELING OF A SUSPENDED-SEDIMENT PULSE.

USGS Publications Warehouse

Schoellhamer, David H.

1987-01-01

The one-dimensional Lagrangian Transport Model (LTM) has been applied in a quasi two-dimensional manner to simulate the transport of a slug injection of microbeads in steady experimental flows. A stationary bed segment was positioned below each parcel location to simulate temporary storage of beads on the bottom of the flume. Only one degree of freedom was available for all three bead simulations. The results show the versatility of the LTM and the ability of the LTM to accurately simulate transport of fine suspended sediment.

On the role of sea-state in bubble-mediated air-sea gas flux during a winter storm

NASA Astrophysics Data System (ADS)

Liang, Jun-Hong; Emerson, Steven R.; D'Asaro, Eric A.; McNeil, Craig L.; Harcourt, Ramsey R.; Sullivan, Peter P.; Yang, Bo; Cronin, Meghan F.

2017-04-01

Oceanic bubbles play an important role in the air-sea exchange of weakly soluble gases at moderate to high wind speeds. A Lagrangian bubble model embedded in a large eddy simulation model is developed to study bubbles and their influence on dissolved gases in the upper ocean. The transient evolution of mixed-layer dissolved oxygen and nitrogen gases at Ocean Station Papa (50°N, 145°W) during a winter storm is reproduced with the model. Among different physical processes, gas bubbles are the most important in elevating dissolved gas concentrations during the storm, while atmospheric pressure governs the variability of gas saturation anomaly (the relative departure of dissolved gas concentration from the saturation concentration). For the same wind speed, bubble-mediated gas fluxes are larger during rising wind with smaller wave age than during falling wind with larger wave age. Wave conditions are the primary cause for the bubble gas flux difference: when wind strengthens, waves are less-developed with respect to wind, resulting in more frequent large breaking waves. Bubble generation in large breaking waves is favorable for a large bubble-mediated gas flux. The wave-age dependence is not included in any existing bubble-mediated gas flux parameterizations.

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

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

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

Functional integral for non-Lagrangian systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

2010-02-01

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

Multiphase Fluid Dynamics for Spacecraft Applications

NASA Astrophysics Data System (ADS)

Shyy, W.; Sim, J.

2011-09-01

Multiphase flows involving moving interfaces between different fluids/phases are observed in nature as well as in a wide range of engineering applications. With the recent development of high fidelity computational techniques, a number of challenging multiphase flow problems can now be computed. We introduce the basic notion of the main categories of multiphase flow computation; Lagrangian, Eulerian, and Eulerian-Lagrangian techniques to represent and follow interface, and sharp and continuous interface methods to model interfacial dynamics. The marker-based adaptive Eulerian-Lagrangian method, which is one of the most popular methods, is highlighted with microgravity and space applications including droplet collision and spacecraft liquid fuel tank surface stability.

Development of a reactive burn model based upon an explicit visco-plastic pore collapse model

NASA Astrophysics Data System (ADS)

Bouton, Eric; Lefrançois, Alexandre; Belmas, Robert

2015-06-01

Our aim in this study is to develop a reactive burn model based upon a microscopic hot spot model to compute the initiation and shock to detonation of pressed TATB explosives. For the sake of simplicity, the hot spots are supposed to result from the viscoplastic collapse of spherical micro-voids inside the composition. Such a model has been incorporated in a lagrangian hydrodynamic code. In our calculations, 8 different pore diameters, ranging from 100 nm to 1.2 μm, have been taken into account and the porosity associated to each pore size has been deduced from the PBX-9502 void distribution derived from the SAXS. The last ingredient of our model is the burn rate that depends on two main variables. The first one is the shock pressure as proposed by the developers of the CREST model. The second one is the number of effective chemical reaction sites calculated by the microscopic model. Furthermore, the function of the reaction progress variable of the burn rate is similar to that in the SURF model proposed by Menikoff. Our burn rate has been calibrated by using pressure profile, material velocities wave forms obtained with embedded particle velocity gauges and run distance to detonation. The comparison between the numerical and experimental results is really good and sufficient to perform a wide variety of simulations including single, double shock waves and the desensitization phenomenon. In conclusion, future works are described.

Turbulent transport with intermittency: Expectation of a scalar concentration.

PubMed

Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D

2016-04-01

Scalar transport by turbulent flows is best described in terms of Lagrangian parcel motions. Here we measure the Eulerian distance travel along Lagrangian trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared Eulerian displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the Eulerian integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the Lagrangian integral time and times longer than the Eulerian integral time. The very short-time enhancement reflects the underlying Lagrangian velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of Lagrangian tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.

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.

Parallel implementation of a Lagrangian-based model on an adaptive mesh in C++: Application to sea-ice

NASA Astrophysics Data System (ADS)

Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar

2017-12-01

We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure Lagrangian scheme or an Arbitrary Lagrangian Eulerian scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.

Nonconservative Lagrangian Mechanics: Purely Causal Equations of Motion

NASA Astrophysics Data System (ADS)

Dreisigmeyer, David W.; Young, Peter M.

2015-06-01

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

Action Principle Derivation of Magnetofluid Models

NASA Astrophysics Data System (ADS)

Wurm, Alexander; Morrison, P. J.

2003-10-01

As it is well-known, ideal MHD possesses an action principle formulation when it is expressed in terms of Lagrangian (or material) variables.^1 Starting with a general magneto-two-fluid Lagrangian, we derive action principles for both MHD approximations and generalizations that contain more complete versions of Ohm's law. ^1 W.A. Newcomb, Nuclear Fusion: 1962 Suppl. Part 2, p. 451

Anyons in an electromagnetic field and the Bargmann-Michel-Telegdi equation

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

Ghosh, S.

1995-05-15

The Lagrangian model for anyons, presented earlier, is extended to include interactions with an external, homogeneous electromagnetic field. Explicit electric and magnetic moment terms for the anyon are introduced in the Lagrangian. The (2+1)-dimensional Bargmann-Michel-Telegdi equation as well as the correct value (2) of the gyromagnetic ratio is rederived, in the Hamiltonian framework.

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.

Single-particle dispersion in stably stratified turbulence

NASA Astrophysics Data System (ADS)

Sujovolsky, N. E.; Mininni, P. D.; Rast, M. P.

2018-03-01

We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuous-time eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbulence, for which single-particle dispersion differs from the well-studied case of homogeneous and isotropic turbulence.

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.

Coupling fluid-structure interaction with phase-field fracture

NASA Astrophysics Data System (ADS)

Wick, Thomas

2016-12-01

In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.

Modeling of combustion processes of stick propellants via combined Eulerian-Lagrangian approach

NASA Technical Reports Server (NTRS)

Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.

1988-01-01

This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined Eulerian-Lagrangian approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the Eulerian approach is obtained; governing equations for the stick propellants are formulated using the Lagrangian approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.

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.

Enhancements to the Branched Lagrangian Transport Modeling System

USGS Publications Warehouse

Jobson, Harvey E.

1997-01-01

The Branched Lagrangian Transport Model (BLTM) has received wide use within the U.S. Geological Survey over the past 10 years. This report documents the enhancements and modifications that have been made to this modeling system since it was first introduced. The programs in the modeling system are arranged into five levels?programs to generate time-series of meteorological data (EQULTMP, SOLAR), programs to process time-series data (INTRP, MRG), programs to build input files for transport model (BBLTM, BQUAL2E), the model with defined reaction kinetics (BLTM, QUAL2E), and post processor plotting programs (CTPLT, CXPLT). An example application is presented to illustrate how the modeling system can be used to simulate 10 water-quality constituents in the Chattahoochee River below Atlanta, Georgia.

Gauging hidden symmetries in two dimensions

NASA Astrophysics Data System (ADS)

Samtleben, Henning; Weidner, Martin

2007-08-01

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine fraktur e9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of fraktur e9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of fraktur e9.

Spatial and Temporal Extrapolation of Disdrometer Size Distributions Based on a Lagrangian Trajectory Model of Falling Rain

NASA Technical Reports Server (NTRS)

Lane, John E.; Kasparis, Takis; Jones, W. Linwood; Metzger, Philip T.

2009-01-01

Methodologies to improve disdrometer processing, loosely based on mathematical techniques common to the field of particle flow and fluid mechanics, are examined and tested. The inclusion of advection and vertical wind field estimates appear to produce significantly improved results in a Lagrangian hydrometeor trajectory model, in spite of very strict assumptions of noninteracting hydrometeors, constant vertical air velocity, and time independent advection during the scan time interval. Wind field data can be extracted from each radar elevation scan by plotting and analyzing reflectivity contours over the disdrometer site and by collecting the radar radial velocity data to obtain estimates of advection. Specific regions of disdrometer spectra (drop size versus time) often exhibit strong gravitational sorting signatures, from which estimates of vertical velocity can be extracted. These independent wind field estimates become inputs and initial conditions to the Lagrangian trajectory simulation of falling hydrometeors.

Detecting reactive islands using Lagrangian descriptors and the relevance to transition path sampling.

PubMed

Patra, Sarbani; Keshavamurthy, Srihari

2018-02-14

It has been known for sometime now that isomerization reactions, classically, are mediated by phase space structures called reactive islands (RI). RIs provide one possible route to correct for the nonstatistical effects in the reaction dynamics. In this work, we map out the reactive islands for the two dimensional Müller-Brown model potential and show that the reactive islands are intimately linked to the issue of rare event sampling. In particular, we establish the sensitivity of the so called committor probabilities, useful quantities in the transition path sampling technique, to the hierarchical RI structures. Mapping out the RI structure for high dimensional systems, however, is a challenging task. Here, we show that the technique of Lagrangian descriptors is able to effectively identify the RI hierarchy in the model system. Based on our results, we suggest that the Lagrangian descriptors can be useful for detecting RIs in high dimensional systems.

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.

A Eulerian-Lagrangian Model to Simulate Two-Phase/Particulate Flows

NASA Technical Reports Server (NTRS)

Apte, S. V.; Mahesh, K.; Lundgren, T.

2003-01-01

Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an Eulerian-Lagrangian technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on Eulerian-Lagrangian technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on Eulerian-Lagrangian techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.

Evaluation of altimetry-derived surface current products using Lagrangian drifter trajectories in the eastern Gulf of Mexico

NASA Astrophysics Data System (ADS)

Liu, Yonggang; Weisberg, Robert H.; Vignudelli, Stefano; Mitchum, Gary T.

2014-05-01

Lagrangian particle trajectory models based on several altimetry-derived surface current products are used to hindcast the drifter trajectories observed in the eastern Gulf of Mexico during May to August 2010 (the Deepwater Horizon oil spill incident). The performances of the trajectory models are gauged in terms of Lagrangian separation distances (d) and a nondimensional skill score (s), respectively. A series of numerical experiments show that these altimetry-based trajectory models have about the same performance, with a certain improvement by adding surface wind Ekman components, especially over the shelf region. However, their hindcast skills are slightly better than those of the data assimilative numerical model output. After 3 days' simulation the altimetry-based trajectory models have mean d values of 75-83 and 34-42 km (s values of 0.49-0.51 and 0.35-0.43) in the Gulf of Mexico deep water area and on the West Florida Continental Shelf, respectively. These satellite altimetry data products are useful for providing essential information on ocean surface currents of use in water property transports, offshore oil and gas operations, hazardous spill mitigation, search and rescue, etc.

Intercomparisons of Aura MLS, ACE, and HALOE Observations of Long-Lived Trace Species Using the Langley Lagrangian Chemistry and Transport Model

NASA Technical Reports Server (NTRS)

Considine, David B.; Natarajan, Murali; Fairlie, T. D.; Lingenfelser, Gretchen S.; Bernath, Peter

2007-01-01

We use the LaRC Lagrangian Chemistry and Transport Model (LCTM) [Considine et al., 2007; Pierce et al., 2003] to intercompare ACE, Aura, and HALOE observations of long-lived trace species. The LCTM calculates the transport, mixing, and photochemical evolution of an ensemble of parcels that have been initialized from ACE-FTS measurements. Here we focus on late November, 2004 comparisons, due to the previous 3-week period of continuous HALOE observations and MLS v2.2 data on November 29, 2004.

Building analytical three-field cosmological models

NASA Astrophysics Data System (ADS)

Santos, J. R. L.; Moraes, P. H. R. S.; Ferreira, D. A.; Neta, D. C. Vilar

2018-02-01

A difficult task to deal with is the analytical treatment of models composed of three real scalar fields, as their equations of motion are in general coupled and hard to integrate. In order to overcome this problem we introduce a methodology to construct three-field models based on the so-called "extension method". The fundamental idea of the procedure is to combine three one-field systems in a non-trivial way, to construct an effective three scalar field model. An interesting scenario where the method can be implemented is with inflationary models, where the Einstein-Hilbert Lagrangian is coupled with the scalar field Lagrangian. We exemplify how a new model constructed from our method can lead to non-trivial behaviors for cosmological parameters.

The Crossover Time as an Evaluation of Ocean Models Against Persistence

NASA Astrophysics Data System (ADS)

Phillipson, L. M.; Toumi, R.

2018-01-01

A new ocean evaluation metric, the crossover time, is defined as the time it takes for a numerical model to equal the performance of persistence. As an example, the average crossover time calculated using the Lagrangian separation distance (the distance between simulated trajectories and observed drifters) for the global MERCATOR ocean model analysis is found to be about 6 days. Conversely, the model forecast has an average crossover time longer than 6 days, suggesting limited skill in Lagrangian predictability by the current generation of global ocean models. The crossover time of the velocity error is less than 3 days, which is similar to the average decorrelation time of the observed drifters. The crossover time is a useful measure to quantify future ocean model improvements.

Lagrangian analysis of multiscale particulate flows with the particle finite element method

NASA Astrophysics Data System (ADS)

Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy

2014-05-01

We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

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.

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.

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

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

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

Polarizable Force Fields and Polarizable Continuum Model: A Fluctuating Charges/PCM Approach. 1. Theory and Implementation.

PubMed

Lipparini, Filippo; Barone, Vincenzo

2011-11-08

We present a combined fluctuating charges-polarizable continuum model approach to describe molecules in solution. Both static and dynamic approaches are discussed: analytical first and second derivatives are shown as well as an extended lagrangian for molecular dynamics simluations. In particular, we use the polarizable continuum model to provide nonperiodic boundary conditions for molecular dynamics simulations of aqueous solutions. The extended lagrangian method is extensively discussed, with specific reference to the fluctuating charge model, from a numerical point of view by means of several examples, and a rationalization of the behavior found is presented. Several prototypical applications are shown, especially regarding solvation of ions and polar molecules in water.

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

PubMed

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

2005-10-01

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

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 domain. The centre of the discussion will be the Lagrangian statistics which is collected from the individual behaviour of the tracked particles.

Evaluation of the Revised Lagrangian Particle Model GRAL Against Wind-Tunnel and Field Observations in the Presence of Obstacles

NASA Astrophysics Data System (ADS)

Oettl, Dietmar

2015-05-01

A revised microscale flow field model has been implemented in the Lagrangian particle model Graz Lagrangian Model (GRAL) for computing flows around obstacles. It is based on the Reynolds-averaged Navier-Stokes equations in three dimensions and the widely used standard turbulence model. Here we focus on evaluating the model regarding computed concentrations by use of a comprehensive wind-tunnel experiment with numerous combinations of building geometries, stack positions, and locations. In addition, two field experiments carried out in Denmark and in the U.S were used to evaluate the model. Further, two different formulations of the standard deviation of wind component fluctuations have also been investigated, but no clear picture could be drawn in this respect. Overall the model is able to capture several of the main features of pollutant dispersion around obstacles, but at least one future model improvement was identified for stack releases within the recirculation zone of buildings. Regulatory applications are the bread-and-butter of most GRAL users nowadays, requiring fast and robust modelling algorithms. Thus, a few simplifications have been introduced to decrease the computational time required. Although predicted concentrations for the two field experiments were found to be in good agreement with observations, shortcomings were identified regarding the extent of computed recirculation zones for the idealized wind-tunnel building geometries, with approaching flows perpendicular to building faces.

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.

Modeling and Numerical Challenges in Eulerian-Lagrangian Computations of Shock-driven Multiphase Flows

NASA Astrophysics Data System (ADS)

Diggs, Angela; Balachandar, Sivaramakrishnan

2015-06-01

The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

PubMed

Townsend, Molly T; Sarigul-Klijn, Nesrin

2016-01-01

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

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.

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

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

DOE PAGES

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2016-10-21

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less

Variational Lagrangian data assimilation in open channel networks

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

On the error propagation of semi-Lagrange and Fourier methods for advection problems☆

PubMed Central

Einkemmer, Lukas; Ostermann, Alexander

2015-01-01

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018

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

The initial value problem in Lagrangian drift kinetic theory

NASA Astrophysics Data System (ADS)

Burby, J. W.

2016-06-01

> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.

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.

Super-Quantum Mechanics in the Integral Form Formalism

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Grassi, P. A.

2018-05-01

We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we retrieve component and superspace actions, and prove their equivalence. The PCO are closed integral forms, and can be interpreted as super Poincar\\'e duals of bosonic submanifolds embedded into a supermanifold.. We use them to construct Lagrangians that are top integral forms, and therefore can be integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$ cases are studied, in a flat and in a curved supermanifold. In this formalism we also consider coupling with gauge fields, Hilbert space of quantum states and observables.

Variational submanifolds of Euclidean spaces

NASA Astrophysics Data System (ADS)

Krupka, D.; Urban, Z.; Volná, J.

2018-03-01

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.

A Lagrangian analysis of the impact of transport and transformation on the ozone stratification observed in the free troposphere during the ESCOMPTE campaign

NASA Astrophysics Data System (ADS)

Colette, A.; Ancellet, G.; Menut, L.; Arnold, S. R.

2006-03-01

The ozone variability observed by tropospheric ozone lidars during the ESCOMPTE campaign is analyzed by means of a hybrid-Lagrangian modeling study. Transport processes responsible for the formation of ozone-rich layers are identified using a semi-Lagrangian analysis of mesoscale simulations to identify the planetary boundary layer (PBL) footprint in the free troposphere. High ozone concentrations are related to polluted air masses exported from the Iberian PBL. The chemical composition of air masses coming from the PBL and transported in the free troposphere is evaluated using a Lagrangian chemistry model. The initial concentrations are provided by a model of chemistry and transport. Different scenarios are tested for the initial conditions and for the impact of mixing with background air in order to perform a quantitative comparison with the lidar observations. For this meteorological situation, the characteristic mixing time is of the order of 2 to 5 days depending on the initial conditions. Ozone is produced in the free troposphere within most air masses exported from the Iberian PBL at an average rate of 0.2 ppbv h-1, with a maximum ozone production of 0.4 ppbv h-1. Transport processes from the PBL are responsible for an increase of 13.3 ppbv of ozone concentrations in the free troposphere compared to background levels; about 45% of this increase is attributed to in situ production during the transport rather than direct export of ozone.

A Lagrangian analysis of the impact of transport and transformation on the ozone stratification observed in the free troposphere during the ESCOMPTE campaign

NASA Astrophysics Data System (ADS)

Colette, A.; Ancellet, G.; Menut, L.; Arnold, S. R.

2006-08-01

The ozone variability observed by tropospheric ozone lidars during the ESCOMPTE campaign is analyzed by means of a hybrid-Lagrangian modeling study. Transport processes responsible for the formation of ozone-rich layers are identified using a semi-Lagrangian analysis of mesoscale simulations to identify the planetary boundary layer (PBL) footprint in the free troposphere. High ozone concentrations are related to polluted air masses exported from the Iberian PBL. The chemical composition of air masses coming from the PBL and transported in the free troposphere is evaluated using a Lagrangian chemistry model. The initial concentrations are provided by a model of chemistry and transport. Different scenarios are tested for the initial conditions and for the impact of mixing with background air in order to perform a quantitative comparison with the lidar observations. For this meteorological situation, the characteristic mixing time is of the order of 2 to 6 days depending on the initial conditions. Ozone is produced in the free troposphere within most air masses exported from the Iberian PBL at an average rate of 0.2 ppbv h-1, with a maximum ozone production of 0.4 ppbv h-1. Transport processes from the PBL are responsible for an increase of 13.3 ppbv of ozone concentrations in the free troposphere compared to background levels; about 45% of this increase is attributed to in situ production during the transport rather than direct export of ozone.

Multisymplectic unified formalism for Einstein-Hilbert gravity

NASA Astrophysics Data System (ADS)

Gaset, Jordi; Román-Roy, Narciso

2018-03-01

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.

PubMed

Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins

2018-04-01

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.

Feature-based component model for design of embedded systems

NASA Astrophysics Data System (ADS)

Zha, Xuan Fang; Sriram, Ram D.

2004-11-01

An embedded system is a hybrid of hardware and software, which combines software's flexibility and hardware real-time performance. Embedded systems can be considered as assemblies of hardware and software components. An Open Embedded System Model (OESM) is currently being developed at NIST to provide a standard representation and exchange protocol for embedded systems and system-level design, simulation, and testing information. This paper proposes an approach to representing an embedded system feature-based model in OESM, i.e., Open Embedded System Feature Model (OESFM), addressing models of embedded system artifacts, embedded system components, embedded system features, and embedded system configuration/assembly. The approach provides an object-oriented UML (Unified Modeling Language) representation for the embedded system feature model and defines an extension to the NIST Core Product Model. The model provides a feature-based component framework allowing the designer to develop a virtual embedded system prototype through assembling virtual components. The framework not only provides a formal precise model of the embedded system prototype but also offers the possibility of designing variation of prototypes whose members are derived by changing certain virtual components with different features. A case study example is discussed to illustrate the embedded system model.

NiftySim: A GPU-based nonlinear finite element package for simulation of soft tissue biomechanics.

PubMed

Johnsen, Stian F; Taylor, Zeike A; Clarkson, Matthew J; Hipwell, John; Modat, Marc; Eiben, Bjoern; Han, Lianghao; Hu, Yipeng; Mertzanidou, Thomy; Hawkes, David J; Ourselin, Sebastien

2015-07-01

NiftySim, an open-source finite element toolkit, has been designed to allow incorporation of high-performance soft tissue simulation capabilities into biomedical applications. The toolkit provides the option of execution on fast graphics processing unit (GPU) hardware, numerous constitutive models and solid-element options, membrane and shell elements, and contact modelling facilities, in a simple to use library. The toolkit is founded on the total Lagrangian explicit dynamics (TLEDs) algorithm, which has been shown to be efficient and accurate for simulation of soft tissues. The base code is written in C[Formula: see text], and GPU execution is achieved using the nVidia CUDA framework. In most cases, interaction with the underlying solvers can be achieved through a single Simulator class, which may be embedded directly in third-party applications such as, surgical guidance systems. Advanced capabilities such as contact modelling and nonlinear constitutive models are also provided, as are more experimental technologies like reduced order modelling. A consistent description of the underlying solution algorithm, its implementation with a focus on GPU execution, and examples of the toolkit's usage in biomedical applications are provided. Efficient mapping of the TLED algorithm to parallel hardware results in very high computational performance, far exceeding that available in commercial packages. The NiftySim toolkit provides high-performance soft tissue simulation capabilities using GPU technology for biomechanical simulation research applications in medical image computing, surgical simulation, and surgical guidance applications.

Atomization simulations using an Eulerian-VOF-Lagrangian method

NASA Technical Reports Server (NTRS)

Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Chen, C. P.

1994-01-01

This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a Lagrangian tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.

The Gaussian streaming model and convolution Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; Castorina, Emanuele; White, Martin

2016-12-05

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

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego

2012-03-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel Lagrangian Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving numerical formulation, which ensures a consistent numerical discretization temporally and spatially for arbitrary χ/χ ratios. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

Comprehensive computational model for combining fluid hydrodynamics, light transport and biomass growth in a Taylor vortex algal photobioreactor: Lagrangian approach.

PubMed

Gao, Xi; Kong, Bo; Vigil, R Dennis

2017-01-01

A comprehensive quantitative model incorporating the effects of fluid flow patterns, light distribution, and algal growth kinetics on biomass growth rate is developed in order to predict the performance of a Taylor vortex algal photobioreactor for culturing Chlorella vulgaris. A commonly used Lagrangian strategy for coupling the various factors influencing algal growth was employed whereby results from computational fluid dynamics and radiation transport simulations were used to compute numerous microorganism light exposure histories, and this information in turn was used to estimate the global biomass specific growth rate. The simulations provide good quantitative agreement with experimental data and correctly predict the trend in reactor performance as a key reactor operating parameter is varied (inner cylinder rotation speed). However, biomass growth curves are consistently over-predicted and potential causes for these over-predictions and drawbacks of the Lagrangian approach are addressed. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

The Gaussian streaming model and convolution Lagrangian effective field theory

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

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

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

Characteristics of the mixing volume model with the interactions among spatially distributed particles for Lagrangian simulations of turbulent mixing

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2016-11-01

The mixing volume model (MVM), which is a mixing model for molecular diffusion in Lagrangian simulations of turbulent mixing problems, is proposed based on the interactions among spatially distributed particles in a finite volume. The mixing timescale in the MVM is derived by comparison between the model and the subgrid scale scalar variance equation. A-priori test of the MVM is conducted based on the direct numerical simulations of planar jets. The MVM is shown to predict well the mean effects of the molecular diffusion under various conditions. However, a predicted value of the molecular diffusion term is positively correlated to the exact value in the DNS only when the number of the mixing particles is larger than two. Furthermore, the MVM is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (ILES/LPS). The ILES/LPS with the present mixing model predicts well the decay of the scalar variance in planar jets. This work was supported by JSPS KAKENHI Nos. 25289030 and 16K18013. The numerical simulations presented in this manuscript were carried out on the high performance computing system (NEC SX-ACE) in the Japan Agency for Marine-Earth Science and Technology.

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

Vorticity-divergence semi-Lagrangian global atmospheric model SL-AV20: dynamical core

NASA Astrophysics Data System (ADS)

Tolstykh, Mikhail; Shashkin, Vladimir; Fadeev, Rostislav; Goyman, Gordey

2017-05-01

SL-AV (semi-Lagrangian, based on the absolute vorticity equation) is a global hydrostatic atmospheric model. Its latest version, SL-AV20, provides global operational medium-range weather forecast with 20 km resolution over Russia. The lower-resolution configurations of SL-AV20 are being tested for seasonal prediction and climate modeling. The article presents the model dynamical core. Its main features are a vorticity-divergence formulation at the unstaggered grid, high-order finite-difference approximations, semi-Lagrangian semi-implicit discretization and the reduced latitude-longitude grid with variable resolution in latitude. The accuracy of SL-AV20 numerical solutions using a reduced lat-lon grid and the variable resolution in latitude is tested with two idealized test cases. Accuracy and stability of SL-AV20 in the presence of the orography forcing are tested using the mountain-induced Rossby wave test case. The results of all three tests are in good agreement with other published model solutions. It is shown that the use of the reduced grid does not significantly affect the accuracy up to the 25 % reduction in the number of grid points with respect to the regular grid. Variable resolution in latitude allows us to improve the accuracy of a solution in the region of interest.

Implications of Lagrangian Tracer Transport for Coupled Chemistry-Climate Simulations

NASA Astrophysics Data System (ADS)

Stenke, A.

2009-05-01

Today's coupled chemistry-climate models (CCM) consider a large number of trace species and feedback processes. Due to the radiative effect of some species, errors in simulated tracer distributions can feed back to model dynamics. Thus, shortcomings of the applied transport schemes can have severe implications for the overall model performance. Traditional Eulerian approaches show a satisfactory performance in case of homogeneously distributed trace species, but they can lead to severe problems when applied to highly inhomogeneous tracer distributions. In case of sharp gradients many schemes show a considerable numerical diffusion. Lagrangian approaches, on the other hand, combine a number of favourable numerical properties: They are strictly mass-conserving and do not suffer from numerical diffusion. Therefore they are able to maintain steeper gradients. A further advantage is that they allow the transport of a large number of tracers without being prohibitively expensive. A variety of benefits for stratospheric dynamics and chemistry resulting from a Lagrangian transport algorithm are demonstrated by the example of the CCM E39C. In an updated version of E39C, called E39C-A, the operational semi-Lagrangian advection scheme has been replaced with the purely Lagrangian scheme ATTILA. It will be shown that several model deficiencies can be cured by the choice of an appropriate transport algorithm. The most important advancement concerns the reduction of a pronounced wet bias in the extra- tropical lowermost stratosphere. In turn, the associated temperature error ("cold bias") is significantly reduced. Stratospheric wind variations are now in better agreement with observations, e.g. E39C-A is able to reproduce the stratospheric wind reversal in the Southern Hemisphere in summer which was not captured by the previous model version. Resulting changes in wave propagation and dissipation lead to a weakening of the simulated mean meridional circulation and therefore a more realistic representation of tropical upwelling. Simulated distributions of chemical tracers in the stratosphere are clearly improved. For example, the vertical distribution of stratospheric chlorine (Cly) is now in agreement with analyses derived from observations and other CCMs. As a consequence the model realistically covers the altitude of maximum ozone depletion in the stratosphere. Furthermore, the simulated temporal evolution of stratospheric Cly in the past agrees is realistically reproduced which is an important step towards more reliable projections of future changes, especially of stratospheric ozone.

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

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

Minier, Jean-Pierre, E-mail: Jean-Pierre.Minier@edf.fr; Chibbaro, Sergio; Pope, Stephen B.

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangianmore » stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.« less

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Ice Accretion Modeling using an Eulerian Approach for Droplet Impingement

NASA Technical Reports Server (NTRS)

Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.

2012-01-01

A three-dimensional Eulerian analysis has been developed for modeling droplet impingement on lifting bodes. The Eulerian model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the Eulerian approach is more efficient because the Lagrangian approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the Lagrangian approach used in an industry standard analysis called LEWICE.

A multiclass vehicular dynamic traffic flow model for main roads and dedicated lanes/roads of multimodal transport network

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

Sossoe, K.S., E-mail: kwami.sossoe@irt-systemx.fr; Lebacque, J-P., E-mail: jean-patrick.lebacque@ifsttar.fr

2015-03-10

We present in this paper a model of vehicular traffic flow for a multimodal transportation road network. We introduce the notion of class of vehicles to refer to vehicles of different transport modes. Our model describes the traffic on highways (which may contain several lanes) and network transit for pubic transportation. The model is drafted with Eulerian and Lagrangian coordinates and uses a Logit model to describe the traffic assignment of our multiclass vehicular flow description on shared roads. The paper also discusses traffic streams on dedicated lanes for specific class of vehicles with event-based traffic laws. An Euler-Lagrangian-remap schememore » is introduced to numerically approximate the model’s flow equations.« less

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.

Simulation of atmospheric dispersion of radionuclides using an Eulerian-Lagrangian modelling system.

PubMed

Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N

2008-12-01

In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a Lagrangian stochastic particle model (LSPM) coupled with an Eulerian regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a Lagrangian stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.

Chiral anomalies and effective vector meson Lagrangian beyond the tree level

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

Dominguez, C.A.

1987-12-01

The decays ..pi../sup O/ ..-->.. ..gamma gamma.., rho ..-->.. ..pi gamma.., ..omega.. ..-->.. ..pi gamma.., ..omega.. ..-->.. 3..pi.. and ..gamma.. ..-->.. 3..pi.. are studied in the framework of the chiral invariant effective Vector Meson Lagrangian beyond the tree level. The standard Lagrangian is enlarged by including an infinite number of radial excitations which are summed according to the dual model. As a result tree level diagrams are modified by a universal form factor at each vertex containing off-mass-shell mesons, but still respecting chiral anomaly low energy theorems. These vertex corrections bring the tree level predictions into better agreement with experiment.more » The presence of the ..omega.. ..-->.. 3..pi.. contact term is confirmed but its strength is considerably smaller than at tree level.« less

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Constraining composite Higgs models using LHC data

NASA Astrophysics Data System (ADS)

Banerjee, Avik; Bhattacharyya, Gautam; Kumar, Nilanjana; Ray, Tirtha Sankar

2018-03-01

We systematically study the modifications in the couplings of the Higgs boson, when identified as a pseudo Nambu-Goldstone boson of a strong sector, in the light of LHC Run 1 and Run 2 data. For the minimal coset SO(5)/SO(4) of the strong sector, we focus on scenarios where the standard model left- and right-handed fermions (specifically, the top and bottom quarks) are either in 5 or in the symmetric 14 representation of SO(5). Going beyond the minimal 5 L - 5 R representation, to what we call here the `extended' models, we observe that it is possible to construct more than one invariant in the Yukawa sector. In such models, the Yukawa couplings of the 125 GeV Higgs boson undergo nontrivial modifications. The pattern of such modifications can be encoded in a generic phenomenological Lagrangian which applies to a wide class of such models. We show that the presence of more than one Yukawa invariant allows the gauge and Yukawa coupling modifiers to be decorrelated in the `extended' models, and this decorrelation leads to a relaxation of the bound on the compositeness scale ( f ≥ 640 GeV at 95% CL, as compared to f ≥ 1 TeV for the minimal 5 L - 5 R representation model). We also study the Yukawa coupling modifications in the context of the next-to-minimal strong sector coset SO(6)/SO(5) for fermion-embedding up to representations of dimension 20. While quantifying our observations, we have performed a detailed χ 2 fit using the ATLAS and CMS combined Run 1 and available Run 2 data.

BRST-BV approach to continuous-spin field

NASA Astrophysics Data System (ADS)

Metsaev, R. R.

2018-06-01

Using BRST-BV approach, massless and massive continuous-spin fields propagating in the flat space are studied. For such fields, BRST-BV gauge invariant Lagrangian is obtained. The Lagrangian and gauge transformations are constructed out of traceless gauge fields and traceless gauge transformation parameters. Interrelation between the BRST-BV Lagrangian and the Lagrangian for the continuous-spin fields in metric-like approach is demonstrated. Considering the BRST-BV Lagrangian in the Siegel gauge, we get gauge-fixed Lagrangian which is invariant under global BRST and antiBRST transformations.

A Lagrangian model for the age of tracer in surface water

NASA Astrophysics Data System (ADS)

Ding, Yu; Liu, Haifei; Yi, Yujun

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

General self-tuning solutions and no-go theorem

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

Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min, E-mail: forste@th.physik.uni-bonn.de, E-mail: jihnekim@gmail.com, E-mail: hyun.min.lee@kias.re.kr

2013-03-01

We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodoxmore » Lagrangians.« less

Fluid Dynamics Lagrangian Simulation Model

NASA Astrophysics Data System (ADS)

Hyman, Ellis

1994-02-01

The work performed by Science Applications International Corporation (SAIC) on this contract, Fluid Dynamics Lagrangian Simulation Model, Contract Number N00014-89-C-2106, SAIC Project Number 01-0157-03-0768, focused on a number of research topics in fluid dynamics. The work was in support of the programs of NRL's Laboratory for Computational Physics and Fluid Dynamics and covered the period from 10 September 1989 to 9 December 1993. In the following sections, we describe each of the efforts and the results obtained. Much of the research work has resulted in journal publications. These are included in Appendices of this report for which the reader is referred for complete details.

Non-material finite element modelling of large vibrations of axially moving strings and beams

NASA Astrophysics Data System (ADS)

Vetyukov, Yury

2018-02-01

We present a new mathematical model for the dynamics of a beam or a string, which moves in a given axial direction across a particular domain. Large in-plane vibrations are coupled with the gross axial motion, and a Lagrangian (material) form of the equations of structural mechanics becomes inefficient. The proposed mixed Eulerian-Lagrangian description features mechanical fields as functions of a spatial coordinate in the axial direction. The material travels across a finite element mesh, and the boundary conditions are applied in fixed nodes. Beginning with the variational equation of virtual work in its material form, we analytically derive the Lagrange's equations of motion of the second kind for the considered case of a discretized non-material control domain and for geometrically exact kinematics. The dynamic analysis is straightforward as soon as the strain and the kinetic energies of the control domain are available. In numerical simulations we demonstrate the rapid mesh convergence of the model, the effect of the bending stiffness and the dynamic instability when the axial velocity gets high. We also show correspondence to the results of fully Lagrangian benchmark solutions.

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

DOE PAGES

Barlow, Andrew; Klima, Matej; Shashkov, Mikhail

2018-04-02

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

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

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

Barlow, Andrew; Klima, Matej; Shashkov, Mikhail

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

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

NASA Astrophysics Data System (ADS)

Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

2013-03-01

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

Segmental Analysis of Cardiac Short-Axis Views Using Lagrangian Radial and Circumferential Strain.

PubMed

Ma, Chi; Wang, Xiao; Varghese, Tomy

2016-11-01

Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a Lagrangian description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis-based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. Lagrangian strain variations demonstrate good agreement with the ideal strain when compared with Eulerian results. Lagrangian radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. Lagrangian radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. © The Author(s) 2015.

Segmental Analysis of Cardiac Short-Axis Views Using Lagrangian Radial and Circumferential Strain

PubMed Central

Ma, Chi; Wang, Xiao; Varghese, Tomy

2016-01-01

Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a Lagrangian description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis–based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. Lagrangian strain variations demonstrate good agreement with the ideal strain when compared with Eulerian results. Lagrangian radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. Lagrangian radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. PMID:26578642

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)

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

NASA Technical Reports Server (NTRS)

Lin, S.-J.; Einaudi, Franco (Technical Monitor)

2000-01-01

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

USGS Publications Warehouse

Jobson, Harvey E.

1980-01-01

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)

Sigma omega meson coupling and properties of nuclei and nuclear matter

NASA Astrophysics Data System (ADS)

Haidari, Maryam M.; Sharma, Madan M.

2008-05-01

We have constructed a Lagrangian model with a coupling of σ and ω mesons in the relativistic mean-field theory. Properties of finite nuclei and nuclear matter are explored with the new Lagrangian model SIG-OM. The study shows that an excellent description of binding energies and charge radii of nuclei over a large range of isospin is achieved with SIG-OM. With an incompressibility of nuclear matter K=265 MeV, it is also able to describe the breathing-mode isoscalar giant monopole resonance energies appropriately. It is shown that the high-density behaviour of the equation of state of nuclear and neutron matter with the σ-ω coupling is much softer than that of the non-linear scalar coupling model.

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.

Experimental determination of the turbulence in a liquid rocket combustion chamber

NASA Technical Reports Server (NTRS)

Hara, J.; Smith, L. O.; Partus, F. P.

1972-01-01

The intensity of turbulence and the Lagrangian correlation coefficient for a liquid rocket combustion chamber were determined experimentally using the tracer gas diffusion method. The results indicate that the turbulent diffusion process can be adequately modeled by the one-dimensional Taylor theory; however, the numerical values show significant disagreement with previously accepted values. The intensity of turbulence is higher by a factor of about two, while the Lagrangian correlation coefficient which was assumed to be unity in the past is much less than unity.

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.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

NASA Astrophysics Data System (ADS)

Khayyer, Abbas; Gotoh, Hitoshi; Falahaty, Hosein; Shimizu, Yuma

2018-02-01

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

Assimilation of drifters' trajectories in velocity fields from coastal radar and model via the Lagrangian assimilation algorithm LAVA.

NASA Astrophysics Data System (ADS)

Berta, Maristella; Bellomo, Lucio; Griffa, Annalisa; Gatimu Magaldi, Marcello; Marmain, Julien; Molcard, Anne; Taillandier, Vincent

2013-04-01

The Lagrangian assimilation algorithm LAVA (LAgrangian Variational Analysis) is customized for coastal areas in the framework of the TOSCA (Tracking Oil Spills & Coastal Awareness network) Project, to improve the response to maritime accidents in the Mediterranean Sea. LAVA assimilates drifters' trajectories in the velocity fields which may come from either coastal radars or numerical models. In the present study, LAVA is applied to the coastal area in front of Toulon (France). Surface currents are available from a WERA radar network (2km spatial resolution, every 20 minutes) and from the GLAZUR model (1/64° spatial resolution, every hour). The cluster of drifters considered is constituted by 7 buoys, transmitting every 15 minutes for a period of 5 days. Three assimilation cases are considered: i) correction of the radar velocity field, ii) correction of the model velocity field and iii) reconstruction of the velocity field from drifters only. It is found that drifters' trajectories compare well with the ones obtained by the radar and the correction to radar velocity field is therefore minimal. Contrarily, observed and numerical trajectories separate rapidly and the correction to the model velocity field is substantial. For the reconstruction from drifters only, the velocity fields obtained are similar to the radar ones, but limited to the neighbor of the drifter paths.

An approach for modeling thermal destruction of hazardous wastes in circulating fluidized bed incinerator.

PubMed

Patil, M P; Sonolikar, R L

2008-10-01

This paper presents a detailed computational fluid dynamics (CFD) based approach for modeling thermal destruction of hazardous wastes in a circulating fluidized bed (CFB) incinerator. The model is based on Eular - Lagrangian approach in which gas phase (continuous phase) is treated in a Eularian reference frame, whereas the waste particulate (dispersed phase) is treated in a Lagrangian reference frame. The reaction chemistry hasbeen modeled through a mixture fraction/ PDF approach. The conservation equations for mass, momentum, energy, mixture fraction and other closure equations have been solved using a general purpose CFD code FLUENT4.5. Afinite volume method on a structured grid has been used for solution of governing equations. The model provides detailed information on the hydrodynamics (gas velocity, particulate trajectories), gas composition (CO, CO2, O2) and temperature inside the riser. The model also allows different operating scenarios to be examined in an efficient manner.

Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

DESCRIPTION OF ATMOSPHERIC TRANSPORT PROCESSES IN EULERIAN AIR QUALITY MODELS

EPA Science Inventory

Key differences among many types of air quality models are the way atmospheric advection and turbulent diffusion processes are treated. Gaussian models use analytical solutions of the advection-diffusion equations. Lagrangian models use a hypothetical air parcel concept effecti...

Numerical modeling of pulsed laser-material interaction and of laser plume dynamics

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

Zhao, Qiang; Shi, Yina

2015-03-10

We have developed two-dimensional Arbitrary Lagrangian Eulerian (ALE) code which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with Lagrangian moving mesh distortion by mesh smoothing and conservative quantities remapping from Lagrangian mesh to smoothed one. A new second order accurate diffusion solver has been implemented for the thermal conduction and radiation transport on distorted mesh. The results of numerical simulation of pulsed laser ablation are presented. The influences of different processes, such as time evolution of the surfacemore » temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas are examined. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.« less

Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term

NASA Astrophysics Data System (ADS)

de la Cruz-Dombriz, Álvaro; Farrugia, Gabriel; Levi Said, Jackson; Sáez-Chillón Gómez, Diego

2017-12-01

In the context of extended teleparallel gravity theories with a 3  +  1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann-Lemaître-Robertson-Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the ΛCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.

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

PubMed

Lindner, Michael; Donner, Reik V

2017-03-01

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

Data Analysis and Non-local Parametrization Strategies for Organized Atmospheric Convection

NASA Astrophysics Data System (ADS)

Brenowitz, Noah D.

The intrinsically multiscale nature of moist convective processes in the atmosphere complicates scientific understanding, and, as a result, current coarse-resolution climate models poorly represent convective variability in the tropics. This dissertation addresses this problem by 1) studying new cumulus convective closures in a pair of idealized models for tropical moist convection, and 2) developing innovative strategies for analyzing high-resolution numerical simulations of organized convection. The first two chapters of this dissertation revisit a historical controversy about the use of convective closures based on the large-scale wind field or moisture convergence. In the first chapter, a simple coarse resolution stochastic model for convective inhibition is designed which includes the non-local effects of wind-convergence on convective activity. This model is designed to replicate the convective dynamics of a typical coarse-resolution climate prediction model. The non-local convergence coupling is motivated by the phenomena of gregarious convection, whereby mesoscale convective systems emit gravity waves which can promote convection at a distant locations. Linearized analysis and nonlinear simulations show that this convergence coupling allows for increased interaction between cumulus convection and the large-scale circulation, but does not suffer from the deleterious behavior of traditional moisture-convergence closures. In the second chapter, the non-local convergence coupling idea is extended to an idealized stochastic multicloud model. This model allows for stochastic transitions between three distinct cloud types, and non-local convergence coupling is most beneficial when applied to the transition from shallow to deep convection. This is consistent with recent observational and numerical modeling evidence, and there is a growing body of work highlighting the importance of this transition in tropical meteorology. In a series of idealized Walker cell simulations, convergence coupling enhances the persistence of Kelvin wave analogs in dry regions of the domain while leaving the dynamics in moist regions largely unaltered. The final chapter of this dissertation presents a technique for analyzing the variability of a direct numerical simulation of Rayleigh-Benard convection at large aspect ratio, which is a basic prototype of convective organization. High resolution numerical models are an invaluable tool for studying atmospheric dynamics, but modern data analysis techniques struggle with the extreme size of the model outputs and the trivial symmetries of the underlying dynamical systems (e.g. shift-invariance). A new data analysis approach which is invariant to spatial symmetries is derived by combining a quasi-Lagrangian description of the data, time-lagged embedding, and manifold learning techniques. The quasi-Lagrangian description is obtained by a straightforward isothermal binning procedure, which compresses the data in a dynamically-aware fashion. A small number of orthogonal modes returned by this algorithm are able to explain the highly intermittent dynamics of the bulk heat transfer, as quantified by the Nusselt Number.

Lagrangian transported MDF methods for compressible high speed flows

NASA Astrophysics Data System (ADS)

Gerlinger, Peter

2017-06-01

This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).

CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation. [hydroelasto-viscoplastic model

NASA Technical Reports Server (NTRS)

Lee, C. H.

1978-01-01

A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

A few words about resonances in the electroweak effective Lagrangian

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

Rosell, Ignasi; Pich, Antonio; Santos, Joaquín

Contrary to a widely spread believe, we have demonstrated that strongly coupled electroweak models including both a light Higgs-like boson and massive spin-1 resonances are not in conflict with experimental constraints on the oblique S and T parameters. We use an effective Lagrangian implementing the chiral symmetry breaking SU (2){sub L} ⊗ SU (2){sub R} → SU (2){sub L+R} that contains the Standard Model gauge bosons coupled to the electroweak Goldstones, one Higgs-like scalar state h with mass m{sub h} = 126 GeV and the lightest vector and axial-vector resonance multiplets V and A. We have considered the one-loop calculationmore » of S and T in order to study the viability of these strongly-coupled scenarios, being short-distance constraints and dispersive relations the main ingredients of the calculation. Once we have constrained the resonance parameters, we do a first approach to the determination of the low energy constants of the electroweak effective theory at low energies (without resonances). We show this determination in the case of the purely Higgsless bosonic Lagrangian.« less

Decoupling the Role of Inertia and Gravity on Particle Dispersion

NASA Technical Reports Server (NTRS)

Rogers, Chris; Squires, Kyle

1996-01-01

Turbulent gas flows laden with small, dense particles are encountered in a wide number of important applications in both industrial settings and aerodynamics applications. Particle interactions with the underlying turbulent flow are exceedingly complex and, consequently, difficult to accurately model. The difficulty arises primarily due to the fact that response of a particle to the local environment is dictated by turbulence properties in the reference frame moving with the particle (particle-Lagrangian). The particle-Lagrangian reference frame is in turn dependent upon the particle relaxation time (time constant) as well as gravitational drift. The combination of inertial and gravitational effects in this frame complicates our ability to accurately predict particle-laden flows since measurements in the particle-Lagrangian reference frame are difficult to obtain. Therefore, in this work we will examine separately the effects of inertia and gravitational drift on particle dispersion through a combination of physical and numerical experiments. In this study, particle-Lagrangian measurements will be obtained in physical experiments using stereo image velocimetry. Gravitational drift will be varied in the variable-g environments of the NASA DC-9 and in the zero-g environment at the drop tower at NASA-Lewis. Direct numerical simulations will be used to corroborate the measurements from the variable-g experiments. We expect that this work will generate new insight into the underlying physics of particle dispersion and will, in turn, lead to more accurate models of particle transport in turbulent flows.

Production of vector resonances at the LHC via WZ-scattering: a unitarized EChL analysis

NASA Astrophysics Data System (ADS)

Delgado, R. L.; Dobado, A.; Espriu, D.; Garcia-Garcia, C.; Herrero, M. J.; Marcano, X.; Sanz-Cillero, J. J.

2017-11-01

In the present work we study the production of vector resonances at the LHC by means of the vector boson scattering WZ → WZ and explore the sensitivities to these resonances for the expected future LHC luminosities. We are assuming that these vector resonances are generated dynamically from the self interactions of the longitudinal gauge bosons, W L and Z L , and work under the framework of the electroweak chiral Lagrangian to describe in a model independent way the supposedly strong dynamics of these modes. The properties of the vector resonances, mass, width and couplings to the W and Z gauge bosons are derived from the inverse amplitude method approach. We implement all these features into a single model, the IAM-MC, adapted for MonteCarlo, built in a Lagrangian language in terms of the electroweak chiral Lagrangian and a chiral Lagrangian for the vector resonances, which mimics the resonant behavior of the IAM and provides unitary amplitudes. The model has been implemented in MadGraph, allowing us to perform a realistic study of the signal versus background events at the LHC. In particular, we have focused our study on the pp → WZjj type of events, discussing first on the potential of the hadronic and semileptonic channels of the final WZ, and next exploring in more detail the most clear signals. These are provided by the leptonic decays of the gauge bosons, leading to a final state with ℓ 1 + ℓ 1 - ℓ 2 + νjj, ℓ = e, μ, having a very distinctive signature, and showing clearly the emergence of the resonances with masses in the range of 1.5-2.5 TeV, which we have explored.

Dredging for dilution: A simulation based case study in a Tidal River.

PubMed

Bilgili, Ata; Proehl, Jeffrey A; Swift, M Robinson

2016-02-01

A 2-D hydrodynamic finite element model with a Lagrangian particle module is used to investigate the effects of dredging on the hydrodynamics and the horizontal dilution of pollutant particles originating from a wastewater treatment facility (WWTF) in tidal Oyster River in New Hampshire, USA. The model is driven by the semi-diurnal (M2) tidal component and includes the effect of flooding and drying of riverine mud flats. The particle tracking method consists of tidal advection plus a horizontal random walk model of sub-grid scale turbulent processes. Our approach is to perform continuous pollutant particle releases from the outfall, simulating three different scenarios: a base-case representing the present conditions and two different dredged channel/outfall location configurations. Hydrodynamics are investigated in an Eulerian framework and Lagrangian particle dilution improvement ratios are calculated for all cases. Results show that the simulated hydrodynamics are consistent with observed conditions. Eulerian and Lagrangian residuals predict an outward path suggesting flushing of pollutants on longer (>M2) time scales. Simulated dilution maps show that, in addition to dredging, the relocation of the WWTF outfall into the dredged main channel is required for increased dilution performance. The methodology presented here can be applied to similar managerial problems in all similar systems worldwide with relatively little effort, with the combination of Lagrangian and Eulerian methods working together towards a better solution. The statistical significance brought into methodology, by using a large number of particles (16000 in this case), is to be emphasized, especially with the growing number of networked parallel computer clusters worldwide. This paper improves on the study presented in Bilgili et al., 2006b, by adding an Eulerian analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling possible spreadings of a buoyant surface plume with lagrangian and eulerian approaches at different resolutions using flow syntheses from 1992-2007 - a Gulf of Mexico study

NASA Astrophysics Data System (ADS)

Tulloch, R.; Hill, C. N.; Jahn, O.

2010-12-01

We present results from an ensemble of BP oil spill simulations. The oil spill slick is modeled as a buoyant surface plume that is transported by ocean currents modulated, in some experiments, by surface winds. Ocean currents are taken from ECCO2 project (see http://ecco2.org ) observationally constrained state estimates spanning 1992-2007. In this work we (i) explore the role of increased resolution of ocean eddies, (ii) compare inferences from particle based, lagrangian, approaches with eulerian, field based, approaches and (ii) examine the impact of differential response of oil particles and water to normal and extreme, hurricane derived, wind stress. We focus on three main questions. Is the simulated response to an oil spill markedly different for different years, depending on ocean circulation and wind forcing? Does the simulated response depend heavily on resolution and are lagrangian and eulerian estimates comparable? We start from two regional configurations of the MIT General Circulation Model (MITgcm - see http://mitgcm.org ) at 16km and 4km resolutions respectively, both covering the Gulf of Mexico and western North Atlantic regions. The simulations are driven at open boundaries with momentum and hydrographic fields from ECCO2 observationally constrained global circulation estimates. The time dependent surface flow fields from these simulations are used to transport a dye that can optionally decay over time (approximating biological breakdown) and to transport lagrangian particles. Using these experiments we examine the robustness of conclusions regarding the fate of a buoyant slick, injected at a single point. In conclusion we discuss how future drilling operations could use similar approaches to better anticipate outcomes of accidents both in this region and elsewhere.

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

Winther, Hans A.; Koyama, Kazuya; Wright, Bill S.

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

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

PubMed

James, Martin; Wilczek, Michael

2018-02-14

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

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.

Meshless Lagrangian SPH method applied to isothermal lid-driven cavity flow at low-Re numbers

NASA Astrophysics Data System (ADS)

Fraga Filho, C. A. D.; Chacaltana, J. T. A.; Pinto, W. J. N.

2018-01-01

SPH is a recent particle method applied in the cavities study, without many results available in the literature. The lid-driven cavity flow is a classic problem of the fluid mechanics, extensively explored in the literature and presenting a considerable complexity. The aim of this paper is to present a solution from the Lagrangian viewpoint for this problem. The discretization of the continuum domain is performed using the Lagrangian particles. The physical laws of mass, momentum and energy conservation are presented by the Navier-Stokes equations. A serial numerical code, written in Fortran programming language, has been used to perform the numerical simulations. The application of the SPH and comparison with the literature (mesh methods and a meshless collocation method) have been done. The positions of the primary vortex centre and the non-dimensional velocity profiles passing through the geometric centre of the cavity have been analysed. The numerical Lagrangian results showed a good agreement when compared to the results found in the literature, specifically for { Re} < 100.00 . Suggestions for improvements in the SPH model presented are listed, in the search for better results for flows with higher Reynolds numbers.

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.

Cine phase contrast MRI to measure continuum Lagrangian finite strain fields in contracting skeletal muscle.

PubMed

Zhou, Hehe; Novotny, John E

2007-01-01

To measure the complex mechanics and Lagrangian finite strain of contracting human skeletal muscle in vivo with cine phase contrast MRI (CPC-MRI) applied to the human supraspinatus muscle of the shoulder. Processing techniques are applied to transform velocities from CPC-MRI images to displacements and planar Lagrangian finite strain. An interpolation method describing the continuity of the velocity field and forward-backward and Fourier transform methods were used to track the displacement of regions of interest during a cyclic abduction motion of a subject's arm. The components of the Lagrangian strain tensor were derived during the motion and principal and maximum in-plane shear strain fields calculated. Derived displacement and strain fields are shown that describe the contraction mechanics of the supraspinatus. Strains vary over time during the cyclic motion and are highly nonuniform throughout the muscle. This method presented overcomes the physical resolution of the MRI scanner, which is crucial for the detection of detailed information within muscles, such as the changes that might occur with partial tears of the supraspinatus. These can then be used as input or validation data for modeling human skeletal muscle.

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.

Multiple quay cranes scheduling for double cycling in container terminals

PubMed Central

Chu, Yanling; Zhang, Xiaoju; Yang, Zhongzhen

2017-01-01

Double cycling is an efficient tool to increase the efficiency of quay crane (QC) in container terminals. In this paper, an optimization model for double cycling is developed to optimize the operation sequence of multiple QCs. The objective is to minimize the makespan of the ship handling operation considering the ship balance constraint. To solve the model, an algorithm based on Lagrangian relaxation is designed. Finally, we compare the efficiency of the Lagrangian relaxation based heuristic with the branch-and-bound method and a genetic algorithm using instances of different sizes. The results of numerical experiments indicate that the proposed model can effectively reduce the unloading and loading times of QCs. The effects of the ship balance constraint are more notable when the number of QCs is high. PMID:28692699

Multiple quay cranes scheduling for double cycling in container terminals.

PubMed

Chu, Yanling; Zhang, Xiaoju; Yang, Zhongzhen

2017-01-01

Double cycling is an efficient tool to increase the efficiency of quay crane (QC) in container terminals. In this paper, an optimization model for double cycling is developed to optimize the operation sequence of multiple QCs. The objective is to minimize the makespan of the ship handling operation considering the ship balance constraint. To solve the model, an algorithm based on Lagrangian relaxation is designed. Finally, we compare the efficiency of the Lagrangian relaxation based heuristic with the branch-and-bound method and a genetic algorithm using instances of different sizes. The results of numerical experiments indicate that the proposed model can effectively reduce the unloading and loading times of QCs. The effects of the ship balance constraint are more notable when the number of QCs is high.

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

EPA Science Inventory

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

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

NASA Astrophysics Data System (ADS)

Reyes, Jonathan; Shadwick, B. A.

2016-10-01

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

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

PubMed

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

2009-07-01

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

An investigation of turbulent transport in the extreme lower atmosphere

NASA Technical Reports Server (NTRS)

Koper, C. A., Jr.; Sadeh, W. Z.

1975-01-01

A model in which the Lagrangian autocorrelation is expressed by a domain integral over a set of usual Eulerian autocorrelations acquired concurrently at all points within a turbulence box is proposed along with a method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble to investigate the flow in the extreme lower atmosphere. Simultaneous measurements of turbulent velocity on a turbulence line along the wake axis were carried out utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity is approximated as a realization of a weakly self-stationary random process. Based on the Lagrangian autocorrelation it is found that: (1) large diffusion time predominated; (2) ratios of Lagrangian to Eulerian time and spatial scales were smaller than unity; and, (3) short and long diffusion time scales and diffusion spatial scales were constrained within their Eulerian counterparts.

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Smoothed Particle Hydrodynamics Simulations of Ultrarelativistic Shocks with Artificial Viscosity

NASA Astrophysics Data System (ADS)

Siegler, S.; Riffert, H.

2000-03-01

We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing suitable Lagrangian time evolution variables, from which the generic fluid variables of rest-mass density, 3-velocity, and thermodynamic pressure have to be determined. We present the corresponding equations for an ideal gas and show the existence and uniqueness of the solution. On the basis of the Lagrangian formulation we have developed a three-dimensional general relativistic smoothed particle hydrodynamics (SPH) code using the standard SPH formalism as known from nonrelativistic fluid dynamics. One-dimensional simulations of a shock tube and a wall shock are presented together with a two-dimensional test calculation of an inclined shock tube. With our method we can model ultrarelativistic fluid flows including shocks with Lorentz factors of even 1000.

Symmetries of relativistic world lines

NASA Astrophysics Data System (ADS)

Koch, Benjamin; Muñoz, Enrique; Reyes, Ignacio A.

2017-10-01

Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a fundamental symmetry, which is present for any Lagrangian term that involves x˙2. As a basic model that incorporates the fundamental symmetries of quantum gravity and string theory, we consider the Lagrangian action of the relativistic point particle. A path integral quantization for this seemingly simple system has long presented notorious problems. Here we show that those problems are overcome by taking into account the additional symmetry, leading directly to the exact Klein-Gordon propagator.

Towards Interpreting the Signal of CO2 Emissions from Megacities by Applying a Lagrangian Receptor-oriented Model to OCO-2 XCO2 data

NASA Astrophysics Data System (ADS)

Wu, D.; Lin, J. C.; Oda, T.; Ye, X.; Lauvaux, T.; Yang, E. G.; Kort, E. A.

2017-12-01

Urban regions are large emitters of CO2 whose emission inventories are still associated with large uncertainties. Therefore, a strong need exists to better quantify emissions from megacities using a top-down approach. Satellites — e.g., the Orbiting Carbon Observatory 2 (OCO-2), provide a platform for monitoring spatiotemporal column CO2 concentrations (XCO2). In this study, we present a Lagrangian receptor-oriented model framework and evaluate "model-retrieved" XCO2 by comparing against OCO-2-retrieved XCO2, for three megacities/regions (Riyadh, Cairo and Pearl River Delta). OCO-2 soundings indicate pronounced XCO2 enhancements (dXCO2) when crossing Riyadh, which are successfully captured by our model with a slight latitude shift. From this model framework, we can identify and compare the relative contributions of dXCO2 resulted from anthropogenic emission versus biospheric fluxes. In addition, to impose constraints on emissions for Riyadh through inversion methods, three uncertainties sources are addressed in this study, including 1) transport errors, 2) receptor and model setups in atmospheric models, and 3) urban emission uncertainties. For 1), we calculate transport errors by adding a wind error component to randomize particle distributions. For 2), a set of sensitivity tests using bootstrap method is performed to describe proper ways to setup receptors in Lagrangian models. For 3), both emission uncertainties from the Fossil Fuel Data Assimilation System (FFDAS) and the spread among three emission inventories are used to approximate an overall fractional uncertainty in modeled anthropogenic signal (dXCO2.anthro). Lastly, we investigate the definition of background (clean) XCO2 for megacities from retrieved XCO2 by means of statistical tools and our model framework.

Comparisons of Lagrangian and Eulerian PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions

NASA Astrophysics Data System (ADS)

Jaishree, J.; Haworth, D. C.

2012-06-01

Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, Lagrangian particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, Lagrangian particle PDF methods are computationally intensive and are not readily integrated into conventional Eulerian computational fluid dynamics (CFD) codes. Eulerian field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid Lagrangian particle/Eulerian mesh (LPEM) method, a stochastic Eulerian field (SEF) method and a deterministic Eulerian field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 Eulerian fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method, while MEPDF is the most computationally efficient of the three methods. These and other findings are discussed in detail.

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). In cosmology referring to the pancake model of Zel'dovich and the adhesion model of Gurbatov and Saichev, both assuming a clumping of matter at the intersection points of fluid particle trajectories (i.e. at the caustics), the foam-like large-scale structure of our Universe observed recently by Chandra X-ray observatory may be explained by the 3D convection of weakly interacting dark matter. Recent developments in plasma and nanotechnology-the miniaturization and fabrication of nanoelectronic devices being one example-have reinforced the interest in the quasi-ballistic electron transport in diodes and triodes, a field which turns out to be best treated by the Lagrangian fluid description. It is shown that the well-known space-charge-limited flow given by Child-Langmuir turns out to be incorrect in cases of finite electron injection velocities at the emitting electrode. In that case it is an intrinsic bifurcation scenario which is responsible for current limitation rather than electron reflection at the virtual cathode as intuitively assumed by Langmuir. The inclusion of a Drude friction term in the electron momentum equation can be handled solely by the Lagrangian fluid description. Exploiting the formula in case of field emission it is possible to bridge ballistic and drift-dominated transport. Furthermore, the transient processes in the electron transport triggered by the switching of the anode potential are shown to be perfectly accounted for by means of the Lagrangian fluid description. Finally, by use of the Lagrangian ion fluid equations in case of a two component, current driven plasma we derive a system of two coupled scalar wave equations which involve the specific volume of ions and electrons, respectively. It has a small amplitude strange soliton solution with unusual scaling properties. In case of charge neutrality the existence of two types of collapses are predicted, one being associated with a density excavation, the other one with a density clumping as in the laser induced ion expansion problem and in the cosmic sticking matter problem. However, only the latter will survive charge separation and hence be observable. In summary, the Lagrangian method of solving fluid equations turns out to be a powerful tool for compressible media in general. It offers new perspectives and addresses to a broad audience of physicists with interest in fields such as plasma and fluid dynamics, semiconductor- and astrophysics, to mention few of them.

Higher-Order Extended Lagrangian Born–Oppenheimer Molecular Dynamics for Classical Polarizable Models

DOE PAGES

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M. N.

2018-01-09

Generalized extended Lagrangian Born−Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate “shadow” potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential tomore » any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.« less

Development of an analytical Lagrangian model for passive scalar dispersion in low-wind speed meandering conditions

NASA Astrophysics Data System (ADS)

Stefanello, M. B.; Degrazia, G. A.; Mortarini, L.; Buligon, L.; Maldaner, S.; Carvalho, J. C.; Acevedo, O. C.; Martins, L. G. N.; Anfossi, D.; Buriol, C.; Roberti, D.

2018-02-01

Describing the effects of wind meandering motions on the dispersion of scalars is a challenging task, since this type of flow represents a physical state characterized by multiple scales. In this study, a Lagrangian stochastic diffusion model is derived to describe scalar transport during the horizontal wind meandering phenomenon that occurs within a planetary boundary layer. The model is derived from the linearization of the Langevin equation, and it employs a heuristic functional form that represents the autocorrelation function of meandering motion. The new solutions, which describe the longitudinal and lateral wind components, were used to simulate tracer experiments that were performed in low-wind speed conditions. The results of the comparison indicate that the new model can effectively reproduce the observed concentrations of the contaminants, and therefore, it can satisfactorily describe enhanced dispersion effects due to the presence of meandering.

Higher-Order Extended Lagrangian Born-Oppenheimer Molecular Dynamics for Classical Polarizable Models.

PubMed

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M N

2018-02-13

Generalized extended Lagrangian Born-Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate "shadow" potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential to any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.

Higher-Order Extended Lagrangian Born–Oppenheimer Molecular Dynamics for Classical Polarizable Models

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

Albaugh, Alex; Head-Gordon, Teresa; Niklasson, Anders M. N.

Generalized extended Lagrangian Born−Oppenheimer molecular dynamics (XLBOMD) methods provide a framework for fast iteration-free simulations of models that normally require expensive electronic ground state optimizations prior to the force evaluations at every time step. XLBOMD uses dynamically driven auxiliary degrees of freedom that fluctuate about a variationally optimized ground state of an approximate “shadow” potential which approximates the true reference potential. While the requirements for such shadow potentials are well understood, constructing such potentials in practice has previously been ad hoc, and in this work, we present a systematic development of XLBOMD shadow potentials that match the reference potential tomore » any order. We also introduce a framework for combining friction-like dissipation for the auxiliary degrees of freedom with general-order integration, a combination that was not previously possible. These developments are demonstrated with a simple fluctuating charge model and point induced dipole polarization models.« less

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.

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.

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.

The γ p →p η η reaction in an effective Lagrangian model

NASA Astrophysics Data System (ADS)

Liu, Bo-Chao; Chen, Shao-Fei

2017-11-01

In this paper, we investigate the γ p →p η η reaction within an effective Lagrangian approach and isobar model. We consider the contributions from the intermediate N*(1535 ) , N*(1650 ) , N*(1710 ) , and N*(1720 ) isobars which finally decay to the N η state. It is found that the excitation of the N*(1535 ) dominates this reaction close to threshold and ρ meson exchange plays the most important role for the excitation of nucleon resonances. Therefore, this reaction offers a potentially good place to study the properties of nucleon resonances and their couplings to the N ρ channel. Predictions for angular distributions and invariant mass spectra of final particles are also presented for future comparison with data.

Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

PubMed

Suk, Heejun

2016-07-01

MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the Lagrangian concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego

2011-10-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy introduced by the presence of the magnetic field (χ∥ /χ⊥ ~1010 in fusion plasmas). Recently, a novel Lagrangian method has been proposed to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids numerical pollution (in fact, it respects transport barriers -flux surfaces- exactly by construction), is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the Lagrangian approach to include perpendicular transport and sources. We present an asymptotic-preserving numerical formulation that ensures a consistent numerical discretization temporally and spatially for arbitrary χ∥ /χ⊥ ratios. This is of importance because parallel and perpendicular transport terms in the transport equation may become comparable in regions of the plasma (e.g., at incipient islands), while remaining disparate elsewhere. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry. D. del-Castillo-Negrete, L. Chacón, PRL, 106, 195004 (2011); DPP11 invited talk by del-Castillo-Negrete.

Modeling of Quasi-Four-Phase Flow in Continuous Casting Mold Using Hybrid Eulerian and Lagrangian Approach

NASA Astrophysics Data System (ADS)

Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan

2017-04-01

Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The Eulerian approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the Lagrangian way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/ h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/ h is larger than 0.4.

Coupling of Coastal Zone Color Scanner data to a physical-biological model of the southeastern U.S. continental shelf ecosystem. I - CZCS data description and Lagrangian particle tracing experiments. II - An Eulerian model. III - Nutrient and phytoplankton fluxes and CZCS data assimilation

NASA Technical Reports Server (NTRS)

Ishizaka, Joji

1990-01-01

Surface phytoplankton biomass of the southeastern U.S. continental shelf area is discussed based on coastal zone color scanner (CZCS) images obtained in April 1980. Data of chlorophyll distributions are analyzed in conjunction with concurrent flow and temperature fields. Lagrangian particle tracing experiments show that the particles move consistently with the evolution of the chlorophyll patterns. A four-component physical-biological model for a horizontal plane at a nominal depth of 17 m is presented. Model simulations using various physical-biological dynamics and boundary conditions show that the variability of chlorophyll distributions is controlled by horizontal advection. Phytoplankton and nutrient fluxes, calculated using the model, show considerable variability with time. The chlorophyll distributions obtained from the CZCS images are assimilated into the model to improve the phytoplankton flux estimates.

Soliton stability in some knot soliton models

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

Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A.

2007-02-15

We study the issue of stability of static solitonlike solutions in some nonlinear field theories which allow for knotted field configurations. Concretely, we investigate the Aratyn-Ferreira-Zimerman model [Phys. Lett. B 456, 162 (1999); Phys. Rev. Lett. 83, 1723 (1999)], based on a Lagrangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with different (integer) topological charges (Hopf index) are not separated by an infinite energy barrier. Further, if variations which change the topological charge are allowed, then the static solutions are not evenmore » critical points of the energy functional. We also explain why soliton solutions can exist at all, in spite of these facts. In addition, we briefly discuss the Nicole model [J. Phys. G 4, 1363 (1978)], which is based on a sigma-model-type Lagrangian. For the Nicole model we find that different topological sectors are separated by an infinite energy barrier.« less

Sources of Sahelian-Sudan moisture: Insights from a moisture-tracing atmospheric model

NASA Astrophysics Data System (ADS)

Salih, Abubakr A. M.; Zhang, Qiong; Pausata, Francesco S. R.; Tjernström, Michael

2016-07-01

The summer rainfall across Sahelian-Sudan is one of the main sources of water for agriculture, human, and animal needs. However, the rainfall is characterized by large interannual variability, which has attracted extensive scientific efforts to understand it. This study attempts to identify the source regions that contribute to the Sahelian-Sudan moisture budget during July through September. We have used an atmospheric general circulation model with an embedded moisture-tracing module (Community Atmosphere Model version 3), forced by observed (1979-2013) sea-surface temperatures. The result suggests that about 40% of the moisture comes with the moisture flow associated with the seasonal migration of the Intertropical Convergence Zone (ITCZ) and originates from Guinea Coast, central Africa, and the Western Sahel. The Mediterranean Sea, Arabian Peninsula, and South Indian Ocean regions account for 10.2%, 8.1%, and 6.4%, respectively. Local evaporation and the rest of the globe supply the region with 20.3% and 13.2%, respectively. We also compared the result from this study to a previous analysis that used the Lagrangian model FLEXPART forced by ERA-Interim. The two approaches differ when comparing individual regions, but are in better agreement when neighboring regions of similar atmospheric flow features are grouped together. Interannual variability with the rainfall over the region is highly correlated with contributions from regions that are associated with the ITCZ movement, which is in turn linked to the Atlantic Multidecadal Oscillation. Our result is expected to provide insights for the effort on seasonal forecasting of the rainy season over Sahelian Sudan.

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.

Hybrid finite difference/finite element immersed boundary method.

PubMed

E Griffith, Boyce; Luo, Xiaoyu

2017-12-01

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

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.

Lagrangian trajectories, residual currents and rectification process in the Northern Gulf of California

NASA Astrophysics Data System (ADS)

Rodríguez, Pablo Alonso; Carbajal, Noel; Rodríguez, Juan Heberto Gaviño

2017-07-01

Considering a semi-implicit approximation of the Coriolis terms, a numerical solution of the vertically integrated equations of motion is proposed. To test the two-dimensional numerical model, several experiments for the calculation of Euler, Stokes and Lagrange residual currents in the Gulf of California were carried out. To estimate the Lagrangian residual current, trajectories of particles were also simulated. The applied tidal constituents were M2, S2, K2, N2, K1, P1 and O1. At spring tides, strong tidal velocities occur in the northern half of the gulf. In this region of complex geometry, depths change from a few meter in the northern shelf zone to more than 3000 m in the southern part. In the archipelago region, the presence of islands alters amplitude and direction of tidal currents producing a rectification process which is reflected in a clockwise circulation around Tiburón Island in the Lagrangian residual current. The rectification process is explained by the superposition of the Euler and Stokes residual currents. Residual current patterns show several cyclonic and anticyclonic gyres in the Northern Gulf of California. Numerical experiments for individual and combinations of several tidal constituents revealed a large variability of Lagrangian trajectories.

Spatially homogeneous rotating world models.

NASA Technical Reports Server (NTRS)

Ozsvath, I.

1971-01-01

The mathematical problem encountered when looking for the simplest expanding and rotating model of the universe without the compactness condition for the space sections is formulated. The Lagrangian function is derived for four different rotating universes simultaneously. These models correspond in a certain sense to Godel's (1950) ?symmetric case.'

AGDRIFT: A MODEL FOR ESTIMATING NEAR-FIELD SPRAY DRIFT FROM AERIAL APPLICATIONS

EPA Science Inventory

The aerial spray prediction model AgDRIFT(R) embodies the computational engine found in the near-wake Lagrangian model AGricultural DISPersal (AGDISP) but with several important features added that improve the speed and accuracy of its predictions. This article summarizes those c...

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.

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.

Yang-Mills condensate as dark energy: A nonperturbative approach

NASA Astrophysics Data System (ADS)

Donà, Pietro; Marcianò, Antonino; Zhang, Yang; Antolini, Claudia

2016-02-01

Models based on the Yang-Mills condensate (YMC) have been advocated for in the literature and claimed as successful candidates for explaining dark energy. Several variations on this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, the previously attained results relied heavily on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in θ =-Fμν aFa μ ν/2 exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using nonperturbative techniques mutated from the functional renormalization-group procedure, we finally show that the minimum in θ of the effective Lagrangian exists. Thus, a YMC can actually take place. The nonperturbative model has properties similar to the ones in the perturbative model. In the early stage of the Universe, the YMC equation of state has an evolution that resembles the radiation component, i.e., wy→1 /3 . However, in the late stage, wy naturally runs to the critical state with wy=-1 , and the Universe transitions from a matter-dominated into a dark energy dominated stage only at latest time, at a redshift whose value depends on the initial conditions that are chosen while solving the dynamical system.

Unified formalism for higher order non-autonomous dynamical systems

NASA Astrophysics Data System (ADS)

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

2012-03-01

This work is devoted to giving a geometric framework for describing higher order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.

Lagrangian turbulence near walls: Structures and mixing in admissible model flows

NASA Astrophysics Data System (ADS)

Ottino, J. M.

1989-05-01

The general objective of work during this period was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: a perturbed Kelvin cat eyes flow, and prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: production flows capable of producing complex distributions of vorticity, and constructed flow fields, based on solutions of the Navier Stokes equations, which are capable of displaying both Eulerian and Lagrangian turbulence.

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.

Estimation of radionuclide (137Cs) emission rates from a nuclear power plant accident using the Lagrangian Particle Dispersion Model (LPDM).

PubMed

Park, Soon-Ung; Lee, In-Hye; Ju, Jae-Won; Joo, Seung Jin

2016-10-01

A methodology for the estimation of the emission rate of 137 Cs by the Lagrangian Particle Dispersion Model (LPDM) with the use of monitored 137 Cs concentrations around a nuclear power plant has been developed. This method has been employed with the MM5 meteorological model in the 600 km × 600 km model domain with the horizontal grid scale of 3 km × 3 km centered at the Fukushima nuclear power plant to estimate 137 Cs emission rate for the accidental period from 00 UTC 12 March to 00 UTC 6 April 2011. The Lagrangian Particles are released continuously with the rate of one particle per minute at the first level modelled, about 15 m above the power plant site. The presently developed method was able to simulate quite reasonably the estimated 137 Cs emission rate compared with other studies, suggesting the potential usefulness of the present method for the estimation of the emission rate from the accidental power plant without detailed inventories of reactors and fuel assemblies and spent fuels. The advantage of this method is not so complicated but can be applied only based on one-time forward LPDM simulation with monitored concentrations around the power plant, in contrast to other inverse models. It was also found that continuously monitored radionuclides concentrations from possibly many sites located in all directions around the power plant are required to get accurate continuous emission rates from the accident power plant. The current methodology can also be used to verify the previous version of radionuclides emissions used among other modeling groups for the cases of intermittent or discontinuous samplings. Copyright © 2016. Published by Elsevier Ltd.

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 implementation, transport of super-droplets in the physical space, and the coupling between super-droplets and the Eulerian temperature and water vapor field are discussed in detail. Some of these are relevant to the original super-droplet methodology as well and to the ice phase modeling using the Lagrangian approach. As a computational example, the scheme is applied to an idealized moist thermal rising in a stratified environment, with the original super-droplet methodology providing a benchmark to which the new scheme is compared.

Performance estimation of a Venturi scrubber using a computational model for capturing dust particles with liquid spray.

PubMed

Pak, S I; Chang, K S

2006-12-01

A Venturi scrubber has dispersed three-phase flow of gas, dust, and liquid. Atomization of a liquid jet and interaction between the phases has a large effect on the performance of Venturi scrubbers. In this study, a computational model for the interactive three-phase flow in a Venturi scrubber has been developed to estimate pressure drop and collection efficiency. The Eulerian-Lagrangian method is used to solve the model numerically. Gas flow is solved using the Eulerian approach by using the Navier-Stokes equations, and the motion of dust and liquid droplets, described by the Basset-Boussinesq-Oseen (B-B-O) equation, is solved using the Lagrangian approach. This model includes interaction between gas and droplets, atomization of a liquid jet, droplet deformation, breakup and collision of droplets, and capture of dust by droplets. A circular Pease-Anthony Venturi scrubber was simulated numerically with this new model. The numerical results were compared with earlier experimental data for pressure drop and collection efficiency, and gave good agreements.

Stochastic-field cavitation model

NASA Astrophysics Data System (ADS)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A cavitation model based on Eulerian stochastic fields

NASA Astrophysics Data System (ADS)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A Cohomological Perspective on Algebraic Quantum Field Theory

NASA Astrophysics Data System (ADS)

Hawkins, Eli

2018-05-01

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.

Data Assimilation Methods on a Non-conservative Adaptive Mesh

NASA Astrophysics Data System (ADS)

Guider, Colin Thomas; Rabatel, Matthias; Carrassi, Alberto; Jones, Christopher K. R. T.

2017-04-01

Adaptive mesh methods are used to model a wide variety of physical phenomena. Some of these models, in particular those of sea ice movement, are particularly interesting in that they use a remeshing process to remove and insert mesh points at various points in their evolution. This presents a challenge in developing compatible data assimilation schemes, as the dimension of the state space we wish to estimate can change over time when these remeshings occur. In this work, we first describe a remeshing scheme for an adaptive mesh in one dimension. We then develop advanced data assimilation methods that are appropriate for such a moving and remeshed grid. We hope to extend these techniques to two-dimensional models, like the Lagrangian sea ice model neXtSIM te{ns}. \\bibitem{ns} 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.

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.

Stochastic-field cavitation model

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

Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.

2013-07-15

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less

A COCHLEAR MODEL USING THE TIME-AVERAGED LAGRANGIAN AND THE PUSH-PULL MECHANISM IN THE ORGAN OF CORTI.

PubMed

Yoon, Yongjin; Puria, Sunil; Steele, Charles R

2009-09-05

In our previous work, the basilar membrane velocity V(BM) for a gerbil cochlea was calculated and compared with physiological measurements. The calculated V(BM) showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the V(BM) for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase.

A COCHLEAR MODEL USING THE TIME-AVERAGED LAGRANGIAN AND THE PUSH-PULL MECHANISM IN THE ORGAN OF CORTI

PubMed Central

YOON, YONGJIN; PURIA, SUNIL; STEELE, CHARLES R.

2010-01-01

In our previous work, the basilar membrane velocity VBM for a gerbil cochlea was calculated and compared with physiological measurements. The calculated VBM showed excessive phase excursion and, in the active case, a best-frequency place shift of approximately two fifths of an octave higher. Here we introduce a refined model that uses the time-averaged Lagrangian for the conservative system to resolve the phase excursion issues. To improve the overestimated best-frequency place found in the previous feed-forward active model, we implement in the new model a push-pull mechanism from the outer hair cells and phalangeal process. Using this new model, the VBM for the gerbil cochlea was calculated and compared with animal measurements, The results show excellent agreement for mapping the location of the maximum response to frequency, while the agreement for the response at a fixed point as a function of frequency is excellent for the amplitude and good for the phase. PMID:20485540

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

Transport upscaling from pore- to Darcy-scale: Incorporating pore-scale Berea sandstone Lagrangian velocity statistics into a Darcy-scale transport CTRW model

NASA Astrophysics Data System (ADS)

Puyguiraud, Alexandre; Dentz, Marco; Gouze, Philippe

2017-04-01

For the past several years a lot of attention has been given to pore-scale flow in order to understand and model transport, mixing and reaction in porous media. Nevertheless we believe that an accurate study of spatial and temporal evolution of velocities could bring important additional information for the upscaling from pore to higher scales. To gather these pieces of information, we perform Stokes flow simulations on pore-scale digitized images of a Berea sandstone core. First, micro-tomography (XRMT) imaging and segmentation processes allow us to obtain 3D black and white images of the sample [1]. Then we used an OpenFoam solver to perform the Stokes flow simulations mentioned above, which gives us the velocities at the interfaces of a cubic mesh. Subsequently, we use a particle streamline reconstruction technique which uses the Eulerian velocity field previously obtained. This technique, based on a modified Pollock algorithm [2], enables us to make particle tracking simulations on the digitized sample. In order to build a stochastic pore-scale transport model, we analyze the Lagrangian velocity series in two different ways. First we investigate the velocity evolution by sampling isochronically (t-Lagrangian), and by studying its statistical properties in terms of one- and two-points statistics. Intermittent patterns can be observed. These are due to the persistance of low velocities over a characteristic space length. Other results are investigated, such as correlation functions and velocity PDFs, which permit us to study more deeply this persistence in the velocities and to compute the correlation times. However, with the second approach, doing these same analysis in space by computing the velocities equidistantly, enables us to remove the intermittency shown in the temporal evolution and to model these velocity series as a Markov process. This renders the stochastic particle dynamics into a CTRW [3]. [1] Gjetvaj, F., A. Russian, P. Gouze, and M. Dentz (2015), Dual control of flow field heterogeneity and immobile porosity on non-Fickian transport in Berea sandstone, Water Resour. Res., 51, 8273-8293, doi:10.1002/2015WR017645. [2] Mostaghimi, P., Bijeljic, B., Blunt, M. (2012). Simulation of Flow and Dispersion on Pore-Space Images. Society of Petroleum Engineers. doi:10.2118/135261-PA. [3] Dentz, M., P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, Continuous time random walks for the evolution of Lagrangian velocities, Phys. Rev. Fluids, 2016. Keywords: Porescale, particle tracking, transport, Lagrangian velocity, ergodicity, Markovianity, continuous time random walks, upscaling.

Lagrangian-based Backtracking of Oil Spill Dynamics from SAR Images: Application to Montara Case

NASA Astrophysics Data System (ADS)

Gautama, Budhi Gunadharma; Mercier, Gregoire; Fablet, Ronan; Longepe, Nicolas

2016-08-01

Within the framework of INDESO project (Infrastructure Development Space Oceanography), we address the issue of oilspill and aim at developing an operational SAR- based system for monitoring this issue in Indonesian waters from space. In this work, we focus on the backtrack- ing of an oilspill detected from SAR observations. As a case-study, we consider one large oil spill event that happened in Indonesian waters in 2009, referred to as the Montara oilspill. On 21 August 2009, the Montara Wellhead Platform had an uncontrolled release of hydrocarbons from one of the platform wells. It was estimated that 400 barrels (or approximately 64 tonnes) of crude oil were being lost per day. The uncontrolled release continued until 3 November 2009 and response operations continued until 3 December 2009. In this work, we develop a Langragian analysis and associated numerical inversion tools with a view to further analyzing the oil spread due to the Montara Wellhead Platform. Our model relies on a 2D Lagrangian transport model developed by CLS (Collecte Localisation Satellite). Our model involves four main parameters : the weights of wind- related and current-related advection, the origin and the duration of the oil leakage. Given SAR oilspill detections, we propose a numerical inversion of the parameters of the Lagrangian model, so that the simulated drift match the SAR observations of the oil spill. We demonstrate the relevance of the proposed model and numerical scheme for the Montara oilspill and further discuss their operational interest for the space-based oilspill backtracking and forecasting.

Predicting dense nonaqueous phase liquid dissolution using a simplified source depletion model parameterized with partitioning tracers

NASA Astrophysics Data System (ADS)

Basu, Nandita B.; Fure, Adrian D.; Jawitz, James W.

2008-07-01

Simulations of nonpartitioning and partitioning tracer tests were used to parameterize the equilibrium stream tube model (ESM) that predicts the dissolution dynamics of dense nonaqueous phase liquids (DNAPLs) as a function of the Lagrangian properties of DNAPL source zones. Lagrangian, or stream-tube-based, approaches characterize source zones with as few as two trajectory-integrated parameters, in contrast to the potentially thousands of parameters required to describe the point-by-point variability in permeability and DNAPL in traditional Eulerian modeling approaches. The spill and subsequent dissolution of DNAPLs were simulated in two-dimensional domains having different hydrologic characteristics (variance of the log conductivity field = 0.2, 1, and 3) using the multiphase flow and transport simulator UTCHEM. Nonpartitioning and partitioning tracers were used to characterize the Lagrangian properties (travel time and trajectory-integrated DNAPL content statistics) of DNAPL source zones, which were in turn shown to be sufficient for accurate prediction of source dissolution behavior using the ESM throughout the relatively broad range of hydraulic conductivity variances tested here. The results were found to be relatively insensitive to travel time variability, suggesting that dissolution could be accurately predicted even if the travel time variance was only coarsely estimated. Estimation of the ESM parameters was also demonstrated using an approximate technique based on Eulerian data in the absence of tracer data; however, determining the minimum amount of such data required remains for future work. Finally, the stream tube model was shown to be a more unique predictor of dissolution behavior than approaches based on the ganglia-to-pool model for source zone characterization.

On modeling heterogeneous coastal sediment transport - A numerical study using multiphase Eulerian and Euler-Lagrangian approaches

NASA Astrophysics Data System (ADS)

Cheng, Z.; Yu, X.; Hsu, T. J.; Calantoni, J.; Chauchat, J.

2016-02-01

Regional scale coastal evolution models do not explicitly resolve wave-driven sediment transport and must rely on bedload/suspended modules that utilize empirical assumptions. Under extreme wave events or in regions of high sediment heterogeneity, these empirical bedload/suspended load modules may need to be reevaluated with detailed observation and more sophisticated small-scale models. In the past decade, significant research efforts have been devoted to modeling sediment transport using multiphase Eulerian or Euler-Lagrangian approaches. Recently, an open-source multi-dimensional Reynolds-averaged two-phase sediment transport model, SedFOAM is developed by the authors and it has been adopted by many researchers to study momentary bed failure, granular rheology in sheet flow and scour around structures. In this abstract, we further report our recent progress made in extending the model with 3D turbulence-resolving capability and to model the sediment phase with the Discrete Element method (DEM). Adopting the large-eddy simulation methodology, we validate the 3D model with measured fine sediment transport is oscillatory sheet flow and demonstrate that the model is able to resolve sediment burst events during flow reversals. To better resolve the intergranular interactions and to model heterogeneous properties of sediment (e.g., mixed grain sizes and grain shape), we use an Euler-Lagrangian solver called CFDEM, which couples OpenFOAM for the fluid phase and LIGGGHTS for the particle phase. We improve the model by better enforcing conservation of mass in the pressure solver. The modified CFDEM solver is validated with measured oscillatory sheet flow data for coarse sand and we demonstrated that the model can reproduce the well-known armoring effects. We show that under Stokes second-order wave forcing, the armoring effect is more significant during the energetic positive peak, and hence the net onshore transport is reduced. Preliminary results modeling the shape effects using composite particles will be presented. This research is supported by Office of Naval Research and National Science Foundation.

Using growth and arrest of Richtmyer-Meshkov instabilities and Lagrangian simulations to study high-rate material strength

NASA Astrophysics Data System (ADS)

Prime, M. B.; Vaughan, D. E.; Preston, D. L.; Buttler, W. T.; Chen, S. R.; Oró, D. M.; Pack, C.

2014-05-01

Experiments applying a supported shock through mating surfaces (Atwood number = 1) with geometrical perturbations have been proposed for studying strength at strain rates up to 107/s using Richtmyer-Meshkov (RM) instabilities. Buttler et al. recently reported experimental results for RM instability growth in copper but with an unsupported shock applied by high explosives and the geometrical perturbations on the opposite free surface (Atwood number = -1). This novel configuration allowed detailed experimental observation of the instability growth and arrest. We present results and interpretation from numerical simulations of the Buttler RM instability experiments. Highly-resolved, two-dimensional simulations were performed using a Lagrangian hydrocode and the Preston-Tonks-Wallace (PTW) strength model. The model predictions show good agreement with the data. The numerical simulations are used to examine various assumptions previously made in an analytical model and to estimate the sensitivity of such experiments to material strength.

Pressure oscillations and instability of working processes in the combustion chambers of solid rocket motors

NASA Astrophysics Data System (ADS)

Emelyanov, V. N.; Teterina, I. V.; Volkov, K. N.; Garkushev, A. U.

2017-06-01

Metal particles are widely used in space engineering to increase specific impulse and to supress acoustic instability of intra-champber processes. A numerical analysis of the internal injection-driven turbulent gas-particle flows is performed to improve the current understanding and modeling capabilities of the complex flow characteristics in the combustion chambers of solid rocket motors (SRMs) in presence of forced pressure oscillations. The two-phase flow is simulated with a combined Eulerian-Lagrangian approach. The Reynolds-averaged Navier-Stokes equations and transport equations of k - ε model are solved numerically for the gas. The particulate phase is simulated through a Lagrangian deterministic and stochastic tracking models to provide particle trajectories and particle concentration. The results obtained highlight the crucial significance of the particle dispersion in turbulent flowfield and high potential of statistical methods. Strong coupling between acoustic oscillations, vortical motion, turbulent fluctuations and particle dynamics is observed.

Comment on: "Corrections to the Mathematical Formulation of a Backwards Lagrangian Particle Dispersion Model" by Gibson and Sailor (2012: Boundary-Layer Meteorology 145, 399-406)

NASA Astrophysics Data System (ADS)

Stöckl, Stefan; Rotach, Mathias W.; Kljun, Natascha

2018-01-01

We discuss the results of Gibson and Sailor (Boundary-Layer Meteorol 145:399-406, 2012) who suggest several corrections to the mathematical formulation of the Lagrangian particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367-389, 1996). While most of the suggested corrections had already been implemented in the 1990s, one suggested correction raises a valid point, but results in a violation of the well-mixed criterion. Here we improve their idea and test the impact on model results using a well-mixed test and a comparison with wind-tunnel experimental data. The new approach results in similar dispersion patterns as the original approach, while the approach suggested by Gibson and Sailor leads to erroneously reduced concentrations near the ground in convective and especially forced convective conditions.

Complete Hamiltonian analysis of cosmological perturbations at all orders

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2016-06-01

In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the 'gauge-fixing' issues and extend the analysis to scalar field models and show that our approach can be applied to any order of perturbation for any first order derivative fields. In the case of Galilean scalar fields, our procedure can extract constrained relations at all orders in perturbations leading to the fact that there is no extra degrees of freedom due to the presence of higher time derivatives of the field in themore » Lagrangian. We compare and contrast our approach to the Lagrangian approach (Chen et al. [2006]) for extracting higher order correlations and show that our approach is efficient and robust and can be applied to any model of gravity and matter fields without invoking slow-roll approximation.« less

Torus Knots and the Topological Vertex

NASA Astrophysics Data System (ADS)

Jockers, Hans; Klemm, Albrecht; Soroush, Masoud

2014-08-01

We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S 3. The key role is played by the transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S 3, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi-Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.

Reference level winds from balloon platforms

NASA Technical Reports Server (NTRS)

Lally, Vincent E.

1985-01-01

The superpressure balloon was developed to provide a method of obtaining global winds at all altitudes from 5 to 30 km. If a balloon could be made to fly for several weeks at a constant altitude, and if it could be tracked accurately on its global circuits, the balloon would provide a tag for the air parcel in which it was embedded. The Lagrangian data on the atmospheric circulation would provide a superior data input to the numerical model. The Global Atmospheric Research Program (GARP) was initiated in large part based on the promise of this technique coupled with free-floating ocean buoys and satellite radiometers. The initial name proposed by Charney for GARP was SABABURA 'SAtellite BAlloon BUoy RAdiometric system' (Charney, 1966). However, although the superpressure balloon exceeded its designers' expectations for flight duration in the stratosphere (longest flight duration of 744 days), flight duration below 10 km was limited by icing in super-cooled clouds to a few days. The balloon was relegated to a secondary role during the GARP Special Observing Periods. The several major superpressure balloon programs for global wind measurement are described as well as those new developments which make the balloon once again an attractive vehicle for measurement of global winds as a reference and bench-mark system for future satellite systems.

Monte Carlo charged-particle tracking and energy deposition on a Lagrangian mesh.

PubMed

Yuan, J; Moses, G A; McKenty, P W

2005-10-01

A Monte Carlo algorithm for alpha particle tracking and energy deposition on a cylindrical computational mesh in a Lagrangian hydrodynamics code used for inertial confinement fusion (ICF) simulations is presented. The straight line approximation is used to follow propagation of "Monte Carlo particles" which represent collections of alpha particles generated from thermonuclear deuterium-tritium (DT) reactions. Energy deposition in the plasma is modeled by the continuous slowing down approximation. The scheme addresses various aspects arising in the coupling of Monte Carlo tracking with Lagrangian hydrodynamics; such as non-orthogonal severely distorted mesh cells, particle relocation on the moving mesh and particle relocation after rezoning. A comparison with the flux-limited multi-group diffusion transport method is presented for a polar direct drive target design for the National Ignition Facility. Simulations show the Monte Carlo transport method predicts about earlier ignition than predicted by the diffusion method, and generates higher hot spot temperature. Nearly linear speed-up is achieved for multi-processor parallel simulations.

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

Impact of data assimilation on ocean current forecasts in the Angola Basin

NASA Astrophysics Data System (ADS)

Phillipson, Luke; Toumi, Ralf

2017-06-01

The ocean current predictability in the data limited Angola Basin was investigated using the Regional Ocean Modelling System (ROMS) with four-dimensional variational data assimilation. Six experiments were undertaken comprising a baseline case of the assimilation of salinity/temperature profiles and satellite sea surface temperature, with the subsequent addition of altimetry, OSCAR (satellite-derived sea surface currents), drifters, altimetry and drifters combined, and OSCAR and drifters combined. The addition of drifters significantly improves Lagrangian predictability in comparison to the baseline case as well as the addition of either altimetry or OSCAR. OSCAR assimilation only improves Lagrangian predictability as much as altimetry assimilation. On average the assimilation of either altimetry or OSCAR with drifter velocities does not significantly improve Lagrangian predictability compared to the drifter assimilation alone, even degrading predictability in some cases. When the forecast current speed is large, it is more likely that the combination improves trajectory forecasts. Conversely, when the currents are weaker, it is more likely that the combination degrades the trajectory forecast.

A novel method for unsteady flow field segmentation based on stochastic similarity of direction

NASA Astrophysics Data System (ADS)

Omata, Noriyasu; Shirayama, Susumu

2018-04-01

Recent developments in fluid dynamics research have opened up the possibility for the detailed quantitative understanding of unsteady flow fields. However, the visualization techniques currently in use generally provide only qualitative insights. A method for dividing the flow field into physically relevant regions of interest can help researchers quantify unsteady fluid behaviors. Most methods at present compare the trajectories of virtual Lagrangian particles. The time-invariant features of an unsteady flow are also frequently of interest, but the Lagrangian specification only reveals time-variant features. To address these challenges, we propose a novel method for the time-invariant spatial segmentation of an unsteady flow field. This segmentation method does not require Lagrangian particle tracking but instead quantitatively compares the stochastic models of the direction of the flow at each observed point. The proposed method is validated with several clustering tests for 3D flows past a sphere. Results show that the proposed method reveals the time-invariant, physically relevant structures of an unsteady flow.

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

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).

The Hamiltonian and Lagrangian approaches to the dynamics of nonholonomic systems

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Marsden, Jerrold E.

1997-08-01

This paper compares the Hamiltonian approach to systems with nonholonomic constraints (see [31, 2, 4, 29] and references therein) with the Lagrangian approach (see [16, 27, 9]). There are many differences in the approaches and each has its own advantages; some structures have been discovered on one side and their analogues on the other side are interesting to clarify. For example, the momentum equation and the reconstruction equation were first found on the Lagrangian side and are useful for the control theory of these systems, while the failure of the reduced two-form to be closed (i.e., the failure of the Poisson bracket to satisfy the Jacobi identity) was first noticed on the Hamiltonian side. Clarifying the relation between these approaches is important for the future development of the control theory and stability and bifurcation theory for such systems. In addition to this work, we treat, in this unified framework, a simplified model of the bicycle (see [12, 13]), which is an important underactuated (nonminimum phase) control system.

Influence of Installation Effects on Pile Bearing Capacity in Cohesive Soils - Large Deformation Analysis Via Finite Element Method

NASA Astrophysics Data System (ADS)

Konkol, Jakub; Bałachowski, Lech

2017-03-01

In this paper, the whole process of pile construction and performance during loading is modelled via large deformation finite element methods such as Coupled Eulerian Lagrangian (CEL) and Updated Lagrangian (UL). Numerical study consists of installation process, consolidation phase and following pile static load test (SLT). The Poznań site is chosen as the reference location for the numerical analysis, where series of pile SLTs have been performed in highly overconsolidated clay (OCR ≈ 12). The results of numerical analysis are compared with corresponding field tests and with so-called "wish-in-place" numerical model of pile, where no installation effects are taken into account. The advantages of using large deformation numerical analysis are presented and its application to the pile designing is shown.

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.

What If We Had A Magnetograph at Lagrangian L5?

NASA Technical Reports Server (NTRS)

Pevtsov, Alexei A.; Bertello, Luca; MacNeice, Peter; Petrie, Gordon

2016-01-01

Synoptic Carrington charts of magnetic field are routinely used as an input for modelings of solar wind and other aspects of space weather forecast. However, these maps are constructed using only the observations from the solar hemisphere facing Earth. The evolution of magnetic flux on the "farside" of the Sun, which may affect the topology of coronal field in the "nearside," is largely ignored. It is commonly accepted that placing a magnetograph in Lagrangian L5 point would improve the space weather forecast. However, the quantitative estimates of anticipated improvements have been lacking. We use longitudinal magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) to investigate how adding data from L5 point would affect the outcome of two major models used in space weather forecast.

Inverse constraints for emission fluxes of atmospheric tracers estimated from concentration measurements and Lagrangian transport

NASA Astrophysics Data System (ADS)

Pisso, Ignacio; Patra, Prabir; Breivik, Knut

2015-04-01

Lagrangian transport models based on times series of Eulerian fields provide a computationally affordable way of achieving very high resolution for limited areas and time periods. This makes them especially suitable for the analysis of point-wise measurements of atmospheric tracers. We present an application illustrated with examples of greenhouse gases from anthropogenic emissions in urban areas and biogenic emissions in Japan and of pollutants in the Arctic. We asses the algorithmic complexity of the numerical implementation as well as the use of non-procedural techniques such as Object-Oriented programming. We discuss aspects related to the quantification of uncertainty from prior information in the presence of model error and limited number of observations. The case of non-linear constraints is explored using direct numerical optimisation methods.

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 particulate matter and some toxic compounds, such as formaldehyde and 1,3-butadiene.

Topological characteristics underpin intermittency and anomalous transport behavior in soil-like porous media

NASA Astrophysics Data System (ADS)

Holzner, M.; Morales, V.; Willmann, M.; Jerjen, I.; Kaufmann, R.; Dentz, M.

2016-12-01

Continuum models of porous media are based on the validity of the Darcy equation for fluid and Fick's law for scalar fluxes on a representative elementary volume. Fluctuations of pore-scale flow and scalar transport are averaged out and represented in terms of effective parameters such as hydrodynamic dispersion. However, the intermittent behavior of pore-scale flow impacts on the nature of particle and scalar transport, and it determines the way dissolved substances mix and react. The understanding of the origin of these processes is of both fundamental and practical importance in applications ranging from reactive transport in groundwater flow to diffusion in fuel cells or biological systems. A central issue in porous medium flow is therefore to relate intermittent behavior of Lagrangian velocity at pore scale imposed by the complex pore network geometry to transport properties at larger scales. Lagrangian measurements in porous systems are nonetheless scarce and most experimental techniques do not provide access to all three velocity components. In this contribution we report 3D measurements of Lagrangian velocity in soil-like porous media. We complement these measurements with detailed X-ray scans of the pore network. We find sharp velocity 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 and a superlinear evolution of particle dispersion. We demonstrate that porosity and pore size distribution alone cannot explain the observed features of the flow. Rather, anomalous transport is better interpreted in terms of how pores of various geometries are interconnected. We reproduce the main observations using a continuous-time random walk (CTRW) model revealing the main features that control the system and showing the potential of this simple model to capture transport in complex geometries.

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.

Water Temperature changes in the Mississippi River Basin

EPA Science Inventory

In this study, we demonstrate the transfer of a physically based semi-Lagrangian water temperature model (RBM) to EPA, its linkage with the Variable Infiltration Capacity (VIC) hydrology model, and its calibration to and demonstration for the Mississippi River Basin (MRB). The r...

AN OPTIMAL ADAPTIVE LOCAL GRID REFINEMENT APPROACH TO MODELING CONTAMINANT TRANSPORT

EPA Science Inventory

A Lagrangian-Eulerian method with an optimal adaptive local grid refinement is used to model contaminant transport equations. pplication of this approach to two bench-mark problems indicates that it completely resolves difficulties of peak clipping, numerical diffusion, and spuri...

An extended transfer operator approach to identify separatrices in open flows

NASA Astrophysics Data System (ADS)

Lünsmann, Benedict; Kantz, Holger

2018-05-01

Vortices of coherent fluid volume are considered to have a substantial impact on transport processes in turbulent media. Yet, due to their Lagrangian nature, detecting these structures is highly nontrivial. In this respect, transfer operator approaches have been proven to provide useful tools: Approximating a possibly time-dependent flow as a discrete Markov process in space and time, information about coherent structures is contained in the operator's eigenvectors, which is usually extracted by employing clustering methods. Here, we propose an extended approach that couples surrounding filaments using "mixing boundary conditions" and focuses on the separation of the inner coherent set and embedding outer flow. The approach refrains from using unsupervised machine learning techniques such as clustering and uses physical arguments by maximizing a coherence ratio instead. We show that this technique improves the reconstruction of separatrices in stationary open flows and succeeds in finding almost-invariant sets in periodically perturbed flows.

Superconformal Algebraic Approach to Hadron Structure

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

de Teramond, Guy F.; Brodsky, Stanley J.; Deur, Alexandre

2017-03-01

Fundamental aspects of nonperturbative QCD dynamics which are not obvious from its classical Lagrangian, such as the emergence of a mass scale and confinement, the existence of a zero mass bound state, the appearance of universal Regge trajectories and the breaking of chiral symmetry are incorporated from the onset in an effective theory based on superconformal quantum mechanics and its embedding in a higher dimensional gravitational theory. In addition, superconformal quantum mechanics gives remarkable connections between the light meson and nucleon spectra. This new approach to hadron physics is also suitable to describe nonperturbative QCD observables based on structure functions,more » such as GPDs, which are not amenable to a first-principle computation. The formalism is also successful in the description of form factors, the nonperturbative behavior of the strong coupling and diffractive processes. We also discuss in this article how the framework can be extended rather successfully to the heavy-light hadron sector.« less

Lagrangian particles with mixing. I. Simulating scalar transport

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2009-06-01

The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by Lagrangian particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by Lagrangian particles with localized mixing is specifically considered.

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.

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.

Estimating cosmic velocity fields from density fields and tidal tensors

NASA Astrophysics Data System (ADS)

Kitaura, Francisco-Shu; Angulo, Raul E.; Hoffman, Yehuda; Gottlöber, Stefan

2012-10-01

In this work we investigate the non-linear and non-local relation between cosmological density and peculiar velocity fields. Our goal is to provide an algorithm for the reconstruction of the non-linear velocity field from the fully non-linear density. We find that including the gravitational tidal field tensor using second-order Lagrangian perturbation theory based upon an estimate of the linear component of the non-linear density field significantly improves the estimate of the cosmic flow in comparison to linear theory not only in the low density, but also and more dramatically in the high-density regions. In particular we test two estimates of the linear component: the lognormal model and the iterative Lagrangian linearization. The present approach relies on a rigorous higher order Lagrangian perturbation theory analysis which incorporates a non-local relation. It does not require additional fitting from simulations being in this sense parameter free, it is independent of statistical-geometrical optimization and it is straightforward and efficient to compute. The method is demonstrated to yield an unbiased estimator of the velocity field on scales ≳5 h-1 Mpc with closely Gaussian distributed errors. Moreover, the statistics of the divergence of the peculiar velocity field is extremely well recovered showing a good agreement with the true one from N-body simulations. The typical errors of about 10 km s-1 (1σ confidence intervals) are reduced by more than 80 per cent with respect to linear theory in the scale range between 5 and 10 h-1 Mpc in high-density regions (δ > 2). We also find that iterative Lagrangian linearization is significantly superior in the low-density regime with respect to the lognormal model.

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.

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.

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

"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.

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

Coupled Eulerian-Lagrangian transport of large debris by tsunamis

NASA Astrophysics Data System (ADS)

Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos

2016-04-01

Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the conservativeness of the model. This way, in highly resolved meshes and high quantities of debris, the model approaches full conservativeness only if the two-way coupling feature is present, an effect that is attenuated in coarse meshes or with small debris quantities. Aknownledgements: This work was partially funded by FEDER, program COMPETE, and by national funds through the Portuguese Foundation for Science and Technology (FCT) with project RECI/ECM-HID/0371/2012. References: Baptista M.A. & Miranda, J.M. (2009) Revision of the Portuguese catalog of tsunamis. Nat. Hazards Earth Syst. Sci., 9, 25-42. Conde, D. A. S.; Baptista, M. A. V.; Sousa Oliveira, C. & Ferreira, R. M. L. (2013) A shallow-flow model for the propagation of tsunamis over complex geometries and mobile beds, Nat. Hazards Earth Syst. Sci., 13, 2533-2542. Conde, D. A. S.; Baptista, M. A. V.; Sousa Oliveira, C. & Ferreira, R. M. L. (2015) Mathematical modelling of tsunami impacts on critical infrastructures: exposure and severity associated with debris transport at Sines port. EGU General Assembly 2015, Vienna, Austria. Ferreira, R. M. L.; Franca, M. J.; Leal, J. G. & Cardoso, A. H. (2009) Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics, Can. J. Civil. Eng., 36, 1604-1621. LeVeque, R. J., George, D. L., & Berger, M. J. (2011) Tsunami modelling with adaptively refined finite volume methods, Acta Numerica, pp. 211-289.

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 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.

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.

3DFATMIC: THREE DIMENSIONAL SUBSURFACE FLOW, FATE AND TRANSPORT OF MICROBES AND CHEMICALS MODEL - USER'S MANUAL VERSION 1.0

EPA Science Inventory

This document is the user's manual of 3DFATMIC, a 3-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals Model using a Lagrangian-Eulerian adapted zooming and peak capturing (LEZOOMPC) algorithm.

A semi-Lagrangian advection scheme for radioactive tracers in a regional spectral model

NASA Astrophysics Data System (ADS)

Chang, E.-C.; Yoshimura, K.

2015-06-01

In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) regional spectral model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

Numerical Modeling of Inclusion Behavior in Liquid Metal Processing

NASA Astrophysics Data System (ADS)

Bellot, Jean-Pierre; Descotes, Vincent; Jardy, Alain

2013-09-01

Thermomechanical performance of metallic alloys is directly related to the metal cleanliness that has always been a challenge for metallurgists. During liquid metal processing, particles can grow or decrease in size either by mass transfer with the liquid phase or by agglomeration/fragmentation mechanisms. As a function of numerical density of inclusions and of the hydrodynamics of the reactor, different numerical modeling approaches are proposed; in the case of an isolated particle, the Lagrangian technique coupled with a dissolution model is applied, whereas in the opposite case of large inclusion phase concentration, the population balance equation must be solved. Three examples of numerical modeling studies achieved at Institut Jean Lamour are discussed. They illustrate the application of the Lagrangian technique (for isolated exogenous inclusion in titanium bath) and the Eulerian technique without or with the aggregation process: for precipitation and growing of inclusions at the solidification front of a Maraging steel, and for endogenous inclusions in the molten steel bath of a gas-stirred ladle, respectively.

Attractor scenarios and superluminal signals in k-essence cosmology

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

Kang, Jin U; Arnold Sommerfeld Center, Department of Physics, Ludwig-Maximilians University, Theresienstrasse 37, 80333 Munich; Vanchurin, Vitaly

Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the Universe. These scenarios avoid the need for fine-tuned initial conditions (the 'coincidence problem') because of the attractorlike dynamics of the k-essence field {phi}. It was recently shown that all k-essence scenarios with Lagrangians p=L(X){phi}{sup -2}, where X{identical_to}(1/2){phi}{sub ,{mu}}{phi}{sup ,{mu}}, necessarily involve an epoch where perturbations of {phi} propagate faster than light (the 'no-go theorem'). We carry out a comprehensive study of attractorlike cosmological solutions ('trackers') involving a k-essence scalar field {phi} and another matter component. The result of this study is a complete classificationmore » of k-essence Lagrangians that admit asymptotically stable tracking solutions, among all Lagrangians of the form p=K({phi})L(X). Using this classification, we select the class of models that describe the late-time acceleration and avoid the coincidence problem through the tracking mechanism. An analogous 'no-go theorem' still holds for this class of models, indicating the existence of a superluminal epoch. In the context of k-essence cosmology, the superluminal epoch does not lead to causality violations. We discuss the implications of superluminal signal propagation for possible causality violations in Lorentz-invariant field theories.« less

The Route to Raindrop Formation in a Shallow Cumulus Cloud Simulated by a Lagrangian Cloud Model

NASA Astrophysics Data System (ADS)

Noh, Yign; Hoffmann, Fabian; Raasch, Siegfried

2017-11-01

The mechanism of raindrop formation in a shallow cumulus cloud is investigated using a Lagrangian cloud model (LCM). The analysis is focused on how and under which conditions a cloud droplet grows to a raindrop by tracking the history of individual Lagrangian droplets. It is found that the rapid collisional growth, leading to raindrop formation, is triggered when single droplets with a radius of 20 μm appear in the region near the cloud top, characterized by a large liquid water content, strong turbulence, large mean droplet size, a broad drop size distribution (DSD), and high supersaturations. Raindrop formation easily occurs when turbulence-induced collision enhancement(TICE) is considered, with or without any extra broadening of the DSD by another mechanism (such as entrainment and mixing). In contrast, when TICE is not considered, raindrop formation is severely delayed if no other broadening mechanism is active. The reason leading to the difference is clarified by the additional analysis of idealized box-simulations of the collisional growth process for different DSDs in varied turbulent environments. It is found that TICE does not accelerate the timing of the raindrop formation for individual droplets, but it enhances the collisional growth rate significantly afterward. KMA R & D Program (Korea), DFG (Germany).

Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

USGS Publications Warehouse

Cox, T.J.; Runkel, R.L.

2008-01-01

Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

Upscaling anomalous reactive kinetics (A+B-->C) from pore scale Lagrangian velocity analysis

NASA Astrophysics Data System (ADS)

De Anna, P.; Tartakovsky, A. M.; Le Borgne, T.; Dentz, M.

2011-12-01

Natural flow fields in porous media display a complex spatio-temporal organization due to heterogeneous geological structures at different scales. This multiscale disorder implies anomalous dispersion, mixing and reaction kinetics (Berkowitz et al. RG 2006, Tartakovsky PRE 2010). Here, we focus on the upscaling of anomalous kinetics arising from pore scale, non Gaussian and correlated, velocity distributions. We consider reactive front simulations, where a component A displaces a component B that saturates initially the porous domain. The reactive component C is produced at the dispersive front located at interface between the A and B domains. The simulations are performed with the SPH method. As the mixing zone grows, the total mass of C produced increases with time. The scaling of this evolution with time is different from that which would be obtained from the homogeneous advection dispersion reaction equation. This anomalous kinetics property is related to spatial structure of the reactive mixture, and its evolution with time under the combined action of advective and diffusive processes. We discuss the different scaling regimes arising depending on the dominant process that governs mixing. In order to upscale these processes, we analyze the Lagrangian velocity properties, which are characterized by the non Gaussian distributions and long range temporal correlation. The main origin of these properties is the existence of very low velocity regions where solute particles can remain trapped for a long time. Another source of strong correlation is the channeling of flow in localized high velocity regions, which created finger-like structures in the concentration field. We show the spatial Markovian, and temporal non Markovian, nature of the Lagrangian velocity field. Therefore, an upscaled model can be defined as a correlated Continuous Time Random Walk (Le Borgne et al. PRL 2008). A key feature of this model is the definition of a transition probability density for Lagrangian velocities across a characteristic correlation distance. We quantify this transition probability density from pore scale simulations and use it in the effective stochastic model. In this framework, we investigate the ability of this effective model to represent correctly dispersion and mixing.

Episodes of Cross-Polar Transport in the Arctic Troposphere During July 2008 as Seen from Models, Satellite, and Aircraft Observations

NASA Technical Reports Server (NTRS)

Sodemann, H.; Pommier, M.; Arnold, S. R.; Monks, S. A.; Stebel, K.; Burkhart, J. F.; Hair, J. W.; Diskin, G. S.; Clerbaux, C.; Coheur, P.-F.;

Modeling Water Waves with Smoothed Particle Hydrodynamics

DTIC Science & Technology

2013-09-30

SPH Model for Water Waves and Other Free Surface Flows ...Lagrangian nature of SPH allows the modeling of wave breaking, surf zones, ship waves, and wave-structure interaction, where the free surface becomes...proving to be a competent modeling scheme for free surface flows in three dimensions including the complex flows of the surf zone. As the GPU

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.

Using Global Plate Velocity Boundary Conditions for Embedded Regional Geodynamic Models: Application to 3-D Modeling of the Early Rifting of the South Atlantic

NASA Astrophysics Data System (ADS)

Taramón, Jorge M.; Morgan, Jason P.; Pérez-Gussinyé, Marta

2016-04-01

The treatment of far-field boundary conditions is one of the most poorly resolved issues for regional modeling of geodynamic processes. In viscous flow, the choice of far-field boundary conditions often strongly shapes the large-scale structure of a geosimulation. The mantle velocity field along the sidewalls and base of a modeling region is typically much more poorly known than the geometry of past global motions of the surface plates as constrained by global plate motion reconstructions. For regional rifting models it has become routine to apply highly simplified 'plate spreading' or 'uniform rifting' boundary conditions to a 3-D model that limits its ability to simulate the geodynamic evolution of a specific rifted margin. One way researchers are exploring the sensitivity of regional models to uncertain boundary conditions is to use a nested modeling approach in which a global model is used to determine a large-scale flow pattern that is imposed as a constraint along the boundaries of the region to be modeled. Here we explore the utility of a different approach that takes advantage of the ability of finite element models to use unstructured meshes than can embed much higher resolution sub-regions. Here we demonstrate the workflow and code tools that we created to generate this unstructured mesh: solver based on springs, guide-mesh and routines to improve the quality, e.g., closeness to a regular tetrahedron, of the tetrahedral elements of the mesh. Note that the same routines are used to generate a new mesh in the remeshing of a distorted Lagrangian mesh. In our initial project to validate this approach, we create a global spherical shell mesh in which a higher resolution sub-region is created around the nascent South Atlantic Rifting Margin. Global Plate motion BCs and plate boundaries are applied for the time of the onset of rifting, continuing through several 10s of Ma of rifting. Thermal, compositional, and melt-related buoyancy forces are only non-zero within the high-resolution sub-region, elsewhere, motions are constrained by surface plate-motion constraints. The total number of unknowns needed to solve an embedded regional model with this approach is less than 1/3 larger than that needed for a structured-mesh solution on a Cartesian or spherical cap sub-regional mesh. Here we illustrate the steps within this workflow for modeling the potential mantle flow associated with the early rifting evolution of the South Atlantic, in particular studying the potential effects of a 'Parana Plume' during the transition from rift to drift.

MODELING ASSESSMENT OF TRANSPORT AND DEPOSITION PATTERNS OF MERCURY AIR EMISSIONS FROM THE U.S. AND CANADA

EPA Science Inventory

In December 1997, the U.S. EPA submitted the Mercury Study Report to Congress which included a regional-scale modeling assessment of the transport and deposition of U.S. air emissions of mercury. This modeling was performed with a modified version of the Regional Lagrangian Mode...

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

NASA Astrophysics Data System (ADS)

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-11-01

Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.

Canonical Descriptions of High Intensity Laser-Plasma Interaction

NASA Astrophysics Data System (ADS)

Le Cornu, B. J.

The problem of laser-plasma interaction has been studied extensively in the context of inertial confinement fusion (ICF). These studies have focussed on effects like the nonlinear force, self-focusing, Rayleigh- Taylor instabilities, stimulated Brillouin scattering and stimulated Raman scattering observed in ICF schemes. However, there remains a large discrepancy between theory and experiment in the context of nuclear fusion schemes. Several authors have attempted to gain greater understanding of the physics involved by the application of standard or 'canonical' methods used in Lagrangian and Hamiltonian mechanics to the problem of plasma physics. This thesis presents a new canonical description of laser-plasma interaction based on the Podolsky Lagrangian. Finite self-energy of charged particles, incroporation of high-frequency effects and an ability to quantise are the main advantages of this new model. The nature of the Podolsky constant is also analysed in the context of plasma physics, specifically in terms of the plasma dispersion relation. A new gauge invariant expression of the energy-momentum tensor for any gauge invariant Lagrangian dependent on second order derivatives is derived for the first time. Finally, the transient and nontransient expressions of the nonlinear ponderomotive force in laser-plasma interaction are discussed and shown to be closely approximated by a canonical derivation of the electromagnetic Lagrangian, a fact that seems to have been missed in the literature.

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.

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

NASA Technical Reports Server (NTRS)

Yeh, Kao-San; Lin, Shian-Jiann; Rood, Richard B.

2002-01-01

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

A model of icebergs and sea ice in a joint continuum framework

NASA Astrophysics Data System (ADS)

Vaňková, Irena; Holland, David M.

2017-04-01

The ice mélange, a mixture of sea ice and icebergs, often present in front of tidewater glaciers in Greenland or ice shelves in Antarctica, can have a profound effect on the dynamics of the ice-ocean system. The current inability to numerically model the ice mélange motivates a new modeling approach proposed here. A continuum sea-ice model is taken as a starting point and icebergs are represented as thick and compact pieces of sea ice held together by large tensile and shear strength selectively introduced into the sea ice rheology. In order to modify the rheology correctly, a semi-Lagrangian time stepping scheme is introduced and at each time step a Lagrangian grid is constructed such that iceberg shape is preserved exactly. With the proposed treatment, sea ice and icebergs are considered a single fluid with spatially varying rheological properties, mutual interactions are thus automatically included without the need of further parametrization. An important advantage of the presented framework for an ice mélange model is its potential to be easily included in existing climate models.

Source-receptor matrix calculation with a Lagrangian particle dispersion model in backward mode

NASA Astrophysics Data System (ADS)

Seibert, P.; Frank, A.

2003-04-01

A method for the calculation of source-receptor (s-r) relationships (sensitivity of a trace substance concentration at some place and time to emission at some place and time) with Lagrangian particle models has been derived and presented previously (Air Pollution Modeling and its Application XIV, Proc. of ITM Boulder 2000). Now, the generalisation to any linear s-r relationship, including dry and wet deposition, decay etc., is presented. It was implemented in the model FLEXPART and tested extensively in idealised set-ups. These tests turned out to be very useful for finding minor model bugs and inaccuracies, and can be recommended generally for model testing. Recently, a convection scheme has been integrated in FLEXPART which was also tested. Both source and receptor can be specified in mass mixing ratio or mass units. Properly taking care of this is quite relevant for sources and receptors at different levels in the atmosphere. Furthermore, we present a test with the transport of aerosol-bound Caesium-137 from the areas contaminated by the Chernobyl disaster to Stockholm during one month.

Superluminality in dilatationally invariant generalized Galileon theories

NASA Astrophysics Data System (ADS)

Kolevatov, R. S.

2015-12-01

We consider small perturbations about homogeneous backgrounds in dilatationally invariant Galileon models. The issues we address are stability (absence of ghosts and gradient instabilities) and superluminality. We show that in the Minkowski background, it is possible to construct the Lagrangian in such a way that any homogeneous Galileon background solution is stable and small perturbations about it are subluminal. On the other hand, in the case of Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds, for any Lagrangian functions there exist homogeneous background solutions to the Galileon equation of motion and time dependence of the scale factor, such that the stability conditions are satisfied, but the Galileon perturbations propagate with superluminal speed.

Lagrangian Form of the Self-Dual Equations for SU(N) Gauge Fields on Four-Dimensional Euclidean Space

NASA Astrophysics Data System (ADS)

Hou, Boyu; Song, Xingchang

1998-04-01

By compactifying the four-dimensional Euclidean space into S2 × S2 manifold and introducing two topological relevant Wess-Zumino terms to Hn ≡ SL(n,c)/SU(n) nonlinear sigma model, we construct a Lagrangian form for SU(n) self-dual Yang-Mills field, from which the self-dual equations follow as the Euler-Lagrange equations. The project supported in part by the NSF Contract No. PHY-81-09110-A-01. One of the authors (X.C. SONG) was supported by a Fung King-Hey Fellowship through the Committee for Educational Exchange with China

Meson properties in magnetized quark matter

NASA Astrophysics Data System (ADS)

Wang, Ziyue; Zhuang, Pengfei

2018-02-01

We study neutral and charged meson properties in the magnetic field. Taking the bosonization method in a two-flavor Nambu-Jona-Lasinio model, we derive effective meson Lagrangian density with minimal coupling to the magnetic field, by employing derivative expansion for both the meson fields and Schwinger phases. We extract from the effective Lagrangian density the meson curvature, pole and screening masses. As the only Goldstone mode, the neutral pion controls the thermodynamics of the system and propagates the long range quark interaction. The magnetic field breaks down the space symmetry, and the quark interaction region changes from a sphere in vacuum to a ellipsoid in magnetic field.

Particle Tracking Model (PTM) with Coastal Modeling System (CMS)

DTIC Science & Technology

2015-11-04

Coastal Inlets Research Program Particle Tracking Model (PTM) with Coastal Modeling System ( CMS ) The Particle Tracking Model (PTM) is a Lagrangian...currents and waves. The Coastal Inlets Research Program (CIRP) supports the PTM with the Coastal Modeling System ( CMS ), which provides coupled wave...and current forcing for PTM simulations. CMS -PTM is implemented in the Surface-water Modeling System, a GUI environment for input development

Unified Dark Matter scalar field models with fast transition

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

Bertacca, Daniele; Bruni, Marco; Piattella, Oliver F.

2011-02-01

We investigate the general properties of Unified Dark Matter (UDM) scalar field models with Lagrangians with a non-canonical kinetic term, looking specifically for models that can produce a fast transition between an early Einstein-de Sitter CDM-like era and a later Dark Energy like phase, similarly to the barotropic fluid UDM models in JCAP01(2010)014. However, while the background evolution can be very similar in the two cases, the perturbations are naturally adiabatic in fluid models, while in the scalar field case they are necessarily non-adiabatic. The new approach to building UDM Lagrangians proposed here allows to escape the common problem ofmore » the fine-tuning of the parameters which plague many UDM models. We analyse the properties of perturbations in our model, focusing on the the evolution of the effective speed of sound and that of the Jeans length. With this insight, we can set theoretical constraints on the parameters of the model, predicting sufficient conditions for the model to be viable. An interesting feature of our models is that what can be interpreted as w{sub DE} can be < −1 without violating the null energy conditions.« less

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Lagrangian Turbulence and Transport in Semi-Enclosed Basins and Coastal Regions

DTIC Science & Technology

2008-09-30

P.M. Poulain, R. Signell, J. Chiggiato , S. Carniel, 2008: Variational analysis of drifter positions and model outputs for the reconstruction of... Chiggiato , S. Carniel, 2008: Variational analysis of drifter positions and model outputs for the reconstruction of surface currents in the Central

Nonlinear soil parameter effects on dynamic embedment of offshore pipeline on soft clay

NASA Astrophysics Data System (ADS)

Yu, Su Young; Choi, Han Suk; Lee, Seung Keon; Park, Kyu-Sik; Kim, Do Kyun

2015-06-01

In this paper, the effects of nonlinear soft clay on dynamic embedment of offshore pipeline were investigated. Seabed embedment by pipe-soil interactions has impacts on the structural boundary conditions for various subsea structures such as pipeline, riser, pile, and many other systems. A number of studies have been performed to estimate real soil behavior, but their estimation of seabed embedment has not been fully identified and there are still many uncertainties. In this regards, comparison of embedment between field survey and existing empirical models has been performed to identify uncertainties and investigate the effect of nonlinear soil parameter on dynamic embedment. From the comparison, it is found that the dynamic embedment with installation effects based on nonlinear soil model have an influence on seabed embedment. Therefore, the pipe embedment under dynamic condition by nonlinear parameters of soil models was investigated by Dynamic Embedment Factor (DEF) concept, which is defined as the ratio of the dynamic and static embedment of pipeline, in order to overcome the gap between field embedment and currently used empirical and numerical formula. Although DEF through various researches is suggested, its range is too wide and it does not consider dynamic laying effect. It is difficult to find critical parameters that are affecting to the embedment result. Therefore, the study on dynamic embedment factor by soft clay parameters of nonlinear soil model was conducted and the sensitivity analyses about parameters of nonlinear soil model were performed as well. The tendency on dynamic embedment factor was found by conducting numerical analyses using OrcaFlex software. It is found that DEF was influenced by shear strength gradient than other factors. The obtained results will be useful to understand the pipe embedment on soft clay seabed for applying offshore pipeline designs such as on-bottom stability and free span analyses.

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.

Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems

NASA Astrophysics Data System (ADS)

Narayan, A.; Singh, Nutan

2014-10-01

This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤ μ≤ μ ∗, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.

Impact of data assimilation on Eulerian versus Lagrangian estimates of upper ocean transport

NASA Astrophysics Data System (ADS)

Sperrevik, Ann Kristin; Röhrs, Johannes; Christensen, Kai Hâkon

2017-07-01

Using four-dimensional variational analysis, we produce an estimate of the state of a coastal region in Northern Norway during the late winter and spring in 1984. We use satellite sea surface temperature and in situ observations from a series of intensive field campaigns, and obtain a more realistic distribution of water masses both in the horizontal and the vertical than a pure downscaling approach can achieve. Although the distribution of Eulerian surface current speeds are similar, we find that they are more variable and less dependent on model bathymetry in our reanalysis compared to a hindcast produced using the same modeling system. Lagrangian drift currents on the other hand are significantly changed, with overall higher kinetic energy levels in the reanalysis than in the hindcast, particularly in the superinertial frequency band.

Constraining estimates of methane emissions from Arctic permafrost regions with CARVE

NASA Astrophysics Data System (ADS)

Chang, R. Y.; Karion, A.; Sweeney, C.; Henderson, J.; Mountain, M.; Eluszkiewicz, J.; Luus, K. A.; Lin, J. C.; Dinardo, S.; Miller, C. E.; Wofsy, S. C.

2013-12-01

Permafrost in the Arctic contains large carbon pools that are currently non-labile, but can be released to the atmosphere as polar regions warm. In order to predict future climate scenarios, we need to understand the emissions of these greenhouse gases under varying environmental conditions. This study presents in-situ measurements of methane made on board an aircraft during the Carbon in Arctic Reservoirs Vulnerability Experiment (CARVE), which sampled over the permafrost regions of Alaska. Using measurements from May to September 2012, seasonal emission rate estimates of methane from tundra are constrained using the Stochastic Time-Inverted Lagrangian Transport model, a Lagrangian particle dispersion model driven by custom polar-WRF fields. Preliminary results suggest that methane emission rates have not greatly increased since the Arctic Boundary Layer Experiment conducted in southwest Alaska in 1988.

From medium heterogeneity to flow and transport: A time-domain random walk approach

NASA Astrophysics Data System (ADS)

Hakoun, V.; Comolli, A.; Dentz, M.

2017-12-01

The prediction of flow and transport processes in heterogeneous porous media is based on the qualitative and quantitative understanding of the interplay between 1) spatial variability of hydraulic conductivity, 2) groundwater flow and 3) solute transport. Using a stochastic modeling approach, we study this interplay through direct numerical simulations of Darcy flow and advective transport in heterogeneous media. First, we study flow in correlated hydraulic permeability fields and shed light on the relationship between the statistics of log-hydraulic conductivity, a medium attribute, and the flow statistics. Second, we determine relationships between Eulerian and Lagrangian velocity statistics, this means, between flow and transport attributes. We show how Lagrangian statistics and thus transport behaviors such as late particle arrival times are influenced by the medium heterogeneity on one hand and the initial particle velocities on the other. We find that equidistantly sampled Lagrangian velocities can be described by a Markov process that evolves on the characteristic heterogeneity length scale. We employ a stochastic relaxation model for the equidistantly sampled particle velocities, which is parametrized by the velocity correlation length. This description results in a time-domain random walk model for the particle motion, whose spatial transitions are characterized by the velocity correlation length and temporal transitions by the particle velocities. This approach relates the statistical medium and flow properties to large scale transport, and allows for conditioning on the initial particle velocities and thus to the medium properties in the injection region. The approach is tested against direct numerical simulations.

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 discretization. A 2-stage Runge–Kutta method is used to evolve the solution in time. The details of the new hydrodynamic scheme are discussed; likewise, results from numerical test problems are presented.« less

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 discretization. A 2-stage Runge–Kutta method is used to evolve the solution in time. The details of the new hydrodynamic scheme are discussed; likewise, results from numerical test problems are presented.« less

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.

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.

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

Employing backward Lagrangian stochastic (bLS) dispersion modelling to infer emission strengths from confined areas using trace gas concentration measurements is a convenient way of emission estimation from field measurements (see Wilson et al., 2012 and references therein). The freely available software 'WindTrax' (www.thunderbeachscientific.com), providing a graphical interface for the application of a bLS model, has spurred its utilisation in the past decade. Investigations include mainly methane (CH4) and ammonia (NH3) emissions based on experimental plots with dimensions between approximately 102 to 104 m2. Whereas for CH4 deposition processes can be neglected, NH3 has a strong affinity to any surface and is therefore efficiently deposited. Neglecting dry deposition will underestimate NH3 emissions, e.g. with a standard WindTrax approach. We extended the bLS model described in Flesch et al. (2004) by a dry deposition process using a simple, one-directional deposition velocity approach. At every contact of the model trajectories with ground level (here at the height of the roughness length Zo), deposition is modelled as: Fdep = vdep × CT raj (1) where vdep represents deposition velocity, and CTraj is the actual concentration of the specific trajectory at contact. A convenient way to model vdep is given by a resistances approach. The deposition velocity is modelled as the inverse of the sum of a series of different resistances to deposition. The aerodynamic resistance is already implicitly included in the bLS model, thus vdep is given as: v = ---1--- dep Rb + Rc (2) Rb and Rc represent resistances of different model layers between Zo and the surfaces where deposition take place. With this approach we analysed a dataset from measurements with an artificial NH3 source that consisted of 36 individual orifices mimicking a circular area source with a radius of 10 m. The use of three open-path miniDOAS (Sintermann et al., submitted to AMT) systems allowed to measure 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.

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.

LSPRAY-IV: A Lagrangian Spray Module

NASA Technical Reports Server (NTRS)

Raju, M. S.

2012-01-01

LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.

A Backward-Lagrangian-Stochastic Footprint Model for the Urban Environment

NASA Astrophysics Data System (ADS)

Wang, Chenghao; Wang, Zhi-Hua; Yang, Jiachuan; Li, Qi

2018-02-01

Built terrains, with their complexity in morphology, high heterogeneity, and anthropogenic impact, impose substantial challenges in Earth-system modelling. In particular, estimation of the source areas and footprints of atmospheric measurements in cities requires realistic representation of the landscape characteristics and flow physics in urban areas, but has hitherto been heavily reliant on large-eddy simulations. In this study, we developed physical parametrization schemes for estimating urban footprints based on the backward-Lagrangian-stochastic algorithm, with the built environment represented by street canyons. The vertical profile of mean streamwise velocity is parametrized for the urban canopy and boundary layer. Flux footprints estimated by the proposed model show reasonable agreement with analytical predictions over flat surfaces without roughness elements, and with experimental observations over sparse plant canopies. Furthermore, comparisons of canyon flow and turbulence profiles and the subsequent footprints were made between the proposed model and large-eddy simulation data. The results suggest that the parametrized canyon wind and turbulence statistics, based on the simple similarity theory used, need to be further improved to yield more realistic urban footprint modelling.

SPARSE—A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure

PubMed Central

Davis, Sean L.; Sen, Oishik; Udaykumar, H. S.

2017-01-01

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles. PMID:28413341

SPARSE-A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure.

PubMed

Davis, Sean L; Jacobs, Gustaaf B; Sen, Oishik; Udaykumar, H S

2017-03-01

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian-Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.

A hybridizable discontinuous Galerkin method for modeling fluid-structure interaction

NASA Astrophysics Data System (ADS)

Sheldon, Jason P.; Miller, Scott T.; Pitt, Jonathan S.

2016-12-01

This work presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid-structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian-Eulerian Navier-Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid-solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.

A modified Brownian force for ultrafine particle penetration through building crack modeling

NASA Astrophysics Data System (ADS)

Chen, Chen; Zhao, Bin

2017-12-01

Combustion processes related to industry, traffic, agriculture, and waste treatment and disposal increase the amount of outdoor ultrafine particles (UFPs), which have adverse effects on human health. Given that people spend the majority of their time indoors, it is critical to understand the penetration of outdoor UFPs through building cracks in order to estimate human exposure to outdoor-originated UFPs. Lagrangian tracking is an efficient approach for modeling particle penetration. However, the Brownian motion for Lagrangian tracking in ANSYS Fluent®, a widely used software for particle dispersion modeling, is not able to model UFP dispersion accurately. In this study, we modified the Brownian force by rewriting the Brownian diffusion coefficient and particle integration time step with a user-defined function in ANSYS Fluent® to model particle penetration through building cracks. The results obtained using the modified model agree much better with the experimental results, with the averaged relative error less than 14% for the smooth crack cases and 21% for the rough crack case. We expect the modified Brownian force model proposed herein to be applied for UFP dispersion modeling in more indoor air quality studies.

Non-linear duality invariant partially massless models?

DOE PAGES

Cherney, D.; Deser, S.; Waldron, A.; ...

2015-12-15

We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Lastly, our models mimic Dirac–Born–Infeld theory but it is unclear whether they are Lagrangian.

Lagrangian Turbulence and Transport in Semi-enclosed Basins and Coastal Regions

DTIC Science & Technology

2007-09-30

Adriatic Sea using NCOM. Ocean Modelling, 17, 68-91 Taillandier V., A. Griffa, P.M. Poulain, R. Signell, J. Chiggiato , S. Carniel. Variational...A. Griffa, P.M. Poulain, R. Signell, J. Chiggiato , S. Carniel. Variational analysis of drifter positions and model outputs for the reconstruction of

EVALUATION AND SENSITIVITY ANALYSES RESULTS OF THE MESOPUFF II MODEL WITH CAPTEX MEASUREMENTS

EPA Science Inventory

The MESOPUFF II regional Lagrangian puff model has been evaluated and tested against measurements from the Cross-Appalachian Tracer Experiment (CAPTEX) data base in an effort to assess its abilIty to simulate the transport and dispersion of a nonreactive, nondepositing tracer plu...

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 simulation results. A set of calibration runs were performed and the model accuracy in reproducing the surface circulation were defined. Therefore, a numerical simulation was conducted to predict the wind induced lagoon water circulation and the paths followed by numerical particles inside the lagoon domain. The simulated particles paths was analyzed and the optimal configuration for the buoys deployment was designed in real-time. The selected deployment geometry was then tested during a further field campaign. The obtained dataset revealed that the chosen measurement strategy provided a near-synoptic survey with the longest records for the considered specific observing experiment. This work is aimed to emphasize the mutual usefulness of observations and numerical simulations in coastal ocean applications and it proposes an efficient approach to harmonize different expertise toward the investigation of a given specific research issue. A Cucco, M Sinerchia, A Ribotti, A Olita, L Fazioli, A Perilli, B Sorgente, M Borghini, K Schroeder, R Sorgente. 2012. A high-resolution real-time forecasting system for predicting the fate of oil spills in the Strait of Bonifacio (western Mediterranean Sea). Marine Pollution Bulletin. 64. 6, 1186-1200. Kallos, G., Nickovic, S., Papadopoulos, A., Jovic, D., Kakaliagou, O., Misirlis, N., Boukas, L., Mimikou, N., G., S., J., P., Anadranistakis, E., and Manousakis, M.. 1997. The regional weather forecasting system Skiron: An overview, in: Proceedings of the Symposium on Regional Weather Prediction on Parallel Computer Environments, 109-122, Athens, Greece. Umgiesser, G., Melaku Canu, D., Cucco, A., Solidoro, C., 2004. A finite element model for the Venice Lagoon. Development, set up, calibration and validation. Journal of Marine Systems 51, 123-145.

Constraining regional scale carbon budgets at the US West Coast using a high-resolution atmospheric inverse modeling approach

NASA Astrophysics Data System (ADS)

Goeckede, M.; Michalak, A. M.; Vickers, D.; Turner, D.; Law, B.

2009-04-01

The study presented is embedded within the NACP (North American Carbon Program) West Coast project ORCA2, which aims at determining the regional carbon balance of the US states Oregon, California and Washington. Our work specifically focuses on the effect of disturbance history and climate variability, aiming at improving our understanding of e.g. drought stress and stand age on carbon sources and sinks in complex terrain with fine-scale variability in land cover types. The ORCA2 atmospheric inverse modeling approach has been set up to capture flux variability on the regional scale at high temporal and spatial resolution. Atmospheric transport is simulated coupling the mesoscale model WRF (Weather Research and Forecast) with the STILT (Stochastic Time Inverted Lagrangian Transport) footprint model. This setup allows identifying sources and sinks that influence atmospheric observations with highly resolved mass transport fields and realistic turbulent mixing. Terrestrial biosphere carbon fluxes are simulated at spatial resolutions of up to 1km and subdaily timesteps, considering effects of ecoregion, land cover type and disturbance regime on the carbon budgets. Our approach assimilates high-precision atmospheric CO2 concentration measurements and eddy-covariance data from several sites throughout the model domain, as well as high-resolution remote sensing products (e.g. LandSat, MODIS) and interpolated surface meteorology (DayMet, SOGS, PRISM). We present top-down modeling results that have been optimized using Bayesian inversion, reflecting the information on regional scale carbon processes provided by the network of high-precision CO2 observations. We address the level of detail (e.g. spatial and temporal resolution) that can be resolved by top-down modeling on the regional scale, given the uncertainties introduced by various sources for model-data mismatch. Our results demonstrate the importance of accurate modeling of carbon-water coupling, with the representation of water availability and drought stress playing a dominant role to capture spatially variable CO2 exchange rates in a region characterized by strong climatic gradients.

Blast Fragmentation Modeling and Analysis

DTIC Science & Technology

2010-10-31

weapons device containing a multiphase blast explosive (MBX). 1. INTRODUCTION The ARL Survivability Lethality and Analysis Directorate (SLAD) is...velocity. In order to simulate the highly complex phenomenon, the exploding cylinder is modeled with the hydrodynamics code ALE3D , an arbitrary...Lagrangian-Eulerian multiphysics code, developed at Lawrence Livermore National Laboratory. ALE3D includes physical properties, constitutive models for

Simulations of Sea-Ice Dynamics Using the Material-Point Method

NASA Technical Reports Server (NTRS)

Sulsky, D.; Schreyer, H.; Peterson, K.; Nguyen, G.; Coon, G.; Kwok, R.

2006-01-01

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

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)

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

Implications of heavy quark-diquark symmetry for excited doubly heavy baryons and tetraquarks

NASA Astrophysics Data System (ADS)

Mehen, Thomas

2017-11-01

We give heavy quark-diquark symmetry predictions for doubly heavy baryons and tetraquarks in light of the recent discovery of the Ξcc ++ by LHCb. For five excited doubly charm baryons that are predicted to lie below the ΛcD threshold, we give predictions for their electromagnetic and strong decays using a previously developed chiral Lagrangian with heavy quark-diquark symmetry. Based on the mass of the Ξcc ++, the existence of a doubly heavy bottom I =0 tetraquark that is stable to strong and electromagnetic decays has been predicted. If the mass of this state is below 10405 MeV, as predicted in some models, we argue using heavy quark-diquark symmetry that the JP=1+ I =1 doubly bottom tetraquark state will lie just below the open bottom threshold and likely be a narrow state as well. In this scenario, we compute strong decay width for this state using a new Lagrangian for doubly heavy tetraquarks which is related to the singly heavy baryon Lagrangian by heavy quark-diquark symmetry.

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.

Implementation of extended Lagrangian dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model.

PubMed

Lemkul, Justin A; Roux, Benoît; van der Spoel, David; MacKerell, Alexander D

2015-07-15

Explicit treatment of electronic polarization in empirical force fields used for molecular dynamics simulations represents an important advancement in simulation methodology. A straightforward means of treating electronic polarization in these simulations is the inclusion of Drude oscillators, which are auxiliary, charge-carrying particles bonded to the cores of atoms in the system. The additional degrees of freedom make these simulations more computationally expensive relative to simulations using traditional fixed-charge (additive) force fields. Thus, efficient tools are needed for conducting these simulations. Here, we present the implementation of highly scalable algorithms in the GROMACS simulation package that allow for the simulation of polarizable systems using extended Lagrangian dynamics with a dual Nosé-Hoover thermostat as well as simulations using a full self-consistent field treatment of polarization. The performance of systems of varying size is evaluated, showing that the present code parallelizes efficiently and is the fastest implementation of the extended Lagrangian methods currently available for simulations using the Drude polarizable force field. © 2015 Wiley Periodicals, Inc.

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.

Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows

PubMed Central

Green, Melissa A.; Rowley, Clarence W.; Smits, Alexander J.

2010-01-01

We use direct Lyapunov exponents to identify Lagrangian coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used Eulerian criteria, the Lagrangian method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Kármán vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location. PMID:20370300

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

New developments in FEYNRULES

NASA Astrophysics Data System (ADS)

Alloul, Adam; Christensen, Neil D.; Degrande, Céline; Duhr, Claude; Fuks, Benjamin

2014-06-01

The program FEYNRULES is a MATHEMATICA package developed to facilitate the implementation of new physics theories into high-energy physics tools. Starting from a minimal set of information such as the model gauge symmetries, its particle content, parameters and Lagrangian, FEYNRULES provides all necessary routines to extract automatically from the Lagrangian (that can also be computed semi-automatically for supersymmetric theories) the associated Feynman rules. These can be further exported to several Monte Carlo event generators through dedicated interfaces, as well as translated into a PYTHON library, under the so-called UFO model format, agnostic of the model complexity, especially in terms of Lorentz and/or color structures appearing in the vertices or of number of external legs. In this work, we briefly report on the most recent new features that have been added to FEYNRULES, including full support for spin-1 fermions, a new module allowing for the automated diagonalization of the particle spectrum and a new set of routines dedicated to decay width calculations.

Wake modeling in complex terrain using a hybrid Eulerian-Lagrangian Split Solver

NASA Astrophysics Data System (ADS)

Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind

2016-09-01

Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid Eulerian- Lagrangian approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.

Modern Elementary Particle Physics

NASA Astrophysics Data System (ADS)

Kane, Gordon

2017-02-01

1. Introduction; 2. Relativistic notation, Lagrangians, and interactions; 3. Gauge invariance; 4. Non-abelian gauge theories; 5. Dirac notation for spin; 6. The Standard Model Lagrangian; 7. The electroweak theory and quantum chromodynamics; 8. Masses and the Higgs mechanism; 9. Cross sections, decay widths, and lifetimes: W and Z decays; 10. Production and properties of W± and Zᴼ; 11. Measurement of electroweak and QCD parameters: the muon lifetime; 12. Accelerators - present and future; 13. Experiments and detectors; 14. Low energy and non-accelerator experiments; 15. Observation of the Higgs boson at the CERN LHC: is it the Higgs boson?; 16. Colliders and tests of the Standard Model: particles are pointlike; 17. Quarks and gluons, confinement and jets; 18. Hadrons, heavy quarks, and strong isospin invariance; 19. Coupling strengths depend on momentum transfer and on virtual particles; 20. Quark (and lepton) mixing angles; 21. CP violation; 22. Overview of physics beyond the Standard Model; 23. Grand unification; 24. Neutrino masses; 25. Dark matter; 26. Supersymmetry.

Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field

DOE PAGES

Ruiz, D. E.; Ellison, C. L.; Dodin, I. Y.

2015-12-16

Here, we report a point-particle ponderomotive model of a Dirac electron oscillating in a high-frequency field. Starting from the Dirac Lagrangian density, we derive a reduced phase-space Lagrangian that describes the relativistic time-averaged dynamics of such a particle in a geometrical-optics laser pulse propagating in vacuum. The pulse is allowed to have an arbitrarily large amplitude provided that radiation damping and pair production are negligible. The model captures the Bargmann-Michel-Telegdi (BMT) spin dynamics, the Stern-Gerlach spin-orbital coupling, the conventional ponderomotive forces, and the interaction with large-scale background fields (if any). Agreement with the BMT spin precession equation is shown numerically.more » The commonly known theory in which ponderomotive effects are incorporated in the particle effective mass is reproduced as a special case when the spin-orbital coupling is negligible. This model could be useful for studying laser-plasma interactions in relativistic spin-1/2 plasmas.« less

Non-minimally coupled scalar field cosmology with torsion

NASA Astrophysics Data System (ADS)

Cid, Antonella; Izaurieta, Fernando; Leon, Genly; Medina, Perla; Narbona, Daniela

2018-04-01

In this work we present a generalized Brans-Dicke lagrangian including a non-minimally coupled Gauss-Bonnet term without imposing the vanishing torsion condition. In the resulting field equations, the torsion is closely related to the dynamics of the scalar field, i.e., if non-minimally coupled terms are present in the theory, then the torsion must be present. For the studied lagrangian we analyze the cosmological consequences of an effective torsional fluid and we show that this fluid can be responsible for the current acceleration of the universe. Finally, we perform a detailed dynamical system analysis to describe the qualitative features of the model, we find that accelerated stages are a generic feature of this scenario.

BRST theory without Hamiltonian and Lagrangian

NASA Astrophysics Data System (ADS)

Lyakhovich, S. L.; Sharapov, A. A.

2005-03-01

We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.

Reconstructing f(R) modified gravity with dark energy parametrization

NASA Astrophysics Data System (ADS)

Morita, Masaaki; Takahashi, Hirotaka

2014-03-01

We demonstrate the reconstruction of f(R) modified gravity theory with late-time accelerated cosmic expansion. A second-order differential equation for Lagrangian density is obtained from the field equation, and is solved as a function of the cosmic scale factor in two cases. First we begin with the case of a wCDM cosmological model, in which a dark-energy equation-of-state parameter w is constant, for simplicity. Next we extend the method to a case in which the parameter w is epoch-dependent and is expressed as the Chevallier-Polarski-Linder parametrization. Thus we can represent Lagrangian density of f(R) modified gravity theory in terms of dark energy parameters.

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.

Supersymmetry, Supergravity, and Unification

NASA Astrophysics Data System (ADS)

Nath, Pran

2016-12-01

Dedication; Preface; 1. A brief history of unification; 2. Gravitation; 3. Non-abelian gauge theory; 4. Spontaneous breaking of global and local symmetries; 5. The Standard Model; 6. Anomalies; 7. Effective Lagrangians; 8. Supersymmetry; 9. Grand unification; 10. MSSM Lagrangian; 11. N = 1 supergravity; 12. Coupling of supergravity with matter and gauge fields; 13. Supergravity grand unification; 14. Phenomenology of supergravity grand unification; 15. CP violation in supergravity unified theories; 16. Proton stability in supergravity unified theories; 17. Cosmology, astroparticle physics and SUGRA unification; 18. Extended supergravities and supergravities from superstrings; 19. Specialized topics; 20. The future of unification; 21. Appendices; 22. Notations, conventions, and formulae; 23. Physical constants; 24. List of books and reviews for further reading; Index.

A time-parallel approach to strong-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Rao, Vishwas; Sandu, Adrian

2016-05-01

A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple sub-intervals that allows parallelization of cost function and gradient computations. The solutions to the continuity equations across interval boundaries are added as constraints. The augmented Lagrangian approach leads to a different formulation of the variational data assimilation problem than the weakly constrained 4D-Var. A combination of serial and parallel 4D-Vars to increase performance is also explored. The methodology is illustrated on data assimilation problems involving the Lorenz-96 and the shallow water models.

Baryon number violation and novel canonical anti-commutation relations

NASA Astrophysics Data System (ADS)

Fujikawa, Kazuo; Tureanu, Anca

2018-02-01

The possible neutron-antineutron oscillation is described by an effective quadratic Lagrangian analogous to the BCS theory. It is shown that the conventional equal-time anti-commutation relations of the neutron variable n (t , x →) are modified by the baryon number violating terms. This is established by the Bjorken-Johnson-Low prescription and also by the canonical quantization combined with equations of motion. This novel canonical behavior can give rise to an important physical effect, which is illustrated by analyzing the Lagrangian that violates the baryon number but gives rise to the degenerate effective Majorana fermions and thus no neutron-antineutron oscillation. Technically, this model is neatly treated using a relativistic analogue of the Bogoliubov transformation.

Lagrangian turbulence: Structures and mixing in admissible model flows

NASA Astrophysics Data System (ADS)

Ottino, Julio M.

1991-12-01

The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both Eulerian and Lagrangian turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.

Bounded fractional diffusion in geological media: Definition and Lagrangian approximation

USGS Publications Warehouse

Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang

2016-01-01

Spatiotemporal Fractional-Derivative Models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a Lagrangian solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New Lagrangian schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the non-local and non-symmetric fractional diffusion. For a non-zero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded Lagrangian solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite do mains to those with any size and boundary conditions.

A variational approach to behavioral and neuroelectrical laws.

PubMed

Noventa, Stefano; Vidotto, Giulio

2012-09-01

Variational methods play a fundamental and unifying role in several fields of physics, chemistry, engineering, economics, and biology, as they allow one to derive the behavior of a system as a consequence of an optimality principle. A possible application of these methods to a model of perception is given by considering a psychophysical law as the solution of an Euler-Lagrange equation. A general class of Lagrangians is identified by requiring the measurability of prothetic continua on interval scales. The associated Hamiltonian (the energy of the process) is tentatively connected with neurophysiological aspects. As an example of the suggested approach a particular choice of the Lagrangian, that is a sufficient condition to obtain classical psychophysical laws, while accounting for psychophysical adaptation and the stationarity of neuronal activity, is used to explore a possible relation between a behavioral law and a neuroelectrical ,response based on the Naka-Rushton model.

Time irreversibility and multifractality of power along single particle trajectories in turbulence

NASA Astrophysics Data System (ADS)

Cencini, Massimo; Biferale, Luca; Boffetta, Guido; De Pietro, Massimo

2017-10-01

The irreversible turbulent energy cascade epitomizes strongly nonequilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power, whose moments display a power-law dependence on the Reynolds number, as recently shown by Xu et al. [H. Xu et al., Proc. Natl. Acad. Sci. USA 111, 7558 (2014), 10.1073/pnas.1321682111]. Here Lagrangian power statistics are rationalized within the multifractal model of turbulence, whose predictions are shown to agree with numerical and empirical data. Multifractal predictions are also tested, for very large Reynolds numbers, in dynamical models of the turbulent cascade, obtaining remarkably good agreement for statistical quantities insensitive to the asymmetry and, remarkably, deviations for those probing the asymmetry. These findings raise fundamental questions concerning time irreversibility in the infinite-Reynolds-number limit of the Navier-Stokes equations.

Surf zone Exchange on a Rip Channeled Beach

NASA Astrophysics Data System (ADS)

Reniers, A.; Macmahan, J.

2008-12-01

The dispersion and surf zone exchange of GPS-equipped surface drifters observed during the Rip Current EXperiment (RCEX) is examined with help of Lagrangian Coherent Structures (LCSs). LCSs allow for the detection of transport barriers in unsteady flows and are typically applied to shelf-scale circulation systems. Here LCSs are specifically computed to detect the effects of surfzone-originated Very Low Frequency motions (VLFs) with O(10) minute time scale on the cross-shore exchange of floating material using numerical model calculations of the Lagrangian surface velocity at the wave group timescale. After verification with RCEX field observations, the model is run for a range of environmental conditions experienced during the field experiment to assess the effects of VLFs on the cross-shore surf zone exchange. Results are relevant for (but not restricted to) sediment and nutrient exchange, human health, water clarity, and swimmer safety.

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

Resonance phenomena in a time-dependent, three-dimensional model of an idealized eddy

NASA Astrophysics Data System (ADS)

Rypina, I. I.; Pratt, L. J.; Wang, P.; Äe; -zgökmen, T. M.; Mezic, I.

2015-08-01

We analyze the geometry of Lagrangian motion and material barriers in a time-dependent, three-dimensional, Ekman-driven, rotating cylinder flow, which serves as an idealization for an isolated oceanic eddy and other overturning cells with cylindrical geometry in the ocean and atmosphere. The flow is forced at the top through an oscillating upper lid, and the response depends on the frequency and amplitude of lid oscillations. In particular, the Lagrangian geometry changes near the resonant tori of the unforced flow, whose frequencies are rationally related to the forcing frequencies. Multi-scale analytical expansions are used to simplify the flow in the vicinity of resonant trajectories and to investigate the resonant flow geometries. The resonance condition and scaling can be motivated by simple physical argument. The theoretically predicted flow geometries near resonant trajectories have then been confirmed through numerical simulations in a phenomenological model and in a full solution of the Navier-Stokes equations.

The Role of Multiphysics Simulation in Multidisciplinary Analysis

NASA Technical Reports Server (NTRS)

Rifai, Steven M.; Ferencz, Robert M.; Wang, Wen-Ping; Spyropoulos, Evangelos T.; Lawrence, Charles; Melis, Matthew E.

1998-01-01

This article describes the applications of the Spectrum(Tm) Solver in Multidisciplinary Analysis (MDA). Spectrum, a multiphysics simulation software based on the finite element method, addresses compressible and incompressible fluid flow, structural, and thermal modeling as well as the interaction between these disciplines. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena. Interaction constraints are enforced in a fully-coupled manner using the augmented-Lagrangian method. Within the multiphysics framework, the finite element treatment of fluids is based on Galerkin-Least-Squares (GLS) method with discontinuity capturing operators. The arbitrary-Lagrangian-Eulerian method is utilized to account for deformable fluid domains. The finite element treatment of solids and structures is based on the Hu-Washizu variational principle. The multiphysics architecture lends itself naturally to high-performance parallel computing. Aeroelastic, propulsion, thermal management and manufacturing applications are presented.

Lagrangian model for the evolution of turbulent magnetic and passive scalar fields

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

Hater, T.; Grauer, R.; Homann, H.

2011-01-15

In this Brief Report we present an extension of the recent fluid deformation (RFD) closure introduced by Chevillard and Meneveau [L. Chevillard and C. Meneveau, Phys. Rev. Lett. 97, 174501 (2006)] which was developed for modeling the time evolution of Lagrangian fluctuations in incompressible Navier-Stokes turbulence. We apply the RFD closure to study the evolution of magnetic and passive scalar fluctuations. This comparison is especially interesting since the stretching term for the magnetic field and for the gradient of the passive scalar are similar but differ by a sign such that the effect of stretching and compression by the turbulentmore » velocity field is reversed. Probability density functions (PDFs) of magnetic fluctuations and fluctuations of the gradient of the passive scalar obtained from the RFD closure are compared against PDFs obtained from direct numerical simulations.« less

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.

Chaotic micromixer utilizing electro-osmosis and induced charge electro-osmosis in eccentric annulus

NASA Astrophysics Data System (ADS)

Feng, Huicheng; Wong, Teck Neng; Che, Zhizhao; Marcos

2016-06-01

Efficient mixing is of significant importance in numerous chemical and biomedical applications but difficult to realize rapidly in microgeometries due to the lack of turbulence. We propose to enhance mixing by introducing Lagrangian chaos through electro-osmosis (EO) or induced charge electro-osmosis (ICEO) in an eccentric annulus. The analysis reveals that the created Lagrangian chaos can achieve a homogeneous mixing much more rapidly than either the pure EO or the pure ICEO. Our systematic investigations on the key parameters, ranging from the eccentricity, the alternating time period, the number of flow patterns in one time period, to the specific flow patterns utilized for the Lagrangian chaos creation, present that the Lagrangian chaos is considerably robust. The system can obtain a good mixing effect with wide ranges of eccentricity, alternating time period, and specific flow patterns utilized for the Lagrangian chaos creation as long as the number of flow patterns in one time period is two. As the electric field increases, the time consumption for homogenous mixing is reduced more remarkably for the Lagrangian chaos of the ICEO than that of the EO.

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.

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates

NASA Astrophysics Data System (ADS)

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

Influence of boundary-layer dynamics on pollen dispersion and viability

NASA Astrophysics Data System (ADS)

Arritt, Raymond W.; Viner, Brian J.; Westgate, Mark E.

2013-04-01

Adoption of genetically modified (GM) crops has raised concerns that GM traits can accidentally cross into conventional crops or wild relatives through the transport of wind-borne pollen. In order to evaluate this risk it is necessary to account both for dispersion of the pollen grains and environmental influences on pollen viability. The Lagrangian approach is suited to this problem because it allows tracking the environmental temperature and moisture that pollen grains experience as they travel. Taking advantage of this capability we have combined a high-resolution version of the WRF meteorological model with a Lagrangian particle dispersion model to predict maize pollen dispersion and viability. WRF is used to obtain fields of wind, turbulence kinetic energy, temperature, and humidity which are then used as input to the Lagrangian dispersion model. The dispersion model in turn predicts transport of a statistical sample of a pollen cloud from source plants to receptors. We also use the three-dimensional temperature and moisture fields from WRF to diagnose changes in moisture content of the pollen grains and consequent loss of viability. Results show that turbulent motions in the convective boundary layer counteract the large terminal velocity of maize pollen grains and lift them to heights of several hundred meters, so that they can be transported long distances before settling to the ground. We also found that pollen lifted into the upper part of the boundary layer remains more viable than has been inferred using surface observations of temperature and humidity. This is attributed to the thermal and moisture structure that typifies the daytime atmospheric boundary layer, producing an environment of low vapor pressure deficit in the upper boundary layer which helps maintain pollen viability.

An individual-based model of skipjack tuna (Katsuwonus pelamis) movement in the tropical Pacific ocean

NASA Astrophysics Data System (ADS)

Scutt Phillips, Joe; Sen Gupta, Alex; Senina, Inna; van Sebille, Erik; Lange, Michael; Lehodey, Patrick; Hampton, John; Nicol, Simon

2018-05-01

The distribution of marine species is often modeled using Eulerian approaches, in which changes to population density or abundance are calculated at fixed locations in space. Conversely, Lagrangian, or individual-based, models simulate the movement of individual particles moving in continuous space, with broader-scale patterns such as distribution being an emergent property of many, potentially adaptive, individuals. These models offer advantages in examining dynamics across spatiotemporal scales and making comparisons with observations from individual-scale data. Here, we introduce and describe such a model, the Individual-based Kinesis, Advection and Movement of Ocean ANimAls model (Ikamoana), which we use to replicate the movement processes of an existing Eulerian model for marine predators (the Spatial Ecosystem and Population Dynamics Model, SEAPODYM). Ikamoana simulates the movement of either individual or groups of animals by physical ocean currents, habitat-dependent stochastic movements (kinesis), and taxis movements representing active searching behaviours. Applying our model to Pacific skipjack tuna (Katsuwonus pelamis), we show that it accurately replicates the evolution of density distribution simulated by SEAPODYM with low time-mean error and a spatial correlation of density that exceeds 0.96 at all times. We demonstrate how the Lagrangian approach permits easy tracking of individuals' trajectories for examining connectivity between different regions, and show how the model can provide independent estimates of transfer rates between commonly used assessment regions. In particular, we find that retention rates in most assessment regions are considerably smaller (up to a factor of 2) than those estimated by this population of skipjack's primary assessment model. Moreover, these rates are sensitive to ocean state (e.g. El Nino vs La Nina) and so assuming fixed transfer rates between regions may lead to spurious stock estimates. A novel feature of the Lagrangian approach is that individual schools can be tracked through time, and we demonstrate that movement between two assessment regions at broad temporal scales includes extended transits through other regions at finer-scales. Finally, we discuss the utility of this modeling framework for the management of marine reserves, designing effective monitoring programmes, and exploring hypotheses regarding the behaviour of hard-to-observe oceanic animals.

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, similarly to CMAQ, it can simulate concentrations of many species, including particulate matter and some toxic compounds, such as formaldehyde and 1,3-butadiene.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Let's Have a Coffee with the Standard Model of Particle Physics!

ERIC Educational Resources Information Center

Woithe, Julia; Wiener, Gerfried J.; Van der Veken, Frederik F.

2017-01-01

The Standard Model of particle physics is one of the most successful theories in physics and describes the fundamental interactions between elementary particles. It is encoded in a compact description, the so-called "Lagrangian," which even fits on t-shirts and coffee mugs. This mathematical formulation, however, is complex and only…

A semi-Lagrangian advection scheme for radioactive tracers in the NCEP Regional Spectral Model (RSM)

NASA Astrophysics Data System (ADS)

Chang, E.-C.; Yoshimura, K.

2015-10-01

In this study, the non-iteration dimensional-split semi-Lagrangian (NDSL) advection scheme is applied to the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection scheme is replaced by the NDSL advection scheme, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.

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

NASA Astrophysics Data System (ADS)

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

2009-02-01

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

SPH simulations of WBC adhesion to the endothelium: the role of haemodynamics and endothelial binding kinetics.

PubMed

Gholami, Babak; Comerford, Andrew; Ellero, Marco

2015-11-01

A multiscale Lagrangian particle solver introduced in our previous work is extended to model physiologically realistic near-wall cell dynamics. Three-dimensional simulation of particle trajectories is combined with realistic receptor-ligand adhesion behaviour to cover full cell interactions in the vicinity of the endothelium. The selected stochastic adhesion model, which is based on a Monte Carlo acceptance-rejection method, fits in our Lagrangian framework and does not compromise performance. Additionally, appropriate inflow/outflow boundary conditions are implemented for our SPH solver to enable realistic pulsatile flow simulation. The model is tested against in-vitro data from a 3D geometry with a stenosis and sudden expansion. In both steady and pulsatile flow conditions, results show close agreement with the experimental ones. Furthermore we demonstrate, in agreement with experimental observations, that haemodynamics alone does not account for adhesion of white blood cells, in this case U937 monocytic human cells. Our findings suggest that the current framework is fully capable of modelling cell dynamics in large arteries in a realistic and efficient manner.

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.

Model-free simulations of turbulent reactive flows

NASA Technical Reports Server (NTRS)

Givi, Peyman

1989-01-01

The current computational methods for solving transport equations of turbulent reacting single-phase flows are critically reviewed, with primary attention given to those methods that lead to model-free simulations. In particular, consideration is given to direct numerical simulations using spectral (Galerkin) and pseudospectral (collocation) methods, spectral element methods, and Lagrangian methods. The discussion also covers large eddy simulations and turbulence modeling.

Ground Vehicle CFD at TARDEC

DTIC Science & Technology

2012-05-21

Cooling Sytem: StarCCM+ Blast / Crew Safety: LS- Dyna Fatigue & FEA: Abaqus / NCode Each code run with ~40-80 CPUs on TARDEC HPC Models...suppression, blast solid modeling have particular scaling problems because of the use of Lagrangian particles Example: Dust modeling for engine...for technology demonstrator vehicles UNCLASSIFIED 9 Example CFD Interest Areas • Underbody mine blast • HVAC design / interior cooling

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

A study of the sources and sinks of methane and methyl chloroform using a global three-dimensional Lagrangian tropospheric tracer transport model

NASA Technical Reports Server (NTRS)

Taylor, John A.; Brasseur, G. P.; Zimmerman, P. R.; Cicerone, R. J.

1991-01-01

Sources and sinks of methane and methyl chloroform are investigated using a global three-dimensional Lagrangian tropospheric tracer transport model with parameterized hydroxyl and temperature fields. Using the hydroxyl radical field calibrated to the methyl chloroform observations, the globally averaged release of methane and its spatial and temporal distribution were investigated. Two source function models of the spatial and temporal distribution of the flux of methane to the atmosphere were developed. The first model was based on the assumption that methane is emitted as a proportion of net primary productivity (NPP). The second model identified source regions for methane from rice paddies, wetlands, enteric fermentation, termites, and biomass burning based on high-resolution land use data. The most significant difference between the two models were predictions of methane fluxes over China and South East Asia, the location of most of the world's rice paddies, indicating that either the assumption that a uniform fraction of NPP is converted to methane is not valid for rice paddies, or that NPP is underestimated for rice paddies, or that present methane emission estimates from rice paddies are too high.

Tall-tower observations of pollution from near-field sources in central Texas during the Texas Air Quality Study 2006

NASA Astrophysics Data System (ADS)

Andrews, A. E.; Kort, E.; Hirsch, A.; Eluszkiewicz, J.; Nehrkorn, T.; Michalak, A. M.; Petron, G.; Frost, G. J.; Gurney, K. R.; Stohl, A.; Wofsy, S. C.; Angevine, W. M.; White, A. B.; Oltmans, S. J.; Montzka, S. A.; Tans, P. P.

2008-12-01

The NOAA Earth System Research Laboratory has been measuring CO2, CO and basic meteorology from a television transmitter tower outside of Waco, TX since 2001. Sample intakes are located at 30, 122 and 457 meters above ground level. From July through November 2006, O3 measurements were added at 9 and 457 magl to support the Texas Air Quality Study (TexAQS 2006). There are several large point sources and metropolitan areas in the vicinity of the tower with distinct chemical signatures. Here, we evaluate the extent to which the Stochastic Time Inverted Lagrangian Transport (STILT) model reproduces pollution events that were observed at the tower during summer and fall 2006. For this study, STILT is driven by customized output from the WRF model v2.2, which was run with a 2km nested grid surrounding the tower embedded in a 10km nest that covers most of the southern and eastern US and a 40km nest that includes all of North America. Inaccurate representation of atmospheric transport is a major source of error in inverse estimates of fluxes of CO2 and other gases, and we selected this period for in depth analysis in part because a dense network of radar profilers was deployed for TexAQS 2006. The radar profilers report wind and boundary layer height, which can be used to evaluate the fidelity of the simulated transport. STILT is a particle dispersion model that can be run either forward or backward in time, which allows us to compare the agreement between forward runs from individual pollution sources and backward runs from the tower. We will also quantitatively compare the STILT-WRF results with similar output from the FLEXPART particle dispersion model driven by high-resolution ECMWF meteorological fields. We will use several different emissions inventories to evaluate model-to-model differences and differences between modeled and observed pollution influences.

Water Impact Test and Simulation of a Composite Energy Absorbing Fuselage Section

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Sparks, Chad; Sareen, Ashish

2003-01-01

In March 2002, a 25-ft/s vertical drop test of a composite fuselage section was conducted onto water. The purpose of the test was to obtain experimental data characterizing the structural response of the fuselage section during water impact for comparison with two previous drop tests that were performed onto a rigid surface and soft soil. For the drop test, the fuselage section was configured with ten 100-lb. lead masses, five per side, that were attached to seat rails mounted to the floor. The fuselage section was raised to a height of 10-ft. and dropped vertically into a 15-ft. diameter pool filled to a depth of 3.5-ft. with water. Approximately 70 channels of data were collected during the drop test at a 10-kHz sampling rate. The test data were used to validate crash simulations of the water impact that were developed using the nonlinear, explicit transient dynamic codes, MSC.Dytran and LS-DYNA. The fuselage structure was modeled using shell and solid elements with a Lagrangian mesh, and the water was modeled with both Eulerian and Lagrangian techniques. The fluid-structure interactions were executed using the fast general coupling in MSC.Dytran and the Arbitrary Lagrange-Euler (ALE) coupling in LS-DYNA. Additionally, the smooth particle hydrodynamics (SPH) meshless Lagrangian technique was used in LS-DYNA to represent the fluid. The simulation results were correlated with the test data to validate the modeling approach. Additional simulation studies were performed to determine how changes in mesh density, mesh uniformity, fluid viscosity, and failure strain influence the test-analysis correlation.

A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

NASA Astrophysics Data System (ADS)

Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

2013-02-01

In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

Nitrate Sources, Supply, and Phytoplankton Growth in the Great Australian Bight: An Eulerian-Lagrangian Modeling Approach

NASA Astrophysics Data System (ADS)

Cetina-Heredia, Paulina; van Sebille, Erik; Matear, Richard J.; Roughan, Moninya

2018-02-01

The Great Australian Bight (GAB), a coastal sea bordered by the Pacific, Southern, and Indian Oceans, sustains one of the largest fisheries in Australia but the geographical origin of nutrients that maintain its productivity is not fully known. We use 12 years of modeled data from a coupled hydrodynamic and biogeochemical model and an Eulerian-Lagrangian approach to quantify nitrate supply to the GAB and the region between the GAB and the Subantarctic Australian Front (GAB-SAFn), identify phytoplankton growth within the GAB, and ascertain the source of nitrate that fuels it. We find that nitrate concentrations have a decorrelation timescale of ˜60 days; since most of the water from surrounding oceans takes longer than 60 days to reach the GAB, 23% and 75% of nitrate used by phytoplankton to grow are sourced within the GAB and from the GAB-SAFn, respectively. Thus, most of the nitrate is recycled locally. Although nitrate concentrations and fluxes into the GAB are greater below 100 m than above, 79% of the nitrate fueling phytoplankton growth is sourced from above 100 m. Our findings suggest that topographical uplift and stratification erosion are key mechanisms delivering nutrients from below the nutricline into the euphotic zone and triggering large phytoplankton growth. We find annual and semiannual periodicities in phytoplankton growth, peaking in the austral spring and autumn when the mixed layer deepens leading to a subsurface maximum of phytoplankton growth. This study highlights the importance of examining phytoplankton growth at depth and the utility of Lagrangian approaches.

A review of the LATEX project: mesoscale to submesoscale processes in a coastal environment

NASA Astrophysics Data System (ADS)

Petrenko, Anne A.; Doglioli, Andrea M.; Nencioli, Francesco; Kersalé, Marion; Hu, Ziyuan; d'Ovidio, Francesco

2017-04-01

The main objective of the LAgrangian Transport EXperiment (LATEX) project was to study the influence of coastal mesoscale and submesoscale physical processes on circulation dynamics, cross-shelf exchanges, and biogeochemistry in the western continental shelf of the Gulf of Lion, Northwestern Mediterranean Sea. LATEX was a five-year multidisciplinary project based on the combined analysis of numerical model simulations and multi-platform field experiments. The model component included a ten-year realistic 3D numerical simulation, with a 1 km horizontal resolution over the gulf, nested in a coarser 3 km resolution model. The in situ component involved four cruises, including a large-scale multidisciplinary campaign with two research vessels in 2010. This review concentrates on the physics results of LATEX, addressing three main subjects: (1) the investigation of the mesoscale to submesoscale processes. The eddies are elliptic, baroclinic, and anticyclonic; the strong thermal and saline front is density compensated. Their generation processes are studied; (2) the development of sampling strategies for their direct observations. LATEX has implemented an adaptive strategy Lagrangian tool, with a reference software available on the web, to perform offshore campaigns in a Lagrangian framework; (3) the quantification of horizontal mixing and cross-shelf exchanges. Lateral diffusivity coefficients, calculated in various ways including a novel technique, are in the range classically encountered for their associated scales. Cross-shelf fluxes have been calculated, after retrieving the near-inertial oscillation contribution. Further perspectives are discussed, especially for the ongoing challenge of studying submesoscale features remotely and from in situ data.

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.

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.

Three-dimensional simulation of the motion of a single particle under a simulated turbulent velocity field

NASA Astrophysics Data System (ADS)

Moreno-Casas, P. A.; Bombardelli, F. A.

2015-12-01

A 3D Lagrangian particle tracking model is coupled to a 3D channel velocity field to simulate the saltation motion of a single sediment particle moving in saltation mode. The turbulent field is a high-resolution three dimensional velocity field that reproduces a by-pass transition to turbulence on a flat plate due to free-stream turbulence passing above de plate. In order to reduce computational costs, a decoupled approached is used, i.e., the turbulent flow is simulated independently from the tracking model, and then used to feed the 3D Lagrangian particle model. The simulations are carried using the point-particle approach. The particle tracking model contains three sub-models, namely, particle free-flight, a post-collision velocity and bed representation sub-models. The free-flight sub-model considers the action of the following forces: submerged weight, non-linear drag, lift, virtual mass, Magnus and Basset forces. The model also includes the effect of particle angular velocity. The post-collision velocities are obtained by applying conservation of angular and linear momentum. The complete model was validated with experimental results from literature within the sand range. Results for particle velocity time series and distribution of particle turbulent intensities are presented.

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.

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.

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

NASA Astrophysics Data System (ADS)

Wiedermann, Marc; Donges, Jonathan F.; Kurths, Jürgen; Donner, Reik V.

2016-04-01

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve certain global and local statistics associated with the nodes' embedding in a metric space. Comparing the original network's and the resulting surrogates' global characteristics allows one to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes' spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling the underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology.

Observation of Dust Aging Processes During Transport from Africa into the Caribbean - A Lagrangian Case Study

NASA Astrophysics Data System (ADS)

Weinzierl, B.; Sauer, D. N.; Walser, A.; Dollner, M.; Reitebuch, O.; Gross, S.; Chouza, F.; Ansmann, A.; Toledano, C.; Freudenthaler, V.; Kandler, K.; Schäfler, A.; Baumann, R.; Tegen, I.; Heinold, B.

2014-12-01

Aerosol particles are regularly transported over long distances impacting air quality, health, weather and climate thousands of kilometers downwind of the source. During transport, particle properties are modified thereby changing the associated impact on the radiation budget. Although mineral dust is of key importance for the climate system many questions such as the change of the dust size distribution during long-range transport, the role of wet and dry removal mechanisms, and the complex interaction between mineral dust and clouds remain open. In June/July 2013, the Saharan Aerosol Long-range Transport and Aerosol-Cloud-Interaction Experiment (SALTRACE: http://www.pa.op.dlr.de/saltrace) was conducted to study the transport and transformation of Saharan mineral dust. Besides ground-based lidar and in-situ instruments deployed on Cape Verde, Barbados and Puerto Rico, the DLR research aircraft Falcon was equipped with an extended aerosol in-situ instrumentation, a nadir-looking 2-μm wind lidar and instruments for standard meteorological parameters. During SALTRACE, five large dust outbreaks were studied by ground-based, airborne and satellite measurements between Senegal, Cape Verde, the Caribbean, and Florida. Highlights included the Lagrangian sampling of a dust plume in the Cape Verde area on 17 June which was again measured with the same instrumentation on 21 and 22 June 2013 near Barbados. Between Cape Verde and Barbados, the aerosol optical thickness (500 nm) decreased from 0.54 to 0.26 and the stratification of the dust layers changed significantly from a rather homogenous structure near Africa to a 3-layer structure with embedded cumulus clouds in the Caribbean. In the upper part of the dust layers in the Caribbean, the aerosol properties were similar to the observations near Africa. In contrast, much more variability in the dust properties was observed between 0.7 and 2.5 km altitude probably due to interaction of the mineral dust with clouds. In our presentation, we show vertical profiles of dust size distributions, CCN and dust optical properties. Based on the Lagrangian measurements, we discuss the effects of dust aging processes during long-range transport. Special attention will be given on changes in fine and coarse mode size distribution and aerosol mixing state.

Variable Density Effects in Stochastic Lagrangian Models for Turbulent Combustion

DTIC Science & Technology

2016-07-20

PDF methods in dealing with chemical reaction and convection are preserved irrespective of density variation. Since the density variation in a typical...combustion process may be as large as factor of seven, including variable- density effects in PDF methods is of significance. Conventionally, the...strategy of modelling variable density flows in PDF methods is similar to that used for second-moment closure models (SMCM): models are developed based on

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.

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.